key: cord- -ju bq authors: last, john title: a brief history of advances toward health date: journal: understanding the global dimensions of health doi: . / - - - _ sha: doc_id: cord_uid: ju bq three major discoveries determined the health and history of the human species. the first occurred almost a million years ago, when our hominid precursors discovered how to use fire to cook the meat they had hunted. they found that cooked meat tasted better, it didn’t go bad so quickly, and eating it was less likely to make them ill. our understanding of nutrition, a basic tenet of public health science, and the art of cooking have been improving ever since. as humans grew fruitful and multiplied, so did the variety and number of their diseases. permanent human settlements transformed ecosystems, and abiding by epidemic theory, the probability of respiratory and fecal-oral transmission of infection rose as population density increased. ecological and evolutionary changes in micro-organisms account for the origins of diarrhea , measles, malaria, smallpox, plague, and many other diseases. micro-organisms evolve rapidly because of their brief generation time and prolific reproduction rates. many that previously had lived in symbiosis with animals began to invade humans, where they became pathogenic. some evolved complex life cycles involving several host species, such as humans and other mammals, humans and arthropods, and humans and freshwater snails. these evolutionary changes in host-parasite relationships occurred at least several millennia before we had created written histories. our oldest written records that have a bearing on health date back about , years. the code of hammurabi (c. bce) contains ideas indicative of insight into the effects on health of diet and behaviour. it also suggests rewards and punishments for physicians who did their jobs well or poorly. information about the impact of diseases, especially of epidemic diseases, from those ancient times has come down to us in myths and biblical accounts of pestilences and plagues, although we cannot reliably identify the nature of the epidemics that afflicted ancient populations. the greek historian thucydides provided a meticulously careful description of an epidemic that struck the athenians in the second year of the peloponnesian war in bce, from which the forces of athens perhaps never fully recovered. modern infectious disease specialists have puzzled over this epidemic. was it typhus, a virulent form of epidemic streptococcal infection, that is, a variant form of scarlet fever, or something completely different? similar questions have been raised about other ancient epidemics, for instance the sweating sickness that recurred many times in mediaeval europe then vanished, never to be seen again, almost , years ago. there has been debate too about the exact nature of the black death, the terrible pandemic that devastated asia minor and the whole of europe in - . this is usually attributed to the plague bacillus, yersinia pestis, but revisionist historians and epidemiologists have raised the possibility that other pathogens, for instance, the anthrax bacillus, might have been responsible. here, as with the plague of the athenians, the plague of justinian, the medieval sweating sickness, the accounts of apparent fulminating epidemic syphilis (that may really have been another sexually transmitted disease or may have been caused by a highly virulent variant of the causative organism of syphilis, treponema pallidum, which has slowly lost its extreme virulence and infectivity), and, indeed, as with all other great epidemics of historical times before the rise of modern microbiology, we can only speculate about the exact aetiology and pathogenesis. this is a rather sterile, albeit fascinating, quest. it is more productive and useful to focus on what we know with reasonable certainty, and it is simplest to describe this knowledge in relation to some of the heroic figures who have contributed to advances in our understanding of epidemics and other diseases that have helped to shape history. this account therefore concentrates on a handful of the heroes of public health through the course of written history. hippocrates , the father of medicine, was also the father of public health. he practised and taught in a school of medicine at the temple of asklepios, near epidaurus in greece, and alone or with members of his school, laid the foundations of rational clinical medicine with careful descriptions of diseases and common sense ideas about ways to manage them. the hippocratic writings contain rich medical wisdom based on careful observation of sick and healthy people and their habits and habitats. epidemics is a series of case records of incidents of diseases, many of which we now know to be caused by infectious agents. the accounts of tetanus, rabies, and mumps, for instance, could have been written by a modern clinician. airs, waters, places outlines environmental health as it was understood two-and-a-half thousand years ago. the relationships of environment, social conditions, and behaviours to health and sickness is made explicit in the timeless advice of the opening paragraph: whoever would study medicine must learn of the following. first, consider the effect of each of the seasons . . . and the differences between them. . . . study the warm and cold winds . . . and the effect of water on health . . . when a physician comes to a district previously unknown to him he should consider its situation and its aspect to the winds . . . and the nature of its water supply . . . whether the land be bare and waterless or thickly covered with vegetation and well-watered, whether in a hollow and stifling, or exposed and cold. lastly, consider the life of the inhabitants-are they heavy drinkers and eaters and consequently unable to stand fatigue, or being fond of work and exercise, eat wisely but drink sparely. in short, study environment and life style, which are very modern concepts. for well over a thousand years after hippocrates' lifetime, human communities were afflicted with ever-present respiratory and gastrointestinal infections that cut deeply into the lives of everyone, and most deeply, as a rule, into the lives of young children who all too often died before they reached adolescence, carried off by measles, scarlet fever, diphtheria, bronchitis, croup, pneumonia, gastroenteritis, or typhoid. from time to time, this steady drain on long life and good health was punctuated by great and terrifying epidemics-smallpox, typhus, influenza, and, most terrible of all, the plague, or the "black death." the causes of these periodic devastations, the contributing reasons to why they happened, were a mystery. many at the time believed they were god' s punishment for sin, or the work of evil spirits. ideas about contagion were rudimentary, even though it had been dimly understood since antiquity that leprosy, perhaps the least contagious of all the infectious diseases, was associated with propinquity and uncleanliness. the th century italian monk, fracastorius, recognized some ways infection can spread. his conclusion, that disease could pass by intimate direct contact from one person to others, was easy to draw because he saw the dramatic epidemic of syphilis that was so obviously spread by sexual intercourse. he described this in a mock heroic poem, syphilis, sive morbis gallicus ( ) about the swineherd syphilis, and how he got and passed on to others the "french disease" then raging in europe. his anti-hero, of course, gave us the name of the disease. fracastorius' s other concepts, contamination by droplet spread and by way of shared contaminated articles, such as clothing and kitchen utensils, were published in de contagione in . fracastorius is important because he made a conceptual breakthrough-he brought about what thomas kuhn calls a paradigm shift in understanding of infection and some ways to control it. after fracastorius, the pathfinders on the road to health became numerous, but mention here will be made of only a handful of public health heroes: paracelsus, john graunt, antoni van leeuwenhoek, bernardino ramazzini, james lind, edward jenner, johann peter frank, john snow, ignaz semmelweiss, and louis pasteur. the swiss alchemist theophrastus bombastus von hohenheim, known as paracelsus ( - ), occupies the junction of medieval alchemy with scientific chemistry, pharmacy, medicine, and environmental health. he was a colourful character, a foul-mouthed drunkard who insulted and sometimes fought those who disagreed with him, whom he considered superstitious nincompoops. he recognized the relationship of goitre to cretinism, the fact that inhaled dusts caused lung disease, and that some common mental disorders were diseases, not caused by witchcraft or 'possession' by evil spirits. he experimented with chemical remedies containing compounds of mercury, lead, and other galenicals, observed their effects, and, thus, could be considered also a founding figure of pharmacology. john graunt ( graunt ( - , a london merchant haberdasher, was an amateur scientist and an early fellow of the royal society. he was interested in the impact of epidemics, especially the plague, and how plague outbreaks caused the numbers of deaths, and the age at death, to vary from one year to another. for over years before his time, parishes had kept records of baptisms and deaths, and what was then understood about causes of death was inscribed in the bills of mortality. graunt collected and analyzed these bills of mortality. he demonstrated statistical differences between males and females, between london and rural areas, and the ebb and flow of epidemics of plague. he published his work in natural and political observations ... upon the bills of mortality (london, ). this work was the foundation for the science of vital statistics. john graunt demonstrated the importance of gathering facts in a systematic manner, to identify, characterize and classify health conditions of public health importance. the diagnostic categories in the bills of mortality tell us what was understood years ago about the variety of human ailments and their causes. the nature of diseases caused by things not visible to the naked eye was long a mystery that began to unravel when antoni van leeuwenhoek ( - ), a dutch linen draper and amateur lens-grinder in delft, perfected the first functioning microscopes, with which he viewed drops of water, vaginal secretions, feces, his own semen, and the detailed structures of plants and insects. he lacked any formal scholarly training but in a series of letters to the royal society of london, he described accurately and in detail all that he saw. he did not suggest that the tiny creatures he was the first to see with his microscope were capable of causing diseases, but he is nonetheless regarded as the first of the 'microbe hunters' who sought and identified the pathogenic micro-organisms responsible for many diseases. bernardino ramazzini ( - ) was an italian physician who observed and classified workers in many occupations, and reported his observations and conclusions about the diseases to which workers in each of these were vulnerable in de morbis artificum diatribe (on the diseases of workers, ). it is a tour de force, a masterly account in the form of sweeping generalizations, and although the evidence supporting these generalizations was often flimsy, ramazzini introduced a new way of thinking about ways in which work conditions can affect health. james lind ( lind ( - was born and educated in edinburgh. he was apprenticed to a surgeon when he was , and spent nine years as a naval surgeon, during which time he saw many cases of scurvy, a disease that disabled and often killed sailors on long ocean voyages. lind thought this disease might be caused by a diet lacking fresh fruit and vegetables. he conducted an experiment, giving different diets to each of several pairs of sailors. this was the first clinical trial ever conducted-although the sample sizes were very small, there was no random allocation, and no informed consent was obtained from the sailors. the two sailors who received fresh oranges and lemons recovered rapidly from the scurvy, the others did not, or got worse. lind also initiated the first effective measures aimed at enhancing hygiene in the british navy, but he is best known for his work on scurvy, reported in a treatise of the scurvy ( ). not only was this the first reported clinical trial, it also was proof that a dietary deficiency can cause disease, that a well-balanced diet is essential for good health. thus lind, like fracastorius, was responsible for an important paradigm shift in the understanding of causes and control of disease. johann peter frank ( - ) studied medicine in heidelberg and strasburg, was a professor of medicine at göttingen and pavia, and taught in many other centres of learning including st petersburg, before he ended his career in vienna where he was professor of medicine at the allegemeines krankenhaus. early in his career he began writing system einer vollständigen medicinischen polizey, his great work on ways to improve population health. this appeared in a series of nine volumes from to . it was, as the title indicates, a system dealing with every then-known way to protect and preserve good health, including community hygiene, personal health protection by cleanliness, and a suggested set of laws and regulations to govern the control of conditions in lodging houses and inns, medical inspection of prostitutes, and so on. edward jenner ( jenner ( - was an english family doctor who practised throughout his life in the village of berkeley, gloucestershire. in his days, smallpox was a ubiquitous threat to life and health. in severe epidemics, it killed up to a quarter of all it attacked. when it did not kill, it often left disfiguring facial pockmarks and if it infected the eyes it caused blindness. the practice of variolation, inoculation into the skin of dried secretions from a smallpox bleb, was invented in china about years ago and spread along the silk route, reaching asia minor in the th century. lady mary wortley montague, wife of the british ambassador to constantinople, described the practice in a letter dated april , , and imported the idea to england when she came home. by the time jenner was a child, variolation had become popular among educated english families as a way to provide some protection against smallpox. jenner knew the popular belief in gloucestershire that people who had been infected with cowpox, a mild disease acquired from cattle, did not get smallpox. he reasoned that since smallpox in mild form was transmitted by variolation, it might be possible similarly to transmit cowpox. a smallpox outbreak in gave him an opportunity to confirm this notion. in he began a courageous and unprecedented experiment-one that would now be unethical, but that has had incalculable benefit for humankind. he inoculated a boy, james phipps, with secretions from a cowpox lesion. in succeeding months, until the summer of , he inoculated others, most of them children, to a total of . all survived unharmed, and none got smallpox. jenner published an inquiry into the causes and effects of the variolae vaccinae in -perhaps the most influential public health treatise of all time. the importance of jenner' s work was immediately recognized and although there were sceptics and hostile opponents, vaccination programs began at once. the frequency and ferocity of smallpox epidemics began to decline early in the th century, but the disease remained a menace until the mid- th century. in , the american epidemiologist donald soper worked out the strategy of containment, in other words, vaccinating all known contacts of every diagnosed case. in , who embarked on a global campaign to eradicate smallpox. the last naturally occurring case was a girl in somalia in . in , the world health assembly proclaimed that smallpox, one of the most deadly scourges of mankind, had been eradicated. at the beginning of the new millennium, samples of smallpox virus are preserved in secure biological laboratories in several countries, but, thanks to edward jenner, this terrible disease need never again take a human life-unless it is used illegally in biological warfare. john snow ( - ) was a london physician, and a founding father of modern epidemiology. (he was also a pioneer anesthetist who invented a new kind of mask to administer chloroform, which he gave to queen victoria to assist at the births of her two youngest children.) snow' s work on cholera demonstrated fundamental intellectual steps that must be part of every epidemiological investigation. he began with a logical analysis of the available facts, which proved that cholera could not be caused by a 'miasma' (emanations from rotting organic matter) as proposed in a theory popular at that time, but must be caused by a transmissible agent, most probably in drinking water. he confirmed the proof with two epidemiological investigations into the great cholera epidemic of . he studied a severe localized epidemic in soho, using analysis of descriptive epidemiological data and spot maps to demonstrate that the cause was polluted water from a pump in broad street. his investigation of a more widespread epidemic in south london involved an inquiry into the source of drinking water used in over households. he compared the water source in houses where cholera had occurred with that in others where it had not. his analysis of the information about cases and their sources of drinking water showed beyond doubt that the cause of the cholera outbreak was water that was being supplied to houses by the southwark and vauxhall water company, which drew its water from the thames downriver, where many effluent discharges polluted the water. very few cases occurred in households supplied with water by the lambeth company, which collected water upstream from london, where there was little or no pollution. john snow reasoned correctly that the cholera must be caused by some sort of agent in the contaminated water supply. this was a remarkable feat, completed years before robert koch identified the cholera bacillus. snow published his work in a monograph, on the mode of communication of cholera ( ). this book has been reprinted in modern editions and is still used as a teaching text. the hungarian physician ignaz semmelweiss ( - ) was a great but tragic figure. working in the obstetric wards of the allgemeines krankenhaus in vienna, he tried to transform traditional but ineffective treatment methods by using logic and statistical analysis to demonstrate the efficacy, or lack of it, when he compared treatment regimens. he believed in the germ theory of disease and was convinced that the terrible death rates from puerperal sepsis must be caused by germs introduced into the raw uterine tissues by birth attendants who did not disinfect their hands. he carried out a meticulous comparative mortality study in his own wards, where he insisted that all birth attendants must cleanse their hands in a disinfectant solution of bleach, and other wards run by senior obstetricians where hand-washing was not routine. his senior colleagues regarded his findings as a gross insult to their professional competence. semmelweiss' s rather abrasive nature and his jewish origins in the anti-semitic atmosphere of th century vienna made matters worse for him. he was hounded out of his hospital post, and ended his life in a mental hospital. his belatedly published comparative statistical analyses of the death rates from puerperal sepsis in his own and other wards of the allgemeines krankenhaus are a model of how to conduct such studies, but, unfortunately, no one in vienna heeded him and young women continued to die of childbed fever for another generation. medical science advanced rapidly in the second half of the th century, applying the exciting discoveries of a new science, bacteriology, which transformed public health. the great bacteriologists of the late th century identified many pathogenic bacteria, classified them, developed ways to cultivate them, and, most important, worked out ways to control their harmful effects, using sera, vaccines, and "magic bullets" such as the arsenical preparations that ehrlich developed to treat syphilis. it would be useful to discuss each of them, but i will focus on just one, louis pasteur ( - ). this french chemist evolved into a bacteriologist, and was a towering figure of th century bacteriology and preventive medicine. in , he had recently been appointed professor of chemistry in lille, and was invited to solve the problem of aberrant fermentation of beer that caused it to taste bad and made it undrinkable. he showed that the problem was caused by bacteria that were killed by heat. in this way he invented the process for heat treatment to kill harmful bacteria, first applied to fermentation of beer, then to milk-the process known ever since as pasteurization that has saved innumerable children from an untimely death. he went on to study and solve many other bacteriological problems in industry and animal husbandry. he developed attenuated vaccines, first to prevent chicken cholera, then, in , to control anthrax, which was a serious threat to livestock and, as well, occasionally to humans. before this, in , he began experiments on rabies, seeking a vaccine to control this disease, which without treatment is invariably fatal. as a result of the success of the anthrax vaccine, he believed that an attenuated rabies vaccine could be made. this, of course, was many decades before the virus was visualized. he prepared and successfully tested his rabies vaccine in on a boy, joseph meister, who had been bitten by a rabid dog. pasteur became not just a national but an international celebrity. born in the same year as louis pasteur, the austro-hungarian monk gregor mendel ( - ) was another amateur scientist, a botanist. experimenting with varieties of garden peas, he cross-pollinated them and observed and recorded the results. unfortunately, he published his findings in an obscure journal where they remained un-noticed for many years, but when they were unearthed about years after his death, gregor mendel was retroactively honoured as the father of a new science, genetics, which soon found many applications in clinical medicine, with the recognition of the fact that many inherited diseases were caused by genetic disorders. almost years after mendel' s death, other discoveries with great public health relevance include development of genetically modified sterile insect vectors of disease, genetically resistant strains of rice, wheat, and so on, and applications of genetic engineering to limit and even control and prevent some recessive inherited disorders. pasteur, henle, koch, virchow, and, soon after, battalions of bacteriologists and pathologists firmly established the fact that micro-organisms caused many diseases-the germ theory was a proven fact, not theory. however, many germ diseases require much more than germs before they can cause their worst damage. tuberculosis is caused by the tubercle bacillus acting in conjunction with poverty, ignorance, overcrowding, poor nutrition, adverse social and economic circumstances, and other enabling and predisposing factors. the diarrheal diseases, including cholera, are caused by various microorganisms, but these get into the gut when ingested with contaminated water or food, that is, they are really caused by poor sanitary and hygienic practices. by late in the th century, many of these factors had been clarified. the stage was set for the health reforms that included the sanitary revolution, the beginnings of a social safety net, provision of immunizations, nutritional supplements for school children, prenatal care for pregnant women, and other essential public health functions we take for granted years later. it required a dedicated army of public health workers to achieve all this. i have singled out and mentioned a mere handful of the public health pathfinders on the road to good health. many others could be added, but that would turn this brief chapter into a weighty monograph. often the physician−pathfinders used their own patients as experimental subjects for their path-finding discoveries. lind' s sailors, jenner' s young friends starting with james phipps, pasteur' s patient joseph meister, and all others known and unknown by name who provided the material for the great discoveries of robert koch and other members of the austrian and german schools of bacteriology, should be remembered and honored too. many others belong in their company: the great german pathologist rudolph virchow recognized that political action as well as rational science are necessary to initiate effective action to control public health problems; edwin chadwick and lemuel shattuck reported on the appalling sanitary conditions associated with the unacceptably high infant and child death rates that prevailed in th century industrial towns; william farr established vital statistics in england as a model for other nations to follow. and so the list grows from a handful of public health pathfinders to whole armies. more was needed than scientific discoveries. such discoveries had to be applied, and this often required drastic changes in the established social and economic order. so, other pathfinders appear on the road to health. they include politicians, administrators, journalists, creative writers, performing artists, and cartoonists. the journalists, creative writers, and artists who transmit the scientific concepts of public health to the general public and to the politicians are indispensable partners in the team that makes it possible for us to advance up the road to better health. the process continues in modern times with investigative journalism and tv documentaries. i have identified five essential ingredients of the processes that brought about the public health reforms called the sanitary revolution of the late th and early th century, and have shown that these five features are essential for the control of all public health problems. . awareness that the problem exists. john graunt began this process with natural and political observations. others consolidated his conceptual breakthrough, and it was applied to great effect after the establishment of formal national vital statistics in england and wales under the inspired leadership of william farr. by farr' s time, widespread literacy, the proliferation of daily newspapers, and word of mouth helped to enhance awareness among thoughtful people everywhere that there were massive public health problems in society at that time. modern computer-based record-keeping and effective health information systems with instantaneous worldwide notification of contagious disease outbreaks with public health significance continue to enhance the process. . understanding the causes. in the second half of the th century, understanding rapidly increased, as epidemiology and bacteriology, and nutritional and environmental sciences explored previously unknown landscapes of aetiology and pathogenesis. the new mass media-daily newspapers-propagated this understanding among literate people throughout the country. from the middle of the th century, news magazines and tv have ensured that knowledge of causal connections-smoking to cancer, diet and lack of exercise to coronary heart disease, alcohol-impaired driving to traffic fatalities, and many more-are very widely disseminated. this, however, has not necessarily led to effective control measures. . capability to control the causes. with astonishing speed, once the initial breakthroughs had occurred, sera and vaccines were developed to control many of the lethal microbial diseases that had plagued earlier generations. improved dietary practices, pasteurization of milk, improved personal hygiene and, above all, environmental sanitation to rid drinking water of polluting pathogens, all advanced rapidly in the final quarter of the th century and the first few decades of the th century. thus many ancient infectious disease scourges have been controlled, most dramatically being, perhaps , the eradication of smallpox. unfortunately, new infectious pathogens including the human immunodeficiency virus, viral tropical haemorrhagic fevers, the coronavirus of severe acute respiratory syndrome, and a score or more of others, have emerged to take their place . . . this is an essential prerequisite to the determination to act upon the problem. it is the most fascinating and challenging aspect of the essential features. this belief is the moral imperative that drives public health reforms. geoffrey vickers described the history of public health as a process of redefining the unacceptable-an endless process of identifying conditions, behaviors, and circumstances that individuals, communities, and cultures must no longer tolerate. throwing the contents of the chamber pot into the street, clearing one' s nostrils on the tablecloth, coughing and spitting on the living-room floor, all became unacceptable in the late th century. many people outside the boundaries of traditional medical science and public health practice played a role in this process. in the era of the great reforms of the th century, they included social reformers like edwin chadwick, journalists like henry mayhew and charles kingsley, novelists like charles dickens, cartoonists in punch and other periodicals-all of whom were aided by the rise of literacy in that period. collectively, they inspired a mood of public outrage that became an irresistible force for reform. in the second half of the th century, this sense of moral outrage found new targets-lighting a cigarette without permission in someone else' s home, carrying infant and child passengers in a car without safety equipment, dumping toxic industrial waste where it harms others, and more. yet, much else remains to be done. . political will. there is always resistance to change, there are always interest groups-often rich and powerful withal-who will do whatever it takes to obstruct necessary improvement. in the era of the sanitary revolution, it was the owners of water companies, factories, and tenement housing who resisted most vigorously. since the s it has been tobacco companies and a host of manufacturers of toxic petrochemical and other dangerous compounds released into the air and water. legislation and regulation are almost always necessary, and inevitably generate opposition. nevertheless, when the other four features-awareness, understanding, capability, and values-are in place, the political will to bring about reforms gathers momentum and usually succeeds eventually. these five essential ingredients required for public health reforms apply to several public health problems that have waxed and waned over time: tobacco addiction, impaired driving, domestic violence, child abuse, irresponsible domestic and industrial waste disposal, and so on. lately, mountainous barriers-of our own making-to maintaining our public health have appeared. the most formidable is a cluster of human-induced changes to global ecosystems and the global commons-the atmosphere, the oceans, wilderness regions, and stocks of biodiversity-that threaten all life and health on earth, not just the life and health of humans. another barrier is perhaps an inherent flaw in the human character that leads many individuals and national leaders to believe that disputes can be settled by violent means. currently, we have so many terrible weapons that violence done by them can and does cause immense suffering, innumerable deaths ( % or more of these deaths, as well as a similar proportion of permanent maiming and disability, are among non-combatants), and appalling damage to ecosystems, the environment, and the fabric of society. sadly, this is rarely recognized as a public health problem. the very first essential ingredient, awareness of the problem, is lacking. both these massive public health problems, in my view, are linked to the insatiable human craving for petroleum fuels, an addiction far more pervasive and dangerous to mankind and the earth than addiction to tobacco. so far in our only partially sentient and insightful civilization, this particular addiction is not even recognized as a public health problem. one public health problem that has been recognized is a worldwide pandemic of tobacco addiction and its many adverse effects on health and long life. recognition of this problem led the delegates to the world health assembly of to approve the framework convention on tobacco control. another universally recognized public health problem is the global pandemic of hiv/aids. tobacco addiction and the hiv/aids pandemic are both associated with the values of modern life and social behavior, including the marketing practices of transnational corporations. surmounting these barriers to health will require social, cultural, and behavioral changes and political action. i am an optimist. i believe that the pace of scientific advances will be maintained in the future, and that values will continue to shift in favor of essential changes towards global ecosystem sustainability. i do not know whether those who follow us will ever reach the ultimate summit or idealized who vision of halfdan mahler' s "health for all," but i am confident that they will continue to climb towards it. de contagione et contagiosis morbis et eorum curatione, libri iii natural and political observations mentioned in a following index and made upon the bills of mortality with reference to the government, religion, trade, growth, air, diseases and the several changes in the said city an inquiry into the causes and effects of the variolae vaccinae a treatise of the scurvy hippocratic writings. harmondsworth: penguin a green history of the world; the environment and the collapse of great civilizations the greatest benefit to mankind; a medical history of humanity from antiquity to the present a history of medicine, . primitive and archaic medicine on the mode of communication of cholera key: cord- -deogedac authors: ochab, j. k.; g'ora, p. f. title: shift of percolation thresholds for epidemic spread between static and dynamic small-world networks date: - - journal: nan doi: . /epjb/e - - sha: doc_id: cord_uid: deogedac the aim of the study was to compare the epidemic spread on static and dynamic small-world networks. the network was constructed as a -dimensional watts-strogatz model ( x square lattice with additional shortcuts), and the dynamics involved rewiring shortcuts in every time step of the epidemic spread. the model of the epidemic is sir with latency time of time steps. the behaviour of the epidemic was checked over the range of shortcut probability per underlying bond - . . the quantity of interest was percolation threshold for the epidemic spread, for which numerical results were checked against an approximate analytical model. we find a significant lowering of percolation thresholds for the dynamic network in the parameter range given. the result shows that the behaviour of the epidemic on dynamic network is that of a static small world with the number of shortcuts increased by . +/- . %, while the overall qualitative behaviour stays the same. we derive corrections to the analytical model which account for the effect. for both dynamic and static small-world we observe suppression of the average epidemic size dependence on network size in comparison with finite-size scaling known for regular lattice. we also study the effect of dynamics for several rewiring rates relative to latency time of the disease. the epidemic modelling has become a significant and needed branch of complex systems research, as we have witnessed the recent epidemic threats and outbreaks of human diseases (h n and h n influenzas [ , ] or severe acute respiratory syndrome [ , ] ) or animal (foot-and-mouth disease [ ] ) and plant diseases alike (e.g. dutch elm disease [ ] or rhizomania [ ] ). there are two crucial characteristics of the epidemic spread that make it complicated to be modelled on the one hand, and costly to be prevented in reality on the other: firstly, a number of infectious diseases exhibit long-range transmissions of varied model we adopt watts-strogatz model of a small-world network [ ] : first we take a -dimensional square lattice with n = l nodes and n undirected edges. to avoid some finite-size effects we impose periodic boundary conditions for the lattice (i.e. we get a torus). then, we add a number of undirected edges between random pairs of nodes. the number of additional edges ('shortcuts') is set as φn , hence φ is shortcut probability per underlying bond. network with φ = is just a regular lattice. for nonzero φ we call the network a static small-world. the third type of network is a dynamic small-world. one can construct it by randomly distributing shortcuts in every time step of simulation. here, we choose φn nodes randomly, and keep them fixed for the whole run of the epidemic. in every time step we randomly launch shortcuts anchored in these nodes, which means the dynamics consists in rewiring one end of these shortcuts. for the sake of simplicity we allow for multiple shortcuts being incident with the same node, for shortcuts leading to nearest neighbours, and for loops being formed. the construction of the source nodes launching shortcuts allows for an easier interpretation of the network: the fixed nodes could correspond to centres of activity that can be identified as in the real world networks. the sir (susceptible-infectious-removed) model is adopted, where the disease is transmitted along the edges of the network in discrete time steps. the probability p of infecting a susceptible node by an infectious neighbour during one time step is set equal for short-and long-range links, both static and dynamic. the latency time l of the disease is measured in discrete time units (we take l = , ). thus, an infectious node can transmit disease to susceptible nodes with probability p every turn for the period of l turns, and after that time it is removed, i.e. it cannot infect nor be reinfected. every simulation starts with only one initially infecting node, all others being susceptible, and it ends when no node in the infectious state is left. sample snapshots of the epidemic time development are presented in fig. . grassberger [ ] related the probability of infection to the probability t in bond percolation through t = l t= p( − p) t− = − ( − p) l , where t is the so called transmissibility (it is the total probability of a node infecting one of its neighbours during the whole latency time). in the case of -dimensional square lattice the bond percolation threshold is t c = . . numerical data the linear lattice size used for most calculations is l = √ n = . in section . we take sizes l = , , , , , , , , , , . the disease latency is set to l = (for faster simulations reported in sec. ) or l = (in sec. . in order to get larger set of dynamic rates). the range of probability p scanned is p = . − . (depending on φ) with resolution of / , which translates to around t = . − . . for every p and φ the epidemic is run times with random distributions of shortcuts each time. the fraction of shortcuts is φ = − . , with steps of . . the simulations are performed for both static and dynamic small-world network. in the study of the epidemic spread on networks, we stick to the percolation theory as a reference point. in the theory, a percolation threshold would be the value of p that generates an epidemic cluster spanning between the boundaries of the whole system. otherwise, it is possible to define percolation as the point at which a cluster of macroscopic size forms (i.e. it occupies a finite fraction of the system for n → ∞). we employ the latter to define percolation threshold (numerically) as the point at which the average epidemic's size divided by n rises above a certain value (here, set to . ). the average is taken over a number of reruns for different shortcut drawings. as we can perform simulations only for finite sizes, we take the results for a relatively large network of √ n = . the choice of the threshold value is taken so as to calibrate the results for the static network to the previously confirmed analytical result. we take as the theoretical model [ ] , where the generating function and series expansion methods were used to find the approximate position of bond percolation transition in d small-world network, which corresponds to the epidemic spread on what we refer to as static small-world. we can account for the change between static and dynamic networks analytically using the model known for static small-world network [ ] . as the original theory has no time variable, it would be a hard task to introduce dynamics explicitly. the solution, however, is astonishingly simple. one can estimate the average number of nodes infected through shortcuts during latency time l: i.e. the number of shortcuts in the static network multiplied by the total probability of infecting a neighbouring node (this probability is the same for both regular links and shortcuts). the analogous expression for the dynamic network is found easily where the sum is an average number of infections transmitted by a single source of dynamic shortcuts for a given latency time. it comes from the fact that a dynamic shortcut can pass infection several times (the factor p i ), while in the static case a node could infect only once (since nodes cannot be reinfected in the sir model). this expression predicts lowering percolation thresholds, although numerical values of the shift are considerably smaller than the ones obtained from simulations. figures (a) - (c) explain why the above expression is not yet correct: it is derived only for the source nodes passing the disease on, while it disregards the fact that the node may itself become infected via long-range link. since on the static network there is no difference between shortcuts' source and target nodes, we can attach the factor φn/ to both infection graphs presented in fig. (a) . for dynamic network, the graphs in fig. (b)- (c) for infecting a source node through a regular link and through a dynamic link give different counts of how many shortcuts were used. the former was given in eq. as lp, and the latter actually utilises the same formula, but with the substitution l → l + . in total, we get we assume that n dyn = n stat if the epidemic on both networks has the same percolation threshold. thus, we can obtain the ratio of the two shortcut densities where p is the probability of infection in one time step and l latency time of a disease. now, we can calculate t c (rφ)) numerically, just as we do it with the fitted fig. . the ratio in eq. was used to plot the lower solid line in fig. . in figure we plot numerical and theoretical values of percolation thresholds t c for both static and dynamic small-worlds. the resulting t c (φ) data points for static small-world network agree with the analytical approximation [ ] , which confirms the validity of calibration procedure. as the lower dataset marks the effect of network dynamics, the difference between the two networks proves to be systematic and significant. the dashed line is a fit t c [( + v)φ] of the analytical model for the static network, where the fitted parameter v may be interpreted as a virtual percentage of additional shortcuts needed to obtain the dynamic network percolation thresholds. it follows from the fit that percolation thresholds for dynamic network are lower as if the shortcut density were ( +v)φ (where v = . ± . is the fitted parameter). nonetheless, qualitatively the epidemic on dynamic small world behaves in the same way as on the static one for the given range of parameters (φ = . corresponds to every node in the network having on average two additional links). the analytical correction slightly exceeds the values of simulation data points, but the overall agreement is satisfactory. the difference between the analytical solution and the observed behaviour does not exceed the shift between static and dynamic networks obtained from simulations. the discrepancy might be due to the method of calculating percolation thresholds from numerical data or due to the approximate nature of the correction. the primary motivation of checking finite-size scaling for the system was to utilise it to determine the percolation thresholds very accurately (as the shift of thresholds observed in fig. is relatively small), and to arrive at threshold value for infinite system size. yet, it is worth noting at this point that the knowledge of thresholds for infinite system sizes would not usually be appropriate for evaluation of risks in the real epidemic, given the sizes of some real networks. to study the size of finite-size effects is thus vital on its own right. in figure (b) the convergence of the average epidemic size to the threshold behaviour can be observed, and the significant dependence on system size ranges up to the epidemic size of around . n and interval of transmissibility of length around . (the numbers are very rough estimates). as presented in fig. (a) where t n are the values of transmissibility for a given system size n and a set section position, and t ∞ is the percolation threshold for infinite system size. for regular lattice t ∞ is fitted correctly for various section positions as . ± . (the error may vary for different sections, but does not exceed the given value). it appears that the dependence on system size for small-world networks (both static and dynamic) is dissimilar to the one of regular lattices, as can be seen in fig. . (φ = . ) . it is suppressed to smaller values of the average epidemic size. for the shortcuts density φ = . the dependence on system size is already visible only below the epidemic size of . . because the dependence of the epidemic size on size of the system becomes of the order of magnitude of statistical fluctuations (the quality of the data can already be seen in the fig. . ), any attempts to utilise finite-size scaling for determining percolation threshold are not viable. indeed, the errors do not allow us to check if the same form of finite-size dependence as in eq. holds. dependence on the rate of dynamics one can generalise the theoretical analysis for various rates of dynamics, given the formula in eq. . to explain this, let us notice that there are two time scales in the model: the latency time l of the infection and the duration /d between consecutive rewirings of dynamic links (both measured in discrete time steps of the epidemic spread). as the choice of latency l only rescales the total probability of infection t = t (p, l), we can dispose of it, and the crucial parameter ld that accounts for the shift of percolation thresholds is defined as the number of shortcut movements during latency time. obviously, for a static network we get d = , while for all the above analysis of dynamic network we have ld = (l = and the rewiring was performed every turn, so d = ). depending on the interpretation of the model, we could also consider d > . however, if p is to be the probability of infection during one time step it is reasonable that shortcuts rewiring faster than one time step would infect with appropriately smaller probability, and there would be no further shift of percolation thresholds. since the epidemic spreads with discrete time, which results in sums as in eq. , we are interested in rational numbers d ∈ [ , ]∩q, particularly of the form /i, i ∈ z. what we need is n dyn calculated in a similar way to that in eq. . here, we take l = , d = , / , . . . , / , and we plot both the numerical and theoretical results for φ = . in fig. . theoretical derivation is to be found in the appendix. the theoretical approach gives slightly exceeding values (the scale should be noted), which is the same effect as discussed at the end of section . . we have shown that introducing dynamics of the long-range links in a smallworld network significantly lowers an epidemic threshold in terms of probability of disease transmission, although the overall dependence on number of shortcuts stays the same. consequently, the risk of an epidemic outbreak is higher than in any calculations involving static models. the effect remains secondary to the influence that the introduction of additional of shortcuts has on the spread of the disease. it should be noted that the shift of percolation thresholds depends on the relative measure of dynamics of the network with respect to the process on the network (rewiring rate and latency time, respectively). any accurate analytical calculation or simulation should take this quantity as a significant parameter, to be estimated for a particular disease and type of the network. as in reality we consider only finite-size networks, and real epidemic sizes do not usually reach values of the order of even % of the system size, the information on finite-size effects seemed very much needed. that the epidemic outbreak magnitude does not depend on the system size for small-world networks as much as it does for regular lattices means that we should not expect the epidemic outbreaks below transmissibility threshold value. thus, finite-size effects seem to become secondary, as well. the usefulness of such a model for risk prediction still depends on our knowledge of the probability of transmission (p or t ) of a given disease, which is not easy to obtain for diseases spreading outside of well controlled environments like hospitals. relatively good estimates, thanks to the nature of transmission, exist for syphilis. transmissibility of the disease is reviewed in [ ] , where authors give values ranging from . % to % per partner, and decide on % as the lower boundary for untreated disease. this seems to be well above the epidemic threshold, irrespective of very different network topology for such diseases. however, this also shows that errors on estimates of transmission probabilities exceed the effect of threshold shifting studied here. though the -dimensional network structure used here may be said to correspond mainly to that of plantations, it is worth noting its generality: nodes may be interpreted as plants, animals or humans, but also on a larger scale as farms, households, or cities and airports; in turn, long-range links could mean wind (on farms), disease vectors, occasional human contacts, or airline connections. still, it has some other fairly realistic characteristics: according to [ ] , who analysed the structure of human social interactions, 'the majority of encounters ( . %; . - . ) occur with individuals never again encountered by the participant during the days of the survey.' this may mean that about % of the repeated contacts corresponds roughly to our regular underlying lattice with z = neighbours for each node, while the % correspond to around z dynamic contacts distributed over over days. this gives on average φ ≈ . for simulation with daily time steps, which lies within the parameter range studied in this paper. a (p, ) = · · · · · a (p, ) = ·| · · · · + · · · · |· = · | · · · · a (p, ) = · · | · · · + · · · | · · = · ·| · · · ( ) a (p, ) = ·| · · · | · a (p, ) = ·| · ·| · · + · · | · ·|· = · | · ·| · · where the symbol '|' marks rewiring, and '·' one epidemic time step during latency period. for instance ·| · · would correspond to three turns with one rewiring, during which either , or infections are possible. the derivation involves only very easy combinatorics, but for longer latency periods one would need to repeat these calculations to obtain more terms and different prefactors. now, one can easily obtain expressions for n dyn for any /d ∈ z. below we give only the general expression for /d ≥ l: where l = . the first term in the brackets corresponds to fig. (b) and the second to fig. (c) . for greater numbers of rewiring per turn d, we need to consider the terms a , a . the result is plotted against simulated data in fig. . modelling control of epidemics spreading by long-range interactions modeling the sars epidemic the natural history of syphilis: implications for the transmission dynamics and control of infection on the critical behavior of the general epidemic process and dynamical percolation epidemic dynamics on an adaptive network dynamics of the uk foot and mouth epidemic: stochastic dispersal in a heterogeneous landscape percolation and epidemics in a two-dimensional small world world health organization. avian influenza (h n ) world health organization. severe acute respiratory syndrome (sars) world health organization. swine influenza (h n ) dynamic social networks and the implications for the spread of infectious disease modelling development of epidemicswith dynamic small-world networks a model for the invasion and spread of rhizomania in the united kingdom: implications for disease control strategies dutch elm disease and the future of the elm in the uk: a quantitative analysis susceptible-infected-recovered epidemics in dynamic contact networks collective dynamics of 'small-world' networks this work is supported by the international phd projects programme of the foundation for polish science within the european regional development fund of the european union, agreement no. mpd/ / . below we present the way to calculate n dyn for latency periods l = , (in the simulation we set l = , but we need to take into account also the process from fig. (c) , which in a sense increases latency by ). let us definewhere we substituted t ( ) for p on the right-hand sides, and we leave out the argument p in t (p, l) to simplify the notation. those quantities correspond to the average number of infections during one latency period depending on when the rewiring takes place. one can present those diagrammatically (here for l = ) as key: cord- - v i rk authors: chen, deng; zhu, lina; lin, xin; hong, zhen; li, shichuo; liu, ling; zhou, dong title: epilepsy control during an epidemic: emerging approaches and a new management framework date: - - journal: acta epileptologica doi: . /s - - -z sha: doc_id: cord_uid: v i rk epidemics are a big threat to world health. the ongoing pandemic of corona virus disease (covid- ) has caused a series of challenges to public health. one such challenge is the management of chronic diseases such as epilepsy during an epidemic event. studies on this topic are rather limited and the related medical practice is full of uncertainty. here we review recent development of potential approaches for epilepsy control during an epidemic and propose a new three-level management framework to address these challenges. epidemics were and still are a dreadful threat to public health. despite continuous efforts by scientists, health providers and even the whole society, the incidence of infectious diseases is still rising [ ] . in alone, the who has documented over disease outbreaks affecting more than countries [ ] . although most of these outbreaks occurred in resource-limited regions such as africa, middle east and south america, other countries are not excluded from the risk. the outbreak of corona virus disease (covid- ) beginning in december is the most recent ongoing pandemic, which has affected millions of people worldwide [ ] . by april th, , this disease has affected over . million people and caused deaths worldwide. epidemics, even not reaching a pandemic level, have dramatic impacts on society that are far beyond disease itself. during the severe acute respiratory syndrome (sars) outbreak in beijing, international transportation, cargo exchange and tourism were ruined by the epidemic, leading to an estimated loss of . bn usd, times higher than the cost for controlling the disease itself [ ] . besides economic loss, the crisis in management of chronic diseases such as epilepsy has long been underestimated. as the world's fourth common neurological disorder, epilepsy has affected over million people worldwide and has a prevalence of . ‰ in china, which means that nearly out of people, no matter within or out of an epidemic area, suffers from epilepsy [ ] . more importantly, cases of epilepsy are not evenly distributed in the world, as a significantly higher portion of patients with epilepsy (pwes) live in resource-limited regions [ , ] , places that are also vulnerable to epidemic outbreaks, thus bringing a new problem as to how to manage epilepsy during an epidemic. similar to many other chronic diseases, epilepsy management requires regular follow-up and sustainable medicine supply [ ] . however, these medical resources are difficult to obtain during an epidemic. on the other hand, successful control of epidemics such as covid- epidemic demands the cut-off of routes of the possible transmission [ ] . in such case, controlling the flow of population as well as community containment would be inevitable, which may affect medical interactivity between neurologists and pwes, restrict patient access to medical resources, and make the management of epilepsy more difficult than ever. to address these challenges, some approaches must be considered, including expanding self-management, using smartphone application-based communications and maximizing the availability of anti-epileptic drugs (aeds) by all means. above all, a systematic epilepsy management framework is critical for dynamically responding to epidemic changes. unfortunately, current epilepsy management framework is generally a periodic outpatient assessment model [ ] , where a certain medical center is the node for almost all medical services and patients actively transport themselves from home to hospital periodically. due to the uncertainty of patient flow and unbalanced accessibility of medical resources, such system is less adaptable and cannot cooperate with disease control policies in epidemic areas. furthermore, the current framework causes a huge waste of medical resources in that the preference of both doctors and patients, rather than objective need, acts as a major driving force for medical service [ ] . hence, a new framework that avoids unnecessary transportation while maximizing the availability of medical resources according to demand is needed. here we review approaches that help control epilepsy during an epidemic event and raise a new conceptual management framework. although not so efficient as many caregivers expect, self-management has its value for chronic diseases [ ] . self-management is characterized by abilities of patients to detect and manage their own conditions. these abilities include management of both medical and nonmedical issues such as emotion or role changing [ ] . luedke et al. summarized six aspects of selfmanagement for pwes based on a systematic review, which are knowledge acquisition, problem solving, medication management, health behavior changing, symptom monitoring, and safety promotion [ ] . pwes have educational needs on two major classes of information for self-management. the first is predesigned knowledge on epilepsy and related issues while the second being a practical guide to self-management of other conditions, especially the psychosocial therapy, and applying it in pwes [ ] . the predesigned epilepsy-specific program largely involves basic knowledge on epilepsy, medication management, and problem-solving suggestions, while psychosocial therapy mainly focuses on health behaviors and related knowledge. to be noted, the details of selfmanagement differ among studies [ ] [ ] [ ] , making it difficult to evaluate the efficacy. a potential solution to this problem is to establish a network that integrates different programs and evaluate their efficacy, effectiveness and dissemination [ ] . however, during an epidemic, the content of these programs requires upgrading. information on the epidemic should be incorporated into the knowledge education and health behavior changing programs. sufficient information on transmission routes and prevention approaches of epidemics is critical for epidemic control [ ] . strong mental and emotional health support is another aspect of importance [ ] due to the fact that an estimate of - % of pwes suffer from anxiety even without an epidemic [ ] [ ] [ ] . on the other hand, epidemic itself can raise public stress. one example is that during the sars outbreak in , the suicide rate in hong kong increased significantly due to loneliness and disconnectedness [ , ] . more recent data during the covid- outbreak showed that . % of people suffer moderate to severe stress from epidemic and . % to . % develop anxiety [ , ] . behavioral intervention taught through the self-management program has been proven beneficial for anxiety in both epilepsy [ ] and epidemic [ , ] . approaches to deliver self-management knowledge can also be influenced by the epidemic. face-to-face training, including group design, is the major method of teaching for pwe self-management, which is usually conducted for to h [ ] . however, it is unclear during an epidemic that whether these trainings are still available and to what extent can they reach pwes. another concern is that bringing patients together to a teaching class could increase the risk of infection. an alternative method is to group and train them through internet [ ] , although it would be hard to cover elder people [ ] . the advantages of self-management during an epidemic could be more than epilepsy control only. the self-management program and pwes can form a network of information exchange, which may be helpful in the control of epidemic. such network, especially that online [ ] , provides a direct route for caregivers to contact pwes, thus paving the way for gathering selfreported information on health and other epidemicrelated information. furthermore, pwes in the system are trained to cope with epilepsy-related issues, thus avoiding repeated visits to the hospital, lowering the risk of exposure to the epidemic. even under circumstances that require hospital support, the problem-solving training can help perform reasonable decision-making and avoid unnecessary blindness in seeking for medical help. however, self-management has limits. studies have suggested that the efficacy of self-management from different programs varies significantly [ ] . some studies [ ] even showed that group education is less effective in improving the quality of pwe's life. patients in the program should be aware of the side-effects of over-reliance on self-management and exaggeration of its role in medical system [ ] . they must understand that they still in many ways require professional medical support, including hospitalization. several concise thresholds for seeking medical help must be emphasized in order to keep pwes safe. it is also not recommended in any condition to self-manage epidemic at any time! smartphone application and remote medical care in epilepsy management smartphone applications (apps) and other remote medical care approaches are familiar things to patients with chronic disease. in epilepsy alone, a series of studies [ ] [ ] [ ] have tested the value of apps in management of seizures and other issues. digital technology in the management of epilepsy features a new trend in epilepsy control. there has been a rapid increase of available apps for pwes. from the end of to , the number of epilepsy-related apps increased from ground zero to [ ] . additionally, an overwhelming majority of these apps are free for use. in , escoffery et al. reviewed over apps from apple store for their functionality, esthetics, and information contained. they found that most apps in epilepsy management are designed for adults and focused on treatment, seizure tracking, response and safety, which cover a significant portion of self-management [ ] . although the population sampled was small, apps for epilepsy management significantly improved users' epilepsy knowledge, personal safety management and adherence to aeds [ , ] . apps are considered as a new tool for the selfmanagement program for delivering information and the potentials of apps on pwe management may be underestimated. however, many new attempts have been made to develop more efficient epilepsy-related apps. for example, to raise social awareness of epilepsy and meet the social needs of pwes, an app has been developed to offer social network function for pwes. other think-out-of-box attemps include a specifically-designed game for vegus nerve stimulation (vns) education [ ] . in an exciting study aimed to facilitate diagnosis of epilepsy in community by non-professional local caregivers using an app, researchers revealed a roughly equal specificity for correct diagnosis to physicians [ ] . these new attempts expanded the traditional concept of epilepsy control and fulfilled different levels of needs for pwes, even for caregivers. during an epidemic, the apps stand out for the convenience of communication, thus significantly reducing unnecessary transportation in seeking for medical assistance while providing necessary information in dealing with epilepsy and epidemic. however, surprisingly, the function of making appointment with or consulting a doctor only exists in two out of apps in escoffery's study [ ] , suggesting that most epilepsy apps are unable to provide sufficient medical support to pwe. meanwhile, apps with these important functions are designed either by hospitals or health organizations, indicating a necessity for strong collaboration between doctors and program developers. in addition, a recent study in west china found that although only . % of caregivers were using apps for management of epilepsy, . % of them were willing to do so [ ] , suggesting a promising future of app-based management. to fully control an epidemic, additional functions of apps are needed. since information gathering from individuals during an epidemic is critical, self-reporting of personal well being is promising. self-reporting has been widely practiced in china to control covid- outbreak. in china, a health qr code will be generated once a user completes self-report of his (or her) health through an app in the smart phone, which grants the access to train, subway, airline and other public places. however, these reports are not compulsory due to ethical considerations and must be gathered with consensus, limiting its reliability. transparency of official information on the distribution and number of infected patients in certain areas also helps control epidemics [ , , ] . during the covid- epidemic in china, apps such as alipay or baidu provide this official information on their pages. they post up-to-date information through data-mining and list distributions of confirmed patients according to areas. in addition to digital mapping, these apps even provide the exact buildings in which patients were discovered. although this may raise ethical concern, people can be guided to keep a distance from epidemic areas. to be noted, these apps are not specifically designed for epidemic, but rather flexible in their functions due to modular design. they may provide reference for epilepsy management apps to meet different needs. apps aiming at improving mental and emotional health are also important. mental health services are nowadays largely available online, even during epidemics [ ] , facilitating the route for intervention. hence, the proposed new approaches for treatment such as structured letter therapy [ ] for consultation on mental problem during covid- epidemic can be easily deployed in app. these apps are largely available online and have helped different groups of patients improving their mental and emotional health. in a review, apps on mental health were evaluated for their functions [ ] , suggesting that mental health apps with cognitive behavior treatment targeting depression and anxiety are available. these apps also included self-reporting function which not only keeps caregivers informed about patient's mental status, but also has great potentials in sharing epidemic information. apps with integrated epidemic control, mental health and epilepsy management functions are feasible and applicable. however, there are several controversial issues on apps. first is the acceptance rate of apps among pwes. a study performed in [ ] found that . % of mobile-phone users had tried at least health app. also, people who are more likely to use health apps are those younger, more educated and with higher income. interestingly, a more recent survey found that those with good or excellent health condition turned out to be the largest user group for health apps [ ] . for pwes, according to liu's study [ ] , . % of surveyed pwes considered apps in epilepsy beneficial and . % would like to accept using free apps. again, young people and urban pwes are more likely to use apps. another interesting finding of this study is that the attitude of patients with poor seizure control or having adherence issues turned out to be more positive towards apps. overall, these data indicated that health apps have a promising acceptance rate in the general population, but their use may still be refused or failed in the elder population and those who live in resource-limited areas. the second problem is withdrawl from apps. in krebs's study [ ] , up to . % of those who ever used health apps had stopped using some of these apps. the primary reasons are high data entry burden, hidden cost as well as degenerating interest [ ] . this tells again for developers that the quality of programming, content and visualization is important for a successful app. moreover, as we demonstrated above, the lack of direct communication with doctors as well as the lack of many other appealing functions may be potentially relevant to the withdrawal. studies must be done to further understand the core need from pwe before designing an app. although new therapies are emerging continuously, aeds still are the very bases of epilepsy treatment [ ] . there are currently two major commercial ways for pwes to obtain aeds: getting medicine in hospital and buying aeds from pharmacy. theoretically, pwes can access aeds according to their preference. however, practically, there are some factors influencing their buying decision, including price, distance from home, insurance coverage, brand and, above all, availability of aeds. availability of aeds is a major concern of epilepsy management, especially in resource-limited areas. a study in zambia carried out in found that . % of pharmacies did not even have aeds and only kinds of first-generation aeds were available [ ] . the same situation also occurs in other middle-and low-income countries. a study in reported that the available rate of basic aeds such as phenytoin, carbamazepine, valproic acid and phenobarbital is less than % in countries [ ] . what makes the matter worse is that these developing countries are also susceptible to epidemics, which can further deteriorate the availability of aeds, if not all medical resources. during the sars outbreak, even in major cities, there was a shortage of certain medicines [ ] , suggesting that the hospital-and pharmacy-centered supply of medicine has limits, and could not adapt to changes during an epidemic. another problem of this system is the requirement of active transportation of patients: in order to obtain necessary aeds, pwes have to go to pharmacies or hospitals regularly. such frequent flow of patients is unfavorable for epidemic control and may further aggravate the situation due to the lack of medicine. keeping daily supply of aeds for hospitals and pharmacies could also be challenging. particularly, transporting medical resource into quarantine areas during an epidemic is difficult. in addition, the focus at such time is always on gathering resources to control the infectious disease, threatening the supplement priority of aeds. however, there have been some new ways to solve this paradox. online pharmacy with non-contact express delivery service is a promising option. one such example is the major online shopping websites taobao.com and jd. com in china. both sites sell aeds as online pharmacies with permission. aeds including carbamazepine, valproic acid, phenytoin, lamotrigine, levetiracetam, topiramate, oxcarbazepine, gabapentin pregabalin, lacosamide and perampanel are all available online, except phenobarbital, which is considered a psychotropic medicine requesting special prescript from professionals. moreover, these aeds could be sent to any street address (except those in compete quarantine) in any county by express. there are some potential risks for such online shopping during epidemic. first is the concern that express may cause spread of disease, especially by the final door-todoor dispatching. during the covid- epidemic, companies in china established a way called 'non-contact approach' to deal with this concern. to be brief, the delivering system consists of two parts: intelligent express cabinet placed in the community and certain sets of protective equipment for couriers. in this non-contact system, all packages are delivered to the cabinet instead of to the door. the customer will receive an encrypted code corresponding to a cell of the cabinet where the package is stored, thus preventing direct contact with couriers. on the other hand, couriers are provided with masks, gloves, and glasses in order to prevent direct contact with contaminated goods. the efficiency of such system has been proven in recent covid- epidemic and express companies worldwide have referred to this approach. the second concern for online aed shopping is the time cost for shipping, which may be further prolonged during an epidemic. a reasonable solution is to post the estimated time for shipping on the buying page so that the pwe could know roughly the time for shipment. another solution is to establish a ranking system for express companies that provide expedited shipping for medicines. however, such ideas might not come into reality without the support of governmental policy, since these acts will inevitably raise the cost for express companies. a combination of local and online pharmacies could further solve this problem. local pharmacy has the advantage of sustainable source of aeds, while the websites could provide information on where aeds are available in local pharmacy, offering reserving services to further complete local availability. express to certain pharmacy is easier and faster to achieve, and also is an alternative way for non-contact express service, where pharmacy itself becomes an intelligent express cabinet. still, systematical reforms of both pharmacies and the government are needed to maximize efficiency and balance the operating cost. however, under the epidemic situation, it is highly recommended that pwe keep sufficient storage of aeds at all time and be readily resupplied with aeds through all available sources. in resource-limited areas where aed availability is extremely limited, strategies described above are difficult to carry out. the convulsive epilepsy management program in rural west of china may offer an answer to this crisis [ ] . the program enrolled any patient with convulsive epilepsy through a door-to-door interview conducted by local central disease control and primary care physicians, fully covering the population in the program area. the patients received phenobarbital as initial treatment and were followed up monthly for efficacy and safety. phenobarbital in the program was purchased directly from the pharmaceutical company by program fund, which thus ensured the long-term availability. although pwes in this program had limited options of aeds, convulsive epilepsy was successfully managed in over pwes with convulsive seizures with acceptable adverse events. during the covid- epidemic in , there was no report of aed insufficiency in any of the program areas. this suggests that official act, rather than dependence on local resources, is applicable for management of epilepsy during an epidemic in resourcelimited areas. there are limited studies on different management frameworks under different conditions, and only one framework was specifically designed for epilepsy during an epidemic [ ] . here we establish a new three-level framework for epilepsy management during an epidemic according to literature and based on our experience (fig. ) . generally, different levels refer to different institutions or medical entities with unequal capability of epilepsy treatment. added to these levels is the aeds availability and delivery system, both online and local, which determines what kind of treatment could be used during an epidemic. the whole framework is boxed by a secured medical information system which intends to minimize the unnecessary flow of patients while maximizing the continuous communication among different compartments. these three levels, namely, patient & family level, community support level and hospital level, are geographically independent, making quarantine of certain level possible during an epidemic. also, they conceptually represent different management measures in epilepsy. the patient & family level focuses on self-management, including all six components mentioned above [ ] and is facilitated by epilepsy-related apps, while the community support level, consisting of general physicians and other local caregivers from the community, acts both as a threshold for hospitalization and an outpost for providing basic intervention, including education, adjusting aed doses, rehabilitation and mental health management. by emphasizing the role of the community, this system requires patient to report their health problems to community supporters for evaluation before going to hospital. the top hospital-level provides medical support for patients with new-onset epilepsy and those in urgent needs. normally, patients with first seizure-like onset, either provoked or unprovoked [ ] , should be sent to hospital for systematic examination if possible. however, such active response to epilepsy as a chronic disease during an epidemic is debatable. since a clear medical history is key to the diagnosis, online consulting with community caregivers or even epileptologists is recommended before directly visiting a hospital. this approach could avoid blind seeking for medical support and ease the psychological impact from first seizure. considering that neuroimaging and electroencephalogram are both necessary for diagnosis of new-onset epilepsy, it is important to make an appointment for these tests during an epidemic. patients must be informed the importance of these examinations for determining the etiology and diagnosis. however, they should also understand that (a) a number of patients will not suffer second seizure in a relatively long period of time, which will even not recur at all [ ] ; (b) if the medical history is typical, the diagnosis of epilepsy can be made without these tests [ ] ; (c) some provoked seizures (i.e. alcohol-induced seizures) can be prevented by avoiding triggering factors [ ] ; (d) even with neuroimaging and electroencephalogram tools, the etiology of some onsets may be still controversial due to many factors. since online prescription systems have already been in legal use, a further decision as whether to start aeds immediately can also be discussed during online consulting. on the other hand, in the presence of any clue of the following situations, hospitalization should be recommended (thresholds of transfer to hospital for patients with first onset) (any of below): . evidence of prolonged seizures which last for more than min . seizures are accompanied by other symptoms, including developmental problems, impaired cognitive function, paralysis, psychological syndrome, and other neurological problems that cannot be explained by seizure itself . recurrent seizures that cannot be explained by a specific cause or triggering factor . patient has a clear family history of epilepsy . atypical onset that could not distinguish seizures from syncope . elder patient (> years) under such scenarios, community support is needed to secure a safe transfer route to the hospital in order to lower the risk of epidemic infection. for the ongoing pandemic, there is no evidence that covid- could directly induce epilepsy [ ] . a recent study in wuhan identified only one seizure in a severe case [ ] . another report from japan described a covid- related meningitis/encephalitis case presenting with seizures [ ] . however, in this case, the rna test was only partially positive in cerebral spinal fluid and was negative on nasopharyngeal swabs sample. follow up during an epidemic is achieved through a medical information system consisting of two parts. the first is a unified smartphone app for patients with daily reminder for medicine adherence, seizure recording, a patient outcomereporting system and an online communication function. it works not only as a tool for self-management, but also as a node for epidemic education, emotional intervention and other potentials, such as social function. all information gathered from app will be presented regularly (i.e. every month) as patient-reported outcomes for evaluation by community caregivers. the second part targets those who do not have the ability or are unwilling to use apps. regular followup through telephone by community is recommended. two sets of thresholds are set for community caregivers to screen for patients requiring further interventions: first set: requesting community medical intervention (primary physicians & caregivers) (any of below): fig. schematic diagram of the three-level management framework for epilepsy control during an epidemic . efficacy issue (the patient did not reach seizure free in the last month) . adherence issue (the patient failed to understand protocol or had more than protocol-violence in the last follow-up period) . adverse events (any event that has mild or moderate influence on patient's daily activity) . emotional instability (patient presented with mild to moderate anxiety or depression symptoms, or obvious stress in response to the epidemic) second set: requesting intervention by hospital and transfer to hospital (any of below): . patient presented with status epilepticus (defined as any tonic-clonic seizure lasting for more than min, focal or other types of seizure for more than min, or patient did not recover between two seizures [ ] ) . serious adverse events (events that significantly influence patient's daily activity, or require additional medicine, or require inpatient treatment) . lack of efficacy (a reduction of seizure frequency in the last month of less than % of baseline or any deterioration of seizures, either in frequency or in manifestation) emotional impact (severe anxiety or depression) by reviewing patient-reported data, such system allows community caregivers to filter and separate patients into different subgroups according to their actual medical demand. patients below such threshold would maintain their current management and stay within the first level. those beyond the first threshold need to contact, either in an online or in a face-to-face manner, the community caregivers to acquire appropriate intervention. since the community-based medical care is within a certain geographical range and patients have no necessity to blindly seek for medical care, this framework can theoretically minimize the mobility of patients, thus contributing to epidemic management as well. however, if a patient reaches the second threshold, he (or she) would be in need of hospital care. a transport arranged by community is recommended to secure a safe and swift pathway. another important part of this framework is the aed availability, which stands beside the three levels. as discussed above, multiple measures are taken to achieve high availability of aeds, including maintaining storage for local pharmacy, online reservation of aeds, priority shipment and non-contact express delivery service. finally, fodjo's [ ] practice as well as our own experience [ ] in rural west of china suggests that strong governmental act is needed for successful management of both epidemics and epilepsy, especially in resource-limited areas. practical test is needed for further refinement of this framework. the management of epilepsy as well as many other chronic diseases under an epidemic is largely unknown. emerging approaches such as self-management, apps and non-contact delivery service are promising solutions to this problem and can be integrated into future management frameworks. meanwhile, a joint effort from health providers, society and government is essential for addressing the challenges. global trends in emerging infectious diseases the economic impact of sars in beijing prevalence of epilepsy in china between and : a systematic review and meta-analysis estimation of the burden of active and life-time epilepsy: a meta-analytic approach epilepsy in poor regions of the world characteristics of and important lessons from the coronavirus disease (covid- ) outbreak in china: summary of a report of , cases from the chinese center for disease control and prevention digital care in epilepsy: a conceptual framework for 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consultation on novel coronavirus (covid- )-related psychological and mental problems: structured letter therapy mental health smartphone apps: review and evidence-based recommendations for future developments health app use among us mobile phone owners: a national survey health app use among us mobile phone users: analysis of trends by chronic disease status feasibility and acceptability of smartphone applications for seizure self-management in china: questionnaire study among people with epilepsy drug development for refractory epilepsy: the past years and beyond the current availability of antiepileptic drugs in zambia: implications for the ilae/who "out of the shadows" campaign mapping the availability, price, and affordability of antiepileptic drugs in countries the operational model of a network for managing patients with convulsive epilepsy in rural west china comprehensive management of epilepsy in onchocerciasis-endemic areas: lessons learnt from community-based surveys is the first seizure epilepsy--and when? evidence-based guideline: management of an unprovoked first seizure in adults: report of the guideline development subcommittee of the american academy of neurology and the ilae official report: a practical clinical definition of epilepsy new-onset acute symptomatic seizure and risk factors in corona virus disease : a retrospective multicenter study neurologic manifestations of hospitalized patients with coronavirus disease a first case of meningitis/encephalitis associated with sars-coronavirus- a definition and classification of status epilepticus--report of the ilae task force on classification of status epilepticus the authors want to thank all medical staff for fighting against covid- outbreak. the topic of this review and the management framework were proposed by ling liu and dong zhou. the manuscript was drafted by deng chen, lina zhu, and xin lin. the construction of the framework and the manuscript were further improved by zhen hong and shichuo li. the authors read and approved the final manuscript. key: cord- - su uan authors: lynteris, christos title: introduction: infectious animals and epidemic blame date: - - journal: framing animals as epidemic villains doi: . / - - - - _ sha: doc_id: cord_uid: su uan the introduction to the edited volume summarises the chapters of the volume and discusses their contribution in the context of current historical and anthropological studies of zoonotic and vector-borne disease, with a particular focus on how epidemic blame is articulated in different historical, social and political contexts. of 'emerging infectious diseases' (eid), which configures the rise of new diseases as carrying with it a potential for human extinction. this volume examines the history of the emergence and transformation of epidemiological and public health framings of non-human disease vectors and hosts across the globe. providing original studies of rats, mosquitoes, marmots, dogs and 'bushmeat', which at different points in the history of modern medicine and public health have come to embody social and scientific concerns about infection, this volume aims to elucidate the impact of framing non-human animals as epidemic villains. underlining the ethical, aesthetic, epistemological and political entanglement of non-human animals with shifting medical perspectives and agendas, ranging from tropical medicine to global health, the chapters in this volume come to remind us that, in spite of the rhetoric of one health and academic evocations of multispecies intimacies, the image and social life of non-human animals as epidemic villains is a constitutive part of modern epidemiology and public health as apparatuses of state and capitalist management. whereas the above approaches (including microbiome studies, and 'entanglement' frameworks in medical anthropology) do contribute to a much-needed shift in the intellectual landscape as regards the impact of animals on human health, their practical and political limitations are revealed each time there is an actual epidemic crisis. then, all talk of one health, multispecies relationships and partnerships melts into thin air, and what is swiftly put in place, to protect humanity from zoonotic or vector-borne diseases, is an apparatus of culling, stamping out, disinfection, disinfestation, separation and eradication; what we may call the sovereign heart of public health in relation to animal-borne diseases. for the maintenance and operation of this militarised apparatus, the framing of specific animals as epidemic villains is ideologically and biopolitically indispensable, even when blame of the 'villain' in question lacks conclusive scientific evidence (see thys, this volume). going against the grain of scholarship that in recent years has sought to portray the vilification of animals as hosts and spreaders of disease as a thing of the past, histories of non-human disease hosts and vectors aims to illuminate the continuous importance of this ideological and biopolitical cornerstone of modern epidemiology and public health. representations of animals as enemies, antagonists or sources of danger have, in different forms, shapes and degrees, been part and parcel of human interactions with the non-human world across history. it is, however, only at the turn of the nineteenth century that, as a result of bacteriological breakthroughs, non-human animals began to be systematically identified and framed as reservoirs and spreaders of diseases affecting humans. to take one famous example, before the end of the nineteenth century, rats were not believed to be carriers or spreaders of plague or any other infectious disease. whereas rats had long been considered to be damaging to human livelihood, due to consuming and spoiling food resources, their only redeeming characteristic was, erroneously, widely believed to be their supposed disease-free nature. hence while mid-seventeenth-century plague treatises noted the rat's destructive impact on fabrics and food, no mention of its connection with the disease was made. equally, two centuries later, when in - british colonial officers in india observed that, at the first sight of rat epizootics, garhwali villagers fled to the himalayan foothills in fear of the 'mahamari' disease, they dismissed this behaviour as merely superstitious. however, the bacteriological identification of rats as carriers of plague or mosquitoes as carriers and spreaders of yellow fever and malaria, at the end of the nineteenth century, was itself enabled and indeed complicated by an already-existing stratum of signification which, by the mid-seventeenth century, had led to the introduction of new symbolic, ontological and legal frameworks of thinking about animals as 'vermin'. vermin, in mary fissell's definition, 'are animals whom it is largely acceptable to kill', not because of some inherent characteristic they possess, but because, in specific historical contexts, 'they called into question some of the social relations which humans had built around themselves and animals'. paraphrasing fissell, we may say that, arising in early modern europe, the category 'vermin' problematised animals which devoured or destroyed the products of human labour and the means of human subsistence in terms of an agency or intentionality that confounded human efforts to control them. departing from the structuralist influences of mary douglas, which dominated animal studies in the s (see, for example, robert danton's work on the great cat massacre in france), and from keith thomas' 'modernisation' reading of vermin as simply animals that were of no use in an increasingly utilitarian world, fissell's discourse analysis of popular texts on vermin from seventeenth-century england was the first to dwell in the social historical reality of the emergence of this notion. however, more recent studies have opposed fissell's idea that what made vermin a threat to 'human civility' was their perceived 'greed and cunning', or their overall 'trickster' character. lucinda cole's recent monograph imperfect creatures argues that, 'what made vermin dangerous was less their breedspecific cleverness or greed than their prodigious powers of reproduction through which individual appetites took on new, collective power, especially in relation to uncertain food supplies'. the two approaches are not mutually exclusive. indeed, if approached anthropologically, they point to an entanglement between symbolic and economic aspects of vermin as threats to 'social integrity', something that is further supported by the association of vermin at the time with vagrancy and the poor. medical historians have in turn noted the association of vermin with miasma in disease aetiologies and public health practices of early modern europe, especially in times of epidemics when extensive legislation against them and prescriptions for their destruction are recorded. this was particularly the case in the context of plague outbreaks that had long been associated with 'putrid' and 'corrupt' vapours, which certain animals, like dogs, pigs, cats and poultry (and their excrements and carcasses), were believed to emanate. as in the late middle ages, the fear of pestilential miasmata emanating from offal and other meat products had led to the spatial regulation of butchery in england and other parts of europe (cf concerns with 'bushmeat' in relation to ebola; thys, this volume), william riguelle has shown that, in the course of the seventeenth century, concerns with 'noxious' animals played an important role in instituting limits of where these could be kept and where they could be allowed to roam in urban environments. the idea of miasma would continue to impact medical thinking into the nineteenth century. as a part of ontologies that escape both the straightjacket of recent anthropological classifications and classical medicalhistorical dichotomies of contagionism/anti-contagionism, the idea of miasma was malleable, adaptable and ambiguous enough to be compatible with, rather than antagonistic to, that of infection and contagion. however, as new medical and biopolitical challenges arose in the context of colonial conquest, the problematisation of animal-derived miasma or 'febrile poison' gave way to concerns about the climate as the driving force of epidemic disease. thus while the dawn of bacteriology, by the s, did not introduce understandings of animals as sources of disease ex nihilo, it did mark a drastic return to this idea, and, at the same time, led to a significant conceptual shift as regards the ontology of the diseases transmitted, and the mechanism involved in this transmission. this transformation was catalysed by an intense medical, economic and political interest and concern over cattle epizootics, which, as historians have shown, catalysed both the emergence of veterinary medicine and the medicalisation of animals across the globe in the second half of the century. as regards infectious diseases affecting humans, the medicalisation of non-human animals and their transformation into 'epidemic villains' involved an interlinked, two-part framing of their epidemiological significance: on the one hand, as spreaders and, on the other hand, as reservoirs of diseases. the historiography of the identification and study of non-human animals as spreaders of infectious diseases has for some time now stopped being the foray of heroic biographies of men like ronald ross, paul-louis simond or carlos chagas. focused on the social, political and epistemological histories of scientific studies of zoonosis and vector-borne diseases, historians, anthropologists and sts scholars have underlined the ways in which, within epidemiology, bacteriology and parasitology, non-human animals constituted active agents in complex networks of power and knowledge, and how they assumed different epistemic value in diverse colonial and metropolitan contexts. framed as spreaders of infectious diseases, animals also came to play an important role in what charles rosenberg has famously described as the dramaturgy of epidemics. assuming a protagonistic role in a series of epidemic and public health dramas, animals came to be seen as the ultimate source of disease outbreaks. no longer simply a nuisance or 'pests', the transformed image of a series of animals (mosquitos, rats, ticks, lice and flies in particular) as enemies of humanity was invested with militaristic tropes and colonial moralities. these animals formed as it were a global repertoire of disease spreaders, while at the same time assuming importantly diverse local forms, often in interaction with concerns and social imaginaries about other, regionally specific, disease hosts and vectors (beetles, bats, sandflies, etc.). while it is not in the scope of this introduction to map these 'glocal' interactions, deborah nadal's chapter in this volume provides a detailed picture of the longue durée of dogs as spreaders of rabies in india. nadal's chapter underlines the complex and important semiotic and ontological workings and re-workings on dogs as spreaders of rabies from colonial india to our times. with dog-borne rabies being recognised as an important public health problem across the globe since the s, in india, where rabies is endemic, human understandings of the particular zoonosis were linked to practices of classifying dogs. for british colonials, distinguishing between rabies-prone and rabies-impervious dogs was key to the imperial project of mastery over both indian society and 'nature'. within the confines of tropical medicine and its biopolitical imperatives, the management of rabies made crucial the definition of dog-human relations in terms of ownership. believed to be able to spontaneously develop rabies, for the british, 'ownerless' dogs presented a distinct danger for the colony. seen as the source of infection amongst owned dogs (which were considered unable to develop spontaneous rabies), these animals, nadal argues, challenged victorian morality and were associated with two key notions: on the one hand the notion of 'stray', with its overtones of vagrancy, and, on the other hand, the notion of the 'pariah'-an anglicised caste term used by british colonials to refer to outcaste or untouchable communities. at the heart of these classifications lied ideas about domesticity and wildness, as well as a pervasive social hierarchical mentality. perceiving street life in general as a threat to colonial rule grouped dogs of distinct social status and social life under one, infectious category. transforming 'strays' from 'vermin' and 'nuisance' into epidemic villains that should be sacrificed in the name of human health was not, however, a frictionless process but, as nadal shows us, one that embroiled indian society in debates about the value of life and compassion (led by both anti-vivisectionists and mahatma gandhi). after , 'catch-and-kill' of dogs for the control of rabies continued unabated but also involved indian society in renewed debate involving civil society activists, animal welfarists and political parties. in nadal's reading, these dog-related conflicts underlined a lingering problem pertaining to the classification of dogs vis-à-vis rabies: the persistence of the term 'stray' (inclusive of its 'pariah' associations). the solution since , nadal argues, has been the emergence of a discourse around 'street dogs', which has marked a shift towards an accommodation between different attitudes towards the particular animals, allowing for the concept that they can be both masterless and hygienic. nadal's chapter thus points out that, at the same time as what we may call high-epidemiology redefined experiences of non-human animals as spreaders of disease, it also instituted regimes of hygienic hope. envisioning and putting in place programs of increasing separation between humans and non-human disease vectors became the hallmark of public health from onwards. whether this involved rat-proofing, ddt spraying, mosquito nets, the cleaning of streets from stray dogs or the drying of swamps, this sanitary-utopian aspiration to liberate humanity of zoonotic and vectorborne diseases was based on a vision of universal breaking of the 'chains of infection'; a separation and, at the same time, unshackling of humans from disease vectors that was aimed at confining pathogens in the animal realm. in this way, whereas separation from animals was seen as a sufficient means of protection of humans from zoonotic and vector-borne diseases, animals themselves were defined as ultimately hygienically unredeemable-they were, in other words, rendered indistinct from disease. hence, the naturalist ontology of the enlightenment, which in philippe descola's anthropological model defines humans and animals as unified under the rubric of nature, was unsettled by a radical divide that saw disease as a mode of being which was only inherently proper to non-human animals, and only tentatively, or, as sanitary utopians would have it, temporarily, part of the human species. sayer's chapter in this volume focuses on the - plague outbreak in freston (suffolk, uk)-the last outbreak of plague in the history of england-and excavates the epistemological, political, class and colonial history of such a regime of prevention and hope. analysing what she calls 'the vermin landscape' of the outbreak, sayer focuses on non-human animal actors so as to show that, in spite of the widespread epidemiological acceptance of the rat flea (xenopsylla cheopis ) as the true spreader of plague, ideas about locality and class created a medico-juridical matrix where it was the rat that constituted the main object of scientific investigation and public health intervention. situating the suffolk outbreak both within the third plague pandemic and within british imperial science politics, sayer stresses the ways in which suffolk was connected to india, as the prime locus of the pandemic and of plague science in the empire. as the outbreak in suffolk was experienced as an echo of the ongoing devastating epidemic in india, the rat became an object of epidemiological concern and fear. what if infected rats moved from the rural hotspots of the epidemic into urban areas, transforming them into the equivalents of plague-ravaged bombay on english soil? such fears were fostered not just by the perceived natural traits of rats (as invasive of migratory animals), but also through their association with the rural poor. tapping into complex imaginary registers involving victorian systems of class-related disgust, the english rural idyll, and the image of 'the labourer's country cottage […] as literal and figurative representation of the state of the nation', sayer argues that, 'because this rested in turn on the state of the rural labouring class, and that class were said here to be unsanitary and their cottages invaded by rat and plague, the indian racial other therefore ghosted a new category of (dead) undeserving poor'. as epidemic villains, in the eyes of epidemiologists and public health authorities, rats indianised the dwellings of rural labourers in suffolk. as 'plague was equated with "rat plague"', plague also became indian plague, and in turn necessitated control measures and legislation aimed at 'codif [ying] the rat in law and normalis[ing] its destruction'. formulated around an entanglement of class and interspecies relations, the suffolk plague crisis led, on the one hand, to an increasing medico-juridical investment of the rat in england, while, on the other hand, to a systematic neglect of 'the hares, cats, dogs that featured in gamekeepers' and labourers' narratives of the disease'. identifying and investing on a non-human epidemic protagonist (the rat) led to, and indeed required, a disinvestment and neglect of other species involved in the spread of the disease, and-perhaps most crucially-to overlooking the ecological complexity of disease persistence and transmission between different species in any given ecosystem. the rats and mice (destruction) act , 'which tasked every british citizen with a legal obligation to remove rats from their property', was the pinnacle of the configuration of the rat as an epidemic villain in england and of the institutionalisation of sanitary regimes of hope as regards the prevention of animal-borne infection. having conquered the globe by the mid- s, this regime of prevention and hope came to an end with the dawn of the emerging infectious diseases framework in the early s, when scientists began to focus on processes leading to new diseases, hitherto of non-human animals, infecting humans and to the 'specie-jump' processes (so-called spillover) leading to this phenomenon: 'rather than revolving around already-existing pathogens and how they circulate in specific ecological contexts, the focus on emergence required a shift of attention to what we may call "viral ontogenesis"'. over the past years, the rise of 'emergence' as the central framework of studying and understanding infectious diseases has led to a radical shift of scales and a reinvestment on zoonotic diseases that has been tied to a shift away from prevention towards preparedness. this is a regime of biosecurity that, as anthropologists like andrew lakoff, frédéric keck and carlo caduff have shown, is based on the anticipation of an unavoidable pandemic catastrophe, and which sets in place technologies of biosecurity that have come to increasingly dominate the realm of global health. envisioned as inevitable and catastrophic, 'emergence' has thus radically transformed the status of animals as epidemic villains. on the one hand, whereas in the sanitary-utopian framework of highepidemiology, animals were considered to be isolatable carriers of disease, in the eid framework infection is rendered inevitable. and, on the other hand, whereas for the sanitary-utopian framework, animal-human infection posed a limited threat to humanity, for eid it poses an unlimited one, or to be precise one associated with existential risk. it is telling that the mytho-historical event defining the conceptual horizon of the sanitaryutopian framework was the black death. believed by to have been rat-borne bubonic plague, the fourteenth-century pandemic was used by moderns as a key cautionary tale, and at the same time as a potent medical metaphor: black death was something that could 'return' (as hundreds of reports and news items made clear during the third plague pandemic) but whose impact would be effectively limited by grace of modern medicine and sanitation. on the other hand, as caduff has shown, the mytho-historical event defining the conceptual horizon of eid is the flu pandemic. the political ontology of this event for our contemporary pandemic imaginary is distinctly different from that of the black death for the early-tomid-twentieth-century public. for, as every contemporary epidemiological report and news broadcast makes clear, were an event like 'the spanish flu' to occur again today, globalisation and modern transport would transform it to an event of human extinction proportions; something not only nonpreventable, but whose control, once it has begun, is not guaranteed. both of these mytho-historical events have non-human animals at the heart of their causation narrative: the black death (at least so scientists believed at the time) rats, while the flu birds, probably chicken. however, while the sanitary myth of origin of the black death portrayed the rat as an ancient enemy of humanity whose days were numbered due to the advancement of science, the eid myth of origin frames chicken as just one example of a host of unknown species from which the 'killer virus' may emerge and against which the only action we can take is being prepared. séverine thys' chapter in this volume explores the consequences of the eid approach to non-human animals, as it applied to 'bushmeat' in the context of the recent ebola epidemic in west africa ( - ), with a focus on the impact of epidemiological and public health framings of 'bushmeat' hunting, butchering and consumption. especially affecting 'forest people' in macenta, guinea-conakry, the framing of a fluid host of animals as the source of epidemiologically illicit meat relies on persistent colonial tropes that imagine the 'tropical jungle' as an originally natural realm whose disturbance by human activity leads to the emergence of killer viruses. rehearsed time and again in films like outbreak ( ), this mortal link between nature and culture, thys reminds us, is currently being mediated by the figure of the bat-the in-between figure of a 'rogue' animal, which, james fairhead has shown, is being increasingly deployed as an epidemiological bridge in several zoonotic scenarios (ebola, mers, sars). thys follows other anthropologists in pointing out that this insistence on 'bushmeat' and contact with fruit-bats frames local cultures as pathogenic, in line with paul ewald's notion of 'culture vectors', and thus 'obscure[s] the actual, political, economic, and political-economic drivers of infectious disease patterns'. framed in terms of a 'transgression of species boundaries', ebola spillover events are thus pictured as resulting from a life led according to 'traditional' (and the implication is irrational) classificatory systems that fail to maintain 'us vs. them' boundaries. replete with visual and affective structures of disgust, this view, thys argues, is not challenged by the one health framework, which 'should provide a more nuanced and expanded account of the fluidity of bodies, categories and boundaries' so as to 'generate novel ways of addressing zoonotic diseases, which have closer integration with people's own cultural norms and understandings of human-animal dynamics'. key to this, according to thys, is to recognise and examine the historically dynamic nature of these classificatory and more broadly ontological systems (a view shared by nadal, this volume), and the explanatory models with which they are entangled. thys outlines the complex matrix of uses of non-farmed meat in the region (for nourishment, medicaments, trophies, etc.) and their transformation under the weight of regional and global commodity market networks. one may add that what is often neglected is the fact that 'bushmeat' was used by colonial authorities as a reward to local communities; in angola, for example, the portuguese rewarded local communities with 'bushmeat' for rat-catching in the colonial power's effort to contain plague during the s. the political investments of non-human animals as disease spreaders are further explored in gabriel lopes' and luísa reis-castro's chapter in this volume on the history of the aedes aegypti mosquito in modern brazil. following the social life of the particular mosquito species from the s until today, lopes and reis-castro stress that, while recognising that it has always constituted an 'epidemic villain', we need to pay closer attention to the particular diseases to which this villainous character has been linked to, and to the corresponding political system under which this identification has been undertaken, over the course of modern brazilian history. at the beginning of the twentieth century, aedes aegypti was associated with 'underdevelopment' as a key overarching ailment of brazil, with 'the image of a plagued country swarming with mosquitoes' filled with yellow fever playing an important role in bringing health under the rubric of the state and its modernising agenda. lopes and reis-castro follow gilberto hochman's classic work on the linkage between sanitation and nationbuilding in brazil in stressing that what began as a project of 'civilizing the tropics' by eliminating yellow fever across the country transformed by the early s into a more modest programme of preventing outbreaks in urban centres. by contrast to the liberal nation-building sanitary-utopian visions of oswaldo cruz and his collaborators in the first decades of the twentieth century, in the second half of the s a renewed focus on aedes aegypti was underscored by the politics of democratisation, following the end of the -year-long military dictatorship in . as by april it had become identified with dengue fever, as a new disease to plague urban 'areas marked by racialised histories of state abandonment and violence', the aedes aegypti became associated with a disease that was not as lethal as yellow fever, and which bore with it the sign of social, political and economic restitution. as public health had been the pejorative of left-wing and other democratic forces during the last decade of the dictatorship, calls to control dengue-carrying aedes aegypti as an embodiment of state violence and neglect contributed to the success of the 'sanitary reform movement' and the establishment, in , of brazil's sistema Único de saúde. lopes and reis-castro then turn their attention to the latest incarnation of aedes aegypti as a spreader of the zika virus. unfolding during the years of the impeachment (or judicial coup, depending on one's point of view) against dilma rousseff, the appearance of zika in brazil involved aedes aegypti in an international emergency. lopes and reis-castro examine the political struggles around zika-related mosquito control and argue that, focused on social inequality and the 'uneven effects of climate change', this new framing of the aedes aegypti on the one hand continues a longestablished practice of problematising it as a disease vector with specific political and political-economic parameters, while, on the other hand, introducing important gender-related critiques of public health. hence, while the authors claim that, 'the specific kind of virus in mosquitoes' bodies shaped what kind of epidemic villain the mosquito became', they also stress that, 'the mosquito as a vector carried not only three epidemiologically distinct viruses but very different political desires, struggles, and debates'. focusing on the recent zika crisis, in their chapter to this volume gustavo corrêa matta, lenir nascimento da silva, elaine teixeira rabello and carolina de oliveira nogueira in turn argue that the focus on mosquitoes' guilt and on the technological strategies developed to control these vectors unfolded within a context of profound political instability, and at the same time of epistemic uncertainty regarding key epidemiological traits of the disease. framing aedes aegypti as epidemic villains in this context, diverted attention from issues of social, economic and environmental injustice and inequality that were driving determinants of the outbreak, and legitimised the absence of governmental measures regarding the latter in response to the epidemic. the 'enactment of a global enemy, aedes aegypti, as the villain of the epidemic' thus allowed the brazilian government to paint an all-too-familiar and deceptive picture of a promethean struggle of the country as a unified whole (notwithstanding its enormous and often violent class, race, gender and ideological discrepancies and antagonisms) against a vile creature, which was solely held responsible for the disease. drawing on critical medical anthropological perspectives, matta et al. thus underline the structural violence inherent in both the discourse of epidemic villains and in the policies built and legitimated by this discourse. brazil's mosquitocentred policy in the face of zika, financially, politically and morally boosted by the declaration of public health emergency of international concern (pheic) by the who, relied on a securitisation framework that rhymed well with the broader neoliberal turn of the country and mobilised the image of the mosquito as a public enemy to create a spectacle of national unity that obscured 'iniquities, poverty, the skin colour of those bitten by mosquitoes, the house and streets where these fly, and the environment where they lay their eggs'. as mark honigsbaum has shown, disease ecology frameworks, arising in the usa in the s, framed non-human animals not simply as spreaders of infectious diseases but also as their 'reservoirs'. the 'great parrot fever epidemic' of - involved pet parrots in an epidemic panic across the globe, with a particular focus in the usa. as readers of the colonialist bande dessiné exemplar, tintin in the congo (published in the shadow of the epidemic in ), may remember, psittacosis (caused by chlamydia psittaci) is a zoonotic disease carried by parrots and parakeets that can infect humans. however, for karl f. meyer, a key contributor to the development of disease ecology, the ability of parrots and parakeets (popular pets at the time in the usa) to be asymptomatic carriers of the disease posed a more important problem that the immediate epidemic crisis; especially, honigsbaum explains, as '[t]hese latent infections were a particular problem in california where during the depression many people supplemented their incomes by breeding parakeets in backyard aviaries'. the discovery that psittacosis was not simply an 'exotic' disease imported to the usa by parrot traders, but one that had established itself endemically in american aviaries transformed the structure of epidemic blame from one focused on an outbreak to one focused on an endemic and, at the same time, from one revolving around an exotic invasion to one regarding unhygienic infrastructures at home. more profoundly, it also contributed to a shift towards a reframing of animal-borne disease in terms of disease ecology, a process which involved several decades of studies and interdisciplinary exchanges, but was ultimately triggered by an integration of charles elton's pathbreaking understanding of animal zoology in the realm of epidemiology. what is less well recognised historically is that the notion of the reservoir had a long history in epidemiological reasoning predating disease ecology. rats in particular were suspected, from as early as , as not only spreading plague (via their flea, xenopsylla cheopis ) but as also contributing to the maintenance of persistence of the disease in given urban settings. indeed, elton's interest in the role of disease in the regulation of animal populations was itself stimulated by earlier russian and chinese studies of the siberian marmot as a host of plague in the inner asian steppes. in chapter of this volume, christos lynteris returns to these studies to examine how the so-called tarbagan became the subject of investigations regarding plague's ability to survive the harsh winters of the region. the question was related to ideas about 'chronic plague', which in the case of the siberian marmot were linked to its hibernation between october and april. using an abundance of visual material, lynteris argues that, on the one hand, tarbagan burrows, which had been epistemic objects ever since the discovery of the species in , and, on the other hand, marmot hibernation, which had been the focus of scientific investigation in relation to host immunity already by , were tied together into an epidemiological duet as a result of the emergency of the manchurian plague epidemic of - . there is indeed a crucial metonymic work involved in this tying together the 'mystery of the survival of plague' over winter to marmot hibernation, and marmot underground dwellings. for the three actants in this network of what following genese sodikoff, we may call 'zoonotic semiotics'-latent plague, hibernating marmots, underground burrows-shared and maintained between them an image of 'mystery' and occultation which has been key both to epidemiological reasoning regarding infectious diseases and to the 'pandemic imaginary' underlying understandings of zoonosis. this image of plague taking advantage of unseen biological processes, materialities or infrastructures so it can assume an imperceptible form that would allow it to persevere over either human action against it or environmentally adverse conditions is of course reliant on pasteurian notions virulence, latency and attenuation. yet, more than simply illuminating a reiteration of bacteriological doctrine, what the tarbagan example points out to is a pervasive aspect of epidemiological reasoning; for the assumption that, when plague (or indeed any other disease) is not seen, this is because it is 'hiding', is part of what we may call a cynegetic complex in epidemiology. as john berger once noted, admittedly in a very different context, a key principle (and, one may add, a mythic structure) of cynegetic worlds is that, 'what has vanished has gone into hiding'. in the case of epidemiology, as with other cynegetic cosmologies, this implies an ambivalent relation. on the one hand, microbes are seen as predators of humanity, who lurk and hide so as to better ambush their prey. and on the other hand, as the enduring metaphor of 'virus hunters' amply illustrates, microbes are also seen as humanity's pray-which thus 'hide' to escape being caught and vanquished by us. as frédéric keck has stressed (following chamayou), '[w]hereas pastoral techniques are asymmetrical, relying on the pastor's superior gaze over the flock manifested by sacrifice, cynegetic techniques are symmetrical, as hunters and prey constantly change perspectives when displayed in rituals'. maurits meerwijk's chapter in the present volume shows that this is indeed a historically pervasive framework, which in the case of mosquitoes is carried over from tropical medicine into global health. comparing the discourses of ronald ross and bill gates, meerwijk shows how the cynegetic metaphor comes to encompass not only the pathogens in question but also their vectors. this points out at a transformative ontology underlying epidemiological reasoning, and its obsession with the 'invisibility' of disease, insofar as pathogens are seen, on the one hand, as able to persist by transforming themselves inside non-human animal hosts (by means of attenuation or mutation) and, on the other hand, as able to spread by transforming their hosts into bestial man-hunters. more than simply blaming non-human animals, in epidemiological reasoning, this double transformative ability configures the former into the loci par excellence of pathogenesis and, at the same time, necessitates techniques of rendering host-pathogen relations visible. visual images of non-human animals have played a historically important role in their configuration as epidemic villains. since the dawn of bacteriology, the scientific identification and examination of non-human hosts and vectors of infectious diseases have heavily relied on photographic technologies (including microphotography), diagrams and epidemic cartography. following sayer (this volume), animals have been 'fed into a data-focused visual regime', combining photography, mapping, diagrams and statistical graphs, that seeks to establish points of contact, habitats, interspecies boundaries and other forms of what hannah brown and ann h. kelly have called human/non-human 'material proximities'. in the context of high-modern epidemiology as well as in today's eid framework, these visualisations are part of a project of mastery aimed not so much at the subjugation of nature, as to the control of humanity's relations with nature. diagrammatic images of dissected mosquitoes played a key role in ronald ross' examination of the insects as malaria vectors, as, in later years, the microphotography of anopheles gambiae dissected ovaries would prove an indispensable, soviet-led method for identifying the capacity of a given mosquito to transmit the malaria plasmodium to humans. similarly, nicholas evans has shown, in the course of the third plague pandemic, comparative images between healthy and plague-infected rats became standard visual objects in epidemiological investigations and their published reports. but the visualisation of 'epidemic villains' did not always necessitate their direct representation. in her chapter for this volume, sayer draws an insightful comparison between two sets of visualising rat control, the first in the english port of liverpool and the second in british india. in both cases, the actual rats are imperceptible, with the photographic focus being on humans undertaking carefully orchestrated epidemiological work (rat dissection, flea collection); a fact which, in the case of liverpool, is underlined by the staged poses of the sanitary officers in questions, and, in the case of india, was permeated by colonial racial hierarchies in the representation of lab work. as representations of the relation between pandemic plague, medical science and empire, these images provide reassuring portraits of control in direct dialogue with the image of objectified rats, described by evans, thus 'making rats an integral part of plague'. similarly, with a focus on this relational aspect of human/non-human mastery and its visual regimes, in the second chapter of this volume lynteris illustrates how the epidemic framing of siberian marmots as reservoirs of plague in inner asia relied on photography and the diagrammatic cartography of their burrows. comprising in survey photographs of excavated marmot burrows and diagrammatic depictions of burrow systems, the visual regime constructed around this suspected host of plague following the manchurian plague outbreak of - comes to show, on the one hand, that intrusive practices of epidemiological visualisation were not limited to human dwellings, but also included those of non-human animals (photographing the marmot burrows required their prior excavation), and, on the other hand, that the visual framing of 'epidemic villains' is not limited to the representation of their role as spreaders of diseases. at the same time, the popularisation of the identity of specific mammals, birds and insects as disease spreaders has and continues to be mediated by their visual representation through photography, film and illustration. photographs of 'wet markets' in south china during and in the aftermath of the sars pandemic have been shown to incorporate a key principle of 'epidemic photography': the depiction of animal-related spaces as potential ground zeros of the 'next pandemic'. the practice of the public vilification of non-human animals and the framing of contact spaces between them and humans as infection hotspots was established for the first time in the course of anti-malarial and anti-yellow fever campaigns in the first decades of the twentieth century, but also during complex public health operations against plague in the context of the third plague pandemic ( - ) when the dreaded disease was often visually personified as the rat. indeed, quite often, the image of animals as enemies of humanity assumed anthropomorphic aspects, which under a colonialist gaze, involved racist inflections. in australian newspaper illustrations, for example, plague-carrying rats were depicted having chinese faces, thus both making an aetiological connection between plague and china (plague as an 'oriental disease' arriving from china, by chinese migrants) and fostering broader sinophobic bigotry at the time. in his examination of the framing of 'tiger mosquitoes' (aedes aegypti and aedes albopictus ) in this volume, meerwijk explores the rich visual culture supporting progressive framings of the specific mosquito species as infectious enemies of humanity. in a striking example, meerwijk shows how the diagrammatic juxtaposition of a mosquito and a tiger was used in a public health poster, meant to underline the predatory, man-eating qualities of aedes mosquitos. pointing at a pervasive tendency to talk about and visualise mosquitoes in terms of great predators (tigers, sharks) or 'enemies of humanity' (terrorists, vampires, prostitutes), meerwijk elucidates the work of the fusion between military, cynegetic and sexual metaphors and visual tropes employed in the depiction of mosquitoes across epidemiological paradigms. this is all the more important as the visualisation of animals as 'epidemic villains' was a trope that found application and success beyond epidemiology and public health. non-human animals were charismatic protagonists of political caricatures since the turn of the eighteenth century. in particular, lukas englemann notes, 'the "political bestiary", as gombrich calls the long tradition of depicting political issues through animal characters, acquired widespread popularity in the nineteenth century. the meaning many animals inhabited could be easily exploited to convey strong messages and almost always suggested degradation'. what changed at the turn of the nineteenth century was the introduction of a new aspect in the use of animals in caricature: their infectious nature. with political discourse utilising more and more medical terms at the time, the use of the visual form of the infectious animal to portray one's political enemies became an exemplary field of vilification. to mention only one example, in the course of the moscow trials, soon after the soviet state prosecutor, andrey vyshinsky, publicly pledged 'to stamp out the accursed vermin' who 'should be shot down like rabid dogs', the prolific cartoonist of the pravda, boris efimov (who was present at the trial), produced a striking caricature of leon trotsky and nikolai bukharin as a two-headed rabid dog held on the leash by the hand of the gestapo. however, as engelmann has shown in his examination of caricatures in the course of the plague outbreak in san francisco, the aim of depicting animals in the context of epidemic crises has not been limited to practices of blaming the former as spreaders or reservoirs of disease. in fact, animals were also used to critique and ridicule bacteriology itself. for example, in the case of san francisco, newspaper caricatures used animals to portray bacteriology 'as a science that formulated its judgments through experiments with animals, not in the treatment of people'. by visualising laboratory animals as 'vermin and pest', englemann argues, bacteriology was portrayed as 'a wasteful expenditure of public funds' and 'the medical laboratory was stripped of its progressive potential and instead appeared as an infliction of damage on the public good'. at the same time, as dawn day biehler has shown in her monograph on pests in twentieth-century us history, images of disease hosts, like rats, have also been used for subaltern purposes, such as the campaigns by the black panther party in the s- s against slumlords and the living conditions in african american neighbourhoods. for example, biehler argues, the well-known illustration by emory douglas, 'black misery! ain't we got right to the tree of life?', 'constrast[ed] with images of women afraid of rats; the woman's grip on the rat suggests determination, courage and fury'. here, the rat represented the unhygienic, exploitative and pestilential conditions imposed by white capital on working-class african americans, and the latter's determination to face up to this social injustice. the prolific use of images of non-human animals as 'epidemic villains' in diverse fields of social practice as public health campaigns, political propaganda, the critique of bacteriology and subaltern critiques of power and domination, points at the importance placed on the infectious nature or potential of animals both as a reality and as a metaphor in the modern world. however, whether it is to convey a threat to the national body, or to mock science, the use of these images also points at the fascination and discomfort of moderns towards non-human agency. underlining how epidemiology and public health emerged in relation to, and continue to be informed by framings of non-human animals as epidemic villains, the chapters in this volume explore the layered political, symbolic and epistemic investments of non-human animals, as these have become rhetorically and visually enabled in distinct ways over the past years. whether it is stray dogs as spreaders of rabies in colonial and contemporary india, bushmeat as the source of ebola in west africa, mosquitoes as vectors of malaria, dengue, zika and yellow fever in the global south, or rats and marmots as hosts of plague during the third pandemic, this volume shows framings of non-human animals to be entangled in local webs of signification and, at the same time, to be global agents of modern epidemic imaginaries. civet cats, fried grasshoppers, and david beckham's pajamas: unruly bodies after sars' the pandemic perhaps: dramatic events in a public culture of danger the scale politics of emerging diseases more than one world more than one health: reconfiguring inter-species health i am using animal-borne diseases here as a term inclusive of zoonotic and vector-borne diseases the rat-catcher's prank: interspecies cunningness and scavenging in henry mayhew's for an influential example of the rat being described as disease-free, see cristofano and the plague: a study in the history of public health in the age of galileo the rat would become suspect of carrying plague for the first time during the inaugural outbreak of the third plague pandemic, in hong kong, with another decade elapsing before the universal acceptance of the link between the animal and human plague. the first scientific study showing the role of the rat and its flea in the propagation of plague was: p. l. simond, 'la propagation de la peste imagining vermin in early modern england the great cat massacre and other episodes in french cultural history religion and the decline of magic: studies in popular beliefs in sixteenth and seventeenth century england imagining vermin in early modern england imperfect creatures: vermin, literature, and the sciences of life on vermin and the poor, see p. camporesi, bread of dreams: food and fantasy in early modern europe animal bodies, renaissance culture filth is the mother of corruption". plague, the poor and the environment in early modern florence que la peste soit de l'animal! la législation à l'encontre des animaux en période d'épidémies dans les villes des pays-bas méridionaux et de la principauté de liège ( - ) que la peste soit de l'animal!'; on ideas of miasma emanating from butchered meat see d. r. carr, 'controlling the butchers in late medieval english towns great stenches, horrible sights and deadly abominations": butchery and the battle against plague in late medieval english towns infection," and the logic of quarantine in the nineteenth century fractured states: smallpox, public health and vaccination policy in british india toxic histories: poison and pollution in modern india as kathleen kete has shown, the modern transformation of this connection, before the dawn of bacteriology, was fostered by a sexualisation of the disease, which rendered it comparable to uncontrollable impulses or lust. commenting on kete's work, linda kalof writes: 'since nymphomania and uncontrollable sexual desire in men were considered the result of prolonged sexual abstinence the beast in the boudoir: petkeeping in nineteenth-century paris looking at animals in human history healing the herds: disease, livestock economies, and the globalization of veterinary medicine veterinary research and the african rinderpest epizootic: the cape colony the great epizootic of - : networks of animal disease in north american urban environments' beastly encounters of the raj: livelihoods, livestock and veterinary health in india animals and disease: an introduction to the history of comparative medicine from coordinated campaigns to watertight compartments: diseased sheep and their investigation in britain, c. - unpacking the politics of zoonosis research and policy catching the rat: understanding multiple and contradictory human-rat relations as situated practices blaming the rat? accounting for plague in colonial indian medicine the bacteriological city and its discontents' malarial subjects: empire, medicine and nonhumans in british india what is an epidemic? aids in historical perspective wartime rat control, rodent ecology, and the rise and fall of chemical rodenticides urban mosquitoes, situational publics, and the pursuit of interspecies separation in dar es salaam the colonial disease: a social history of sleeping sickness in northern zaire the mobile workshop: the tsetse fly and african knowledge production cat and mouse: animal technologies, trans-imperial networks and public health from below building out the rat: animal intimacies and prophylactic settlement in s south africa'. american anthropological association (engagement modern" management of rats: british agricultural science in farm and field during the twentieth century of rats, rice, and race: the great hanoi rat massacre, an episode in french colonial history for a more detailed discussion of this process, see c. lynteris, 'zoonotic diagrams: mastering and unsettling human-animal relations' curing their ills: colonial power and african illness rethinking human-nonhuman primate contact and pathogenic disease spillover the scale politics of emerging diseases the pandemic perhaps avian preparedness: simulations of bird diseases and reverse scenarios of extinction in hong kong unprepared: global health in a time of emergency the pandemic perhaps great anticipations human extinction and the pandemic imaginary for discussion, see k. ostherr, cinematic prophylaxis: globalization and contagion in the discourse of world health inclusivity and the rogue bats and the war against "the invisible enemy as fairhead argues, this entanglement of 'native culture' with 'rogue animals' has the effect of transferring the status of the 'rogue' to the 'culture' in question; fairhead, 'technology, inclusivity and the rogue bats and the war against "the invisible enemy"'. see also m. leach and i. scoones, 'the social and political lives of zoonotic disease models: narratives for a discussion of disgust and animal disease, see a. l. olmstead, arresting contagion. science, policy and conflicts over animal disease control it needs to be noted here that, following fissell, the emergence of the early modern notion of 'vermin' was not associated with disgust-something that points to the introduction of this affective and sensory structure in the nineteenth century imagining vermin in early modern england serviço permanente de prevenção e combate à peste bubónica no sul de angola: relatório (lisboa: agência geral das colónias the sanitation of brazil: nation, state, and public health latent infections, and the birth of modern ideas of disease ecology' tipping the balance blaming the rat? plague and the regulation of numbers in wild mammals Évolution de la peste chez la marmotte pendant l'hibernation'. comptes rendus hebdomadaires des séances de l'académie des sciences for a more detailed examination of zoosemiotics in the case of marmots, see c. lynteris, 'speaking marmots, deaf hunters: animal-human semiotic breakdown as the cause of the manchurian pneumonic plague of - on the ambivalence as applies to hunters and gatherers, see r. willerslev lessons in medical nihilism. virus hunters, neoliberalism and the aids pandemic in cameroon on chamayou's theory, see grégoire chamayou, manhunts: a philosophical history for a discussion of the mythic ability of pathogens to transform their hosts into man-hunters, see c. lynteris, 'the epidemiologist as culture hero: visualizing humanity in the age of "the next pandemic on diagrams and the configuration of zoonosis, see lynteris the evolution of ebola zoonotic cycles'. contagion material proximities and hotspots: toward an anthropology of viral hemorrhagic fevers' human extinction and the pandemic imaginary seeing cellular debris, remembering a soviet method' blaming the rat? on the practice of intrusive epidemic photography as regards human dwellings, see r. peckham, 'plague views. epidemic, photography and the ruined city the prophetic faculty of epidemic photography: chinese wet markets and the imagination of the next pandemic this 'global visual economy' was so pervasive in fact so as to lead to a retrospective diagnosis of the presence of rats in paintings such as nicholas poussin's the plague of ashdod as evidence of a pre-bacteriological knowledge of this zoonotic connection; for a critique, see s. barker yellow peril epidemics: the political ontology of degeneration and emergence a plague of kinyounism: the caricatures of bacteriology in san francisco the sharp weapon of soviet laughter: boris efimov and visual humor a plague of kinyounism', p. . . ibid pests in the city: flies, bedbugs, cockroaches, and rats (washington key: cord- -kqfyasmu authors: tagore, somnath title: epidemic models: their spread, analysis and invasions in scale-free networks date: - - journal: propagation phenomena in real world networks doi: . / - - - - _ sha: doc_id: cord_uid: kqfyasmu the mission of this chapter is to introduce the concept of epidemic outbursts in network structures, especially in case of scale-free networks. the invasion phenomena of epidemics have been of tremendous interest among the scientific community over many years, due to its large scale implementation in real world networks. this chapter seeks to make readers understand the critical issues involved in epidemics such as propagation, spread and their combat which can be further used to design synthetic and robust network architectures. the primary concern in this chapter focuses on the concept of susceptible-infectious-recovered (sir) and susceptible-infectious-susceptible (sis) models with their implementation in scale-free networks, followed by developing strategies for identifying the damage caused in the network. the relevance of this chapter can be understood when methods discussed in this chapter could be related to contemporary networks for improving their performance in terms of robustness. the patterns by which epidemics spread through groups are determined by the properties of the pathogen carrying it, length of its infectious period, its severity as well as by network structures within the population. thus, accurately modeling the underlying network is crucial to understand the spread as well as prevention of an epidemic. moreover, implementing immunization strategies helps control and terminate theses epidemics. for instance, random networks, small worlds display lesser variation in terms of neighbourhood sizes, whereas spatial networks have poisson-like degree distributions. moreover, as highly connected individuals are of more importance considering disease transmission, incorporating them into the current network is of outmost importance [ ] . this is essential in case of capturing the complexities of disease spread. architecturally, scale-free networks are heterogenous in nature and can be dynamically constructed by adding new individuals to the current network structure one at a time. this strategy is similar to naturally forming links, especially in case of social networks. moreover, the newly connected nodes or individuals link to the already existent ones (with larger connections) in a manner that is preferential in nature. this connectivity can be understood by a power-law plot with the number of contacts per individual, a property which is regularly observed in case of several other networks like that of power grids, world-wide-web, to name a few [ ] . epidemiologists have worked hard on understanding the heterogeneity of scalefree networks for populations for a long time. highly connected individuals as well as hub participants have played essential roles in the spread and maintenance of infections and diseases. figure . illustrates the architecture of a system consisting of a population of individuals. it has several essential components, namely, nodes, links, newly connected nodes, hubs and sub-groups respectively. here, nodes correspond to individuals and their relations are shown as links. similarly, newly connected nodes correspond to those which are recently added to the network, such as initiation of new relations between already existing and unknown individuals [ ] . hubs are fig. . a synthetic scale-free network and its characteristics those nodes which are highly connected, such as individuals who are very popular among others and have many relations and/or friends. lastly, sub-groups correspond to certain sections of the population which have individuals with closely associated relationships, such as group of nodes which are highly dense in nature, or having high clustering coefficient. furthermore, it is important in having large number of contacts as the individuals are at greater risk of infection and, once infected, can transmit it to others. for instance, hub individuals of such high-risk individuals help in maintaining sexually transmitted diseases (stds) in different populations where majority belong to long-term monogamous relationships, whereas in case of sars epidemic, a significant proportion of all infections are due to high risk connected individuals. furthermore, the preferential attachment model proposed by barabási and albert [ ] defined the existence of individuals of having large connectivity does not require random vaccination for preventing epidemics. moreover, if there is an upper limit on the connectivity of individuals, random immunization can be performed to control infection. likewise, the dynamics of infectious diseases has been extensively studied in case of scale-free as well as small-world and random networks. in small-world networks, most of the nodes may not be direct neighbors, but can be reached from all other nodes via less number of hops, that are number of nodes between start and terminating nodes. also, in these networks distance, dist, between two random nodes increases proportionally to the logarithm of the number of nodes, tot, in the network [ ] , i.e., dist ∝ log tot ( . ) watts and strogatz [ ] identified a class of small-world networks and categorized them as random graphs. these were classified on the basis of two independent features, namely, average shortest path length and clustering coefficient. as per erdős-rényi model, random graphs have a smaller average shortest path length and small clustering coefficient. watts and strogatz on the other hand demonstrated that various real-world networks have a smaller average shortest path length along with high clustering coefficient greater than expected randomly. it has been observed that it is difficult to block and/or terminate an epidemic in scale-free networks with slow tails. it has especially been seen in case the network correlations among infections and individuals are absent. another reason for this effect is the presence of hubs, where infections could be sustained and reduced by target-specific selections [ ] . it has been well known that real-world networks ranging from social to computers are scale-free in nature, whose degree distribution follows an asymptotic power-law. these are characterized by degree distribution following a power law, for the number of connections, conn for individuals and η is an exponent. barabási and albert [ ] analyzed the topology of a portion of the world-wide-web and identified 'hubs'. the terminals had larger number of connections than others and the whole network followed a power-law distribution. they also found that these networks have heavy-tailed degree distributions and thus termed them as 'scale-free'. likewise, models for epidemic spread in static heavy-tailed networks have illustrated that with a degree distribution having moments resulted in lesser prevalence and/or termination for smaller rates of infection [ ] . moreover, beyond a particular threshold, this prevalence turns to non-zero. similarly, it has been seen that for networks following power-law, does not exist and the prevalence is non-zero for any infection rates. due to this reason, epidemics are difficult to handle and terminate in static networks having powerlaw degree distributions. likewise, in various instances, networks are not static but dynamic (i.e., they evolve in time) via some rewiring processes, in which edges are detached and reattached according to some dynamic rule. steady states of rewiring networks have been studied in the past. more often, it has been observed that depending on the average connectivity and rewiring rates, networks reach a scale-free steady state, with an exponent, η , represented using dynamical rates [ ] . the study of epidemics has always been of interest in areas where biological applications coincide with social issues. for instance, epidemics like influenza, measles, and stds, can pass through large group of individuals, populations, and/or persist over longer timescales at low levels. these might even experience sudden changes of increasing and decreasing prevalence. furthermore, in some cases, single infection outbreaks may have significant effects on a complete population group [ ] . epidemic spreading can also occur on complex networks with vertices representing individuals and the links representing interactions among individuals. thus, spreading of diseases can occur over the network of individuals as spreading of computer viruses occur over the world-wide-web. the underlying network in epidemic models is considered to be static while the individual states vary from infected to non-infected individuals according to certain probabilistic rules. furthermore, the evolution of an infected group of individuals in time can be studied by focusing on the average density of infected individuals in steady state. lastly, the spread as well as growth of epidemics can also be monitored by studying the architecture of the network of individuals as well as its statistical properties [ ] . one of the essential properties of epidemic spread is its branching pattern, thereby infecting healthy individuals over a time period. this branching pattern of epidemic progression can be classified on the basis of their infection initiation, spread and further spread ( fig. . ) [ ]. . infection initiation: if an infected individual comes in contact with a group of individuals, the infection is transmitted to each with a probability p, independent of one another. furthermore, if the same individual meets k others while being infected, these k individuals form the infected set. due to this random disease transmission from the initially infected individual, those directly connected to it get infected. if infection in a branching process reaches an individual set and fails to infect healthy individuals, then termination of the infection occurs, which leads to no further progression and infection of other healthy individuals. thus, there may be two possibilities for an infection in a branching process model. either it reaches a site infecting no further and terminating out, or it continues to infect healthy individuals through contact processes. the quantity which can be used to identify whether an infection persist or fades out is defined as basic reproductive number [ ] . this basic reproductive number, τ, is the expected number of newly infected individuals caused by a single already infected individual. in case where every individual meets k new people and infects each with probability p, the basic reproductive number is represented as it is quite essential as it helps in identifying whether or not an infection can spread through a population of healthy individuals. the concept of τ was first proposed by alfred lotka, and applied in the area of epidemiology by macdonald [ ] . for non-complex population models, τ can be identified if information for 'death rate' is present. thus, considering death rate, d, and birth rate, b, at the same time, moreover, τ can also be used to determine whether an infection will terminate, i.e., τ < or it becomes an epidemic, i.e., τ > . but, it cannot be used for comparing different infections at the same time on the basis of multiple parameters. several methods, such as identifying eigenvalues, jacobian matrix, birth rate, equilibrium states, population statistics can well be used to analyze and handle τ [ ] . there are some standard branching models that are existent for analyzing the progress of infection in a healthy population or network. the first one, reed-frost model, considers a homogeneous close set consisting of total number of individuals, tot. let num designate the number of individuals susceptible to infection at time t = and m num the number of individuals infected by the infection at any time t [ ] . here, here, eq. . is in case of a smaller population. it is assumed that an individual x is infected at time t, whereas any individual y comes in contact with x with a probability a num , where a > . likewise, if y is susceptible to infection then it becomes infected at time t + and x is removed from the population ( fig. . a ). in this figure, x or v ( * ) represents the infection start site, y(v ), v are individuals that are susceptible to infection, num = , tot = , and m num = . the second one, -clique model constructs a -clique sub-network randomly by assigning a set of tot individuals. here, for individual/vertex pair (v i , v j ) with probability p , the pair is included along with vertices triples here, g , g are two independent graphs, where g is a bernoulli graph with edge probability p and g with all possible triangles existing independently with a probability p ( fig. . b ). in this figure, ) are the three -clique sub-networks with tot = , and g = g g g respectively [ ] . the third one, household model assumes that for a given a set of tot individuals or vertices, g is a bernoulli graph consisting of tot b disjoint b−cliques, where b tot with edge probability p . thus, the network g is formed as the superposition of the graphs g and g , i.e., g = g g . moreover, g fragments the population into mutually exclusive groups whereas g describes the relations among individuals in the population. thus, g does not allow any infection spread, as there are no connections between the groups. but, when the relationship structure g is added, the groups are linked together and the infection can now spread using relationship connections ( fig. . c ). in this figure, tot = where the individuals (v to v ) are linked on the basis of randomly assigned p and b = tot = . the fig. . b-d respectively [ ] . thus, it is essential to identify the conditions which results in an epidemic spread in one network, with the presence of minimal isolated infections on other network components. moreover, depending on the parameters of individual sub-networks and their internal connectivities, connecting them to one another creates marginal effect on the spread of epidemic. thus, identifying these conditions resulting in analyzing spread of epidemic process is very essential. in this case, two different interconnected network modules can be determined, namely, strongly and weakly coupled. in the strongly coupled one, all modules are simultaneously either infection free or part of an epidemic, whereas in the weakly coupled one a new mixed phase exists, where the infection is epidemic on only one module, and not in others [ ] . generally, epidemic models consider contact networks to be static in nature, where all links are existent throughout the infection course. moreover, a property of infection is that these are contagious and spread at a rate faster than the initially infected contact. but, in cases like hiv, which spreads through a population over longer time scales, the course of infection spread is heavily dependent on the properties of the contact individuals. the reason for this being, certain individuals may have lesser contacts at any single point in time and their identities can shift significantly with the infection progress [ ] . thus, for modeling the contact network in such infections, transient contacts are considered which may not last through the whole epidemic course, but only for particular amount of time. in such cases, it is assumed that the contact links are undirected. furthermore, different individual timings do not affect those having potential to spread an infection but the timing pattern also influences the severity of the overall epidemic spread. similarly, individuals may also be involved in concurrent partnerships having two or more actively involved ones that overlap in time. thus, the concurrent pattern causes the infection to circulate vigorously through the network [ ] . in the last decade, considerable amount of work has been done in characterizing as well as analyzing and understanding the topological properties of networks. it has been established that scale-free behavior is one of the most fundamental concepts for understanding the organization various real-world networks. this scale-free property has a resounding effect on all aspect of dynamic processes in the network, which includes percolation. likewise, for a wide range of scale-free networks, epidemic threshold is not existent, and infections with low spreading rate prevail over the entire population [ ] . furthermore, properties of networks such as topological fractality etc. correlate to many aspects of the network structure and function. also, some of the recent developments have shown that the correlation between degree and betweenness centrality of individuals is extremely weak in fractal network models in comparison with non-fractal models [ ] . likewise, it is seen that fractal scale-free networks are dis-assortative, making such scale-free networks more robust against targeted perturbations on hubs nodes. moreover, one can also relate fractality to infection dynamics in case of specifically designed deterministic networks. deterministic networks allow computing functional, structural as well as topological properties. similarly, in case of complex networks, determination of topological characteristics has shown that these are scale-free as well as highly clustered, but do not display small-world features. also, by mapping a standard susceptible, infected, recovered (sir) model to a percolation problem, one can also find that there exists certain finite epidemic threshold. in certain cases, the transmission rate needs to exceed a critical value for the infection to spread and prevail. this also specifies that the fractal networks are robust to infections [ ] . meanwhile, scale-free networks exhibit various essential characteristics such as power-law degree distribution, large clustering coefficient, large-world phenomenon, to name a few [ ] . network analysis can be used to describe the evolution and spread of information in the populations along with understanding their internal dynamics and architecture. specifically, importance should be given to the nature of connections, and whether a relationship between x and y individuals provide a relationship between y and x as well. likewise, this information could be further utilized for identifying transitivitybased measures of cohesion ( fig. . ). meanwhile, research in networks also provide some quantitative tools for describing and characterizing networks. degree of a vertex is the number of connectivities for each vertex in the form of links. for instance, degree(v ) = , degree(v ) = (for undirected graph (fig. . a) ). similarly for fig. likewise, shortest path is the minimum number of links that needs to be parsed for traveling between two vertices. for instance, in fig. diameter of network is the maximum distance between any two vertices or the longest of the shortest walks. thus, in fig. [ ] . radius of a network is the minimum eccentricity (eccentricity of a vertex v i is the greatest geodesic distance), i.e., distance between two vertices in a network is the number of edges in a shortest path connecting them between v i and any other vertex of any vertex. for instance, in fig. . b, radius of network = . betweenness centrality (g(v i )) is equal to the number of shortest paths from all vertices to all others that pass through vertex v i , i.e., is the number of those paths that pass through v i . thus, in fig. similarly, closeness centrality (c(v i )) of a vertex v i describes the total distance of v i to all other vertices in the network, i.e., sum the shortest paths of v i to all other vertices in the network. for instance, in fig. . b, c( lastly, stress centrality (s(v i )) is the simple accumulation of the number of shortest paths between all vertex pairs, sometimes interchangeable with betweenness centrality [ ] . use of 'adjacency matrix', a v i v j , describing the connections within a population is also persistent. likewise, various network quantities can be ascertained from the adjacency matrix. for instance, size of a population is defined as the average number of contacts per individual, i.e., the powers of adjacency matrix can be used to calculate measures of transitivity [ ] . one of the key pre-requisites of network analysis is initial data collection. for performing a complete mixing network analysis for individuals residing in a population, every relationship information is essential. this data provides great difficulty in handling the entire population, as well as handling complicated network evaluation issues. the reason being, individuals have contacts, and recall problems are quite probable. moreover, evaluation of contacts requires certain information which may not always be readily present. likewise, in case of epidemiological networks, connections are included if they explain relationships capable of permitting the transfer of infection. but, in most of the cases, clarity of defining such relations is absent. thus, various types of relationships bestow risks and judgments that needs to be sorted for understanding likely transmission routes. one can also consider weighted networks in which links are not merely present or absent but are given scores or weights according to their strength [ ] . furthermore, different infections are passed by different routes, and a mixing network is infection specific. for instance, a network used in hiv transmission is different from the one used to examine influenza. similarly, in case of airborne infections like influenza and measles, various networks need to be considered because differing levels of interaction are required to constitute a contact. the problems with network definition and measurement imply that any mixing networks that are obtained will depend on the assumptions and protocols of the data collection process. three main standard techniques can be employed to gather such information, namely, infection searching, complete contact searching and diary-based studies [ ] . after an epidemic spread, major emphasis is laid on determining the source and spread of infection. thus, each infected individual is linked to one other from whom infection is spread as well as from whom the infection is transmitted. as all connections represent actual transmission events, infection searching methods do not suffer from problems with the link definition, but interactions not responsible for this infection transmission are removed. thus, the networks observed are of closed architecture, without any loops, walks, cliques and complete sub-graphs [ ] . infection searching is a preliminary method for infectious diseases with low prevalence. these can also be simulated using several mathematical techniques based on differential equations, control theories etc., assuming a homogeneous mixing of population. it can also be simulated in a manner so that infected individuals are identified and cured at a rate proportional to the number of neighbors it has, analogous to the infection process. but, it does not allow to compare various infection searching budgets and thus a discrete-event simulation need to be undertaken. moreover, a number of studies have shown that analyses based on realistic models of disease transmission in healthy networks yields significant projections of infection spread than projections created using compartmental models [ ] . furthermore, depending on the number of contacts for any infected individuals, their susceptible neighbors are traced and removed. this is followed by identifying infection searching techniques that yields different numbers of newly infected individuals on the spread of the disease. contact searching identifies potential transmission contacts from an initially infected individual by revealing some new individual set who are prone to infection and can be subject of further searching effort. nevertheless, it suffers from network definition issues; is time consuming and depends on complete information about individuals and their relationships. it has been used as a control strategy, in case of stds. its main objective of contact searching is identifying asymptomatically infected individuals who are either treated or quarantined. complete contact searching deals with identifying the susceptible and/or infected individuals of already infected ones and conducting simulations and/or testing them for degree of infection spread, treating them as well as searching their neighbors for immunization. for instance, stds have been found to be difficult for immunization. the reason being, these have specifically long asymptomatic periods, during which the virus can replicate and the infection is transmitted to healthy, closely related neighbors. this is rapidly followed by severe effects, ultimately leading to the termination of the affected individual. likewise, recognizing these infections as global epidemic has led to the development of treatments that allow them to be managed by suppressing the replication of the infection for as long as possible. thus, complete contact searching act as an essential strategy even in case when the infection seems incurable [ ] . diary-based studies consider individuals recording contacts as they occur and allow a larger number of individuals to be sampled in detail. thus, this variation from the population approach of other tracing methods to the individual-level scale is possible. but, this approach suffers from several disadvantages. for instance, the data collection is at the discretion of the subjects and is difficult for researchers to link this information into a comprehensive network, as the individual identifies contacts that are not uniquely recorded [ ] . diary-based studies require the individuals to be part of some coherent group, residing in small communities. also, it is quite probable that this kind of a study may result in a large number of disconnected sub-groups, with each of them representing some locally connected set of individuals. diary-based studies can be beneficial in case of identifying infected and susceptible individuals as well as the degree of infectivity. these also provide a comprehensive network for diseases that spread by point-to-point contact and can be used to investigate the patterns infection spread. robustness is an essential connectivity property of power-law graph. it defines that power-law graphs are robust under random attack, but vulnerable under targeted attack. recent studies have shown that the robustness of power-law graph under random and targeted attacks are simulated displaying that power-law graphs are very robust under random errors but vulnerable when a small fraction of high degree vertices or links are removed. furthermore, some studies have also shown that if vertices are deleted at random, then as long as any positive proportion remains, the graph induced on the remaining vertices has a component of order of the total number of vertices [ ] . many a times it can be observed that a network of individuals may be subject to sudden change in the internal and/or external environment, due to some perturbation events. for this reason, a balance needs to be maintained against perturbations while being adaptable in the presence of changes, a property known as robustness. studies on the topological and functional properties of such networks have achieved some progress, but still have limited understanding of their robustness. furthermore, more important a path is, higher is the chance to have a backup path. thus, removing a link or an individual from any sub-network may also lead to blocking the information flow within that sub-network. the robustness of a model can also be assessed by means of altering the various parameters and components associated with forming a particular link. robustness of a network can also be studied with respect to 'resilience', a method of analyzing the sensitivities of internal constituents under external perturbation, that may be random or targeted in nature [ ] . basic disease models discuss the number of individuals in a population that are susceptible, infected and/or recovered from a particular infection. for this purpose, various differential equation based models have been used to simulate the events of action during the infection spread. in this scenario, various details of the infection progression are neglected, along with the difference in response between individuals. models of infections can be categorized as sir and susceptible, infected, susceptible (sis) [ ] . the sir model considers individuals to have long-lasting immunity, and divides the population into those susceptible to the disease (s), infected (i) and recovered (r). thus, the total number of individuals (t ) considered in the population is the transition rate from s to i is κ and the recovery rate from i to r is ρ . thus, the sir model can be represented as likewise, the reproductivity (θ) of an infection can be identified as the average number of secondary instances a typical single infected instance will cause in a population with no immunity. it determines whether infections spreads through a population; if θ < , the infection terminates in the long run; θ > , the infection spreads in a population. larger the value of θ, more difficult is to control the epidemic [ ] . furthermore, the proportion of the population that needs to be immunized can be calculated by known as endemic stability can be identified. depending upon these instances, immunization strategies can be initiated [ ] . although the contact network in a general sir model can be arbitrarily complex, the infection dynamics can still being studied as well as modeled in a simple fashion. contagion probabilities are set to a uniform value, i.e., p, and contagiousness has a kind of 'on-off' property, i.e., an individual is equally contagious for each of the t i steps while it has the infection, where is present state of the system. one can extend the idea that contagion is more likely between certain pairs of individuals or vertices by assigning a separate probability p v i ,v j to each pair of individuals or vertices v i and v j , for which v i is linked to v j in a directed contact network. likewise, other extensions of the contact model involves separating the i state into a sequence of early, middle, and late periods of the infection. for instance, it could be used to model an infection with a high contagious incubation period, followed by a less contagious period while symptoms are being expressed [ ] . in most of the cases, sir epidemics are thought of dynamic processes, in which the network state evolves step-by-step over time. it captures the temporal dynamics of the infection as it spreads through a population. the sir model has been found to be suitable for infections, which provides lifelong immunity, like measles. in this case, a property termed as the force of infection is existent, a function of the number of infectious individuals is. it also contains information about the interactions between individuals that lead to the transmission of infection. one can also have a static view of the epidemics where sir model for t i = . this means that considering a point in an sir epidemic when a vertex v i has just become infectious, has one chance to infect v j (since t i = ), with probability p. one can visualize the outcome of this probabilistic process and also assume that for each edge in the contact network, a probability signifying the relationship is identified. the sis model can be represented as removed state is absent in this case. moreover, after a vertex is over with the infectious state, it reverts back to the susceptible state and is ready to initiate the infection again. due to this alternation between the s and i states, the model is referred to as sis model. the mechanics of sis model can be discussed as follows [ ] . . at the initial stage, some vertices remain in i state and all others are in s state. . each vertex v i that enters the i state and remains infected for a certain number of steps t i . . during each of these t i steps, v i has a probability p of passing the infection to each of its susceptible directly linked neighbors. . after t i steps, v i no longer remains infected, and returns back to the s state. the sis model is predominantly used for simulating and understanding the progress of stds, where repeat infections are existent, like gonorrhoea. moreover, certain assumptions with regard to random mixing between individuals within each pair of sub-networks are present. in this scenario, the number of neighbors for each individual is considerably smaller than the total population size. such models generally avoid random-mixing assumptions thereby assigning each individual to a specific set of contacts that they can infect. an sis epidemic, can run for long time duration as it can cycle through the vertices multiple number of times. if at any time during the sis epidemic all vertices are simultaneously free of the infection, then the epidemic terminates forever. the reason being, no infected individuals exist that can pass the infection to others. in case if the network is finite in nature, a stage would arise when all attempts for further infection of healthy individuals would simultaneously fail for t i steps in a row. likewise, for contact networks where the structure is mathematically tractable, a particular critical value of the contagion probability p is existent, an sis epidemic undergoes a rapid shift from one that terminates out quickly to one that persists for a long time. in this case, the critical value of the contagion probability depends on the structure of the problem set [ ] . the patterns by which epidemics spread through vertex groups is determined by the properties of the pathogen, length of its infectious period, severity and the network structures. the path for an infection spread are given by a population state, with existence of direct contacts between the individuals or vertices. the functioning of network system depends on the nature of interaction between their individuals. this is essentially because of the effect of infection-causing individuals and topology of networks. to analyze the complexity of epidemics, it is important to understand the underlying principles of its distribution in the history of its existence. in recent years it has been seen that the study of disease dynamics in social networks is relevant with the spread of viruses and the nature of diseases [ ] . moreover, the pathogen and the network are closely intertwined with even within the same group of individuals, the contact networks for two different infections are different structures. this depends on respective modes of transmission of infections. for instance, a highly contagious infection, involving airborne transmission, the contact network includes a huge number of links, including any pair of individuals that are in contact with one another. likewise, for an infection requiring close contact, the contact network is much sparser, with fewer pairs of individuals connected by links [ ] . immunization is a site percolation problem where each immunized individual is considered to be a site which is removed from the infected network. its aim is to transfer the percolation threshold that leads to minimization of the number of infected individuals. the model of sir and immunization is regarded as a site-bond percolation model, and immunization is considered successful if the infected a network is below a predefined percolation threshold. furthermore, immunizing randomly selected individuals requires targeting a large fraction, frac, of the entire population. for instance, some infections require - % immunization. meanwhile, targetbased immunization of the hubs requires global information about the network in question, rendering it impractical in many cases, which is very difficult in certain cases [ ] . likewise, social networks possess a broad distribution of the number of links, conn, connecting individuals and analyzing them illustrate that that a large fraction, frac, of the individuals need to be immunized before the integrity of the infected network is compromised. this is essentially true for scale-free networks, where p(conn) ≈ conn − η , < η < , where the network remains connected even after removal of most of its individuals or vertices. in this scenario, a random immunization strategy requires that most of the individuals need to be immunized before an epidemic is terminated [ ] . for various infections, it may be difficult to reach a critical level of immunization for terminating the infection. in this case, each individual that is immunized is given immunity against the infection, but also provides protection to other healthy individuals within the population. based on the sir model, one can only achieve half of the critical immunization level which reduces the level of infection in the population by half. a crucial property of immunization is that these strategies are not perfect and being immunized does not always confer immunity. in this case, the critical threshold applies to a portion of the total population that needs to be immunized. for instance, if the immunization fails to generate immunity in a portion, por, of those immunized, then to achieve immunity one needs to immunize a portion here, im denotes immunity strength. thus, in case if por is huge it is difficult to remove infection using this strategy or provides partial immunity. it may also invoke in various manners: the immunization reduces the susceptibility of an individual to a particular infection, may reduce subsequent transmission if the individual becomes infected, or it may increase recovery. such immunization strategies require the immunized individuals to become infected and shift into a separate infected group, after which the critical immunization threshold (s i ) needs to be established. thus, if cil is the number of secondary infected individuals affected by an initial infectious individual, then thus, s i needs to be less than one, else it is not possible to remove the infection. but, one also needs to note that an immunization works equally efficiently if it reduces the transmission or susceptibility and increases the recovery rate. moreover, when the immunization strategy fails to generate any protection in a proportion por of those immunized, the rest −por are fully protected. in this scenario, it can be not possible to remove the infection using random immunization. thus, targeted immunization provides better protection than random-based [ ] . in case of homogenous networks, the average degree, conn, fluctuates less and can assume conn conn, i.e., the number of links are approximately equal to average degree. however, networks can also be heterogeneous. likewise, in a homogeneous network such as a random graph, p(conn) decays faster exponentially whereas for heterogenous networks it decays as a power law for large conn. the effect of heterogeneity on epidemic behavior studied in details for many years for scale-free networks. these studies are mainly concerned with the stationary limit and existence of an endemic phase. an essential result of this analysis is the expression of basic reproductive number which in this case is τ ∞ conn conn . here, τ is proportional to the second moment of degree, which finally diverges for increasing network sizes [ ] . it has been noticed that the degree of interconnection in between individuals for all form of networks is quite unprecedented. whereas, interconnection increases the spread of information in social networks, another exhaustively studied area contributes to the spread of infection throughout the healthy network. this rapid spreading is done due to less stringency of its passage through the network. moreover, initial sickness nature and time of infection are unavailable most of the time, and the only available information is related to the evolution of the sick-reporting process. thus, given complete knowledge of the network topology, the objective is to determine if the infection is an epidemic, or if individuals have become infected via an independent infection mechanism that is external to the network, and not propagated through the connected links. if one considers a computer network undergoing cascading failures due to worm propagation whereas random failures due to misconfiguration independent of infected nodes, there are two possible causes of the sickness, namely, random and infectious spread. in case of random sickness, infection spreads randomly and uniformly over the network where the network plays no role in spreading the infection; and infectious spread, where the infection is caused through a contagion that spreads through the network, with individual nodes being infected by direct neighbors with a certain probability [ ] . in random damage, each individual becomes infected with an independent probability ψ . at time t, each infected individual reports damage with an independent probability ψ . thus, on an average, a fraction ψ of the network reports being infected, where it is already known that social networks possess a broad distribution of the number of links, k, originating from an individual. computer networks, both physical and logical are also known to possess wide, scale-free, distributions. studies of percolation on broad-scale networks display that a large fraction, fc, of the individuals need to be immunized before the integrity of the network is compromised. this is particularly true for scale-free networks, where the percolation threshold tends to , and the network remains contagious even after removal of most of its infected individuals [ ] . when the hub individuals are targeted first, removal of just a fraction of these results in the breakdown of the network. this has led to the suggestion of targeted immunization of hubs. to implement this approach, the number for connections of each individual needs to be known. during infection spread, at time , a randomly selected individual in the network becomes infected. when a healthy individual becomes infected, a time is set for each outgoing link to an adjacent individual that is not infected, with expiration time exponentially distributed with unit average. upon expiration of a link's time, the corresponding individual becomes infected, and in-turn begins infecting its neighbors [ ] . in general, for an epidemic to occur in a susceptible population the basic reproductive rate must be greater than . in many circumstances not all contacts will be susceptible to infection. in this case, some contacts remain immune, due to prior infection which may have conferred life-long immunity, or due to some previous immunization. therefore, not all individuals are infected and the average number of secondary infections decrease. similarly, the epidemic threshold in this case is the number of susceptible individuals within a population that is required for an epidemic to occur. similarly, the herd immunity is the proportion of population immune to a particular infection. if this is achieved due to immunization, then each case leads to a new case and the infection becomes more stable within the population [ ] . one of the simplest immunization procedure consists of random introduction of immune individuals in the population for achieving uniform immunization density. in this case, for a fixed spreading rate, ξ , the relevant control parameter in the density of immune individuals present in the network, the immunity, imm. at the meanfield level, the presence of a uniform immunity reduces ξ by a factor − imm, i.e., the probability of identifying and infecting a susceptible and non-immune individual becomes ξ( −imm). for homogeneous networks, one observes that, for aconstant ξ , the stationary prevalence is given by for imm > imm c and for imm ≤ imm c here imm c is the critical immunization value above which the density of infected individuals in the stationary state is null and depends on ξ as thus, for a uniform immunization level larger than imm c , the network is completely protected and no large epidemic outbreaks are possible. on the contrary, uniform immunization strategies on scale-free heterogenous networks are totally ineffective. the presence of uniform immunization elocally depresses the infections prevalence for any value of ξ , and it is difficult to identify any critical fraction of immunized individuals that ensures the eradication of infection [ ] . cascading, or epidemic processes are those where the actions, infections or failure of certain individuals increase the susceptibility of others. this results in the successive spread of infections from a small set of initially infected individuals to a larger set. initially developed as a way to study human disease propagation, cascades ares useful models in a wide range of application. the vast majority of work on cascading processes focused on understanding how the graph structure of the network affects the spread of cascades. one can also focus on several critical issues for understanding the cascading features in network for which studying the architecture of the network is crucial [ ] . the standard independent cascade epidemic model assumes that the network is directed graph g = (v, e), for every directed edge between v i , v j , we say v i is a parent and v j is a child of the corresponding other vertex. parent may infect child along an edge, but the reverse cannot happen. let v denote the set of parents of each vertex v i , and for convenience v i ∈ v is included. epidemics proceed in discrete time where all vertices are initially in the susceptible state. at time , each vertex independently becomes active, with probability p init . this set of initially active vertices are called 'seeds'. in each time step, the active vertices probabilistically infects its susceptible children; if vertex v i is active at time t, it infects each susceptible child v j with probability p v i vj , independently. correspondingly, a vertex v j susceptible at time t becomes active in the next time step, i.e., at time t + , if any one of its parents infects it. finally, a vertex remains active for only one time slot, after which it becomes inactive and does not spread the infection further as well as cannot be infected again either [ ] . thus, in this kind of an sir epidemic, where some vertices remain forever susceptible because the epidemic never reaches them, while others transition, susceptible → active for one time step → inactive. in this chapter, we discussed some critical issues regarding epidemics and their outbursts in static as well as dynamic network structures. we mainly focused on sir and sis models as well as identifying key strategies for identifying the damage caused in networks. we also discussed the various modeling techniques for studying cascading failures. epidemics pass through populations and persists over long time periods. thus, efficient modeling of the underlying network plays a crucial role in understanding the spread and prevention of an epidemic. social, biological, and communication systems can be explained as complex networks with their degree distribution follows a power law, p(conn) ≈ conn − η , for the number of connections, conn for individuals, representing scale-free (sf) networks. we also discussed certain issues on epidemic spreading in sf networks characterized by complex topologies with basic epidemic models describing the proportion of individuals susceptible, infected and recovered from a particular disease. likewise, we also explained the significance of the basic reproduction rate of an infection, that can be identified as the average number of secondary instances a typical single infected instance will cause in a population with no immunity. also, we explained how determining the complete nature of a network required knowledge of every individual in a population and their relationships as, the problems with network definition and measurement depend on the assumptions of data collection processes. nevertheless, we also illustrated the importance of invasion resistance methods, with temporary immunity generating oscillations in localized parts of the network, with certain patches following large numbers of infections in concentrated areas. similarly, we also explained the significance of damages, namely, random, where the damage spreads randomly and uniformly over the network and in particular the network plays no role in spreading the damage; and infectious spread, where the damage spreads through the network, with one node infecting others with some probability. infectious diseases of humans: dynamics and control the mathematical theory of infectious diseases and its applications a forest-fire model and some thoughts on turbulence emergence of scaling in random networks mathematical models used in the study of infectious diseases spread of epidemic disease on networks networks and epidemic models network-based analysis of stochastic sir epidemic models with random and proportionate mixing elements of mathematical ecology intelligent information and database systems propagation phenomenon in complex networks: theory and practice relation between birth rates and death rates the analysis of malaria epidemics graph theory and networks in biology mathematical biology spread of epidemic disease on networks the use of mathematical models in the epidemiology study of infectious diseases and in the design of mass vaccination programmes forest-fire as a model for the dynamics of disease epidemics on the critical behaviour of simple epidemics sensitivity estimates for nonliner mathematical models ensemble modeling of metabolic networks on analytical approaches to epidemics on networks computational modeling in systems biology collective dynamics of 'small-world' networks unifying wildfire models from ecology and statistical physics key: cord- -vm d mj authors: bradt, david a.; drummond, christina m. title: technical annexes date: - - journal: reference manual for humanitarian health professionals doi: . / - - - - _ sha: doc_id: cord_uid: vm d mj this chapter provides guidance on technical issues in the health sector. the annexes contain selective compilations of frequently used reference information. material ( ) financial f. identification of deliverables and timetables g. consolidated reporting and dissemination ( ) group terms of reference ( ) meeting minutes ( ) epidemiology updates ( ) health sitreps ( ) component analysis ( ) field documentation (toolkit) for new arrivals . capacity building of host authorities . civil society partnership and support a. organize community leaders b. encourage gender mainstreaming c. encourage privatization d. discourage entitlements . advocacy . transition to early recovery d. strategy for livelihood/economic relief . restore productive assets (supply side interventions) a. in-kind donations (e.g. food, seeds, tools, fishing nets, etc.) b. types of community projects in food-for-assets programs ( ) natural resources development (a) water harvesting (b) soil conservation ( ) restoration of agri(aqua)culture potential (a) irrigation systems (b) seed systems ( ) infrastructure rehabilitation (a) schools (b) market places (c) community granaries (d) warehouses (e) roads (f) bridges ( ) diversification of livelihoods (a) training and experience sharing . increase individual purchasing power a. cash distribution b. cash for work (cash for assets) c. vouchers d. micro-credit e. job fairs f. artisanal production g. livelihoods/income generation . support market resumption a. market rehabilitation b. infrastructure rehabilitation c. micro-finance institutions e. goals-protect what's left ( month), restore the system ( months), improve the system ( ( ) non-food items c. financial assistance ( ) cash grants ( ) cash for work ( ) microfinance (loans) ( ) livelihood/income generation . ensure responsible resource management a. human resources management ( ) incident management command and control ( ) team structure and function ( ) staff selection (a) internationals (b) homologues ( ) field activities (a) briefing (b) meetings and reports (c) debriefing ( ) operations support (a) comms (b) transport (c) office (d) food and lodging ( ) personal health maintenance and morale b. material resources management c. financial resources management d. supervision e. monitoring and evaluation . scale up coverage of priority health interventions . address bottlenecks of the disrupted health system (otherwise temporary solutions become permanent) . protect essential public health infrastructures . build capacity of local authorities with focus on sustainable systems a. technical oversight-hiring of local experts b. material assistance-production of key commodities c. financial assistance . provide incentives for host government . support host country non-beneficiary population . find new partners in the development community . use health sustainable development goals as targets for recovery activities . seek opportunities and develop mechanisms for transition and phase out f. . programmatic constraints a. staff ( ) western trained ( ) hospital-based ( ) resource intensive ( ) technology dependent ( ) procedurally oriented ( ) invasive ( ) monolingual ( ) hazard naïve b. supervision ( ) limited responsibility ( ) limited authority ( ) limited accountability c. projects ( ) acute ( ) curative ( ) short-term ( ) intermittent d. systems ( ) inadequate security ( ) weak rule of law ( ) limited accountability framework ( ) uncoordinated . international cooperation to protect lives and health . timely and sustained high-level political leadership to the disease . transparency in reporting of cases of disease in humans and in animals caused by strains that have pandemic potential to increase understanding, enhance preparedness, and ensure rapid and timely response to potential outbreaks . immediate sharing of epidemiological data and clinical samples with the world health organization (who) and the international community to characterize the nature and evolution of any outbreaks as quickly as possible . prevention and containment of an incipient epidemic through capacity building and in-country collaboration with international partners . rapid response to the first signs of accelerated disease transmission . work in a manner supportive of key multilateral organizations (who, fao, oie) . timely coordination of bilateral and multilateral resource allocations; dedication of domestic resources (human and financial); improvements in public awareness; and development of economic and trade contingency plans . increased coordination and harmonization of preparedness, prevention, response and containment activities among nations . actions based on the best available science d. program innovations at community level . genocide (article )-acts committed with intent to destroy, in whole or in part, a national, ethnic, racial, or religious group a. killing members of the group b. causing serious bodily or mental harm to members of the group c. inflicting on the group conditions of life calculated to bring about its physical destruction in whole or in part d. imposing measures intended to prevent births within the group e. forcibly transferring children of the group to another group . crimes against humanity (article )-acts committed as part of a widespread or systematic attack against any civilian population, with knowledge of the attack a. murder b. extermination c. enslavement d. deportation e. imprisonment in violation of international law f. torture g. rape, sexual slavery, enforced prostitution, forced pregnancy, enforced sterilization, or other comparable form of sexual violence h. persecution on political, racial, national, ethnic, cultural, religious, gender, or other grounds universally recognized as impermissible under international law i. enforced disappearance j. apartheid k. other inhumane acts intentionally causing great suffering or serious injury to body or to mental or physical health . war crimes (article ) a. grave breaches of the geneva conventions of aug ( ) willful killing ( ) torture or inhumane treatment including biological experiments ( ) willfully causing great suffering ( ) extensive destruction and appropriation of property ( ) compelling a pow to serve in the armed forces of a hostile power ( ) willfully depriving a pow of the right to a fair trial ( ) unlawful deportation ( ) taking of hostages b. serious violations of laws and customs applicable in international armed conflict ( ) intentionally directing attacks against the civilian population or against civilians not taking direct part in hostilities ( ) intentionally directing attacks against civilian objects ( ) intentionally directing attacks against personnel, installations, material, units, or vehicles involved in humanitarian assistance or peacekeeping mission ( ) intentionally launching an attack in the knowledge that it will cause incidental civilian loss of life or severe damage to the natural environment ( ) attacking undefended towns, villages, dwellings, or buildings which are not military targets ( ) killing or wounding a combatant who has surrendered ( ) improper use of a flag of truce, flag or insignia or uniform of the enemy or of the un, or emblems of the geneva conventions resulting in death or serious personal injury ( ) transfer by the occupying power of parts of its own civilian population into the territory it occupies, or the deportation or transfer of all or parts of the population of the occupied territory within or outside the territory ( ) intentionally directing attacks against buildings dedicated to religion, education, art, science, charitable purposes, historic monuments, hospitals, and places where sick are collected, provided they are not military objectives ( ) subjecting persons to physical mutilation or to medical or scientific experiments which are not justified by the medical treatment nor carried out in his/her interest ( ) killing or wounding treacherously individuals belonging to the hostile nation or army ( ) declaring that no quarter will be given ( ) destroying or seizing the enemy's property unless such be imperatively demanded by the necessities of war ( ) declaring abolished, suspended, or inadmissible in a court of law the rights and actions of the nationals of the hostile party ( ) compelling the nationals of the hostile party to take part in the operations of war directed against their own country ( ) pillaging a town or place, even when taken by assault ( ) employing poison or poison weapons ( ) employing asphyxiating, poisonous or other gases, and all analogous liquids, materials, or devices ( ) employing bullets which expand or flatten easily in the human body ( ) employing weapons, projectiles, material and methods of warfare which cause superfluous injury or unnecessary suffering ( ) committing outrages upon personal dignity, in particular humiliating and degrading treatment ( ) committing rape, sexual slavery, enforced prostitution, forced pregnancy, enforced sterilization, or other comparable form of sexual violence ( ) utilizing a civilian or other protected person to render certain areas or military forces immune from military operations ( ) intentionally directing attacks against buildings, material, medical units, transport, and personnel using the emblems of the geneva conventions in conformity with international law ( ) conscripting or enlisting children under the age of years c. serious violations of common article applicable in non-international armed conflict, i.e. acts vs. persons taking no active part in the hostilities, including armed forces placed hors de combat by sickness, wounds, detention, or other cause ( ) violence to life and person ( ) outrages upon personal dignity ( ) taking of hostages ( ) passing of sentences and carrying out of executions d. non-applicability of c (above) to internal disturbances (riots, sporadic violence, etc.) e. other serious violations of laws and customs applicable in non-international armed conflict c. degradation of health system a. ppm = mg/kg (solids) = mg/l (liquids) = μg/ml (liquids) = basic unit of measure for chloroscopes :. , ppm = % a range of generic prevention measures should be considered for its impact on diseases in a biological "all-hazards" environment. overall, excreta disposal, water quantity, personal hygiene, and food hygiene commonly contribute more to environmental health than do other listed measures. epidemic threats will oblige heightened consideration of disease-specific strategies for prevention and control. note: in u , length is the preferred term over height . . this last includes kwashiorkor and marasmatic kwashiorkor in the wellcome classification. • sam = severe wasting cases or bilateral pitting edema cases (where due to malnutrition) • sam = whz < − , muac < . cm, or bilateral pitting edema (who). whm not in definition. • sam prevalence worldwide ≈ , , . • sam mortality ≈ × mortality of normally nourished child and its cfr can be - %. • gam = mam + sam • gam = moderate wasting cases, severe wasting cases, or bilateral pitting edema cases (where due to malnutrition) underweight • underweight is not used for screening or surveys in nutritional emergencies. it reflects past (chronic) and present (acute) undernutrition and is unable to distinguish between them. it encompasses children who are wasted and/or stunted. however, weight gain over time can be a sensitive indicator of growth faltering which is easily tracked on road to health charts. • stunting generally occurs before age . it is irreversible. • stunting prevalence worldwide ≈ , , . • stunting is not a good predictor of mortality, but the cfr from ids in cases of severe stunting ≈ × the cfr from ids in cases without stunting. reference standards can be absolute muac, centile, % of median reference, or z scores: • muac • easy to understand. an excellent predictor of mortality. permits comparisons between age groups insofar as the low growth velocity of muac in the u age group makes data roughly comparable. may be used alone in "quick-and-dirty" convenience samples to estimate local prevalence of wasting. however, not used alone in authoritative anthropometric surveys, and is commonly part of a two stage screening process to determine eligibility for feeding programs. easy to understand. permits comparisons between age groups and outliers. however, data are not convenient to convert. e.g. z - . = . nd percentile • % of median of reference population whm is the preferred indicator to determine eligibility for feeding programs (sphere). calculations are easy and are used in the who road to health charts. however, median reference data are not comparable between ages. eg % wt-for-age = severe malnutrition in infants = moderate malnutrition in school age kids moreover, median reference data are not comparable between indicators. eg % wt-for-age = severe malnutrition in infants % wt-for-ht = death • z scores preferred indicator (sphere, who) for reporting anthropometry survey results because it permits comparisons between age groups and nutritional indices. however, data may be difficult to understand. eg z score wt-for-age for y/o: . . kg kg -= − sd below median for his age overall: whz gives higher prevalence of malnutrition than whm for the same population. this is most marked where there is low baseline prevalence of disease, and especially for adolescents (who get subsequently over-referred). whz is more statistically valid, but whm is better predictor of mortality and is used for admission to tfcs. weight-for-age is influenced by weight-for-height and height-for-age. it can be difficult to interpret. blanket-all hh in geographically targeted catchment area (e.g. where ipc + and gam > % or - % with aggravating factors) targeted-some hh in catchment area (e.g. where gam - % or - % with aggravating factors); u and pregnant or lactating women vs. u alone vs. u alone depending on resources available and challenges with case finding) overall programmatic target- % coverage for sam in rural areas (sphere); % coverage for mam in rural areas admission criteria: pedes: age - mo, muac < . cm, with appetite, discharged from otp, no severe medical complications pregnant & lactating: muac < . cm, and nd- rd trimester or with infant < mo treatment: rusf as dry rations e.g. plumpy'sup ® , csb, csb + (supercereal), csb ++ (supercereal +) nb csb may also be cooked on-site as in emergency school feeding. discharge criteria (pedes): weight gain, muac > . cm, time in program > months community outreach with mobile brigades admission criteria for u : sam (whz < − , muac < . cm, or bilateral pitting edema) discharge criteria for u : whz >− . , no edema, and clinically well (generally takes - weeks) treatment protocol (who, icddr) shock severe dehydration: rl + d , ½ strength darrow's + d , or ½ ns + d dose: cc/kg iv death (~ % sam will die with good care, and % will die with mediocre care) c. measures of association quantify the strength or magnitude of the association between the exposure and the health problem of interest. they are independent of the size of the study and may be thought of as best guess of the true degree of association in the source population. however, they give no indication of the association's reliability. • cohort study-relative risk (rr) = riskexposed/riskunexposed • in acute outbreaks, risk is represented by the attack rate (ar) • case-control study-odds ratio (or) • no denominator with which to calculate an attack rate • cross-sectional-prevalence ratio or prevalence odds ratio c. survey designs (see r magnani [ ] , and f checchi [ ] ) . census-complete enumeration of the entire population . sample a. probability sampling ( ) simple random sampling (srs) it requires a complete enumeration of population n-names and locations of all persons or households (hh)-and sample size n nb much effort is necessary to conform to requirements of random sampling. it is easier to sample less often but take more specimens as a cluster. unfortunately, it is recognized that individuals from a cluster often share characteristics which < the precision of the method. ( ) systematic random sampling it requires a complete enumeration of population n, and sample size n, to calculate the skip interval k = n/n. ( ) stratified random sampling it requires a population size n divided into groups or strata l, then srs within each stratum. the method ensures over-sampling in under-represented groups. it yields separate estimates for each stratum at less cost. however, it requires extra info and has complicated analysis. ( ) cluster sampling, cluster sample survey (css) it is used when you don't have a complete enumeration n of all people in the area, and thus can't do random sampling; or when the area is too big to cover, and thus can't do systematic random sampling. • what should be done to compensate for the bias induced when one samples clusters rather than individuals? use n. empiric data on association within clusters in smallpox immunization suggests doubling n. if n = , n = . • what is the minimum number of clusters that can be selected and still fulfill requirements of the theory on which binomial sampling is based? . statistical theory demonstrates that > clusters help ensure cluster means have a normal distribution. the larger the number of clusters, the smaller the design effect (i.e. study efficiency improves, and the total number of study subjects needed will decrease). e.g. × (n = ) will prove more accurate and efficient than × (n = ). clusters × households will be more precise, but clusters × households may be more logistically feasible. choice of cluster should be driven by what one team can complete in a day. × css leaves . min/hh/team, but × css leaves min/hh/team. if a team can only measure kids/day (which is common), then it's best to increase the number of smaller clusters. • to permit an equal number of children to be selected from each of clusters, children would not achieve the necessary n. therefore, children are selected per cluster ( × = ). b. non-probability sampling ( ) convenience ( ) purposeful/judgment (most affected area, hhs, etc.) ( ) quota bias (see r magnani [ ] , f checchi [ ] , and smart [ ] ) systematic, non-sampling error which lowers accuracy of findings. it is usually not appreciated by the survey team. it is usually not apparent from the survey results. it cannot be arithmetically calculated or corrected. its extent cannot be judged by readers of the report. methods and materials must be explicit. report authors must discuss possible sources of bias as limitations to their study. accuracy depends on validity of findings. it is more important than precision (section e), and bias should be prevented at all costs. awareness of sources of bias is the first step in minimizing its impact on any study. as sample size increases, it is more difficult to control quality. more teams to train and supervise create higher risk of bias. it is better to have smaller sample size with less attendant precision but much less risk of bias. . selection bias-respondents are not representative of the population a. project bias-assessors work where a project may be conceptually familiar to them b. spatial/access bias-assessors work where access is easiest (roadside or "windshield" bias) c. refusal or non-response bias (self-selection) bias-subject nonparticipation may undermine representativeness of the sample d. survivor bias-assessments are conducted where households have disappeared due to family death or migration. mortality rate is thereby underestimated. this bias is most likely where hh size is low, recall period is long, mortality is high, and clustering is present. e. class/ethnic bias-different social classes or ethnic groups are inadequately included if not excluded from the assessment. local assessors may have ethnic bias, or the key informants may be drawn from one particular social class or ethnic group. f. season bias-assessments are conducted during harvest season or periods of weather when segments of the population may be under-represented g. time of day/schedule bias-assessments are conducted at a time of day when segments of the population may be under-represented nb items - below may also be grouped as information/measurement bias. . interview bias a. interviewer bias ( ) cultural bias-assessors cultural norms lead to incorrect assumptions about the interview subjects ( ) mandate or specialty bias-assessors mandate or specialty blinds them to needs outside of that mandate or specialty. e.g., a shelter specialist may only assess shelter needs while neglecting livelihood or nutrition needs. gender bias-assessors interview only one gender ( ) language bias-assessors may have a limited spectrum of people with whom they can communicate ( ) key informant bias-assessors may be partial to key informants who appear credible in ways meaningful to the assessors ( ) information/political bias-assessors focus on information that confirms preconceived notions rather than pursue evidence of alternate beliefs ( ) mistranslation ( ) interviewer error-assessors write down answers incorrectly b. subject (response) bias ( ) event recall bias-retrospective surveys only, esp. with recall periods > yr (a) informants underreport remote events (e.g. neonatal deaths) (b) calendar bias-informants over report events within the recall period ( ) event reporting bias (a) taboos-informants underreport taboo subjects (e.g. neonatal deaths) (b) lies-informants misinterpret surveys as registration activities and over report family members or underreport deaths to maintain assistance (c) political bias-informants present information that conforms to their political agenda ( ) age heaping/digit preference-informants exhibit digit preference . instrument/measurement bias-errors in design or use of instrument (e.g. questionnaire, lab equipment, etc.) a. random errors in measurement random errors in weight measurement, even if yielding equal numbers of high and low measurements, widen the distribution curve without altering the mean. hence, the prevalence of malnutrition is overestimated. the effect is greater for severe malnutrition than for moderate malnutrition, and greater when prevalence is low than when it is high. the data distribution should be checked for normal distribution with an sd between . and . z scores. improving the data quality thus appears to reduce the prevalence of malnutrition. b. systematic errors in measurement systematic errors in weight measurement, even if small (e.g. g error in presence of clothing), may alter the mean, but also widen the distribution curve. hence, the prevalence of malnutrition is overestimated. systematic errors in height measurement, such as erroneous lengthboard, may alter the mean without altering the sd. if the measurement is too short, there will be > stunting, albeit < wasting. if the measurement is too long, there will be < stunting, albeit > wasting. a standardization test is routine before undertaking anthropometric surveys. nb some scholars prefers terms "counted" and "calculated" to "measured" and "derived" . data entry bias . analytic bias a. anchoring bias-focusing on one major piece of information b. confirmation bias-favoring data which confirm underlying beliefs c. familiarity bias-weighing familiar/understandable events and spokespersons more than unfamiliar ones d. recency bias-weighing recent events more than remote ones e. salience bias-weighing vivid events more than mundane ones f. "time will tell" bias-collecting more data or letting time pass instead of making a hard decision e. imprecision (see r magnani [ ] , f checchi [ ] , and smart [ ] ) sampling, non-systematic error which lowers precision of findings and affects the level of certainty in extrapolating sampling estimates to the population's true value. it is always present, unavoidable, and a function of chance. its magnitude depends on sample size, sampling statistics, prevalence of condition, and length of recall period. precision refers to consistency of results obtained from repeated measurements. what is the sample size n of a random sample of binomial variables needed to yield a result of specified accuracy and precision? n = [(z pq)/d ] × design effect e.g. n = first estimate of sample size z = confidence limits (accuracy), or normal deviate. usually set at % :. z "score" = . p = proportion of the target population with attribute p q = proportion of the population without attribute p = -p. usually set at . to maximize the n of a study having a result of specified accuracy and precision. if you knew p and q, you would not need to do a survey. d = confidence interval (precision). usually set at +/− % :. d = . design effect (see e below) . . . once n is calculated, compare it to the size of the target population (n). if n < % of n, then use n as final sample size. if n > % of n, then recalculate the final sample size (n f ) by the following correction (a smaller sample size may be used). n n n n f = + / n f = / . n f = nb n to calculate the mean weight may be much smaller than n to calculate the prevalence of malnourished outliers ( vs. ). . sampling statistics and error measurement a. malnutrition prevalence or death rate the higher the prevalence (or death rate), the lesser the precision (higher d) available through a fixed sample size. (this is a consequence of the formula.) % gam is a common trigger for intervention. but, smart discourages use of this because high survey precision is needed (narrow ci). :. choose highest expected prevalence or rate-tends to > n. nb at levels of malnutrition and mortality generally found in emergencies, precision has much greater effect on sample size than suspected prevalence of malnutrition or death rate. n is related to d . e.g., if the malnutrition rate estimate is %, and assuming a design effect of : • survey statistic with a ci of +/− % requires n = • survey statistic with a ci of +/− % requires n = as rule of thumb, prevalence (%)/ approximates the range of appropriate ci. e.g. malnutrition prevalence of % calls for a precision of +/− % (range of %). it's generally unfeasible to achieve precision greater than +/− %. b. standard deviation (sd, σ). the degree to which individuals within the sample differ from the sample mean (μ); unaffected by sample size c. standard error (se = sd/√n) standard deviation of the sampling distribution of a statistic; decreases with larger sample sizes as estimate of the population mean improves, thus a lower se is more precise ( ) standard error of the mean (sem) is standard deviation of a sample mean's estimate of a population's true mean; an estimate of how close to the population's true mean the sample mean appears to be. ( ) relative standard error (rse)-sem/μ expressed as % • se of g on weight mean of kg = rse of % • se of g on weight mean of kg = rse of % d. confidence interval (ci = μ + z (se)) the margin of error around a point estimate. for normally distributed data, the ci yields the range in which a parameter is % likely to be found. a convention for reporting such data would be: "the most probable estimate of the parameter is x, and we are % confident the parameter lies somewhere between y and z [bounds of the ci]" (paraphrased from checchi, ) . nb in general, the lower the prevalence (or death rate), the greater the precision (lower d) needed to detect it and any subsequent changes in it. (this is intuitive.) overall, there is no benchmark for precision. increasing precision (decreasing d) slightly can dramatically increase n. +/− . deaths/ , /d is a practical limit in precision of mortality surveys. :. choose widest acceptable ci-tends to < n. e. design effect (d eff = variance study design /variance simple random sample ) a measure of the (in)efficiency of a cluster sample survey compared to that of a simple random sample. if d eff > , but the analysis treats it as a srs, then the confidence interval is inappropriately narrowed, and a test for differences is more likely to produce a positive result (type error). • if each child in a cluster had an unrelated probability of immunization, the precision of the sample estimate would match that of a simple random sample in which children were chosen. d eff = . however, this is generally not the case. • if each child in a cluster had an identical probability of immunization, the precision of the sample estimate would match that of a simple random sample in which children were chosen. d eff = cluster size of . nb focal phenomena create clustering of findings which increase the d eff . :. choose largest d eff -tends to > n. . length of recall period a. the shorter the recall period, the more accurate the mortality estimate (more distant events are more likely to be forgotten). b. the longer the recall period, the more precise the mortality estimate for a fixed sample size. the "sample" is effectively the number of person-days. for a fixed level of precision, the length of the recall period is inversely related to number of study subjects needed. if you cannot increase the sample size, you must increase the recall period. confounders are extraneous variables that correlate with both dependent and independent variables of interest (e.g. both the exposure of interest and the outcome of interest), are unevenly distributed across the levels of exposure, but are not causally linked to exposure and outcome. age and sex are the most common confounders. hence, the importance of matching in intervention and control groups. g. validity . study validity a. internal-capacity of the study to yield sound conclusions for the study population after considering bias, imprecision, and confounding (see d-f above) b. external-generalizability beyond the study population (ill-advised) . measurement validity a. criterion validity ( ) concurrent-sensitivity/specificity or correlation with a gold standard ( ) predictive-ability to predict an event b. face validity-common sense c. content validity-all relevant elements of a composite variable are included d. construct validity (usually for a new measure)-extent to which the measure corresponds to theoretical concepts (constructs) e. consensual validity-extent to which experts agree the measure is valid :. strength of evidence: face validity, criterion validity > content, construct, consensual validity. in absence of validity, a measurement may be embraced for its reliability (below). . death rates-calculated incidence of death expressed per , p/d or per p/mo; data collected by retrospective surveys (e.g. month period) to gauge severity of public health emergency particularly where sudden events lead to spike in mortality a. cdr-crude death rate b. asdr-age-specific death rate (e.g. u dr or death rate of children - yr) during a studied time interval (written as m or - dr); age of study cohort, e.g. - yr, should not be confused with study time intervals . mortality rates-calculated probability of dying before a specified age expressed per live births; data collected by national health authorities in periodic (annual) demographic surveys to reflect ongoing health status a. cmr-calculated probability of mortality in given population for specific time b. imr-calculated probability of a live borne child dying before yr c. u mr-calculated probability of a live borne child dying before yr nb mr ≠ dr. e.g. cmr ≠ cdr, u mr ≠ u dr. different rates measure different things and are not directly comparable. however, mrs may be converted into drs by the following: cdr or u dr (deaths/ , /d) = -ln( -p/ ) × . where p = cmr or u mr (deaths/ live births). however, this has little field utility. nb mmr-maternal mortality ratio has different units in numerators (maternal deaths) and denominators (live births), thus is a ratio, not a rate i. . stability-inter/intra-observer variation a. discrete variables-kappa coefficient b. continuous variables-correlation coefficient . internal consistency-correlation among all items in the measure . tests of reliability-cronbach's alpha, kuder-richardson, split halves j. conclusions the application of study findings to an entire population from which the sample was drawn. if the survey was well-conducted, the results may be considered representative of the entire population. this is scientifically justified. however a ci should accompany any parameter estimate of that population. the extension of study findings to a population or period which was not represented in the sample. it works by association-if populations appear to be experiencing similar conditions, the morbidity/mortality experience of one may be imputed to the other. this is not scientifically justified, but is often done where data are insufficient or impossible to collect. .k. • holo-endemic areas (e.g. congo) have an intense level of malaria transmission year-round. epidemics don't occur unless displacement brings in nonimmune populations. infection may be asymptomatic. effective partial immunity develops in adults which enables clinical tolerance of infection and protects against serious episodes. mortality is highest in pedes u and pregnant women. • hyper-endemic areas (e.g. w. africa) have an intense but unstable level of transmission in seasonal peaks when the climatic conditions are favorable. epidemics occur. infection is generally symptomatic. partial immunity fails to develop. mortality occurs across all age groups. • hypo-endemic areas (e.g. thai-burmese border) have a low level of transmission year-round. epidemics occur. infection is generally symptomatic. partial immunity fails to develop. mortality occurs across all age groups. think differential diagnosis (below). know the golden rules of infectious diseases (abstracted from a yung [ ] and used with permission). rigors are always important-serious bacterial infections are the most likely cause. severe muscle pain may be a symptom of sepsis even without fever. elderly patients with sepsis may be afebrile. in elderly patients, fever is rarely caused by a viral infection. septic patients who are hypothermic have a worse prognosis than those with high fever. treat as a medical emergency. fever in a postoperative patient is usually related to the surgical procedure (e.g. pneumonia, uti, wound, or deep infection). fever with jaundice is rarely due to viral hepatitis. think liver abscess, cholangitis, etc. the rash of early meningococcal infection may resemble a viral rash. generalized rashes involving the palms and soles may be due to drugs, viral infections, rickettsial infections, or syphilis. all febrile travelers in or returned from a malaria infected area must have malaria excluded. . disseminated tb must be suspected in all elderly patients with fever and multisystem disease who have been in an area with endemic tb. . septic arthritis may be present even in a joint which is mobile. ddx failure to thrive without f in infants is worked up like f without localizing signs. watch for clinical mimics-malaria presenting as pneumonia or diarrhea in pedes; vl presenting as malaria in adults; lepto presenting as mild df (esp in df endemic areas where the pt has mild onset of illness, worsening course, and no rash but jaundice after a week). do basic things well, use equipment you understand, teach others, delegate. h. count the number of fresh graves or bodies at health facilities and inquire as to cause. . orient the descriptive data-person, place, and time. a. tabulate data on affected patients. b. make a spot map. ( ) when and where was/were the first reported case(s) seen indicating an outbreak? c. plot an epidemic curve. ( ) what is the present # of patients/day or week? ( ) what is the usual # of patients/day or week? ( ) is this an increase? ( ) what is the present # of deaths/week or month? ( ) what is the usual # of deaths/week or month? ( ) is this an increase? d. calculate attack rates and case fatality ratios for total patients, u , o , and gender. . develop hypothesis. a. postulate sources of disease and mechanism of spread. b. estimate the population at risk of contracting disease and of dying from it. consider especially: those with limited access to health services pregnant and lactating ( ) infants not breast fed, children unvaccinated ( ) elderly . initiate control measures considering agent, host, and environment. a. what action has the community taken? b. identify local response capacity. ( ) what number and type of staff are locally available? ( ) what drugs and supplies are locally available? c. determine immediate unmet needs. ( ) specimen collection and lab diagnosis ( ) logistics ( ) support for clinical care-staff, drugs, and supplies ( ) support for environmental health d. undertake further necessary actions. ( ) case management with secondary prevention ( ) patient isolation ( ) health education ( ) agent and reservoir identification ( ) environmental decontamination ( ) primary prevention ( ) public information . inform authorities with investigation report. . initiate ongoing disease surveillance. during epidemic there is no clinical difference between them. other serogroups may cause disease in individuals, but not epidemics. when a suspected cholera serotype (strain) is isolated in the lab, one of the first tests performed is bacterial agglutination with o and o antisera. strains are thereby identified as v. cholerae o , o , or non-o /non-o . • if (+) agglutination to o antisera, then the strain is further tested for agglutination to antiserum of ogawa and inaba serotypes. • if (+) agglutination to o antisera, then the strain is not further subdivided (except as producer or nonproducer of ct as noted below). • if (−) agglutination to o and o antisera, then the strain is known as non-o , non-o v. cholerae. a strain is further identified as a producer or non-producer of cholera toxin (ct). ct production is a major determinant of disease development. strains lacking ct do not produce epidemics even if from the o or o serogroup. • serogroup o exists as main biotypes-classical and el tor-though hybrids also exist. each biotype occurs as two serotypes-ogawa and inaba. classic biotype caused the th and th pandemics but little epidemic disease since the s though it still causes cases in india. el tor biotype caused the th (current) pandemic and almost all recent outbreaks. el tor was first isolated in in el tor, egypt after importation by indonesian pilgrims travelling to mecca. it survives longer in the environment and produces ct similar to the classical biotype. presumably because of ct pathogenicity, the % of cholera patients with severe disease has doubled over the past yrs. these patients tend to require iv fluid therapy. • serogroup o may have evolved from strains of o el tor as they share many properties though not agglutination. in spring of in dhaka, o cases exceeded o el tor cases for the first time, and it was postulated that o may become the cause of an th pandemic. however, since then, o has again become dominant. infective dose depends on individual susceptibility. relevant host factors include immunity produced by prior infection with serogroup o as well as stomach acidity. id may be , orgs, so personal hygiene plays a lesser role than in shigellosis where the id is much lower. shigella has species. • s. dysenteriae type (sd or shiga bacillus) causes the severest disease of all shigella sp because of its neurotoxin (shiga toxin), longer duration of illness, higher abx resistance, higher cfr thru invasive complications, and great epidemic potential. • s. flexneri is the most common, and is generally endemic, in developing countries • s. sonnei is the most common in industrial countries • s. boydii and s. sonnei give mild disease. id may be orgs, so personal hygiene plays a greater role than in cholera. some kinds of e. coli produce a shiga toxin. shiga toxin genes reside in bacteriophage genome integrated into the bacterial chromosome. some abx, e.g. fluoroquinolones, induce expression of phage genes. the bacteria that make these toxins are variously called "shiga toxin-producing e. coli" (stec), "enterohemorrhagic e. coli" (ehec), or "verocytotoxic e. coli" (vtec). all terms refer to the same group of bacteria. • e. coli o :h (often called "e. coli o " or "o ") is the most commonly identified stec in north america, and it causes most e. coli outbreaks. approximately - % of ehec infections result in hus. • non-o stec serogroups also cause disease. in the usa, serogroups o , o , and o are the most commonly identified e. coli pathogens overall. diarrhea epidemiology is seasonally dependent. environmental temperature directly influences biologic activity-∆ °c is proportional to × risk of disease • temperate climates: bacterial diarrhea in warmer, humid season; rotavirus diarrhea in cooler, dry season • tropical climates: bacterial diarrhea in rainy season; rotavirus diarrhea year round with increased incidence in cooler season • most common pathogens for watery diarrhea-rotavirus, etec, v. cholerae; most important pathogen for epidemic watery diarrhea-v. cholerae • most common pathogens for dysentery-shigella species, salmonella species, campylobacter jejuni, clostridium difficile, eiec, ehec, e. coli o :h , entamoeba histolytica, yersinia enterocolitica; most important pathogens for epidemic dysentery-s. dysenteriae serotype (developing countries), e. coli o :h (developed countries) bangladesh has two seasonal cholera peaks: pre-monsoon with hot, humid weather (esp weeks - in apr-may) creating increased biological activity; post-monsoon (esp weeks - in aug-sep) with contamination of water sources. premonsoon epidemics are generally worse than post-monsoon ones. dysentery has low level year-round incidence, but epidemics occur roughly each decade. epidemic strains display new, additive antibiotic resistance which probably triggers the epidemic. once resistant strains have become endemic, antibiotic susceptibility rarely reappears. sd acquires resistance quickly. sf acquires it more slowly, and that resistance may wane with decreasing abx pressure. at icddr, annual proportional incidence approximates the following: • e. coli overall = % of cases, but etec = %. • e. coli tends to dominate before monsoon season and flooding. • cholera tends to dominate after monsoon season and flooding. • overall, - % of diarrhea cases may be vaccine-preventable. • % of pts have no pathogen identified. clean water and waste management for cholera. personal hygiene (hand washing with soap and clean towels) for shigella. water safe drinking water (boiled, chlorinated) nb sphere standards are not enough-you need increased quantities of chlorinated water at household level. san clean latrines for safe disposal of excreta hand washing with soap food safe food (cooked, stored) breast feeding fomites safe disposal of dead bodies with disinfection of clothing nb after outbreak of a fecal-oral pathogen, food hygiene and funereal practices may influence human-tohuman transmission more then water quality. health education to affected population wash hands with soap: after using toilets/latrines. after disposing of children's feces. before preparing food. before eating. before feeding children. is identical for all patients, and thus can't be given to pedes < yr because of volume loading. dukoral has been the main vaccine considered for use in high-risk populations. • morc-vax and shanchol-similar to dukoral except they do not contain the rbs, hence do not require a buffer, and are / the cost to produce. morc-vax, produced in vietnam, is derived from a vaccine administered to millions of people since , but is not who pre-qualified, and is not expected to have international distribution. shanchol, produced in india, has international distribution (e.g. used in the haiti cholera vaccination campaign of ), and is now the agent of choice for who. it confers immunity d p nd dose, effectiveness > % at mo, and protection > % at yr. also confers short-term protection vs etec. dose: . cc vaccine followed by water ingestion but no fasting needed; doses, wks apart; cold chain required except for day of use. orochol-bivalent formulation as in dukoral without rbs of ct. dose: single dose. no longer manufactured. who recommendations: "vaccination should not disrupt the provision of other high-priority health interventions to control or prevent cholera outbreaks. vaccines provide a short-term effect that can be implemented to bring about an immediate response while the longer term interventions of improving water and sanitation, which involve large investments, are put into place" [ ] . icddr recommendations: "because of limitations in terms of transport, formulation, and cost of the current dukoral vaccine, the cots program does not require the utilization of the vaccine during an outbreak; it is not necessary to vaccinate to overcome an outbreak. however, if dukoral is readily available and staff are properly trained in its use according to the guidelines that come with the vaccine, the cots program permits dukoral's use (ideally before an outbreak) in the following high-risk populations: refugee populations in which cholera is present, health care workers managing cholera cases, and communities in which the incidence rate is greater than in annually" [ ] . if undertaken, the following will apply: vaccination campaign requires numerous staff. community mobilizers are key. clinical staff should not be poached from their clinical duties. supervisors must be free to move at will. logistics is key-if the st day goes bad, the campaign goes bad. mark the domiciles which are done. hold after-action meetings each day. last day, use mobilizers with mobile broadcasting to find those missed. second phase vaccination should include chws with multi-purpose messages on water and sanitation. key lessons in epidemic response avoid: press exaggeration abx prophylaxis reliance on ivf and insufficient ors lab investigation of cases once epidemic etiology is ascertained prolonged hospitalization hospital discharge criteria requiring multiple negative stool cultures enthusiasm for ocv during epidemic exaggerated water purification objectives concentration of technical competencies in moh at expense of districts failure to share information with district stakeholders influenza viruses comprise genera-influenza types a, b, and c-each with species. • influenza type a is divided into subtypes based upon serological response to hemagglutinin (ha) and neuraminidase (na) glycoproteins. there are different ha subtypes and different na subtypes. h n , h n , and h n are responsible for the major human pandemics in the last century. h n virus circulated between and but currently does not. only influenza a subtypes infect birds, and all subtypes can do so. bird flu viruses do not usually infect humans. but, in , an outbreak of h n avian influenza in poultry in hong kong marked the first known direct human transmission of avian influenza virus from birds to humans. since then, h , h , and h avian influenza subtypes have been shown to infect humans. • influenza type b is morphologically similar to a and also creates seasonal and epidemic disease. • influenza type c is rare but can cause local epidemics. seasonal human influenza vaccine currently has strains-h n /h n /b. influenza disease in humans has a short incubation period ( - d) . early symptoms are non-specific. it is highly infectious, especially early in the course of the disease, with a large # of asymptomatic carriers. transmission potential (r ) is a function of infectivity, period of contagiousness, daily contact rate, and host immunity. in general, the faster the transmission, the less feasible is interrupting transmission thru usual disease control tools of case finding, isolation, contact tracing, and ring vaccination. case definitions may change and become more specific as epidemic evolves case management guidelines for communicable diseases with epidemic potential outbreak management protocol rapid response teams to investigate case reports epidemic investigation kits to mobilize specimens to collect labs to verify diagnosis and share specimens with peer labs pts to identify, isolate, and treat (ipd and opd settings) contacts to trace and ? quarantine hotline use and rumor investigation secondary prevention specific groups of exposed or at risk in the community-most likely to work when there is limited disease transmission in the area, most cases can be traced to a specific contact or setting, and intervention is considered likely to slow the spread of disease eg quara ntine of groups of people at known common source exposure (e.g. airplane, school, workplace, hospital, public gathering; ensure delivery of medical care, food, and social services to persons in quarantine with special attention to vulnerable groups) (useless once there is community-based spread) eg containment measures at specific sites or buildings of disease exposure (focused measures to > social distance) cancel public events (concerts, sports, movies) close buildings (recreational facilities, youth clubs) restrict access to certain sites or buildings community-wide measures (affecting exposed and non-exposed)-most likely to work where there is moderate to extensive disease transmission in the area, many cases cannot be traced, cases are increasing, and there is delay between sx onset and case isolation. eg infection control measures ari etiquette-cover nose/mouth during cough or sneeze, use tissues, wash hands avoidance of public gatherings by persons at high risk of complications nb use of masks by well persons is not recommended eg "snow" (stay-at-home) days and self-shielding (reverse quarantine) for initial d period of community outbreak-may reduce transmission without explicit activity restrictions eg closure of schools, offices, large group gatherings, public transport (pedes more likely to transmit disease than adults) nb community quarantine (cordon sanitaire)-restriction of travel in and out of an area is unlikely to prevent introduction or spread of disease international travel nb travel advisories to restrict international travel are generally useless in slowing epidemic spread nb health screening for fever and respiratory sx at ports of entry is also generally useless in slowing epidemic spread meningitis is a disease with significant mortality. meningococcus (neisseria meningitides) is renown for its rapid onset, rapid progression (death sometimes within hours), and high mortality ( % untreated). there are serogroups of neisseria meningitides but only (a, b, c, w, x, y) are known to cause epidemics. the bacteria spread from person to person via respiratory and nasal secretions. kissing, sharing eating and drinking utensils, cigarettes, coughing, and sneezing are recognized methods of transmission. close contacts over a period of time, as between household or dormitory residents, are most commonly affected. population movements (e.g. pilgrimages, displacement, military recruitment), poor living conditions, and overcrowding are epidemic risk factors. large, recurring epidemics of meningitis occur in the "meningitis belt" of sub-saharan africa where over million people live. this belt encompasses countries from senegal in the west to ethiopia in the east and as far south as tanzania and the democratic republic of congo. sub-saharan arica has epidemic seasonality. dry seasons and droughts favor epidemics. rains stop them. large regional epidemics, as well as epidemics in displaced populations and refugee camps, have mainly been due to meningococcus serogroup a. since , extensive use of meningococcal type a conjugate vaccine in the meningitis belt has reduced the incidence and case load of type a epidemics by nearly %. in , the most common lab confirmed meningitis isolate was streptococcus pneumoniae. in non-epidemic settings, neisseria.meningitidis, streptococcus pneumoniae, and haemophilus influenzae account for % of all cases of bacterial meningitis. prior to the availability of conjugate vaccines, h. influenza type b (hib) was the most common cause of childhood bacterial meningitis outside of epidemics. where hib vaccines are in the routine infant immunization schedule, hib meningitis has nearly disappeared. polysaccharide vaccines are available with serotypes (a and c), serotypes (a, c and w) or serotypes (a,c, w, and y). duration of immunity is approximately years. meningococcal protein conjugate vaccines confer longer immunity but at higher cost than polysaccharide vaccines. monovalent conjugate vaccine against group c dates from , and tetravalent (a, c, w and y) conjugate vaccine dates from . a group b vaccine made from bacterial proteins has been licensed since but is not readily available. meningococcal vaccines have a very low incidence of side effects. regular disease surveillance is necessary to detect outbreaks. the epidemic threshold is suspected cases/ , population in any given week. two suspected cases of meningitis in the same settlement should trigger an outbreak investigation. nasopharyngeal carriage rates do not predict epidemics. - % of meningococcal disease presents with meningitis. % of cases occur in patients < y/o. peak incidence in meningitis belt is ages - yrs. diagnosis is straightforward when patient presents with signs of meningitis-fever, headache, vomiting, changes in mental status. however, most patients have non-specific illness - days before onset of meningitis. cfr of untreated meningococcal meningitis can be %. cfr of properly treated meningococcal meningitis is < %. - % of meningococcal disease presents with septicemia unaccompanied by meningitis or other focal features. it is a dramatic illness which affects previously healthy children and young adults. it presents with acute fever leading to purpura fulminans (hemorrhagic or purpuric rash), shock, and waterhouse-friderichsen syndrome (acute adrenal failure). etiologic diagnosis can be easily missed. cfr of meningococcal septicemia is % and may be % even with proper treatment. diagnosis may be confirmed by agglutination tests, polymerase chain reaction, culture and sensitivity testing of spinal fluid and blood. in many situations, these tests are not available. throat swabs may be helpful on occasions. do not delay treatment for tests or test results. minutes count. it is more important to have a live patient without a confirmed diagnosis than a dead one with a diagnosis. differential diagnosis in a tropical patient with fever and altered mental status, but without purpura or shock, includes cerebral malaria. co-infection may occur. standardized case management of bacterial meningitis in developed countries involves - days of parenteral antibiotic therapy. drug of choice in adults and older children is ceftriaxone which also rapidly eliminates the carrier state. alternate drugs include ampicillin and benzylpenicillin which do not eliminate the carrier state. in developing countries, days of parenteral antibiotic therapy are empirically shown to be effective. in large epidemics in resource-poor settings, a single im dose of chloramphenicol in oil is the drug of choice. for patients who do not improve in h, a repeat dose may be given. viral meningitis is rarely serious and requires only supportive care, recovery is usually complete. patient isolation and disinfection of the room, clothing, or bedding are not necessary. respiratory precautions are advised particularly early in the course of treatment. chemoprophylaxis of contacts is available in some settings but rarely in the disaster setting. vigilance and education of close contacts is mandatory. epidemic preparedness and early detection of outbreaks are key. vaccines against n. meningitides serogroups a, c, y and w are very effective in controlling epidemics. in epidemic settings, children - are the priority target with serogroups a and c typically the priority antigens. rapid mass vaccination campaigns can contain outbreaks in - weeks. for immunocompetent patients over years, vaccine efficacy rate is % one week after injection. however, duration of immunity may be as little as years in younger children. in some countries, vaccine may also be used with close contacts of sporadic disease cases to prevent secondary cases. chemoprophylaxis of contacts is not recommended in epidemics, but community education and ready access to health care are essential. source control/reduction/elimination avoid unnecessary contact with suspected reservoir animals and known disease carrier species (e.g. primates). avoid direct or close contact with symptomatic patients. undertake quarantine and culling of sick reservoir animals and known disease carrier species. avoid unnecessary contact with or consumption of dead reservoir animals or known disease carrier species. establish appropriate communicable disease controls for burial of the dead. administrative controls environmental and engineering controls avoid needle stick exposure to blood specimens thru automated machine handling ppe use standard precautions-gloves, masks, and protective clothing-if handling infected animals or patients. wash hands after visiting sick patients. active surveillance and contact tracing (enhanced surveillance) through community-based mobile teams active case finding (screening and triage) and contact tracing dedicated isolation facility food provision to isolated patients so they are not dependent on family case definition treatment protocols emphasizing supportive care and treatment of complications essential drugs referral guidelines secondary prevention barrier nursing strictly enforced family and community education ministerial task force to address policy local health authority task force to address procedures national level task forces to comprise guidance note on using the cluster approach to strengthen humanitarian response panel on humanitarian financing report to the united nations secretary-general. too important to fail-addressing the humanitarian financing gap belgian development corporation, government of bulgaria, government of canada, et al. the grand bargain-a shared commitment to better serve people in need available from usaid's development experience clearinghouse gender equality and female empowerment policy national strategy for pandemic influenza selective primary health care-an interim strategy for disease control in developing countries ten great public health achievements-united states ten great public health achievements-united states water and excreta-related diseases: unitary environmental classification infections related to water and excreta: the health dimension of the decade addendum to ipc technical manual version . . tools and procedures for classification of acute malnutrition. rome: ipc global partnership integrated food security phase classification technical manual version . . evidence and standards for better food security decisions nbc domestic preparedness training hospital provider course. undated. curriculum available from the center for domestic preparedness sampling guide interpreting and using mortality data in humanitarian emergencies-a primer for non-epidemiologists. humanitarian practice network, network paper no . london: overseas development institute measuring mortality, nutritional status, and food security in crisis situations: smart methodology. v infectious diseases-a clinical approach cholera vaccines: who position paper cholera outbreak training and shigellosis (cots) program [cd-rom version . , undated history and epidemiology of global smallpox eradication retrieved from us department of health and human services geneva: world health organization. laboratory available? . what tests does it perform? . is there transport to and from the laboratory? . who prepares transport media? . who provides specimen collection material and supplies? . how can these supplies be obtained? . who provides cool packs, transport boxes, car, driver …? . what forms/information must be sent with the specimens? how does the epidemiologist obtain results? if a lab is not available, then you need a sampling strategy that addresses specimen acquisition, preparation, and transportation in compliance with international regulations on the transport of infetious substances. reference . world health organization department of communicable disease surveillance and response. highlights of specimen collection in emergency situations. undated. available from who laboratory and epidemiology capacity strengthening office regulation ) . leak-proof specimen container wrapped with enough absorbent material to absorb the entire content of the st container . leak-proof secondary container usually plastic or metal . outer shipping container whose smallest dimension is mm diagnostic specimens use iata packing instruction without biohazard label. infectious materials use iata packing instruction with biohazard label. what to send with the sample? lab request form with: • sender's name and contact info • patient name, age, sex • sample date, time • suspected clinical diagnosis with main signs and symptoms • sample macroscopic description • context-outbreak confirmation, ongoing verification, outbreak end, etc. • epidemiological or demographic data where to send the sample? a. prior to seasonal epidemic . establish a national coordinating committee (ncc). . designate a lead agency and lead official in the ncc. . establish a local coordinating committee (lcc). . designate a lead official in the lcc. . anticipate roles for partner agencies (e.g. inter-agency and team coordination, disease surveillance, field epidemiological investigation, laboratory identification, case management guideline development, outbreak logistics, public information, and social mobilization). . identify sources of funds. . intensify disease surveillance. . identify reference lab(s) for communicable diseases of epidemic potential. . ensure mechanism for specimen transport. initial response to suspected outbreak . form an emergency team to investigate and manage the outbreak a. identify key roles on the outbreak investigation team(s) ( ) epidemiology and surveillance ( ) case management ( ) water and sanitation ( ) laboratory services ( ) communication b. staff those roles ( ) epidemiologist-to monitor proper data collection and surveillance procedures ( ) physician-to confirm clinical s/sx and train health workers in case management ( ) water and sanitation expert-to develop a plan for reducing sources of contamination ( ) microbiologist-to take environmental/biological samples for laboratory confirmation, train health workers in proper sampling techniques, and confirm use of appropriate methods in the diagnostic laboratory ( ) behavior change communication (bcc) specialist-to assess the population's reaction to the outbreak, create, and disseminate appropriate health messages outbreak investigation protocol in place rapid response teams to investigate case reports epidemic investigation kits to mobilize specimens to collect labs to confirm dx of v. cholerae, s. dysenteriae, other shigella, and e. coli o :h dipstick identification on representative sample of specs is useful for cholera, but c&s is essential because dipsticks are not available for shigella, etec. vibrio are hardy if kept moist and cool. they can survive a week in cary blair media. shigella are fragile and difficult to recover if transport time > d. - isolates initially to confirm outbreak - isolates initially to create abx use policy (bacterial resistance renders cotrimoxazole, amp/amox, nalidixic acid, and tetracycline unusable) - isolates monthly from ipd and opd before abx therapy to assess evolving abx resistance - isolates periodically to reference laboratory to confirm abx resistance patterns and undertake molecular studies isolates at end of the outbreak to confirm that new diarrheas are not epidemic pathogens nb systematic sampling is most representative-e.g. every th pt or all pts q weeks adjusted as needed to collect the necessary specs. sensitivity >> important than specificity in rdt screening during an epidemic. pts from one geographic area are more likely to constitute a cluster involving a new pathogen. an area may be considered cholera-free after incubation periods (total of d) have passed without cholera disease. however, hospital monitoring should continue for a year due to tendency of enteric pathogens to re-emerge long after they are declared gone. cholera may be viable but nonculturable from the environment; environmental monitoring has many false negatives. consider improvements to existing diagnostic labs hotlines set up for reporting of rumor health reference and educational materials in place case definitions case management and referral guidelines for communicable diseases with epidemic potential pt, provider, and community educational materials specimen handling protocols epidemic command & control center established under local health authorities using principles and practices of incident mgmt unified command of multi-disciplinary specialists information channel to government and stakeholders support by government for technical actions coordination with technical sectors-particularly wash (cfr is a function of case mgmt, but ar overall is a function of wash) water supply, purification, and distribution systems bucket chlorination is low tech but reasonable way to reach individual hh or small communities water treatment units need ca hypochlorite, chlorimetric, and colimetric monitoring devices chlorinators worth considering at water sources of high public demand and epidemic activity hygiene promoters with environmental health assessors to address hand and food hygiene in communities around the outbreak area (think ring vaccination with knowledge) safe disposal of medical waste and infectious sludge from treatment facilities medical logistics-resource prepositioning and stockpiles cots (take one and have carpenter make copies) plastic sheets with defecation hole or sleeve buckets ( white color for stool-enables recognition of diarrhea color; different color for emesis; different color for domestic waste) ivf, iv sets, iv poles or suspension cords (cholera kits) key: cord- -c w b authors: cacciapaglia, giacomo; sannino, francesco title: interplay of social distancing and border restrictions for pandemics (covid- ) via the epidemic renormalisation group framework date: - - journal: nan doi: nan sha: doc_id: cord_uid: c w b we demonstrate that the epidemic renormalisation group approach to pandemics provides an effective and simple way to investigate the dynamics of disease transmission and spreading across different regions of the world. the framework also allows for reliable projections on the impact of travel limitations and social distancing measures on global epidemic spread. we test and calibrate it on reported cases while unveiling the mechanism that governs the delay in the relative peaks of newly infected cases among different regions of the globe. we discover that social distancing measures are more effective than travel limitations across borders in delaying the epidemic peak. we further provide the link to compartmental models such as the simplistic and time-honoured sir-like models. we also show how to generalise the framework to account for the interactions across several regions of the world, replacing or complementing large scale simulations. the covid- pandemic is raging around the world with an immense toll in terms of human, economic and social impact. forecasting a pandemic dynamics and its spreading is therefore paramount in helping governments to make informed decisions on a number of social and economic measures, apt at curbing the pandemic and dealing with its aftermath. while different empirical models already exist to describe the epidemic dynamics locally and globally, a coherent framework is missing. using a powerful language and methodology borrowed from high energy physics, we study and forecast the spreading dynamics and containment across different regions of the world. this framework is the renormalisation group approach [ , ] , which was successfully employed for epidemic dynamics in [ ] . here we will generalise the framework to take into account the dynamics in between different regions of the world. the approach is complementary to other methods summarised in [ ] [ ] [ ] [ ] [ ] . as for the widely adopted choice to represent the data by fitting them to simple minded logistic functions we refer to [ ] [ ] [ ] [ ] [ ] [ ] . we will also provide a map between our framework and compartmental models such as the time-honoured sir model [ ] . our epidemic renormalisation group (erg) approach is based * g.cacciapaglia@ipnl.in p .fr † sannino@cp .sdu.dk upon a simpler set of equations, which can be extended in a straightforward way to include interactions between multiple regions of the world, without the need for powerful numerical simulations. as already noted in [ ] , rather than the number of cases, it is convenient to discuss its logarithm, which is a more slowly varying function. we define through it an epidemic strength function where i(t) is the total number of infected cases per million inhabitants in the region, and ln indicates its natural logarithm. the derivative of α with respect to time provides a new quantity that we interpret as the betafunction of an underlying microscopic model. in statistical and high energy physics, the latter governs the time (inverse energy) dependence of the interaction strength among fundamental particles. here it regulates infectious interactions. more specifically, as the renormalisation group equations in high energy physics are expressed in terms of derivatives with respect to the energy µ, it is natural to identify the time as t/t = − ln µ/µ , where t and µ are respectively a reference time and energy scale. we choose t to be one week so that time is measured in weeks, and will drop it in the following. thus, the dictionary between the erg equation for the epidemic strength α and the high-energy physics analog is it has been shown in [ ] that α captures the essential information about the infected population within a sufficiently isolated region of the world. the pandemic beta function can be parametrised as whose solution, for n = , is a familiar logistic-like function the dynamics encoded in eq. ( ) is that of a system that flows from an uv fixed point at t = −∞ where α = to an ir fixed point where α = a. the latter value encodes the total number of infected cases per million expected in the region under study. the coefficient γ is the diffusion slope, while b shifts the entire epidemic curve by a given amount of time. further details, including what parameter influences the flattening of the curve and location of the inflection point and its properties can be found in [ ] . note that here we work with number of cases per million, so that our α corresponds to α − ln n m of [ ] with n m the number of inhabitants per million per each sufficiently isolated region of the world. in this work, we extend the erg formalism to include the diffusion of the epidemic between multiple nearly-isolated regions. our work is organised as follows. in sec. ii we present the formalism in the simple case of two regions, and study how the interaction term influences the delay between the epidemic peak between the first and second regions. we also investigate the effect of closing the borders at different times between the two regions. in sec. iii we map the erg formalism onto time-honoured compartmental models of the sir-type. in sec. iv we test the erg formalism by comparing the predictions to data relative to the covid- epidemic in europe and in the united states, and generalise it to include multiple regions at the same time. we then use the model to simulate a second wave of epidemic diffusion in a sample of european countries. finally, we present a discussion of the results in sec. v and offer our conclusions. here we go beyond the state-of-the-art by considering the diffusion among multiple regions of the world, each characterised by its own α i (t), which in isolation obeys a beta function like eq. ( ), with its own γ i and a i . we exemplify the framework by first considering two regions, and we generalise to multiple ones later. to couple the two equations, we start from the following axiom: there is a constant number of travellers moving from one region to the other, and viceversa, given by ∆n trav each week. our basic simplifying assumption is that the number of travellers is symmetric, i.e. there is no net flow of people between the two regions: this is a reasonable approximation during a short time as immigration only involves a smaller fraction of inhabitants than that involved in the epidemic. we further use the approximation that the rate of infected cases within the travelling subset of people is the same as the rate of infected cases in the total population of each region. thus, the variation in the number of infected cases per million in region- is given by where n m is the population of region- in millions and for region- , we find the analogous where the same k applies. physically, the parameter k measures the number of reciprocal travellers per week in units of million people. for instance, if the number of weekly travellers is ∆n trav = , then k = − . using the identity the effect of this exchange can be encoded in the two beta functions, c.f. eq. ( ), as follows: the above equations describe the evolution of the epidemic across the two regions, once a small fraction of the population travels between the two. however, for large k, they have the interesting property of forcing α = α , which in turn modifies the value of the fixed point for the two regions. the fact that the α's become equal in the long run indicates that the two regions have merged into one. one surprising finding is that the total number of infected cases across the two regions, for large k, may be reduced compared to the isolated case (see details in appendix a). while mathematically intriguing, we do not consider this result physical, as having large k modifies the values of α i and γ i in the two regions compared to the values one would have in case of isolation. in other words it would violate our initial assumption that the two regions are nearly-isolated, with small k. one can [ ] . we use data updated to the th of may (from www.worldometers.info), so the values should be considered as averaged over the whole period of pandemic diffusion. go beyond the realistic case envisioned here by increasing k. this would require modifying the set of equations substantially and goes beyond the scope of this work. to quantitatively estimate the interaction between two regions of the world, we consider benchmark values for the parameters in the two beta functions using the results given in [ ] . we show in table i the values of a and γ for various regions of the world for the covid- pandemic [ ] . a is normalised per million inhabitants and all values are adjourned to the th of may, . the values of γ and a are average values over the whole duration of the epidemic diffusion in each country/region. we observe that the value of γ tends to diminish over time as a consequence of the effect of gradual implementing of social distancing measures in each region. at the early stages of the epidemic, we observe γ ∼ , so that we will consider this as a benchmark value for the epidemic diffusion without any restriction. with the exception of south korea and china (hubei province), the range for a is roughly [ . , . ] , while for γ we find [ . , . ]. thus, we defined the following benchmark scenario for the two regions: while we vary the values of γ and γ as specified in the figures. the value of b = is chosen such that the peak in the two regions in isolation have a relative delay of weeks. the peak is here defined as the week where the maximum number of new infected cases per million is registered and corresponds to the inflection point of the total number of infected cases curve. the explicit formula for the inflection point time as function of the parameters of the theory can be found in [ ] . as a first sanity check, we computed the total number of infected cases across the two regions, per million, at the end of the pandemic, i.e. at infinite time. this is given by as a function of k. the result allows us to determine the largest value of k that does not affect the total number, i.e. the largest value that k can have before the two regions effectively merge into one. in fig. we show the results for two different populations. the plot shows that k as large as . is allowed before our description of the coupled system breaks down. note that the maximal value of k grows linearly with the population in region- , as it enters as the ratio k/n m in the coupled differential equations. to understand how the interaction encoded by k affects the diffusion of the epidemic in the two regions, we study the same benchmark of eq. ( ), except that we set b = ∞, i.e. the region- remains with zero infected cases if isolated. one caveat that should be kept in mind is that the values for γ in table i are obtained by fitting the data during the whole period of the epidemic, i.e. they take into account the effect of social distancing measures in each region. however, at the early stages of the epidemic, when social distancing measures were not yet being enforced, we expect larger values of γ. that is the reason why, in the following, we assume γ = as the natural initial benchmark value. nevertheless, we show how different social distancing measures impact the results for region- by showing also the results for smaller values of γ . we discover that the interaction among the two regions of the world, controlled by the parameter k, is sufficient to ignite the spread of the epidemic to region- and it also controls the timing of the peak. this is shown in fig. , where we plot the time of the peaks in the two regions as a function of k/n m . the result does not depend on n m . also, the time of the peak for region- is unaffected by the value of k (dashed curve) while it affects the timing of the peak for region- (solid curves). note that the kterm in eq. ( ) sparks the epidemic diffusion in region- as soon as k nm e α (t) becomes sizeable. after this point, the epidemic evolution follows the solution of the initial equation ( ), as encoded in the first term of the region- beta function. the numerical results for the peak delay show a linear dependence on ln k, with a change in slope appearing for k/n m ∼ − . this value corresponds to k n m e a = , i.e. it marks the threshold (grey line in the plots) between the regime where the interaction term is always smaller than one, and the one where strength is attainable. to test our approach we consider the covid- epidemic spread from china (hubei province) to europe (italy). from data it is known that the peaks in the two regions are about weeks apart. a reasonable estimate of weekly travellers between the two regions is in the order of the thousands, so we consider k = × − as a benchmark. this means that for this value, the bottom plot in fig. allows us to estimate the peak delay to be around weeks for γ = , i.e. for unrestricted diffusion within italy. this nicely confirms our expectations while validating the model. it is useful to note that both k and b lead to a temporal shift of the epidemic curve for region- , however the underlying mechanisms are distinct. the former is due to an interaction between two different regions of the world, while the latter is a constant of integration that depends on the number of cases at the initial time t = in region- . this also means that a specific peak time for region- relative to region- can emerge as a combination of the two effects, interpolating between the two limiting cases: the peak delay is entirely due to the interaction with region- , or it is due to the presence of cases in region- (which may have different origin) and the coupling to region- is negligible. we will discuss this interplay in more details in the next section. we now turn out attention on the impact of closing the borders between two regions of the globe versus different degree of social distancing. in the erg approach this is implemented by setting to zero k after the closing time t cl . we consider the benchmark values given in eq. ( ) , while the impact of social distancing is encoded in region- in varying the value for γ . furthermore we consider two scenarios: one in which region- has zero initial cases, meaning that the epidemic would not occur for k = (corresponding to b = ∞) and another where we fix the initial condition according to the benchmark (corresponding to b = ). the results are shown in fig. , where we report the delay in the peak of region- caused by closing the borders (i.e., delay relative to the case of t cl = ∞). such a delay depends crucially on the value of γ in region- as shown in the top plot when the epidemic in region- is only driven by the interaction term. in particular the results show that a significant delay in the spreading of the epidemic can be achieved only if the closing is enacted before the peak in region- (which is unaffected by k). in the bottom panel we show the case where region- features already some initial cases, so that t cl = would correspond to isolated regions with both featuring infected cases. in this case, we also see that the effect of the interaction is more pronounced for small values of γ in region- , indicated by the red curve for γ = . . for this value of γ , isolation would yield a delay of . weeks in the peak. for larger values of γ (less social distancing) the peak delay is strongly reduced to within week of closed frontiers, t cl [weeks] one or two weeks. in any case, closing the borders is only relevant if done before the peak in region- is attained. our results, obtained using the simple and effective erg approach, agree qualitatively with the ones presented in [ ] obtained using a numerical analysis. the take home message is that social distancing plays the dominant role in curbing and delaying the epidemic spread in region- with respect to seed region- . epidemic dynamics is often described in terms of simplistic compartmental models introduced long time ago in [ ] . here, the affected population is described in terms of compartmentalised sub-populations that have different roles in the dynamics. then, differential equations are designed to describe the time evolution of the various sub-populations. for an application to the covid- epidemic, see [ , ] . the sub-populations can be chosen to represent (s)usceptible, (i)nfected and (r)ecovered individuals (sir model), obeying the following differential equations: where p = s + i + r is a constant, measuring the total number of individuals affected. as the equations do not depend on the normalisation of the number of individuals, we can consider them for cases per million. due to the constant p , only two equations are independent, so that we can drop the one for s. the total number of infected, i(t), we study in our model is related to the above sub-populations as we can therefore re-write the two independent sir equations as eq. ( ) has a form similar to eq. ( ), except for the following: it is written in terms of the total number i(t) instead of its log α(t); it contains a dependence on the number of recovered cases, r(t). thus, our erg approach would be equivalent to the sir model if we could drop the r(t) dependence in the differential equation for i(t). it is conceivable that this is the case: in fact, in eq. ( ) we can already see that the second factor drives the number of infected cases to the fixed point i(∞) → p ≡ e a , which corresponds to the ir fixed point in the erg approach. r(t), instead, is zero at early times and only grows slowly as long as the recovery rate is small, thus its effect should remain negligible once the dynamics of i(t) is driven towards the fixed point. as investigated in [ ] , the dynamics of i(t) and α(t) can be described by the same equation, as they both are driven to flow between the two fixed points. once a solution for i(t) is found following the erg approach, i.e. eq. ( ), the number of recovered cases can be calculated by solving eq. ( ), with solution to validate this approach and calibrate , we compared the above formula to the number of recovered cases for the united states (us), where i(t) is obtained using the fit values in table i : the results are shown in fig. , where r(t) (in red) reproduces the data for = . . we checked that for other countries, a similarly good fit can be obtained for ∼ . , thus we consider this description consistent. to establish a more quantitative dictionary between the erg approach and the sir model, we compared the numerical solutions of the sir equations ( ) and ( ) to the solutions of the beta function in eq. (with r(t) given by eq. ( )). we find that the solutions overlap as long as matching values of γ andγ are used. in fig. we show the numerical relation between the matching values of the couplings for choices of the recovery rate : the result shows a linear relation between the couplings in the two models. being able to reproduce the number of recovered cases for one region in isolation, we can now address the issue of the effect of the recovered cases in the coupled system. in fact, the transmission of the epidemic due to travel of individuals between the two regions is only due to the presence of people actively infected, namely it depends on thus, it suffices to replace the expression in eq. ( ) with and similarly for eq. ( ). we have compared the solutions of the coupled differential equations with and without taking into account the recovered cases, and found that including r i (t) only affects the epidemic diffusion in region- by a few days. thus, this effect can be neglected in first approximation. we now confront the erg framework to data from the covid- pandemic collected from www.worldometers.info and adjourned to the th of may, . although we are well aware of the pitfalls stemming from comparing data provided by different countries due to the inhomogeneous way infectious cases were tested and reported, it is still possible to extract from these reliable time behaviour and structure. of course, when coupling two regions of the world, part of the initial uncertainty also affects the epidemic transmission probability without affecting the overall picture. nevertheless, we will now see that the erg formalism can be used simultaneously to quantiately project the spreading dynamics across different regions of the world, or as an a-posteriori way to learn how this spreading came to be. we focus on two examples, one intra european (italy-denmark) and the other between europe and the us. the values for γ and a for each country are taken from the fit in table i , which assumes isolation. in the right plot of fig. we show the total number of infected cases in italy and denmark (blue and red dots, respectively), compared to the fit in table i (solid curves) : the latter assumes that the epidemic occurred in the two regions while in isolation. we now wish to understand how and whether the virus spread from italy to denmark: thus, we used the coupled eqs ( ) and ( ), while we set the number of initial cases in denmark to be null, i.e. b = ∞. all the other parameters are fixed to the values in the table. we find that the two curves can be reasonably fit by assuming k = . , as shown in the left plot of fig. : the dashed orange curve, corresponding to italy, overlaps to the isolated fit (solid blue), while the new curve for denmark (dashed green) is close to the isolated fit (solid red). let us now comment on the actual value of k. if we take it literally this it would correspond to a rate of . travellers between the two regions each week. this is an unreasonably large value but it can be alternatively and conservatively interpreted in the following ways: i) more countries contributed to the epidemic spread in denmark; it and dk k= . i) the original spreading dynamics in denmark is due to few very socially active infected individuals that traveled back from italy and/or were superspreaders; iii) a combination of the above. whatever the reason, it is naturally incorporated in a larger value of k. one can also take into account the various scenarios by effectively re-instating an initial value for α at t = while reducing the k value. to further test our model we consider the system consisting of europe as region- and the united states as region- . for simplicity, we modelled europe on the european union (with n m = ) with parameters from the fit of the epidemic diffusion in italy (c.f., table i ). after setting to zero the initial cases in the us, we were able to reproduce the diffusion of the epidemic in region- (us) for k = , as shown in the right plot of fig. . while it is still possible that the large value for k may be interpreted as in the above case, it has the further effect of distorting the epidemic curve for region- , the eu, thus suggesting that it may be hard to explain the diffusion of the covid- epidemic in the us as originating solely from the eu. at this stage, we cannot exclude that adjusting the epidemic parameters in the eu could improve the agreement. this exercise, nevertheless, proves the effectiveness of our simple erg model to describe the diffusion of the epidemic among different regions of the world. a more accurate fit may be obtained if more than one region is included in the analysis, which will be considered in a future work. we now use the erg framework to model the impact of a new wave of epidemic spread of the covid- virus (or a related one) in europe. to do so, we simulate the effect of transmission among countries in a pool of european countries, namely italy, spain, france, the united kingdom, germany, denmark and switzerland. we also include an unspecified "seed region", with a population of n m = , which has some initial cases, while no case is initially present for the simulated european countries. this is achieved by setting b i = ∞, where i = , . . . spans over the sample countries mentioned above. we generate randomly the diffusion factors γ i in the range [ . , . ], based on the data of the current covid- epidemic in europe, and also generate random values of a i in the range [ . , . ] . this also includes the seed region. finally, we provide randomly generated numbers of travellers between each of the regions, including the seed one, giving coupling values k ij in the range [ , ] × − . we then solve the coupled differential equations: where i, j = , . . . and α corresponds to the seed region. the result is shown in the top row of fig. , where black indicates the seed region and the coloured curves correspond to the sample european countries. the top-right plot, where the distribution of new cases is displayed, clearly shows that the peaks in the infected regions occur between to weeks after the peak in the seed region. this effect, however, is mainly due to the values of the γ's in those regions, and not on the values of the interaction couplings k ij . to prove this, we have run the same simulation again, by fixing γ i = , i = , . . . roughly correspond to unrestricted diffusion of the virus in the target regions. the result shows that all the peaks are now occurring within weeks after the peak in the seed region. the results nicely demonstrate that our erg framework not only is useful, simple and effective to understand the current pandemic, but can also be used to model future ones. we extended the epidemic renormalisation group approach to analyse the dynamics of disease transmission and spreading across different regions of the world. we have shown that the erg framework constitutes an effective way to understand the relative impact of border control versus social distancing measures on the global spread of the epidemic. the simplicity of the approach, stemming from an effective description of complex phenomena, make it a reliable alternative to the use of expensive high-performance numerical computations. we calibrated our approach via internationally reported cases. the approach elucidates the underlying mechanism that governs the delay in the relative peaks of newly infected cases across different regions of the world. among our results, we were able to demonstrate that social distancing measures are more efficient than border control in delaying the epidemic peak. in order to connect with widely used time-honoured compartmental models of the sir-like type, we established the proper map with our erg framework. we have also shown how to generalise the erg framework to account for the epidemic interactions across multiple regions of the world. we foresee a number of future applications and extensions of our seed work. from a more phenomenological point of view, of immediate impact for society, we plan on embarking on a world-wide monitoring to make global projections that will help governments and industries make containment plans and strategise about reopening society and how to best implement border control. we also wish to improve on understanding the link between the erg approach and microscopic models of population dynamics and epidemic spread including a number of granular effects that are, by construction, averaged over by effective descriptions such as the erg approach. appendix a: asymptotic behaviour for large k the coupled system of beta functions in eqs ( ) and ( ) has an interesting solution in the limit for large k. while this limit should be considered unphysical, it is intriguing from a mathematical point of view. moreover, it may lead to some insights on the dynamics of two regions merging into a single one. in the limit of large k → ∞, the interaction term in the two beta functions dominates. it thus forces α = α asymptotically. to check if there is a fixed point, we can take the sum of the two functions, eliminating the k-term, and search for zeros: n m e α β(α ) + n m e α β(α ) = e α n m γ α − α a + e α n m γ α − α a = . imposing the condition α = α = α, we find: e α α n m γ − α a + n m γ − α a = (a ) that is solved by α = (uv fixed point) or α * = (n m γ + n m γ )a a n m γ a + n m γ a , which defines the new ir fixed point. it is now interesting to ask: for fixed a and a , is the total number of cases in the two regions in the k → ∞ limit larger or smaller than that in the k → limit? in fact, i tot k→∞ = (n m + n m )e α * = (n m + n m )e similarly, i tot k→ = n m e a + n m a a = e a (n m e δ + n m e −δ ) . thus i tot k→∞ i tot k→ = n m + n m n m e δ + n m e −δ e − δ(δ+ga) a+gδ . (a ) interestingly, as the exponential in the numerator may be negative, it is possible to have a reduction in the total number of cases when the exchange of people is large. in fig. we show numerically the above ratio, for n m = n m (top plot) and n m = n m (bottom plot), and for various values of g (we recall that − < g < ). to make sense of the result, let's consider the case of similar slope in the two countries, i.e. γ = γ . in the case n m = n m , this would give g = , i.e. the blue curve in the top plot: this case features a reduction of the total cases, as long as a = a . for n m = n m , we have g ≈ , corresponding to the orange curve in the bottom plot: again, there is a significant reduction for a > a , k→∞ /i tot k→ as a function of delta for g = (blue), g = . (red), g = − . (purple), and the extreme values g = (orange) and g = − (green). we fixed a = , but the results have a mild dependence on its value. while the increase if minor if a > a . of course, these results are just illustrative, because the values of a i and γ i should be influenced by the policies concerning the movement of people between infected regions. renormalization group and critical phenomena. . renormalization group and the kadanoff scaling picture renormalization group and critical phenomena. . phase space cell analysis of critical behavior renormalization group approach to pandemics: the covid- online here analysis of transmission dynamics for zika virus on networks coupling dynamics of epidemic spreading and information diffusion on complex networks statistical physics of human cooperation coupled disease-behavior dynamics on complex networks: a review statistical physics of vaccination computing applications to differential equations modelling in the physical and social sciences early estimates of epidemic final sizes a note on the derivation of epidemic final sizes interdisciplinary applied mathematics early epidemic dynamics of the west african ebola outbreak: estimates derived with a simple two-parameter model using phenomenological models for forecasting the ebola challenge a contribution to the mathematical theory of epidemics the effect of travel restrictions on the spread of the novel coronavirus (covid- ) outbreak the effect of control strategies to reduce social mixing on outcomes of the covid- epidemic in wuhan, china: a modelling study time, space and social interactions: exit mechanisms for the covid- epidemics we thank michele della morte, christian møller dahl and domenico orlando for comments and helpful discussions. key: cord- -wwpd bx authors: nguyen, vinh-kim title: when the world catches cold: thinking with influenza date: - - journal: biosocieties doi: . /biosoc. . sha: doc_id: cord_uid: wwpd bx nan sars and ebola appear as deadly epidemiological bookends for the chief subject matter of the reviewed publications: pandemic flu. sars and ebola are both zoonoses, but sars emerged from the viral broth of the dense of animal/human interactions ecology of southeast asia, whereas the ebola epidemic in west africa was triggered by a random chain of transmission linking a fruit bat and a -year old in the forest region of guinea. the epidemics differed in other ways: sars was airborne, spreading from southeast china to hong kong to toronto by jet; ebola was touch-borne, spread through the most common gestures of care and carried from village to village to capital city by ambulance and bush-taxi. their common denominator was fear, fuelled by viral speed and deadliness. pandemic flu is also frightening, suspended in historical memory and always threatening to materialize. but a dramatic worldwide epidemic on the scale of the - 'spanish flu' has never recurred, yet continues to haunt current research and public health policy debates. nonetheless, a flu epidemic happens every year, embedding us in an autumnal (at least in europe and north america) cycle of sniffles, sneezes and runny noses (and vaccination for those considered more vulnerable). at the heart of the matter then, lies the question of the fear of an unforeseeable, potentially cataclysmic event lurking behind the regular recurrence of what most of us experience as a benign event. caduff, keck and macphail all write against more sensationalistic accounts of pandemic flu with their dramatic tropes of virus hunters and looming catastrophe, seeking rather to demystify and explain in these ethnographies of influenza research. these works constitute a collective plea for sang-froid, careful engagement with science and paying serious attention to the perspectives of people in everyday life. together, these three monographs point out important directions for future ethnography and theoretical elaboration. caduff constructs the narrative of his book around prophecy, arguing that it is precisely the inscrutability of science that opens up a space for scientists to make bold and conflicting declarations. at least in the case of influenza research, science does little more, it seems, than to furnish yet another set of omens (viral genes, epidemiological signs, previous outbreaks) to be parsed. on the basis of interviews with leading flu scientists and an ethnographic exploration of "preparedness", pandemic prophecy expands and elaborates on the argument (set out in more condensed form in caduff, ) that the threat of the next great flu pandemic creates a zone of uncertainty that allows different science-based forecasts to compete for authority in the public sphere; what caduff calls "scientific prophecy". the argument is deployed in an account that explores, in six chapters, the basic, or laboratory, science of influenza and the evidentiary troubles engendered by the prophetic scene. these troubles essentially concern the way in which the "prophetic scene" sets the stage for evidentiary vinh-kim nguyen is an emergency room physician and medical anthropologist. he teaches in montreal's school of public health and geneva's graduate institute for international and development studies and is currently funded by the erc to conduct research on the elimination of infectious diseases. disputes around laboratory findingsa false alarm based on screening cases for specific strains, the reconstitution of the original epidemic flu virus and other forays into the engineering of more virulent recombinant strainswhich in turn fuel uncertainty and sustain the space of pandemic prophecy. caduff draws mainly on the scientific literature, illuminated by interviews with scientists, snapshots of laboratory life and his own participation in pandemic preparedness drills. fear reveals underlying cultural logics of prediction and control. these logics are best understood in light of the staple of anthropological scholarship on prophecy and oracles and, more broadly, of human efforts to order nature, tame the unpredictable and manage misfortune. macphail in contrast focuses on the work required to "make" pandemics real. this "pathography", with seven chapters ordered according to the genetic structure of the virus, draws on fieldwork principally within the cdc tracking the flu epidemic, along with interviews with scientists in hong kong. macphails's key argument is that viruses and the scientists who study them transmit along global networks, such that the actual phylogenetic structure of the virus mirrors the structure of information exchange between scientists required to map the structure. more boldly, she invokes kroeber's "superorganism" to refer to the global health apparatus as itself the unit out of which viruses and scientists are cleaved. epidemics generate viruses much as globalization produces locality. the analogy between viruses and networks of scientific collaboration is not a metaphor, macphail makes clear, but rather points to how infrastructures of global exchange materialize events, of which epidemics are the symptom. the world truly is "viral", because it is interconnected; in other words, it is the planetary span of infrastructuresof transportation, communication and commercethat produces things that go viral. unlike the previous two books, keck's is aimed at a general audience. departing from a concern with the (non-)eventfulness of flu epidemics, what they do and what it takes to "make" them, keck engages a wideranging investigation into the origins of the flu that takes us from the french food safety agency to hong kong, china, cambodia and back to the laboratory. the investigation exposes the cultural logic of zoonotic danger, and how influenza rehearses the fundamental binary between human and animal. with erudition and humour, keck explores the logics of transformation of this binary across a wide range of practices, in farms, in chinese markets, and in a particularly charming chapter, to those buddhists in hong kong who go about rescuing animals, releasing fish back into the sea or burying dead rats. in a penultimate laboratory chapter, keck encounters the same phylogenetic classificatory schemes as mac-phail, a clear visualization of underlying logics of transformation as they move from human to animal to laboratory and across society. discussing the mass culling of poultry in the context of avian flu epidemics, buddhist cosmology and asian politics, keck skilfully outlines an anthropology of boundaries: that between animal (non-human) and human, between meaning and non-meaning, between production and consumption, between country and city. it is hard not to see the influence here of the anthropology of lévi-strauss, of whom keck is a renowned commentator in france. but un monde grippé updates lévi strauss with actor-network theory, as keck ventures into the laboratory to uncover the work of mediation produced by scientists and engages the broader geopolitics of influenza. an explicit project of these authors is to complicate the seminal distinction, introduced by luhmann ( ) between "provisional foresight" manifest in scientific contingency and the inevitability of "prophetic temporality". what is at stake are the regimes of anticipation (cf adams et al, ) that conjure a dystopian past (that is, the great flu epidemic of - ) to inject a hypothetical future into the present. the temporal modality, perhaps most familiar to readers of this journal from the concept of the experiment as a "machine for producing the future" (rheinberger, , quoting the nobel prize-winning molecular biologist françois jacob), is most explicitly indebted to classical studies of witchcraft, oracles and divination (evans-pritchard, ) to more contemporary examinations of risk and uncertainty in clinical practice, global health and everyday life. these books contribute to elaborate on the anthropology of "preparedness" (collier and lakoff, ) , as is visible in lakoff and keck, considerations of "sentinel devices". how does the articulation of infrastructure with prediction, and the regimes of anticipation that result (as we have seen in these books) compare with that more intimate domain of biomedical forecasting located in the clinic, particularly around markers for future conditions? an increasingly large body of work in medical anthropology and sociology points to the paradoxical generation of uncertainty that clinical diagnostic technologies produce. rescaling biomedical risk assessment from the clinic/individual to the global/ population represents a step-change to an books forum ontologically different level: that of time itself, looping from the future back to the past. this more radical uncertainty opens up the space of prophecy and, because uncertainty has become unmoored from stable systems for predicting and explaining misfortune, perhaps, takes us even beyond divination. thinking about regimes of anticipation can bring in conversations that have emerged in contemporary ethnography around the work of elizabeth povinelli and specifically her notions of social tense and "the future anterior" as a mode of late liberal governmentalitya gesture made by caduff. povinelli ( ) develops social tense and the future anterior to account for how in australia, aboriginal peoples are located within a future anterior, a hypothetical future when past injustices will have been compensated. this "mode of address" is not unique to australia, surfacing in canada's treatment of past injustices foisted on first nations communities, and wherever "truth & reconciliation" commissions have been brought to bear. here we might be concerned with the political work that is done by modes of anticipation, the forms of address they entail and how these inscribe those being addressed into specific temporal-juridical registers. a second issues that arises in reading these books concerns notions of transmissibility or what sampson ( ) has recently termed 'virality'. at the relentlessly empirical and clearly pragmatic level, the notion of transmissibility distinguishes diseases that can be transmitted from those that cannot. this is a distinction increasingly used in global health, previously largely concerned with infectious diseases as top causes of global mortality (these being hiv, malaria and tuberculosis). an identifiable vector is presumed and ultimately identified: a proteinaceous (that is, prions) viral or bacterial pathogen. because of their dramatic potential for contagion viruses are the reference for transmissibility; what gets transmitted goes viral after all. but as macphail points out, viruses are structured like the networks that reveal them; contagion is a consequence of interconnectedness. today growing concern is voiced, based on epidemiological data that shows increasing rates of obesity and hypertension, conjugated with ageing populations worldwide, that a 'tsunami' of non-communicable diseases (ncds) is in store. the moniker of ncds includes a diversity of pathologies that include diabetes and cardiovascular disease (which contribute significantly to stroke and renal failure), cancers and chronic lung diseases. even empirically, however, 'non-communicable' diseases appear to be more transmissible than previously thought. epidemiological studies suggest that conditions such as obesity or diabetes in fact cluster along social networks, that they are in fact 'transmitted'. what is transmitted is unclear, although (usually) not a pathogenic microscopic organism (although many non-communicable diseases appear to have more of an infectious/inflammatory origin than previously thought). it is assumed that it is 'ideas', 'social norms' or 'behaviours' that are pathogenic. the underlying concepts operant in the communicable/non-communicable distinction articulate assumptions about identity, difference and mutability that back up keck's decision to explore the boundaries/ oppositions that are put to work by influenza. but while keck drew on lévi-straussian transformation theory, sampson points to another conversation that explicitly concerns affect, ontology and most recently individuation. the philosophical corpus in this case includes gabriel tarde, gilbert simondon and gilles deleuze. the rush to prepare for the next pandemic, manifestly to no effect as demonstrated by the ebola epidemic, suggests that the world as we know it has already caught cold. the reference to antiessentialist thinking and the ontological pluralism associated with these thinkers suggests a way to depart from the deterministic conventions of languageand indeed representationthat still saturate global health science and have kept us off-balance for coming pandemics. sometimes thinking about the history or ethnography of a disease seems inseparable fromor even reducible toone's own experience of it. as i read alex m. nading's mosquito trails, a vivid account of the ecological and social entanglements of dengue fever outside managua, nicaragua, i kept remembering my own engagement with the mosquito and its virus in solo, indonesia, around . taking a break from graduate school, i was hanging out in that ancient javanese town, spending time with an old friend from college, who was training to be a dalang, or puppet master, in the art of wayang kulit, shadow puppetry. we were living in rough and simple conditions close to one of the two sultans' palaces, or kratons, and my friend, like many others in the neighborhood, was recovering from a prolonged and severe fever. although i was unaware of dengue's epidemiology at the time, i later learned that i had become just one more number in the emerging epidemic of the disease in southeast asia and latin america. development and urbanization were providing ideal conditions for mosquito breeding and for bringing aedes into close contact with vulnerable peoplein particular, the poor in crowded, unfinished, poorly drained, insectnet deficient slums or barrios or favelas. many species of mosquito thrive in such circumstances. since the first dengue infection in adults is rarely fatal, the disease does not receive the attention that killers like malaria, tuberculosis and aids demand. nonetheless, it is a major cause of suffering and malaise among those who live in the regions, mostly tropical, that aedes finds hospitable. re-infection with a different one of the four or so serotypes of the virus is a anticipation: technoscience, life, affect, temporality pandemic prophecy, or how to have faith in reason infrastructure and event: the political technology of preparedness witchcraft, oracles and magic among the azande preface: sentinel devices observations on modernity key: cord- -ay ybcm authors: davies, stephen title: pandemics and the consequences of covid‐ date: - - journal: nan doi: . /ecaf. sha: doc_id: cord_uid: ay ybcm nan pandemics are a regular feature of human history from ancient times onwards (mcneill, ) . as major eruptions of the harsh realities of nature into the settled life of civilisations (for it is civilisations that suffer from them, for various reasons), they loom large in historical accounts and the memoirs of those who lived through them. historically, pandemics have brought about sweeping social, political, and cultural changeor at least they seem to have done so, for the reality is that they give a massive push to movements and trends that were already under way. in the extreme cases, pandemics have figured largely in the collapse of empires and civilisations, as for example in the havoc the bubonic plague wrought on both the eastern roman and sasanian empires in the sixth century (little, ) . in the modern world (since around ) their impact has been less dramatic but it is still considerable. there have been almost pandemics in the modern era and they have played a central part in the development and growth of the modern state. there is also an inescapable economic aspect to pandemics, in terms of both their dynamics (the way they spread and the reasons why they appear when and where they do), and their consequences, among which economic impacts loom large. it is important to understand what a pandemic is and how it is distinct from an ordinary and localised epidemic outbreak. the latter is a constant feature of human life. an infectious disease will break out in a particular location and initially spread rapidly among the local population (which may be large). after a while the rate of growth slows down and eventually stops, with the number of cases peaking. there is then an almost equally rapid decline, so the path of an epidemic resembles an inverted v. sometimes, however, the epidemic spreads widely beyond its original point of origin and becomes extensively dispersed geographically. such an epidemic is commonly called a pandemic, although strictly speaking that term should be used only for the ultimate case of an epidemic that has diffused so widely that outbreaks are found at roughly the same time all over the populated planet. a pandemic has a different pattern from that of a local epidemic. the disease, which is typically novel and caused by a new or mutated pathogen, appears at one point on the planet. it then spreads along trade routes and travel routes to other parts of the world (tatem, rogers, & hay, ) . travellers (tourists today but also pilgrims and business travellers), merchants, and soldiers are historically the major carriers (mcneill, ) . the transmission at this point is not geographically continuous; instead, the disease spreads along trade routes from one trade hub to another, leaping over intervening territory. this leads to widespread and scattered nearsimultaneous outbreaks across the world, which can then in turn lead to further transmission. this is the first phase of the pandemic. eventually these localised outbreaks subside, in the same way as a truly local epidemic does. however, in a pandemic that is not the end of the story. the epidemic now enters a second phase, usually called the 'smouldering' phase (viboud, grais, lafont, miller, & simonsen, ) . in this phase the disease spreads out from the original foci and becomes much more widely and uniformly dispersed. this phase is marked by scattered outbreaks on a small scale, so the overall number of cases does not rise or does so slowly. gradually, however, the local outbreaks start to coalesce, and after some time (which, depending on the pathogen, can be anything from a few months to several years) the third phase is entered. this is a second wave of accelerating infection, but much more widely dispersed and uniform than the first one (although some of the areas most hard hit in the first phase get off lightly, because of higher levels of acquired immunity) (cockburn, delon, & fereira, ; kindrachuk & nickol, ) . this third phase, or second wave, is typically much larger than the first wave in terms of both the number of cases and the geographical spread, and often does far more damage. with viral pathogens the second wave is often more virulent than the first (this happened for example in the spanish flu pandemic of - ) but it can be milder (kilbourne, ; potter, ; spinney, ) . after the third phase the epidemic becomes quiescent again but it often returns in a third and even a fourth wave. these, however, are almost always milder than the earlier waves in terms of their medical effects. how then does the covid- pandemic of fit into that kind of story? clearly it is not on the same scale as the truly massive ones of the past, such as the antonine plague of the second century (probably smallpox) or the plague of justinian in the sixth century and the black death in the fourteenth (both of these being bubonic plague). these all killed upwards of per cent of the affected populations, a truly devastating mortality rate (benedictow, ; horrox, ; little, ; mcneill, ) . by contrast, covid- appears so far to have an infection fatality rate of around . - . per cent (so much milder than those cases but also several times worse than regular seasonal influenza). the medical effect is so far much less than that of the spanish flu pandemic of - , although it may end up being slightly worse than in the asian flu and hong kong flu pandemics ( - and - respectively) . the covid- virus is seemingly less infectious than influenza but has a longer incubation period and a very high proportion of asymptomatic cases, which means it still spreads widely. the major differences from the past are the greater medical capacity available, in terms of both knowledge and actual resources, and the greater administrative capacity of modern states. in - local controls, often sweeping, were imposed, but there were nothing like the national responses seen in (spinney, ) . policies of lockdown initially and testing, tracing and isolating (tti) subsequently may smother the smouldering phase and prevent a second wave or third phase this time, holding the line until a vaccine is developed. (countries that were able to put a programme of tti in place early on, such as south korea, have avoided the need for a strict lockdown.) at the time of writing (may ), we still do not know whether we will escape a third phase. one problem is that the development and spread of the virus is at every stage a complex system in the technical sense of that term. that is, we cannot simply extrapolate existing trends, or predict from initial conditions and parameters how things will work out subsequently. in addition, too much is still not known, most notably the proportions of populations that have already been infected and are consequently now immune. what evidence we have suggests an infection rate in most places of between per cent and per cent (ahlander & pollard, ; urra, ) . the problem is that this means populations are a long way from so-called 'herd immunity' where the number of susceptible people in a given population is at a level where one case will give rise to fewer than one new case, because of the physical difficulty of finding a vulnerable person (this level is at least per cent for a virus with the known features of . all this means that policymakers are operating in a situation analogous to the 'fog of war', with incomplete or absent information and constantly and unpredictably changing circumstances. they face an acute knowledge problem, in other words. given this, it will be a major achievement if controls and other measures do succeed in dousing the smouldering stage of the pandemic. the experience of the past, and the way pandemics have happened, tell us a number of things. because the initial spread beyond a locality is a function of transmission along channels such as trade and travel routes (including pilgrimage ones), very widespread epidemics are almost by definition cases where an epidemic has reached every part of an ecumene, that is, a part of the planet that is economically integrated through trade and exchange. today that means the entire planet. in the past for the entire planet to be reached the pathogen would take several steps geographically, going through the cycle described above in each step (we can see this in the black death, for example). today, because of air travel and things such as austrian ski holidays, the coronavirus was able to spread from wuhan in china to the whole planet in a matter of just weeks. (in - the time it took spanish flu to travel from one part of the world to another was measured in months.) all this leads to the conclusion that several features of the world we live in, such as high levels of economic integration and trade, widespread mass travel, and rapid modes of transport, make it much more vulnerable to a true pandemic. to that list we should add such things as the nature of modern livestock farming and acute pressure on wildlife habitats, both of which contribute significantly to the appearance of novel pathogens and transmission from animals to humans. these and other features of the modern world also mean that the economic impact of an extensive epidemic is going to be much greater than was the case in, for example, - . international travel is now a much more significant and valuable activity, so its curtailment will have much bigger effects. much manufacturing and other economic activity now depends on long and complex supply chains that, again, will be disrupted by both the epidemic itself and the measures taken to contain it. changes in consumption patterns also make contemporary economies more vulnerable. for example, in the last three decades americans have taken to eating out more and more, to the point where just over half of the food consumed is eaten in bars and restaurants. these have been closed down but even before then their trade had collapsed. this has had a much bigger effect than would have been the case in , not least because the entire food supply system is now geared up to sending half its output to restaurants rather than grocery stores, and it is extremely difficult to adjust quickly to restaurant closure (bedford, ) there are similar examples in other areas, such as clothing purchasing. another change is the much greater significance of credit, with far more businesses highly leveraged and operating on very tight margins. this means that a prolonged interruption to normal business conditions will have its effect amplified by finance, in a way that was not true years ago. one social change that also has this effect is the movement of women with children into the labour force in large numbersthis magnifies the economic impact of school closures (keogh-brown, wren-lewis, edmunds, beutels, & smith, ) . all this means that a pandemic such as the hong kong flu is going to have bigger effects if it were to happen today than the original did back in - . the covid- virus is, on the evidence, more medically severe, so we should expect it to have if anything a still larger impact. at first sight it would seem obvious that the measures taken by governments to try to suppress the spread of the virus and head off a second wave (by stamping out the 'smouldering' phase) have in turn increased that impact even further, massively so. certainly, the impact has been dramatic, with a record rise in us unemployment claims and a dramatic rise in claims for universal credit in the uk. most businesses are presently shut down in the uk and elsewhere, and only measures such as the furlough scheme introduced into the uk have prevented a rise in unemployment not seen since the dark days of , given a collapse in gdp that some commentators estimate to be the worst since the s or s (bruce, ; faulconbridge & bruce, ) . however, initial forecasts indicate that the additional impact of lockdowns is far less than most imagine. there is no clear correlation between the severity of lockdown and the size of the hit to gdp, with countries such as sweden that have avoided lockdowns and gone instead for social distancing predicted to see a decline in gdp similar to the ones expected in countries that did impose one (milne, ) . moreover, the early signs are that lockdowns may not have had such a dramatic effect on rates of infection and rapidity of spread during the first phase of this pandemic. it seems that it is measures such as effective tti policy, closing of borders, and successfully protecting vulnerable groups such as the elderly that have had the biggest effect. the tentative but increasingly strong conclusion is that it was the spontaneous responses and reactions of the public that brought about both the medical effect of slower spread and the bulk of the economic impact (this also highlights the fragility of much of the contemporary economy). what kinds of administrative and political effects have pandemics had historically and how might that play out this time? one important point is that pandemics seldom lead to something truly novel: they typically provide a big boost to processes that were already under way. they do not bring down institutions and systems that are in good shape, but they do precipitate the collapse and end of ones that were already in a poor state. so most of the firms or sectors that go under will be ones that were already having serious difficulty or were already vulnerable, such as retail. we will see the same pattern in politics. the pandemic will lead to a resurgence of nationalism and the nation state, while undermining a rules-based international order and supranational forms of governance. unfortunately, it will boost the trend towards protectionism and economic nationalism that is already under way. it will also lead to a decline in international integration as supply chains are shortened and production 'reshored' in response to revealed vulnerabilities (again, this is already under way). it will almost certainly trigger a financial crisis centred on the unsustainable accumulation of private debt, this again being a case of it providing the push that brings down something that is already on the verge of falling over. historically, pandemics have played a central part in the emergence of the modern administrative state, through the creation of modern systems of public health in response to major epidemics. it was the six great cholera pandemics of the nineteenth century that were particularly important for this, leading as they did to governments acquiring extensive powers to inspect, regulate, and register their populations and to the state taking on responsibility for sanitation and providing potable water (wilford, ) . they also led to a profound change in the way large towns and cities were administered and subsequently to the development of an extensive and often coercive set of public health programmes, such as compulsory vaccination, as well as health visitors and district nurses to support but also chivvy and push the general public. it seems likely that the coronavirus pandemic will therefore lead to a reassessment of the extent, power, and functions of government. in some areas this will result in a growth or extension of powers but in others there will likely be a pulling back or withdrawal as public administration is found to be lacking or self-defeating. a lot of regulations, particularly ones to do with medicines and drugs but also things such as occupational licensure (in the united states in particular) are likely to be cut back or abolished. in contrast, surveillance powers are probably going to become more extensive. one likely change is in the area of health services: in most countries (east asian ones and germany are the big exceptions) these have come to be dominated by hospitals and therapeutic medicine at the expense of health maintenance and public health (hawe, yuen, & baillie, ) . this has been revealed as brittle and highly vulnerable to shocks such as a major epidemic (in it was panic about the pressure on hospital systems that led to the decision to impose a lockdown, in most cases). one area where there will be much debate is over the relative performance and effectiveness of decentralised and localised systems as compared to centralised or national ones: this is actually an area where the evidence can support both sides, with the correct answer differing according to local circumstances. the pandemic will also have other, less predictable, effects, but some of these can already be discerned and others can be guessed at from historical experience. one rather grim result will be a heightening of international tensions, particularly between china and both the us and europe. there may be significant consequences for education and higher education in particular. despite what some hope or fear, there are unlikely to be lasting consequences for pedagogy but the financial and organisational structure of the higher education industry is likely to face dramatic disruption and reorganisation, on a worldwide basis. another area that will probably see a major impact in some countries is welfare policy, where the idea of a universal basic income, already gaining support of late, is going to move to the centre of debate. on the historical evidence there will also be unpredictable but extensive cultural effects (cantor, ) . usually there is a simultaneous movement towards both greater seriousness and impatience with intellectual frivolity on the one hand and a desire to live for the moment and take pleasure where it may be found on the other. other things are simply a matter of guesswork (or, too often, projection of hopes and fears). perhaps there will be a revulsion against the way everyday work is organised and away from a system where almost all adults are employed. perhaps working from home will become a new normal, or alternatively people will be desperate for the company of a workplace. there may well be an uptick in the birth rate: as one person observed to me, if lockdown does not get the uk birth rate back above replacement level, nothing will. note for up-to-date information, see worldometer data at https://www.worldometers.info/coronavirus/ swedish antibody study shows long road to immunity as covid- toll mounts. reuters how and why america's food system is cracking. the federalist the black death - : the complete history worst uk slump in 'centuries' looms as lockdown slams business. reuters in the wake of the plague: the black death and the world it made origin and progress of the - hong kong influenza epidemic never had it so bad? plague, weather, and war did worse to the uk economy. reuters ohe guide to uk health and healthcare statistics. london: office of health economics the black death the possible macroeconomic impact on the uk of an influenza pandemic influenza pandemics of the twentieth century plague and the end of antiquity: the pandemic of - plagues and peoples sweden unlikely to feel economic benefit of no-lockdown approach a year of terror and a century of reflection: perspectives on the great influenza pandemic of - pale rider: the spanish flu of and how it changed the world global transport networks and infectious disease spread antibody study shows that just % of spaniards have contracted the coronavirus. el pais multinational impact of the hong kong influenza how epidemics helped shape the modern metropolis how to cite this article: davies s. pandemics and the consequences of covid- key: cord- -kc thr authors: bradt, david a.; drummond, christina m. title: technical annexes date: - - journal: pocket field guide for disaster health professionals doi: . / - - - - _ sha: doc_id: cord_uid: kc thr . humanitarian programs ; . security sector ; . health sector : core disciplines in disaster health . primary health care programs . disease prevention . clinical facilities . reproductive health . water and sanitation . food and nutrition . chemical weapons . epi methods ; . tropical medicine : tropical infectious diseases—vector-borne and zoonotic . tropical infectious diseases—non-vector-borne ; . epidemic preparedness and response ; . communicable disease control : diarrhea . influenza . malaria . measles . meningitis . viral hemorrhagic fever ; . diagnostic laboratory : indications, laboratory tests, and expected availability . specimen handling ; . acronyms ; this section provides guidance on technical issues in the health sector. the annexes contain compilations of frequently used reference information. • humanitarian programs-contains conceptual frameworks on global clusters, relief programs, humanitarian financing, and early recovery. • security sector-contains key definitions from the rome statute of the international criminal court • health sector-contains a broad range of core health technical information including environmental classification of water and excreta-related diseases, disease prevention measures, water treatment end points, anthropometric classifications, micronutrient deficiency states, management of chemical weapon exposures, and epi methods. • tropical medicine-contains clinical summaries of tropical infectious diseases with details on disease vector and host, clinical presentation, diagnostic lab tests, clinical epidemiology, and therapy. • epidemic preparedness and response-contains core principles of epidemic preparedness and response. • communicable disease control-contains an overview of selected communicable diseases of epidemic potential including diarrhea, influenza, malaria, measles, meningitis, and viral hemorrhagic fever. • diagnostic laboratory-contains guidance on lab specimen handling and testing. • acronyms-contains acronyms commonly used in disaster management and humanitarian assistance. a. in-kind donations (eg food, seeds, tools, fishing nets, etc) b. types of community projects in food-for-assets programs ( ) natural resources development (a) water harvesting (b) soil conservation ( ) restoration of agri(aqua)culture potential (a) irrigation systems (b) seed systems ( ) infrastructure rehabilitation (a) schools (b) market places (c) community granaries (d) warehouses (e) roads (f) bridges ( ) diversification of livelihoods (a) training and experience sharing . increase individual purchasing power a. cash distribution b. cash for work (cash for assets) c. vouchers d. micro-credit e. job fairs f . artisanal production g. livelihoods/income generation . support market resumption a. market rehabilitation b. infrastructure rehabilitation c. micro-finance institutions goals-protect what's left ( month), restore the system ( months), improve the system ( . promote transformational development support far-reaching, fundamental changes in relatively stable developing countries, with emphasis on improvements in governance and institutions, human capacity, and economic structure, so that countries can sustain further economic and social progress without depending on foreign aid. focus on those countries with significant need for assistance and with adequate (or better) commitment to ruling justly, promoting economic freedom, and investing in people. reduce fragility and establish the foundation for development progress by supporting stabilization, reform, and capacity development in fragile states when and where u.s. assistance can make a significant difference. . support strategic states help achieve major u.s. foreign policy goals in specific countries of high priority from a strategic standpoint. . international cooperation to protect lives and health . timely and sustained high-level political leadership to the disease . transparency in reporting of cases of disease in humans and in animals caused by strains that have pandemic potential to increase understanding, enhance preparedness, and ensure rapid and timely response to potential outbreaks . immediate sharing of epidemiological data and clinical samples with the world health organization (who) and the international community to characterize the nature and evolution of any outbreaks as quickly as possible . prevention and containment of an incipient epidemic through capacity building and in-country collaboration with international partners . rapid response to the first signs of accelerated disease transmission . work in a manner supportive of key multilateral organizations (who, fao, oie) . timely coordination of bilateral and multilateral resource allocations; dedication of domestic resources (human and financial); improvements in public awareness; and development of economic and trade contingency plans . increased coordination and harmonization of preparedness, prevention, response and containment activities among nations . actions based on the best available science . genocide (article )-acts committed with intent to destroy, in whole or in part, a national, ethnic, racial, or religious group a. killing members of the group b. causing serious bodily or mental harm to members of the group c. inflicting on the group conditions of life calculated to bring about its physical destruction in whole or in part d. imposing measures intended to prevent births within the group e. forcibly transferring children of the group to another group . crimes against humanity (article )-acts committed as part of a widespread or systematic attack against any civilian population, with knowledge of the attack a. murder b. extermination c. enslavement d. deportation e. imprisonment in violation of international law f. torture g. rape, sexual slavery, enforced prostitution, forced pregnancy, enforced sterilization, or other comparable form of sexual violence h. persecution on political, racial, national, ethnic, cultural, religious, gender, or other grounds universally recognized as impermissible under international law i. enforced disappearance j. apartheid k. other inhumane acts intentionally causing great suffering or serious injury to body or to mental or physical health . war crimes (article ) a. grave breaches of the geneva conventions of aug ( ) willful killing ( ) torture or inhumane treatment including biological experiments ( ) willfully causing great suffering ( ) extensive destruction and appropriation of property ( ) compelling a pow to serve in the armed forces of a hostile power ( ) willfully depriving a pow of the right to a fair trial ( ) unlawful deportation ( ) taking of hostages b. serious violations of laws and customs applicable in international armed conflict ( ) intentionally directing attacks against the civilian population or against civilians not taking direct part in hostilities ( ) intentionally directing attacks against civilian objects ( ) intentionally directing attacks against personnel, installations, material, units, or vehicles involved in humanitarian assistance or peacekeeping mission ( ) intentionally launching an attack in the knowledge that it will cause incidental civilian loss of life or severe damage to the natural environment ( ) attacking undefended towns, villages, dwellings, or buildings which are not military targets ( ) killing or wounding a combatant who has surrendered ( ) improper use of a flag of truce, flag or insignia or uniform of the enemy or of the un, or emblems of the geneva conventions resulting in death or serious personal injury ( ) transfer by the occupying power of parts of its own civilian population into the territory it occupies, or the deportation or transfer of all or parts of the population of the occupied territory within or outside the territory ( ) intentionally directing attacks against buildings dedicated to religion, education, art, science, charitable purposes, historic monuments, hospitals, and places where sick are collected, provided they are not military objectives ( ) subjecting persons to physical mutilation or to medical or scientific experiments which are not justified by the medical treatment nor carried out in his/her interest ( ) killing or wounding treacherously individuals belonging to the hostile nation or army ( ) declaring that no quarter will be given ( ) destroying or seizing the enemy's property unless such be imperatively demanded by the necessities of war ( ) declaring abolished, suspended, or inadmissible in a court of law the rights and actions of the nationals of the hostile party ( ) compelling the nationals of the hostile party to take part in the operations of war directed against their own country ( ) pillaging a town or place, even when taken by assault ( ) a range of generic prevention measures should be considered for its impact on diseases in a biological "all-hazards" environment. overall, excreta disposal, water quantity, personal hygiene, and food hygiene commonly contribute more to environmental health than do other listed measures. epidemic threats will oblige heightened consideration of disease-specific strategies for prevention and control. c. water treatment (bold text of particular relevance in clinical facilities) ppm = mg/kg (solids) = mg/l (liquids) = ug/ml (liquids) = basic unit of measure for chloroscopes : , ppm = % • sam = whz < − , muac < . cm, or bilateral pitting edema (who). whm not in definition. • sam prevalence worldwide ≈ , , . • sam mortality ≈ x mortality of normally nourished child and its cfr can be - %. • gam = mam + sam • gam = moderate wasting cases, severe wasting cases, or bilateral pitting edema cases (where due to malnutrition) • underweight is not used for screening or surveys in nutritional emergencies. it reflects past (chronic) and present (acute) undernutrition and is unable to distinguish between them. it encompasses children who are wasted and/or stunted. however, weight gain over time can be a sensitive indicator of growth faltering which is easily tracked on road to health charts. • stunting generally occurs before age . it is irreversible. • stunting prevalence worldwide ≈ , , . • stunting is not a good predictor of mortality, but the cfr from ids in cases of severe stunting ≈ x the cfr from ids in cases without stunting. reference standards can be absolute muac, centile, % of median reference, or z scores: • muac easy to understand. an excellent predictor of mortality. permits comparisons between age groups insofar as the low growth velocity of muac in the u age group makes data roughly comparable. may be used alone in "quick-and-dirty" convenience samples to estimate local prevalence of wasting. however, not used alone in authoritative anthropometric surveys, and is commonly part of a two stage screening process to determine eligibility for feeding programs. • overall whz gives higher prevalence of malnutrition than whm for the same population. this is most marked where there is low baseline prevalence of disease, and especially for adolescents (who get subsequently over-referred). whz is more statistically valid, but whm is better predictor of mortality and is used for admission to tfcs. weight-for-age is influenced by weight-for-height and height-for-age. it can be difficult to interpret. b. adults and adolescents (o ) anthropometrics: bmi = weight (kg) / height (m) . death rates-calculated incidence of death expressed per , p/d or per p/mo; data collected by retrospective surveys (eg month period) to gauge severity of public health emergency particularly where sudden events lead to spike in mortality a. cdr-crude death rate b. asdr-age-specific death rate (eg u dr or death rate of children - yr) during a studied time interval (written as . mortality rates-calculated probability of dying before a specified age expressed per live births; data collected by national health authorities in periodic (annual) demographic surveys to reflect ongoing health status a. cmr-calculated probability of mortality in given population for specific time b. imr-calculated probability of a live borne child dying before yr c. u mr-calculated probability of a live borne child dying before yr nb mr ≠ dr. eg cmr ≠ cdr, u mr ≠ u dr. different rates measure different things and are not directly comparable. however, mrs may be converted into drs by the following: cdr or u dr (deaths/ , /d) = − ln( −p/ ) × . where p = cmr or u mr (deaths/ live births). however, this has little field utility. nb mmr-maternal mortality ratio has different units in numerators (maternal deaths) and denominators (live births), thus is a ratio, not a rate the application of study findings to an entire population from which the sample was drawn. if the survey was well-conducted, the results may be considered representative of the entire population. this is scientifically justified. however a confidence interval should accompany any parameter estimate of that population. extrapolation the extension of study findings to a population or period which was not represented in the sample. it works by association-if populations appear to be experiencing similar conditions, the morbidity/mortality experience of one may be imputed to the other. this is not scientifically justified, but is often done where data are insufficient or impossible to collect. s/sx think differential diagnosis (below). . severe muscle pain may be a symptom of sepsis even without fever. . elderly patients with sepsis may be afebrile. in elderly patients, fever is rarely caused by a viral infection. . septic patients who are hypothermic have a worse prognosis than those with high fever. treat as a medical emergency. . fever in a postoperative patient is usually related to the surgical procedure (eg pneumonia, uti, wound, or deep infection). . fever with jaundice is rarely due to viral hepatitis. think liver abscess, cholangitis, etc. . the rash of early meningococcal infection may resemble a viral rash. . generalized rashes involving the palms and soles may be due to drugs, viral infections, rickettsial infections, or syphilis. . all febrile travelers in or returned from a malaria infected area must have malaria excluded. . disseminated tb must be suspected in all elderly patients with fever and multisystem disease who have been in an area with endemic tb. . septic arthritis may be present even in a joint which is mobile. . back pain with fever may be caused by vertebral osteomyelitis or an epidural abscess. . a patient may have more than one infection requiring treatment (eg malaria and typhoid), especially if they are elderly, immunosuppressed, or have travelled. . always remember common infections, not just opportunistic infections, in aids patients with a fever. understand morbidity multipliers-measles, malnutrition, and tb/hiv. understand occult co-morbidities. for any undifferentiated illness, even in infants, think of hiv, tb, syphilis, and sarcoid. for any child, think of malaria, hookworm, and anemia. malarial anemia usually in pedes < year-old; hookworm anemia usually in pedes > year-old. for any icp, think of tb, vl, histoplasmosis, and strongyloides. must treat early. watch for clinical mimics-malaria presenting as pneumonia or diarrhea in pedes; vl presenting as malaria in adults; lepto presenting as mild df (esp in df endemic areas where the pt has mild onset of illness, worsening course, and no rash but jaundice). tx do basic things well, use equipment you understand, teach others, delegate. this annex profiles selected communicable diseases of epidemic potential whose incidence, management complexity, or mortality obliges particular attention. • if (+) agglutination to o antisera, then the strain is further tested for agglutination to antiserum of ogawa and inaba serotypes. • if (+) agglutination to o antisera, then the strain is not further subdivided (except as producer or non-producer of ct as noted below). • if (−) agglutination to o and o antisera, then the strain is known as non-o , non-o v. cholerae. a strain is further identified as a producer or non-producer of cholera toxin (ct). ct production is a major determinant of disease development. strains lacking ct do not produce epidemics even if from the o or o serogroup. • serogroup o exists as main biotypes-classical and el tor-though hybrids also exist. each biotype occurs as two serotypes-ogawa and inaba. classic biotype caused the th and th pandemics but little epidemic disease since the s though it still causes cases in india. el tor biotype caused the th (current) pandemic and almost all recent outbreaks. el tor was first isolated in in el tor, egypt after importation by indonesian pilgrims travelling to mecca. it survives longer in the environment and produces ct similar to the classical biotype. presumably because of ct pathogenicity, the % of cholera patients with severe disease has doubled over the past yrs. these patients tend to require iv fluid therapy. • serogroup o may have evolved from strains of o el tor as they share many properties though not agglutination. in spring of in dhaka, o cases exceeded o el tor cases for the first time, and it was postulated that o may become the cause of an th pandemic. however, since then, o has again become dominant. infective dose depends on individual susceptibility. relevant host factors include immunity produced by prior infection with serogroup o as well as stomach acidity. id may be , orgs, so personal hygiene plays a lesser role than in shigellosis where the id is much lower. shigella has species. • s. dysenteriae type (sd or shiga bacillus) causes the severest disease of all shigella sp because of its neurotoxin (shiga toxin), longer duration of illness, higher abx resistance, higher cfr thru invasive complications, and great epidemic potential. • s. flexneri is the most common, and is generally endemic, in developing countries • s. sonnei is the most common in industrial countries • s. boydii and s. sonnei give mild disease. some kinds of e. coli produce a shiga toxin. shiga toxin genes reside in a bacteriophage genome integrated into the bacterial chromosome. some abx, eg fluoroquinolones, induce expression of phage genes. the bacteria that make these toxins are variously called "shiga toxin-producing e. coli" (stec), "enterohemorrhagic e. coli" (ehec), or "verocytotoxic e. coli" (vtec). all terms refer to the same group of bacteria. • e. coli o :h (often called "e. coli o " or "o ") is the most commonly identified stec in north america, and it causes most e. coli outbreaks. approximately - % of ehec infections result in hus. • non-o stec serogroups also cause disease. in the usa, serogroups o , o , and o are the most commonly identified e. coli pathogens overall. weather (esp weeks - in apr-may) creating increased biological activity; post-monsoon (esp weeks - in aug-sep) with contamination of water sources. pre-monsoon epidemics are generally worse than postmonsoon ones. dysentery has low level year-round incidence, but epidemics occur roughly each decade. epidemic strains display new, additive antibiotic resistance which probably triggers the epidemic. once resistant strains have become endemic, antibiotic susceptibility rarely reappears. sd acquires resistance quickly. sf acquires it more slowly, and that resistance may wane with decreasing abx pressure. at icddr, annual proportional incidence approximates the following: clean water and waste management especially for cholera. personal hygiene (hand washing with soap and clean towels) especially for shigella. water safe drinking water (boiled, chlorinated) nb sphere standards are not enough-you need increased quantities of chlorinated water at household level. san clean latrines for safe disposal of excreta hand washing with soap food safe food (cooked, stored) breast feeding fomites safe disposal of dead bodies with disinfection of clothing nb after outbreak of a fecal-oral pathogen, food hygiene and funereal practices may influence human-to-human transmission more than water quality. health education to affected population wash hands with soap: after using toilets/latrines. after disposing of children's feces. before preparing food. before eating. before feeding children. dukoral has been the main vaccine considered for use in high-risk populations. • morc-vax and shanchol-similar to dukoral except they do not contain the rbs, hence do not require a buffer, and are / the cost to produce. morc-vax, produced in vietnam, is derived from a vaccine administered to millions of people since , but is not who pre-qualified, and is not expected to have international distribution. • shanchol, produced in india, has international distribution (eg used in the haiti cholera vaccination campaign of ), and is now the agent of choice for who. it confers immunity d p nd dose, effectiveness > % at mo, and protection > % at yr. also confers short-term protection vs etec. dose: . cc vaccine followed by water ingestion but no fasting needed; doses, wks apart; cold chain required except for day of use. • orochol-bivalent formulation as in dukoral without rbs of ct. dose: single dose. no longer manufactured. who recommendations: "vaccination should not disrupt the provision of other high-priority health interventions to control or prevent cholera outbreaks. vaccines provide a short-term effect that can be implemented to bring about an immediate response while the longer term interventions of improving water and sanitation, which involve large investments, are put into place." [ ] icddr recommendations: "because of limitations in terms of transport, formulation, and cost of the current dukoral vaccine, the cots program does not require the utilization of the vaccine during an outbreak; it is not necessary to vaccinate to overcome an outbreak. however, if dukoral is readily available and staff are properly trained in its use according to the guidelines that come with the vaccine, the cots program permits dukoral's use (ideally before an outbreak) in the following high-risk populations: refugee populations in which cholera is present, health care workers managing cholera cases, and communities in which the incidence rate is greater than in annually." [ ] epidemiological surveillance (specific to cholera) epidemiological assumptions (who, cots): estimated attack rates: - % extremely vulnerable hosts and poor environmental health (who) % (refugee camps with malnutrition) (cots) % (rural communities of < p) (cots) % (severe epidemic-good estimate of ultimate disease burden) (who) . % (endemic areas with bad sanitation) (cots) . % (endemic areas in open settings-suitable for initial calculations of early resource requirements) nb overall, % of cases are mild and difficult to distinguish from other types of d. nb asymptomatic carriers are very common ( x # of cases). referral rates for ivs % of cases (much higher- % at icddr as it shortens recovery time) case fatality ratios % (with good care) the following catchment populations will yield acute pts of whom will be severely dehydrated: refugee camp of people (ar of % = pts) open settings in endemic area with , people (ar . % = pts) a population of , infected individuals in an epidemic area will yield the following (who): population infected , clinical cases , ( % of infected population) cases needing early resources ( % of cases) cases needing iv therapy ( % of cases) anticipated deaths ( % cfr) nb in non-endemic areas, ar adults > ar pedes because adults have higher exposure risks. in endemic areas, ar pedes > ar adults because adults have been exposed since childhood delivery of health services shigella are fragile and difficult to recover if transport time > d. - isolates initially to confirm outbreak - isolates initially to create abx use policy (bacterial resistance renders cotrimoxazole, amp/amox, nalidixic acid, and tetracycline unusable) - isolates monthly from ipd and opd before abx therapy to assess evolving abx resistance - isolates periodically to reference laboratory to confirm abx resistance patterns and undertake molecular studies isolates at end of the outbreak to confirm that new diarrheas are not epidemic pathogens nb systematic sampling is most representative-eg every th pt or all pts q weeks adjusted as needed to collect the necessary specs. sensitivity > > important than specificity in rdt screening during an epidemic. pts from one geographic area are more likely to constitute a cluster involving a new pathogen. an area may be considered cholera-free after incubation periods (total of d) have passed without cholera disease. however, hospital monitoring should continue for a year due to tendency of enteric pathogens to re-emerge long after they are declared gone. cholera may be viable but nonculturable from the environment; environmental monitoring has many false negatives. consider improvements to existing diagnostic labs • hotline set up for reporting of rumor this often translates into a hastily conceived vaccination campaign that distracts from core principles of cholera management. for every symptomatic pt, there may be asymptomatic carriers. in an established epidemic, the affected community is already extensively infected. cholera vaccination, under these circumstances, has little public health benefit for the resource investment. if undertaken, the following will apply: • vaccination campaign requires numerous staff. community mobilizers are key. clinical staff should not be poached from their clinical duties. supervisors must be free to move at will. • logistics is key-if the st day goes badly, the campaign goes badly. • mark the domiciles which are done. • hold after-action meetings each day. • last day, use mobilizers with mobile broadcasting to attract those who missed out. • second phase vaccination should include chws with multi-purpose messages on water and sanitation. avoid: press exaggeration abx prophylaxis reliance on ivf and insufficient ors lab investigation of cases once epidemic etiology is ascertained prolonged hospitalization hospital discharge criteria requiring multiple negative stool cultures enthusiasm for ocv during epidemic exaggerated water purification objectives concentration of technical competencies in moh at expense of districts failure to share information with stakeholders influenza viruses comprise genera-influenza types a, b, and c-each with species. • influenza type a is divided into subtypes based upon serological response to hemagglutinin (ha) and neuraminidase (na) glycoproteins. there are different ha subtypes and different na subtypes. h n , h n , and h n are responsible for the major human pandemics in the last century. h n virus circulated between and but currently does not. only influenza a subtypes infect birds, and all subtypes can do so. bird flu viruses do not usually infect humans. but, in , an outbreak of h n avian influenza in poultry in hong kong marked the first known direct human transmission of avian influenza virus from birds to humans. since then, h , h , and h avian influenza subtypes have been shown to infect humans. • influenza type b is morphologically similar to a and also creates seasonal and epidemic disease. • influenza type c is rare but can cause local epidemics. seasonal human influenza vaccine currently has strains-h n /h n /b. influenza disease in humans has a short incubation period ( - d). early symptoms are non-specific. it is highly infectious, especially early in the course of the disease, with a large # of asymptomatic carriers. transmission potential (r ) is a function of infectivity, period of contagiousness, daily contact rate, and host immunity. in general, the faster the transmission, the less feasible is interrupting transmission thru usual disease control tools of case finding, isolation, contact tracing, and ring vaccination. • specific groups of exposed or at risk in the community-most likely to work when there is limited disease transmission in the area, most cases can be traced to a specific contact or setting, and intervention is considered likely to slow the spread of disease eg quarantine of groups of people at known common source exposure (airplane, school, workplace, hospital, public gathering; ensure delivery of medical care, food, and social services to persons in quarantine with special attention to vulnerable groups) (useless once there is community-based spread) eg containment measures at specific sites or buildings of disease exposure (focused measures to > social distance) cancel public events (concerts, sports, movies) close buildings (recreational facilities, youth clubs) restrict access to certain sites or buildings • community-wide measures (affecting exposed and non-exposed)most likely to work where there is moderate to extensive disease transmission in the area, many cases cannot be traced, cases are increasing, and there is delay between sx onset and case isolation. infection control measures ari etiquette-cover nose/mouth during cough or sneeze, use tissues, wash hands avoidance of public gatherings by persons at high risk of complications nb use of masks by well persons is not recommended "snow" (stay-at-home) days and self-shielding (reverse quarantine) for initial d period of community outbreak-may reduce transmission without explicit activity restrictions closure of schools, offices, large group gatherings, public transport (pedes more likely to transmit disease than adults) nb community quarantine (cordon sanitaire)-restriction of travel in and out of an area is unlikely to prevent introduction or spread of disease anopheles vector biology egg becomes adult mosquito in d adult mosquito becomes infective in d after bite on infected host susceptible human host becomes infective in d after bite from infected mosquito :. earliest human clinical disease in d after eggs are laid follow the -d rule: dusk and dawn stay indoors as much as possible with window screens in good repair dress in light colored long sleeve shirts and long pants when outside identify cause of the outbreak undertake vaccination campaign strengthen routine immunization and surveillance meningitis is a disease with significant mortality. meningococcus (neisseria meningitides) is renown for its rapid onset, rapid progression (death sometimes within hours), and high mortality ( % untreated). there are serogroups of neisseria meningitides but only (a, b, c, w, x, y) are known to cause epidemics. the bacteria spread from person to person via respiratory and nasal secretions. polysaccharide vaccines are available with serotypes (a and c), serotypes (a, c, and w) or serotypes (a, c, w, and y). duration of immunity is approximately years. meningococcal protein conjugate vaccines confer longer immunity but at higher cost than polysaccharide vaccines. monovalent conjugate vaccine against group c dates from , and tetravalent (a, c, w, and y) conjugate vaccine dates from . group b vaccine made from bacterial proteins has been licensed since but is not readily available. meningococcal vaccines have a very low incidence of side effects. regular disease surveillance is necessary to detect outbreaks. the epidemic threshold is suspected cases/ , population in any given week. two suspected cases of meningitis in the same settlement should trigger an outbreak investigation. nasopharyngeal carriage rates do not predict epidemics. - % of meningococcal disease presents with meningitis. % of cases occur in patients < y/o. peak incidence in meningitis belt is ages - yrs. diagnosis is straightforward when patient presents with signs of meningitis-fever, headache, vomiting, changes in mental status. however, most patients have non-specific illness - days before onset of meningitis. cfr of untreated meningococcal meningitis can be %. cfr of properly treated meningococcal meningitis is < %. - % of meningococcal disease presents with septicemia unaccompanied by meningitis or other focal features. it is a dramatic illness which affects previously healthy children and young adults. it presents with acute fever leading to purpura fulminans (hemorrhagic or purpuric rash), shock, and waterhouse-friderichsen syndrome (acute adrenal failure). etiologic diagnosis can be easily missed. cfr of meningococcal septicemia is % and may be % even with proper treatment. diagnosis may be confirmed by agglutination tests, polymerase chain reaction, culture and sensitivity testing of spinal fluid and blood. in many situations, these tests are not available. throat swabs may be helpful on occasions. do not delay treatment for tests or test results. minutes count. it is more important to have a live patient without a confirmed diagnosis than a dead one with a diagnosis. differential diagnosis in a tropical patient with fever and altered mental status, but without purpura or shock, includes cerebral malaria. co-infection may occur. standardized case management of bacterial meningitis in developed countries involves - days of parenteral antibiotic therapy. drug of choice in adults and older children is ceftriaxone which also rapidly eliminates the carrier state. alternate drugs include ampicillin and benzylpenicillin which do not eliminate the carrier state. in developing countries, days of parenteral antibiotic therapy are empirically shown to be effective. in large epidemics in resource-poor settings, a single im dose of chloramphenicol in oil is the drug of choice. for patients who do not improve in hours, a repeat dose may be given. viral meningitis is rarely serious and requires only supportive care, recovery is usually complete. patient isolation and disinfection of the room, clothing, or bedding are not necessary. respiratory precautions are advised particularly early in the course of treatment. chemoprophylaxis of contacts is available in some settings but rarely in the disaster setting. vigilance and education of close contacts is mandatory. epidemic preparedness and early detection of outbreaks are key. vaccines against n. meningitides serogroups a, c, y and w are very effective in controlling epidemics. in epidemic settings, children - are the priority target with serogroups a and c typically the priority antigens. rapid mass vaccination campaigns can contain outbreaks in - weeks. for immunocompetent patients over years, vaccine efficacy rate is % one week after injection. however, duration of immunity may be as little as years in younger children. in some countries, vaccine may also be used with close contacts of sporadic disease cases to prevent secondary cases. chemoprophylaxis of contacts is not recommended in epidemics, but community education and ready access to health care are essential. preventive medicine [ ] source control/reduction/elimination undertake quarantine and culling of sick reservoir animals and known disease carrier species. avoid unnecessary contact with or consumption of dead reservoir animals or known disease carrier species. avoid unnecessary contact with suspected reservoir animals and known disease carrier species (eg primates). avoid direct or close contact with symptomatic patients. establish appropriate communicable disease controls for burial of the dead. administrative controls (improve people's work practices) environmental and engineering controls (isolate people from the hazard) avoid needle stick exposure to blood specimens thru automated machine handling. ppe (protect people with ppe) use standard precautions-gloves, masks, and protective clothing-if handling infected animals or patients. wash hands after visiting sick patients. active surveillance and contact tracing (enhanced surveillance) through community-based mobile teams active case finding (screening and triage) and contact tracing dedicated isolation facility food provision to isolated patients so they are not dependent on family case definition treatment protocols emphasizing supportive care and treatment of complications essential drugs referral guidelines secondary prevention barrier nursing strictly enforced family and community education ministerial task force to address policy local health authority task force to address procedures national level task forces to comprise if a lab is not available, then you need a sampling strategy that addresses specimen acquisition, preparation, and transportation in compliance with international regulations on the transport of infectious substances. guidance note on using the cluster approach to strengthen humanitarian response international conference on primary health care selective primary health care-an interim strategy for disease control in developing countries water and excreta-related diseases: unitary environmental classification infections related to water and excreta: the health dimension of the decade world health organization. cholera vaccines: who position paper available from: international centre for diarrhoeal disease research history and epidemiology of global smallpox eradication available from: us department of health and human services communicable disease control in emergencies-a field manual. geneva: world health organization ebola: technical guidance documents for medical staff world health organization. manual for the care and management of patients in ebola care units/community care centers-interim emergency guidance. who/ evd/manual/ecu/ . . geneva: world health organization what tests does it perform? is there transport to and from the laboratory? who prepares transport media? who provides specimen collection material and supplies? how can these supplies be obtained? who provides cool packs, transport boxes, car, driver …? • refrigerate other vials for cytology, chemistry ( °c) leak-proof specimen container wrapped with enough absorbent material to absorb the entire content of the st container . leak-proof secondary container usually plastic or metal . outer shipping container whose smallest dimension is mm diagnostic specimens use iata packing instruction without biohazard label. infectious materials use iata packing instruction with biohazard label. what to send with the sample? lab request form with: • sender's name and contact info • patient name, age, sex • sample date, time • suspected clinical diagnosis with main signs and symptoms • sample macroscopic description • context-outbreak confirmation, ongoing verification, outbreak end, etc • epidemiological or demographic data where to send the sample? • reference lab • contact person what and when to expect results? source: world health organization world health organization department of communicable disease surveillance and response. highlights of specimen collection in emergency situations. undated . designate a lead official in the lcc. . anticipate roles for partner agencies (eg inter-agency and team coordination, disease surveillance, field epidemiological investigation, laboratory identification, case management guideline development, outbreak logistics, public information, and social mobilization). . identify sources of funds. . intensify disease surveillance. . identify reference lab(s) for communicable diseases of epidemic potential. . ensure mechanism for specimen transport. a. initial response to suspected outbreak . form an emergency team to investigate and manage the outbreak a. identify key roles on the outbreak investigation team(s) ( ) epidemiology and surveillance ( ) case management ( ) water and sanitation ( ) laboratory services ( ) communication b. staff those roles ( ) epidemiologist-to monitor proper data collection and surveillance procedures ( ) physician-to confirm clinical s/sx and train health workers in case management ( ) water and sanitation expert-to develop a plan for reducing sources of contamination ( ) microbiologist-to take environmental/biological samples for laboratory confirmation, train health workers in proper sampling techniques, and confirm use of appropriate methods in the diagnostic laboratory ( ) key: cord- -ijlnefz authors: koher, andreas; lentz, hartmut h. k.; gleeson, james p.; hövel, philipp title: contact-based model for epidemic spreading on temporal networks date: - - journal: nan doi: . /physrevx. . sha: doc_id: cord_uid: ijlnefz we present a contact-based model to study the spreading of epidemics by means of extending the dynamic message-passing approach to temporal networks. the shift in perspective from node- to edge-centric quantities enables accurate modeling of markovian susceptible-infected-recovered outbreaks on time-varying trees, i.e., temporal networks with a loop-free underlying topology. on arbitrary graphs, the proposed contact-based model incorporates potential structural and temporal heterogeneities of the contact network and improves analytic estimations with respect to the individual-based (node-centric) approach at a low computational and conceptual cost. within this new framework, we derive an analytical expression for the epidemic threshold on temporal networks and demonstrate the feasibility of this method on empirical data. accurate models of disease progression are valuable tools for public health institutions as they enable detection of outbreak origins [ ] [ ] [ ] [ ] , assessment of epidemic risk and vulnerability [ ] [ ] [ ] [ ] , and containment of the spreading at an early stage [ , ] . mitigation strategies can thus be evaluated and employed without the need to run a large number of monte carlo (mc) realizations. a fundamental challenge to mathematical epidemiologists is the accurate determination of the critical parameters that separate local and global epidemic outbreaks [ ] [ ] [ ] [ ] [ ] [ ] [ ] . to this end, the early kermack-mckendrick model [ ] divides a population according to the disease status into compartments of susceptible, infected, and recovered individuals with mass-action equations to determine the transitions between them. since then, a wide range of improvements has been proposed, including the impact of stochasticity [ ] [ ] [ ] , non-markovian dynamics [ ] [ ] [ ] [ ] [ ] , and, notably, heterogeneity in the contact structure [ , [ ] [ ] [ ] [ ] [ ] . in recent years, the availability of mobility and contact data with a high temporal resolution, so-called temporal networks, offers another opportunity to improve analytical predictions [ ] [ ] [ ] [ ] [ ] [ ] . the timing of links between nodes matters, in particular, when the network evolves on a similar timescale as the spreading dynamics, which led to an increasing interest in the interplay between disease and network dynamics [ ] [ ] [ ] [ ] [ ] [ ] . one approach to model the states of individual nodes in a network takes the corresponding probabilities directly as variables in a set of coupled dynamic equations [ , , , [ ] [ ] [ ] [ ] [ ] . we refer to this approach as the individualbased (ib) model, though it is sometimes also called the n-intertwined model [ ] or quenched mean field [ , ] . however intuitive, the analytic predictability suffers from the simplifying assumption that epidemic states of adjacent nodes are independent. recently, a change from a node-centric to an edgecentric perspective has been discussed within different frameworks in order to overcome the inherent limitation of the ib model. these approaches include branching processes [ ] , message passing [ , ] , belief propagation [ ] , and the edge-based compartmental model [ ] . so far, however, edge-centric models are mostly limited to static topologies. it thus remains an open challenge to simultaneously account for topological and temporal properties of the underlying contact data and hence improve current predictions of the epidemic threshold [ , [ ] [ ] [ ] [ ] [ ] . in this paper, we generalize the dynamic message-passing approach for discrete-time markovian susceptible-infectedrecovered (sir) spreading [ ] to time-evolving networks and derive the epidemic threshold within this new framework. the proposed model takes an edge-centric perspective because the relevant dynamic equations are based on the set of edges. furthermore, the framework integrates the complete temporal and topological information of the underlying network into the epidemic model. we refer to our approach as contact-based (cb) model and compare numerical predictions with the widely used ib model that takes a node-centric perspective. within the cb framework, we then derive a new analytic expression of the epidemic threshold for temporal networks and show that the edge-centric approach improves existing results [ , , , , , ] at a low conceptual and numerical cost. the cb and ib models have been implemented in python with the source code available on github [ ] . the remainder of this paper is structured as follows: first, we summarize the conceptual framework in sec. ii and formulate in sec. iii the dynamic equations of the ib and cb models. then, we derive the epidemic threshold for temporal networks within the cb framework in sec. iv. we compare the edge-and node-centric approaches against mc simulations in sec. v and close with a discussion in sec. vi. appendix a includes an extension to weighted contacts and heterogeneous epidemiological parameters. a network analysis of the german cattle-trade data is given in appendix b. further results and applications of the cb model are summarized in appendix c. we consider a temporal network g ¼ ½gð Þ; gð Þ; …; gðt − Þ with n nodes and t snapshots sampled at a constant rate. although both modeling frameworks can, in principle, account for contact weights that indicate the strength of a connection, we focus on unweighted networks for simplicity and refer to appendix a for an extension of the model. emphasizing the important difference between temporal and static elements, we refer to contacts as time-stamped links ðt; k; lÞ ∈ c ⊂ t × n × n , thereby denoting with n , t , and c the set of nodes, time stamps, and contacts, respectively. we further assume that every contact is of constant duration and equal to the sampling time of the temporal network. by edges, we refer to the corresponding static elements in the time-aggregated network. in other words, an edge ðk; lÞ ∈ e ⊂ n × n exists if and only if at least one (temporal) contact is recorded between k and l. here, we denote with e the set of edges. moreover, we assume directed edges throughout the paper and represent an undirected contact as two reciprocal contacts. following the convention in ref. [ ] , we denote with k → l a directed edge from k to l, and we indicate edge-based quantities in a similar fashion. as the stochastic process, we assume a discrete-time sir model, where a node l ∈ n represents an individual that is either susceptible, infected, or recovered at a given time t with a corresponding probability s l ðtÞ, i l ðtÞ, and r l ðtÞ, respectively. a susceptible node that is in contact with an infected neighbor contracts the disease with a constant and uniform (per time step) probability β. furthermore, we treat the transmission events from multiple infected neighbors as independent, and similarly, we interpret potential (integer) edge weights as independent infection attempts (see appendix a). we do not account for secondary infections within one time step; i.e., only direct neighbors can be affected. once infected, the individual recovers with a uniform and constant probability μ independently of the infection process and henceforth acquires a permanent immunity. concerning the contact data, we focus our numerical analysis first on a face-to-face interaction network between conference participants [ ] . this so-called proximity graph has a resolution of s, and the observation time is limited to the first h. if necessary, we extend the data set with a periodic boundary condition in time. the timeresolved contacts enable the study of spreading of airborne diseases as well as the propagation of ideas and rumors. as an illustrative example, we present in fig. the timedependent probability that a selected node in the proximity graph is either susceptible (yellow), infected (red), or recovered (green). the results are derived from mc simulations fig. . illustrative examples of a simulated epidemic outbreak from a single initially infected node. colors give the probability that another arbitrarily selected node is in the susceptible (yellow), infected (red), or recovered (green) state, respectively. simulation parameters: μ ¼ . × − , β ¼ μ, mc realizations. with the same initially infected node. the trajectories reflect the bursty activity of the underlying temporal network [ ] within the first h and the subsequent inactive nighttime. as a second source of data with direct relevance to public health, we consider an excerpt of the national german livestock database hi-tier [ ] . this temporal network comprises the movement of cattle between farms in germany for the year with daily resolution. within the observation window of days, more than million transactions have been recorded between over farms and traders, respectively. for more details on the graph, see appendix b. cattle trade is considered an important transmission route for livestock-related diseases such as foot-and-mouth disease (fmd), which broke out in the united kingdom in with an estimated cost of billion pounds sterling [ ] . therefore, the analysis of the corresponding spatiotemporal graphs is highly relevant to public health institutions. in this section, we present the mathematical framework to model the stochastic sir process as outlined in the introduction and sec. ii. our main focus is the cb model, but in order to facilitate a direct comparison between the node and the edge-based approach, we begin with a short overview of the ib model. in the ib model, the marginal probabilities s l ðtÞ, i l ðtÞ, and r l ðtÞ for all l ∈ n directly enter a set of × n coupled dynamic equations. the probability for l to contract the infection from k upon a temporal contact is given by βi k ðtÞ. for convenience, we introduce an indicator function with a k→l ðtÞ ¼ if a (directed) contact from k to l exists at time t and a k→l ðtÞ ¼ otherwise. then, the probability for node l to receive no infection at time t from any of its neighbors factorizes by assumption to q k ½ − βa k→l ðtÞi k ðtÞ and k ∈ n . with this result, the marginal probability s l ðt þ Þ can be expressed by the probability s l ðtÞ to be susceptible in the previous time step t and not contract the infection within the interval ½t; t þ Þ. in the ib model, the joint probability factorizes, and we obtain here, the crucial simplification is to treat the epidemic states of l and its neighbors as mutually independent, which is sometimes referred to as neglecting dynamic correlations [ ] . the marginal probability i l ðt þ Þ follows from two independent contributions: (i) the outflux μi l ðtÞ indicates the transition from the infected to the recovered state. (ii) the influx Δs l ðtÞ ¼ s l ðtÞ − s l ðt þ Þ reflects the probability that node l is newly infected at time t þ . combining both contributions leads to the set of × n coupled dynamic equations ( ) and ( ) thus constitutes the ib model for temporal networks. the remaining marginal probability r l ðtÞ to find node l in the recovered state follows from the conservation condition s l ðtÞ þ i l ðtÞ þ r l ðtÞ ¼ for all l ∈ n . finally, we assign a probability z l ¼ s l ð Þ that node l is initially susceptible, as well as i l ð Þ ¼ − z l and r l ð Þ ¼ throughout the paper. though intuitive and, in many cases, sufficient from a modeling perspective, the limits of the ib model are difficult to estimate due to the ad hoc factorization of the joint probability in eq. ( ). even for the simplest network with two nodes connected by an undirected static edge, the ib approach can deviate significantly from the expected outcome as illustrated in ref. [ ] . in their example, recovery is neglected for simplicity, and only the first node is infected initially with some probability < z ≤ . counterintuitively, the probabilities to find each node in the infected state converge to i ð∞Þ ¼ i ð∞Þ ¼ according to the ib model, independent of the initial condition z . this convergence occurs because integrating eqs. ( ) and ( ) admits a probability flux from the outbreak location to the adjacent node and back to its origin again. this mutual reinfection, coined the echo chamber effect in ref. [ ] , appears because we neglect the fact that the probability i to find the second node in the infected state is conditioned on the state of the first node, and thus the factorization in eq. ( ) is not justifiable. in an arbitrary network, an initially infected node leads to a cascade of secondary infections within which all marginal probabilities are highly correlated. an accurate model excludes these previously infected nodes from those that can potentially contract the infection in the future. in the next section, we discuss how a shift from a node-centric to an edge-centric view can take into account some such dependencies. we begin with a slightly different approach to the marginal probability s l ðtÞ. first, we note that l is susceptible at time t, if it was susceptible initially [with probability s l ð Þ ¼ z l ] and has not contracted the infection from any of its neighbors up to time t. we assign the probability Φ l ðtÞ to the latter statement. thus, without introducing any approximation at this stage, we can write in order to determine Φ l ðtÞ, we make the assumption that the underlying time-aggregated graph is a tree (ignoring directionality). then, different branches originating in node l are independent as long as l remains susceptible, and thus Φ l ðtÞ factorizes. however, if node l contracts a disease from a neighbor k with some probability and passes it on to another node k , then the corresponding probabilities i k and i k are clearly correlated. a simple solution that allows different branches to nonetheless be treated as independent is to prevent a probability flow through the root node in the first place. from a graph-theoretic perspective, this solution corresponds to the (virtual) removal of all out-directed contacts from the root node. this approach does not modify the dynamics of the node under consideration because it can still contract the disease, and once infected, the recovery process is independent of the topology. however, the idea considerably reduces the amount of bookkeeping that would otherwise be necessary if we accounted for the correlations directly. the singular node l is said to be a cavity node or in the cavity state [ , ] , a concept closely related to the test-node assumption [ ] and the idea of cut vertices [ ] . with this concept, we can factorize Ψ l ðtÞ and thus obtain here, we introduce the probability θ k→l ðtÞ that no disease has been transmitted from node k to the cavity node l up to time t. the change in perspective towards an edge-centric analysis introduces new auxiliary dynamic quantities such as θ k→l ðtÞ. these quantities are defined on the set of edges e of the time-aggregated network, and thus the number of dynamic variables scales with l, the number of edges. in order to obtain a system of dynamic equations, we focus on our first edge-centric variable θ k→l . initially, no disease was transmitted such that θ k→l ð Þ ¼ for all edges ðk; lÞ ∈ e. henceforth, the dynamic quantity reduces only (i) upon a temporal contact indicated by a k→l ðtÞ and (ii) if the adjacent node k is infected without having transmitted the disease earlier to the cavity node l-we denote the corresponding probability by i k→l ðtÞ. hence, the out-flow of probability is given by βa k→l ðtÞi k→l ðtÞ, leading to our first dynamic equation next, the probability i k→l ðtÞ evolves according to three contributions. (i) it decreases with the recovery probability μ and (ii) with the probability β to infect its target node upon a temporal contact. these processes are independent and may contribute simultaneously with the joint probability βμ. (iii) i k→l ðtÞ increases with the probability Δs k→l ðtÞ ¼ s k→l ðtÞ − s k→l ðt þ Þ that k is newly infected by at least one of its incident neighbors excluding the cavity node l. in sum and with the initial condition i k→l ð Þ ¼ − z k , these contributions lead to finally, we consider the probability s k→l ðtÞ that node k, adjacent to the cavity node l, is susceptible. since k is not affected by the state of l, it stays susceptible if it does not contract the disease from any of its remaining, incident neighbors j ∈ n k nl. it has been shown in ref. [ ] that the corresponding probability Φ k→l ðtÞ ¼ q j∈n k nl θ j→k ðtÞ factorizes, and thus, similar to eq. ( ), we find s k→l ðtÞ ¼ z l Φ k→l ðtÞ or, equivalently, the disease progression in the cb framework is fully characterized by eqs. ( ) and ( ), a set of l coupled equations. equation ( ) is introduced here for convenience only and can be substituted into eq. ( ). next, we return to the node-centric quantities. to this end, we note that s l ðtÞ has already been determined in eq. ( ). the remaining marginals i l and r l are equivalent to the ib model and given by the conservation condition, as well as the transition to the recovered state in eqs. ( ) and ( ), respectively: the cb model is exact for temporal networks, where the undirected, time-aggregated graph has a tree structure and is therefore loop-free. most realistic networks, however, contain a large number of loops such as triangles in social graphs, where two friends are likely to have many more friends in common. here, the cb model nevertheless appears to be "unreasonably effective" (cf. ref. [ ] ) and improves predictions significantly with respect to the ib approach as we will see in sec. v. for further extensions to the model that include heterogeneous infection and recovery probabilities, as well as weighted contacts, see appendix a. the parameters that mark the epidemic threshold can be derived by examining small perturbations around the disease-free state. if such perturbations die out, then any outbreak remains local, but if the perturbation grows, then a global epidemic may occur. we consider a linearization of the dynamic equations ( )-( ), which will give rise to a criticality condition, determining the epidemic threshold. we begin with the ansatz θ k→l ðtÞ ¼ − δ k→l ðtÞ and z l ¼ − ϵ l , where δ k→l ðtÞ; ϵ l ≪ are small perturbations around the disease-free state for all nodes l and edges ðk; lÞ. thus, eq. ( ) becomes in eq. ( ), we keep the linear terms of the taylor expansion, which transforms the product into a corresponding sum: in eq. ( b), we substituted the dynamic equation ( ) and identified s k→l ðtÞ in the next step. from the resulting eq. ( c), we can read the linearized form of Δs k→l , which allows us to decouple the dynamic equations for i k→l : next, we rewrite the remaining set of l dynamic equations in a compact, matrix-based formulation and therefore introduce the vectors iðtÞ and aðtÞ with elements i k→l ðtÞ and a k→l ðtÞ, respectively. to this end, we also express the linear operation p j∈n k nl a j→k ðtÞ in eq. ( ), which acts on the elements i k→l ðtÞ of the state vector, through the temporal unweighted nonbacktracking matrix bðtÞ: in other words, b k→l;j→k ðtÞ ¼ if the contact ðt; j; k Þ at time t is incident on the edge ðk; lÞ (implying k ¼ k), and additionally j ≠ l. otherwise, we have b k→l;j→k ðtÞ ¼ . it is only the nonbacktracking property j ≠ l that sets b apart from the adjacency matrix of the ordinary line graph. for temporal networks, a subtle distinction has to be made between the first and the second index of the l × l dimensional matrix b: the first corresponds to an outdirected (static) edge ðk; lÞ ∈ e of the underlying aggregated network and can be interpreted as a potential contact in the future. the second, however, is an incident (temporal) contact ðt; j; k Þ ∈ c from node j to k at time t. we also introduce the diagonal matrix diag( − βaðtÞ), with diagonal elements given by the vector − βaðtÞ. here, we denote by the vector of all ones. with these definitions, we rewrite eq. ( ) as the explicit solution to the state vector iðtÞ at final observation time t is formally given by iðtÞ ¼ pðβ; μÞið Þ, where the so-called infection propagator p [ ] is introduced for notational convenience: in order to evaluate the asymptotic behavior, we assume a periodic boundary condition in time, i.e., bðtÞ ¼ bðt þ tÞ. this allows us to assess the vulnerability of the temporal network through the spectral radius of the propagator p. in particular, we find that a sir-type outbreak is asymptotically stable under small perturbations, i.e., remains confined to a small set of nodes, as long as the spectral radius satisfies ρ½pðβ; μÞ < . thus, the phase transition is given by the criticality condition note that for irreducible and non-negative matrices, the largest eigenvalue is simple and positive according to the perron-frobenius theorem [ ] . assuming ≤ β, μ < , a sufficient condition for temporal networks is to restrict contacts to the giant strongly connected component (gscc) of the underlying time-aggregated graph. in sec. v b, we fix the recovery probability μ and determine the critical infection probability β crit as the root of fðβÞ ¼ − ρ½pðβ; μÞ for different empirical networks. we conclude this section with a discussion on the static network limit. in the so-called quenched regime, the disease evolves on a much faster timescale than the dynamic topology and thus operates on an effectively static network with bðtÞ ≡ bð Þ ≡ b and aðtÞ ≡ for all times t. as in the temporal analysis, we restrict the network to the gscc so that the perron-frobenius theorem [ ] applies. in this limit, the dynamic equations ( )-( ) reduce to the dynamic message-passing formulation in ref. [ ] . moreover, eq. ( ) now becomes a product q t− t¼ p fast ðβ; μÞ ¼ ½p fast ðβ; μÞ t of t identical, single time-step propagators where ¼ diagð Þ denotes the identity matrix. the spectral radius in eq. ( ) factorizes to ρ½p fast ðβ; μÞ t ¼ ρ½p fast ðβ; μÞ t , and it follows that the criticality condition eq. ( ) reduces to ρ½p fast ðβ; μÞ ¼ . furthermore, we find from basic linear algebra that ρ½p fast ðβ; μÞ ¼ ð − μÞð − βÞ þ βρðbÞ, and hence we obtain the corresponding static threshold condition β β þ μ − βμ the criticality condition in eq. ( ) deviates from the continuous-time result in refs. [ , ] . in the derivation presented here, the term βμ in eq. ( ) accounts for the simultaneous events when a node infects a neighbor and recovers within the same time step. in contrast to the quenched regime, one can also consider the so-called annealed limit. then, parameters β and μ are sufficiently small such that no more than one infection or recovery event can take place within the observation time. therefore, we expand the infection propagator to the first order in β and μ and obtain here,ā ¼ =t p t aðtÞ andb ¼ =t p t bðtÞ denote the corresponding time-averaged quantities. it is insightful to evaluate simple bounds for the set of parameters ðβ; μÞ crit;slow that satisfy the threshold condition ρðp slow Þ ¼ in the annealed limit. with =t ≤ā ≤ for all elements inā, we thus find β assuming the upper bound in eq. ( ) overestimates the outbreak risk and can be considered a conservative choice from an epidemiological perspective. this limit is realized for a temporal network where every edge appears exactly once within the observation time, henceā ¼ =t. the lower bound in eq. ( ) is exact in the case of a static network (thusā ¼ ) and corresponds to the continuoustime result in ref. [ ] . however, this limit underestimates the outbreak risk, and therefore we conclude with a note of caution when applying results from static network theory directly to time-varying topologies. a big advantage common to both the node-centric ib and edge-centric cb modeling framework is a significant reduction in computational complexity compared to mc simulations. the cb model requires iteration through all edges at every time step, and thus the time complexity scales with oðltÞ. the ib formulation and a single mc realization require oðctÞ, wherec denotes the average number of active contacts, which can be significantly smaller than l. stochastic mc simulations, on the other hand, require a large number of realizations in order to provide reliable statistics. the computational disadvantage of mc simulations becomes even more apparent when we consider a complex quantity such as the epidemic threshold, which requires multiple ensemble averages for different sets of epidemic parameters in order to fit the critical infection probability (see sec. v b). equally important, however, is the accuracy of our analytic approach. therefore, in this section, we compare estimations from the ib and cb mean-field model with mc simulations using empirical data as introduced in sec. ii. we begin with an analysis on the level of individual nodes. in fig. , we show the cumulative infection probability for a small number of example nodes from the conference data set given the same outbreak location. the selection is intended to present qualitatively different trajectories, also demonstrating that deviations between the two models vary considerably. the mc result (blue curve) in fig. (a) corresponds to the introductory example in fig. . here, a comparison with the analytic estimation shows that the cb approach leads to a substantial improvement to the ib model. also in figs. (b)- (d), the trajectories are erratic, as they reflect the sudden changes in the underlying topology, highly individual and yet well approximated by the cb model. for all nodes in the network, we find that the cb model gives a closer upper bound to mc simulations because, unlike the ib framework, it accounts for dynamic correlations between nearest-neighbor states. dynamic mean-field models such as the ib and cb framework provide realistic expectation values only if stochastic fluctuations are negligible. in order to illustrate the limitations, we study epidemic outbreaks for three different initially infected nodes in figs. (a)- (c), respectively. the left column gives the time-resolved distribution of the outbreak size, and the right column presents the final distribution at the end of the three-day observation period. for the ensemble average (blue line), we consider only realizations with more than infected nodes overall. this threshold separates outbreaks that die out early due to stochastic fluctuations and thus permits a direct comparison with estimations from the ib and cb frameworks in green and red, respectively. we choose the outbreak locations such that the degree of stochasticity increases from top to bottom. in fig. (a ) , we find a narrow distribution around the ensemble average, which is well approximated by the mean-field models. minor outbreaks due to early extinctions are well separated in fig. (a ) from large epidemics. in fig. (b) , the initially infected node leads to realizations with considerably stronger fluctuations, and in fig. (c) , it is barely possible to separate early extinctions at all. additionally, we observe a second source of stochastic variation, namely, the time at which a disease escalates and hence evolves into a global epidemic. as a consequence, early outbreak sizes may be overestimated significantly before the analytic trajectory approaches the expectation value again [see fig. (c ) ]. remarkably, the performance of both mean-field models varies significantly with the outbreak location, even for the basic reproduction number r well above the epidemic threshold. at the late phase of an outbreak, however, the mean-field models provide good approximations, and consistently with fig. , we find that the cb model outperforms the ib approach. in appendix c, we demonstrate how a sufficiently large number of initially infected individuals significantly improves the predictability. another source of stochasticity is the choice of disease parameters β and μ, respectively. we focus on the final outbreak size, averaged over all outbreak locations. the distribution as a function of the infection probability β (see fig. ) shows a percolation-like transition from localized spreading to epidemics that affect a considerable fraction of the network. we apply the same threshold as in fig. for a direct comparison between the averaged outbreak size and the mean-field models for β > . . here, we find that the difference between the expected size and the cb estimation is close to negligible, whereas the ib model consistently overestimates the expected value. a comparison at low values of the infection probability β becomes unreliable as stochasticity impedes a reasonable distinction between minor and global outbreaks. in order to illustrate the effect, we present in fig. the outbreak-size distribution for different values of β as marked by the arrows in fig. . this representation highlights the transition from the subcritical to the supercritical parameter domain: the unimodal distribution in fig. (a) characterizes localized outbreaks, whereas the bimodal distribution in fig. (d) clearly separates early extinctions and global epidemics. next, we focus on the critical infection probability that marks the transition. in fig. (a) , we present the region of small β from fig. in order to focus on the transition from localized outbreaks to the sudden emergence of global epidemics. we determine the critical infection probability β crit (vertical blue line) from the maximum of the relative standard deviation [ ] , also known as the coefficient of variation [see blue line in fig. here, we denote with hσi and hσ i the first and second moments of the outbreak-size distribution. the coefficient of variation captures the intuition that fluctuations dominate the outbreak-size distribution close to the transition. indeed, c v diverges at the critical point for infinitely large networks, indicating a second-order phase transition [ ] . analytically, we determine β crit from the spectral criterion in eq. ( ) for the cb model and similarly within the ib framework [ , ] . the comparison in fig. shows that the ib and cb models, marked by a red dashed and green dotted line, respectively, underestimate the critical infection probability from mc simulations (blue line) and thus overestimate the outbreak risk. consistent with our previous results, we can state that a shift from a node-to an edge-centric framework improves the analytic prediction. in appendix c, we present similar results for different values of the recovery probability μ. next, we continue with a realistic application of the epidemic threshold to the german cattle-trade network. we now consider a completely different data set, where the system size is large and contacts are sparse over time. our example is a cattle-trade network, where the movements of animals between farms in germany are recorded on a daily basis. next, we isolate the trade within each federal state of germany as visualized in fig. and restrict trade to the gscc of the underlying aggregated graph. disregarding the smallest networks (those with less than nodes), we thus obtain time-varying graphs with sizes varying from to nodes and highly heterogeneous topological and temporal features (see appendix b). as in the previous section, we assume that premises can be either susceptible, infected, or recovered, and trade events facilitate the transmission of a disease. unlike before, however, we take into account the number of traded animals during each transaction, i.e., the weight w k→l of a (temporal) contact from node k to l. to this end, we modify the infection propagator in eq. ( ) and replace β by − ð − βÞ w k→l (see appendix a for more information). in a potential outbreak, we assume that an infected node is detected with a constant probability μ each day, after which it would be isolated and thus removed from the network. as a consequence, highly infectious diseases such as fmd can be modeled as sirtype epidemics [ ] . in fig. , we compare the critical infection probability similar to fig. for six selected federal states with different transition characteristics. the critical value derived from mc simulations varies between β crit ¼ . [bavaria (by)] and β crit ¼ . [saxony (sn)]. the latter indicates that outbreaks remain localized for every choice of β due to sparse intrastate trade. as a potential application to public health institutions, we present in fig. (a) the spatial variation of the epidemic risk in terms of β crit . the quantitative comparison in fig. (b) demonstrates that spectral methods provide a lower bound with a varying degree of accuracy depending on the network details. despite their heterogeneity in size and activity, we find for all networks that the cb model outperforms the ib approach. the detailed results for all states as well as a similar analysis for μ − ¼ are available in appendix c. in this paper, we have presented the cb model for epidemic sir spreading on temporal networks as a conceptually similar framework to the widely used ib approach. derived from the message-passing framework [ , ] , it inherits its accuracy on loop-free topologies and improves analytic estimations with respect to the ib approach for arbitrary time-evolving graphs. moreover, the focus on edge-based quantities that are updated in discrete time steps allows a seamless integration of temporal interactions. structurally similar to the node-centric ib model, the proposed cb approach poses a low conceptual barrier and admits application on large graphs. importantly, the accuracy of the cb model improves existing approximations of the epidemic threshold, which is a crucial risk measure for public health institutions. to this end, we have studied the largest eigenvalue of the infection propagator matrix, which determines the disease propagation in the low prevalence limit and takes into account the full temporal and topological information up to the observation time. the largest eigenvalue can be easily found through repeated matrix multiplications, i.e., the so-called power method. without relying on extensive mc simulations and a subsequent parameter fit, the critical value can thus be estimated with efficient, vectorizable tools from linear algebra that are available for most high-level programming languages. in the application section, we focused first on a social contact graph that can be used to analyze the propagation of airborne diseases as well as the spread of information. our comparison between mc simulations and analytic estimations from the cb and ib models followed a bottom-up approach: we looked at (i) epidemic trajectories of individual nodes, (ii) averaged trajectories given the same outbreak location, and (iii) the final outbreak size for a range of infection probabilities and with random initial condition. in all cases, the cb model provides a closer upper bound to mc simulations than the widely used ib model. all results based on the conference data set can be reproduced using the python code provided in ref. [ ] . table i ). (b) critical infection probability β crit in logarithmic scale, sorted from high (left) to low risk (right). results from mc simulations, and the cb and ib models are presented as groups of blue, red, and green bars, respectively. disclaimer: a realistic vulnerability analysis requires, for instance, heterogeneous recovery probabilities and complex countermeasures (see appendix b for details). as a particularly important application, we then compared analytic estimations of the critical infection probability with extensive mc simulations. to this end, we included a case study of livestock trade within federal states in germany with highly heterogeneous characteristics in terms of size, density, and temporal activity. consistently, we found that the cb model improves the previously proposed lower bound at a low conceptual and computational cost. many excellent results have already been derived within the ib framework for empirical networks and in the context of random graphs (see ref. [ ] for a recent review) that can further improve the cb model. we therefore expect that the conceptual simplicity of the cb framework allows us to integrate features such as non-markovianity [ ] , stochastic effects [ ] , and estimations of uncertainty [ ] that are important to realistic disease models on temporal networks. also, first steps towards higher-order models that go beyond the tree-graph assumption have been proposed in the context of percolation theory [ ] and diffusive transport [ , ] , and we expect these improvements to be applicable to the cb model as well. the data are available on [ ], and using the source code in ref. [ ] , results of this paper can be easily reproduced. in order to improve the predictive power of a network model, it is often required to take into account additional information. in the main article, we focus on the temporal dimension. however, another important piece of information is the weight of a contact. the interpretation of weight can range from passenger numbers in the global air traffic network to the impedance in a network of electric components. the distribution of weights in static as well as temporal empirical networks often shows a broad tail [ ] , and as such, the averaged edge weight can become meaningless because of large fluctuations. it is therefore often required to account for heterogeneous edge weights explicitly in epidemiological models. however, depending on the interpretation, weights may enter the model in different ways. typically, a time-dependent edge weight w k→l ðtÞ is considered similar to the conductivity between two nodes k and l in an electric circuit. translated to an epidemiological context, we would thus scale the infection probability linearly; i.e., βa k→l ðtÞ becomes βw k→l ðtÞ in a weighted network. another approach, popular in the context of random walks and disease spreading, is to interpret an integer-valued weight w k→l ðtÞ as a number of parallel and unweighted edges that connect k with l [ , ] . from an epidemiological viewpoint, this idea would translate to w k→l independent attempts to transmit the disease at time t. here, the infection probability βa k→l ðtÞ becomes − ð − βÞ w k→l ðtÞ in the weighted case. in the main article, we apply the latter interpretation to calculate the epidemic risk in the context of livestock trade (see fig. ). here, weights correspond to the number of animals traded, each of which can infect the target population independently. for small probabilities β ≪ , the adjusted infection probability simplifies to − ð − βÞ w k→l ðtÞ ≈ βw k→l ðtÞ. a second source of heterogeneity that is commonly considered includes heterogeneous infection and recovery probabilities, denoted as β k→l and μ k , respectively. with these modifications, the dynamic equations ( )-( ) from the main text translate to θ k→l ðt þ Þ ¼ θ k→l ðtÞ − Ψ k→l ðtÞi k→l ðtÞ; ða aÞ here, Ψ k→l ðtÞ denotes the probability that k infects l at time t given that the former is infected and has not yet transmitted the disease. for weighted networks, we can choose Ψ k→l ðtÞ ¼ β k→l w k→l ðtÞ or Ψ k→l ðtÞ ¼ − ð − β k→l Þ w k→lðtÞ as discussed above. the linearization of eqs. (a a)-(a c) around the disease-free state leads to here, the circle denotes the elementwise product. moreover, the l-dimensional vectors μ and ΨðtÞ integrate the nodeand edge-dependent values μ k and Ψ k→l ðtÞ, respectively. we also generalize the temporal nonbacktracking matrix b β ðtÞ from eq. ( ) to the weighted one: the largest eigenvalue ρ of the infection propagator determines the asymptotic stability for small perturbations around the disease-free state. accounting for heterogeneity in β, μ, and contact weights, the criticality condition eq. ( ) from the main text reads assuming β ≡ β k→l for all edges k → l, we can determine from eq. (a ) the critical (homogeneous) infection probability β crit given a weighted, temporal network with heterogeneous recovery probabilities μ k . similarly, one can assume μ ≡ μ k for all nodes k and thus derive the critical (homogeneous) value μ crit with heterogeneity in the infection probability β k→l . the system of traceability of cattle in the eu requires that each animal is identified with ear tags and that each movement, birth, or death event has to be reported within days of the event to the national livestock database. we consider an excerpt of the national german livestock database hi-tier [ ] for the year . the database is administered by the bavarian state ministry for agriculture and forestry on behalf of the german federal states. it records . million animal movements with a total of . million traded animals between premises, such as farms, pastures, slaughterhouses, and traders within the observation window. the location of each animal holding was provided at the resolution of the municipality. we consider each trade event between two premises a temporal contact, and we identify an edge if at least one contact has been recorded. the distribution of edges is highly heterogeneous in terms of geography, degree, and weight. in fig. (a) , we observe clusters of trade activity mostly within and between north rhine-westphalia (nw), lower saxony (ni), baden-württemberg (bw), and bavaria (by). the number of trading partners, i.e., the node degree, is broadly distributed as demonstrated in fig. (b) . here, we differentiate between in, out, and total degree. similarly, we find a broad distribution of edge weights in fig. (c) , i.e., the number of traded animals along a given edge. the geographic distribution of nodes in fig. (a) shows dense regions in the northwest and southeast including the above-mentioned federal states nw, ni, bw, and by. here, we also find the largest premises in terms of total traded animals: in fig. (c) , color and size indicate the node strength, i.e., the aggregated trade volume. the heterogeneous distribution of strength also becomes apparent in fig. (d) where in, out, and total strength are analyzed separately. finally, we observe in fig. (b) the net flux, i.e., the difference between in-and out-directed trade volume. we display only nodes with at least traded animals in figs. (b) and (c) . from a temporal perspective, we find that trade fluctuates between and active nodes, i.e., farms with at least one trade event on a given day, whereas minima appear regularly on the weekends [see fig. (a) ]. the weekly pattern is also apparent in the interactivation time distribution, i.e., the time interval between two successive trade events for a given node (see fig. ). here, we find a broad distribution of activity with peaks around , , and days. the geographic risk analysis in sec. v b requires us to separate the network into subgraphs that correspond to the intrastate trade (see fig. ). the largest eigenvalue of the corresponding infection propagator allows us to evaluate the outbreak risk within a federal state due to the local movement of infected animals. in table i , we list the names of all federal states of germany together with the corresponding iso abbreviation and basic statistics: the number of nodes, (static) edges, and (temporal) contacts in the gscc. the city states berlin, hamburg, and bremen as well as saarland, which is a particularly small state in terms of nodes, are marked with an asterisk and are not considered for risk analysis in fig. . separating the trade network into subgraphs as visualized in fig. (b) inevitably reduces the outbreak risk as the neglected cross-border edges would otherwise facilitate the disease transmission. in fig. (a) , we find that a considerable fraction of trade is directed across federal states and has thus been removed. this case applies, in particular, to the federal states ni, nw, and bw. similarly, we find that the ratio between intrastate and in-directed trade lies between . (nw) and . (by). thus, we conclude that a considerable fraction of trade across borders is being neglected in the geographic risk analysis in fig. . it is also important to stress that we use the same parameter μ across all federal states and thus assume a uniform detection probability. in reality, federal states with a large number of premises tend to enforce stricter hygiene and intervention standards so that the actual epidemic risk for states such as by and nw is much lower. a realistic evaluation for public health must therefore include heterogeneous recovery (detection) probabilities on the level of states or individual nodes as discussed in ref. [ ] and appendix a, as well as a complex disease response that table i includes trade restrictions, increased awareness, and higher biosecurity. from the detailed, node-level infection trajectory, we can estimate the infection arrival time from a given outbreak location to all remaining nodes. for that purpose, we extend the contact sequence periodically in time until the infection probabilities are negligible. then, we derive the infection arrival time to a single node from the corresponding cumulative infection probability (see fig. ) as follows: (i) the discrete derivative of the cumulative infection probability gives the probability distribution to contract the infection at a given time step. (ii) the expectation value of the probability distribution gives the mean infection arrival time at a single node, corresponding to a scatter point in fig. (a) . here, we compare the expected values from mc simulations with the estimated infection arrival times given by the cb and ib models, respectively. in a perfect prediction, the scattered values would lie on the diagonal, but, as the contact network is far from a treelike structure, the models estimate infection arrival times smaller than the observed values. the comparison between the ib and cb frameworks in fig. (b) shows a considerably smaller relative deviation of cb estimations from the corresponding mc simulations for the given set of disease parameters and outbreak locations. another application focuses on the vulnerability of nodes with respect to a given outbreak location. again, we assume an infinite time horizon and compare the cumulative probability that a node has been infected in the limit t → ∞. as before, we find a good correlation between simulations and the estimated vulnerability in fig. , whereas the cb model consistently outperforms the ib approach and overestimates the expected values surprisingly little given that the underlying aggregated network is fairly dense (the average degree is hki ≈ ) and far from being treelike. for some applications, we may be interested in the trajectory of a global epidemic, averaged over outbreak locations. a sufficiently large number of initially infected nodes would then avoid complications with the early outbreak phase [ , ] . in this case, we adjust the mc simulations such that every node is infected independently with a given probability − z l ¼ − z, ∀ l ∈ n at t ¼ . as for the analytic approach, we only need to set a corresponding homogeneous initial condition, and thus the computational complexity remains the same as in the previous case of one initially infected node. in fig. (left column), we observe a narrow, timedependent distribution of cumulatively infected nodes around the mean value for three different infection probabilities. without applying any additional threshold, we find a close agreement between the averaged trajectory, and the cb and ib models in all cases. in contrast to fig. of the main text, we observe in fig. (right column) only one peak in the distribution due to the large number of initially infected nodes. one potential application is to calculate the vulnerability of a node as discussed in ref. [ ] . here, the vulnerability is defined as the probability that a given node is eventually infected by a disease that started somewhere in the network. the value can be used to rank nodes in order to prioritize surveillance or vaccination measures to the nodes that are most likely to contract the disease when resources are limited. in fig. , every curve represents the vulnerability fig. . (a) comparison between simulated and estimated mean infection arrival times. we extend the data set periodically in time until the outbreak dies out. the discrete derivative of the cumulative infection probabilities (see fig. ) yields the infection arrival probabilities of which we take the average value for every node. results according to the cb and ib models are visualized as red circles and green crosses, respectively. the epidemic starts from the same outbreak origin and disease parameters as in fig. . . (a) comparison between simulated and estimated vulnerability. we compute the cumulative infection probability in the limit t → ∞, also denoted as vulnerability. the comparison with cb and ib estimations is visualized by red circles and green crosses, respectively. each value corresponds to the vulnerability of a node given the same outbreak location and disease parameters as in fig. . (b) relative deviation of the estimated values with respect to mc simulations. the numerical values are averaged over realizations. of one node as a function of the infection probability β. these results are derived from the cb model, given an initial infection probability of − z ¼ . . the individual colors correspond to the degree of the node in the underlying time-aggregated graph and serve as a guide to the eye. interestingly, we find that the ranking, as estimated by the cb model, may change with increasing infection probabilities β as can be seen from the highlighted curve in fig. . this effect has been observed earlier in the context of static networks [ ] and indicates that network properties alone are often not sufficient to rank nodes as they do not take into account details of the dynamic system. the analysis of the conference data set in the main text was limited to a single value of the recovery probability with μ ¼ . × − . this choice corresponds to an expected infectious period of about . h. in addition to the analysis of the main text, we present in fig. similar results for different values of μ. the left, middle, and right columns correspond to figs. , (a), and (b), respectively. in all cases, the cb model gives a closer bound to mc simulations as compared to the ib approach. next, we complete the analysis in fig. of the main text on the epidemic threshold for the example of the animal trade network. again, we assume μ ¼ = and provide in fig. a detailed analysis of all federal states, excluding the city states berlin, hamburg, and bremen. the left and middle columns in fig. provide a similar analysis to figs. (a) and (b) of the main text, respectively. in other words, we present the distribution of outbreak sizes for different values of the infection probability β (left column) from which we derive the coefficient of variation c v (blue line, middle column). the right column presents values of c v that are close to the peak and a quadratic fit (green line, right column) that determines the numerical estimation of the critical infection probability (blue vertical line). this value can be compared to spectral estimations from the mean-field models. in agreement with previous results, we find that the criticality condition in eq. ( ) of the cb model (see main text) improves previous results of the ib approach. fig. . cumulative infection probability with a large fraction of initially infected nodes for three different values of β and the same outbreak location as in fig. (a) . left column [panels (a )-(c )]: time-evolving distribution (linear scale) of cumulatively infected individuals for infection probabilities β ¼ . , . , and . , respectively. we average over outbreak locations with % of the network initially infected at random. the mean outbreak size (blue line), averaged over realizations and with a standard deviation below − , can thus be compared to the cb and ib models (red dashed and green dotted lines, respectively) with no threshold applied. right column [panels (a )-(c )]: final distribution (logarithmic scale) together with the averaged values. fig. . vulnerability as a function of the infection probability β estimated from the cb model. each curve represents the vulnerability of a node, i.e., the probability to contract the infection from a set of randomly chosen outbreak locations. here, we estimate the vulnerability according to the cb model. starting from an initial infection probability of − z ¼ . , we propagate the infection over time until convergence. we stop when the largest increase in vulnerability after h falls below − . the colors indicate the degree of each node in the underlying time-aggregated graph. moreover, the behavior of one selected node is highlighted. finally, we provide an additional analysis of the epidemic threshold for the cattle-trade data with μ ¼ = . results in fig. are akin to our previous analysis in fig. , except for sl. here, the spectral condition in eq. ( ) of the cb model predicts that every outbreak remains localized, i.e., β cb crit ¼ , whereas mc simulations suggest a transition to global epidemics, hence β mc crit < . we attribute the inconsistency to the small size of the network ( nodes). the spectral approach implicitly assumes an infinitely large network, which is clearly violated in this case. we summarize the results for μ ¼ = in fig. , akin to fig. of the main text. the risk map in fig. (a) visualizes the spatial variability of the outbreak risk, and each group of blue, red, and green bars in fig. 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(herkunftssicherungs-und informationssystem für tiere) is administered by the bavarian state ministry for agriculture and forestry on behalf of the german federal states modeling infectious diseases in humans and animals solving the dynamic correlation problem of the susceptible-infected-susceptible model on networks message-passing approach for recurrent-state epidemic models on networks exact deterministic representation of markovian sir epidemics on networks with and without loops dynamic cavity method and problems on graphs, thesis the unreasonable effectiveness of tree-based theory for networks with clustering introduction to percolation theory predicting epidemic risk from past temporal contact data mathematics of epidemics on networks: from exact to approximate models temporal percolation of the susceptible network in an epidemic spreading the relationships between message passing, pairwise, kermack-mckendrick and stochastic sir epidemic models beyond the locally treelike 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trying to make sense out of these deaths. the epidemic control measures taken by national and international health agencies were soon faced by strong reluctance and a sometimes aggressive attitude of the affected communities. based on ethnographic work in macenta (forest region) in the autumn of for the global outbreak and alert response network (goarn) of the world health organization, this chapter shows that while epidemiologists involved in the outbreak response attributed the first ebola deaths in the forest region to the transmission of a virus from an unknown animal reservoir, local citizens believed these deaths were caused by the breach of a taboo. epidemiological and popular explanations, mainly evolving in parallel, but sometimes overlapping, were driven by different explanatory models: a biomedical model embodying nature in the guise of an animal disease reservoir, which in turn poses as threat to humanity, and a traditional-religious model wherein nature and culture are not dichotomized. the chapter will argue that epidemic responses must be flexible and need to systematically document popular discourse(s), rumours, codes, practices, knowledge and opinions related to the outbreak event. this precious information must be used not only to shape and adapt control interventions and health promotion messages, but also to trace the complex biosocial dynamics of such zoonotic disease beyond the usual narrow focus on wild animals as the sources of infection. at the end of december with the death of a two-year-old child in the village of méliandou in guéckédou prefecture, four days after the onset of symptoms (fever, black stools and vomiting). this patient would be considered from now on as the 'case zero', the index case stemming the severe ebola virus disease (evd) epidemic of west africa from apparently a single zoonotic transmission event. but then, with the idea of the spillover taking central stage the question arises: which animal species, the mythic 'animal zero', came to bear the burden of epidemic blame this time? while this retrospective epidemiological study was perceived as essential for limiting high-risk exposures and for quickly implementing the most appropriate control interventions, these investigations (biomedical experts deployed from the rich north) were tempted to mimic and fulfil the 'outbreak narrative' imposed by the global health governance. in this endeavour, rather than discovering the epidemiological origin, what becomes crucial is to quickly identify the carriers-'these vehicles necessary to drive forward the plot', which often function as the outbreak narrative's scapegoats. historically always located at the boundary of the human social body, the ideal candidate to carry this role in the evd epidemic of - was once again the wild and villainous non-human animal. because the pathways for emergence are in any way 'natural' or 'sylvatic', according to the dominant western biomedical model, the inclusion of wildlife in the epidemiology and the evolution of emerging infectious diseases is justified, yet its role is often misrepresented. although the probability of a humans contracting the disease from an infected animal still remains very low, certain cultural practices sometimes linked with poverty, especially 'bushmeat' hunting, continue to be seen as the main source of transgression of species boundaries. in the african context, research into emerging infections from animal sources implicates nonhuman primate 'bushmeat' hunting as the primary catalyst of new diseases. since the virus of ebola was identified for the first time in zaïre in and qualified as the first 'emerging' virus according to the new world clinic called 'global health', the link between animal and human health appears based on an 'us vs. them'. after the formal confirmation of the aetiological agent in march , the epidemic quickly took on an unprecedented scale and severity in several respects. it was declared by the who as an 'extraordinary event' because of its duration, the number of people infected, and its geographical extent which made it the largest ebola epidemic recorded in history until then. to these quantifiable impact measures were added sociological, ecological, political and economic phenomena that are much more complex to decrypt. these have had a profound impact on society, well beyond the remote rural environment that was typically affected by preceding epidemics. by threatening major urban areas, these 'geographies of blame' or 'hotspots' (usually at the margin of modern civilisation and configuring specific areas of the world or the environment into the breeding grounds of viral ontogenesis) have been mapped by 'virus-hunters' to update 'predictions about where in africa wild animals may harbour the virus and where the transmission of the virus from these animals to humans is possible'. in addition to this epidemic's extraordinary character, by spreading beyond the capacities of humanitarian aid, this new biomedically unsolved complexity conferred upon it a status of 'exceptionality' also by 'proclaiming the danger of putting the past in (geographical) proximity with the present'. this status had the effect, among others, of the most intense involvement, perhaps more visibly than before, of different disciplines, from human and animal health to the social sciences, in the international response. anthropology's response in particular was 'one of the most rapid and expansive anthropological interventions to a global health emergency in the discipline's history'. yet it is very critical that the collective social science experiences acquired during this west african ebola epidemic remained engaged to addressing future outbreaks and beyond. they translated and shared anthropological knowledge between scholars by including translation for public health specialists, transmitting that knowledge to junior scientists, and engaging in ongoing work to develop relevant methodology and theory. among the three west african countries most affected by the epidemic, guinea-conakry has been more marked by this dual 'exceptionality', that is to say, both epidemiological and social. beside the exceptionalism described by the senegalese anthropologist faye on the strong and sometimes violent demonstrations of popular reticence with regard to the activities of the 'riposte', guinea was also marked by a higher case fatality rate, as shown in the who report of march . globally raised up to more than % (while knowing that the number of cases and deaths was probably underreported), this case fatality rate confirmed the seriousness of the disease in a guinean context where the ebola virus had never hit before. neither the medical community, nor the population, nor the authorities had so far experienced it. despite all the measures implemented, to the question, why did we observe a higher case fatality rate in guinea compared to that of other countries, a multitude of factors can be advanced. the latter deserve to be the subject of multidimensional analyses, especially as this global lethality has manifested itself differently according to the geographical region of the country. the highest fatality rate was observed in forest guinea ( . %, / ), the region of origin of the index case and main epicentre of the epidemic. was this due to exclusively biomedical factors, such as a lower level of immunity among the guinean population? or was it because of late care that would have given patients less chance of surviving and fighting the virus? but then, why did people infected with the virus later arrive at ebola treatment centres (etc) in guinea? was it due to a poorer and more limited health system and frailer medical and health infrastructure than liberia and sierra leone at the time of the epidemic? or was it due to less effective coordination work by international and national teams in responding to the epidemic? or simply because in guinea the local communities were much more reluctant and intentionally opposed to the deployment of humanitarian and health assistance? although sharing broadly similar cultural worlds, what can therefore explain this notable difference of social resistance between the affected countries? combined with a divergent political practice and lived experiences of the state, especially between sierra leone and guinea, the working hypothesis drawn from my ethnographic observations in macenta and related literature review is that part of the continuing episodes of hostility and social resistance manifested by guinean communities regarding the adoption of the proposed control measures against the scourge of ebola has its origins in the divergence between explanatory systems of the disease; on the one hand, biomedical explanatory systems, and, on the other hand, popular explanatory systems. in march , when ebola hemorrhagic fever was formally identified a few months after the first death, epidemiologists and local populations each actively began to trace and understand this first human-to-human transmission chain of the disease, as well as its triggering event. evolving most often in parallel, and overlapping at times, these epidemiological and popular investigations generally refer to different explanatory models, some more biomedical ('natural') and others more mysticoreligious ('supernatural'). the purpose of this chapter is to trace and reflect on the interpretations of the origin and transmission of the ebola disease, as perceived and explained by the population, and to contrast them with the explanatory model of epidemiologists. in order to interrupt the two routes of evd transmission, namely from animal reservoirs to humans and between human infection, humanitarian responses followed the following public health logic: 'bushmeat' hunting, butchering and consumption should be banned and the ill should be isolated within etcs and burials should be made safe. yet, the interventions related to this reasoning had unattended consequences and, together with the ebola disease itself, they 'disrupted several intersecting but precarious social accommodations that had hitherto enabled radically different and massively unequal worlds to coexist'. carriers, in the case of human-to-human transmission, are generally perceived as the ones promulgating the epidemics and are marked with transgressive attributes intrinsic to their 'contagiousness' (e.g. wanton or deviant sexuality for the hiv epidemic, uncleanliness for the cholera epidemic, immigration for typhoid). however, in zoonosis-related diagnostic discourses, pathogens have the potential to reverse relations between humans and animals in such a way that the carrier becomes the victim. located at the 'interface' between humans, animals and the (natural) environmentalready proved to be a virtual place where deadly pandemic risks lie waiting for humanity-'forest people' from guinea were rendered both carriers of the disease and victims of the villainous role of nonhuman animals. the response to the fear of pandemics has been made unmistakable: we have to shield off humanity from nature. this mindset strongly adheres to the prevailing 'culture-nature divide' which is also depicted through zoonotic cycles diagrams further operating both as pilots of human mastery over human-animal relations and as crucial sites of unsettlement for the latter. wild animals became public enemy number one, together with those who were supposedly facilitating the transgression of the boundaries between the cultural and natural world with (or because of) their culturally 'primitive' or 'underdeveloped' practices. by framing 'bushmeat' hunting, as well as local burials, as the main persisting cultural practices among the 'forest people' to explain (or to justify) the maintenance of the evd transmission during the west african epidemic, the notion of culture that fuelled sensational news coverage has strongly stigmatised this 'patient zero' community both globally and within guinea, and has been employed to obscure the actual, political, economic and political-economic drivers of infectious disease patterns. appointed by my former institute, the institute of tropical medicine of antwerp, belgium (itm), to the who, i was sent to guinea-conakry from the end of october to the end of november for a four-week mission by the global outbreak alert and response network (goarn). since august , the country had been in the largest and longest phase of the epidemic, the second recrudescence which would also be the most intense one up until january . i first spent a week in conakry to follow the implementation of a social mobilisation project (project of monitoring committees at the level of each commune in the urban area). then, following an evaluation of the situation qualified as catastrophic by the national coordinator of the who, it was in macenta, forest guinea, where i was deployed. macenta, located east of guéckédou, was the prefecture considered to be the epicentre of this new outbreak of ebola and where transmission was the most intense. this district would remain one of guinea's most affected regions. by october , macenta, where catastrophic scenarios seemed possible, had already a cumulative number of almost cases since the beginning of the epidemic. the epidemiological situation was out of control, with a lack of material, human and financial resources. on arrival, there was still only one transit center (cdt). a new etc was being finalised by msf belgium. its management would be taken over a few weeks later by the french red cross. due to the long rainy season, the road used for bringing confirmed cases from macenta to the guéckédou treatment centre was in a deplorable state, slowing down the start of treatment and increasing the risk of transmission during transportation. it is as a medical anthropologist that i have been involved in guinea's national coordination platform for the fight against ebola and this within the commission of 'social mobilization and communities engagement', also named locally the 'communication' unit, in order to document, better understand and help to address the reluctance manifested by the local community. without going into the debate about the instrumentalisation of anthropologists as simple 'cultural mediators' at the service of humanitarians, i will simply recall here the specific objectives assigned for the mission. they consisted, on the one hand, in an analysis of rumours and crisis situations in order to propose responsive actions and, on the other hand, in adapting the responses and protocols of the various national and international institutions to local conditions, giving priority to comprehensive and participatory approaches. by integrating the 'communication' unit, i tried to support and animate the meticulous and sensitive work of a whole team working to rebuild trust with communities and to 'open' villages reluctant to receive care interventions. under the authority of unicef guinea, this communication team also hosted many local associations previously working for the prevention of infectious diseases, such as hiv/aids, in the region. the latter had already been mobilised to serve as a relay and to mitigate the unpredictable consequences of the epidemic not foreseen by the riposte, such as, among other things, sensitisation and reception of healed people and orphans of ebola, food distribution, and support for people and villages stigmatised by the disease for whom access to the market-purchase and sale of products-was forbidden. religious representatives of protestant and muslim communities also voluntarily joined this platform to learn and then preach preventive behaviour, to comfort the population, as well as to deconstruct and addressed rumours. their main message was to convince the public that ebola did indeed exist and 'was a real disease'. subsequently, the communication unit was finally able to associate the prefectural direction of traditional medicine of macenta counting traditional healers and distributed in the subprefectures of macenta. the main objective of this new activity was to engage all traditional healers in the fight against evd by raising the awareness of their patients and their entourage thanks to their high level of credibility in their respective communities. they also undertook to refer their patients directly to the tc if they came to present even one of the symptoms of evd (fever, diarrhoea [with blood], vomiting [with blood], loss of appetite). a 'health promotion' team managed and financed by msf belgium also acted on the ground. each morning, the different commissions and stakeholders of the riposte present in macenta were meeting at the prefectural health directorate (dps) to discuss and coordinate their activities in the field. alongside a guinean sociologist, consultant for the who and the assistant coordinator of the mission philafricaine, i was quickly immersed in the realities of the field and in the local strategies elaborated with respect of traditional hierarchies, despite the emergencies. their goal was to restore dialogue with the various village representatives who, since the officialisation of the epidemic, had decided to resist ebola interventions. this was, for instance, the case of the village of dandano, where deaths had risen to ; a village whose access was authorised the day after my arrival in macenta. although tragic, this coincidence made me earn some legitimacy from the other national and international 'fighters'. it is in this intense and difficult context that the ethnographic observations and their preliminary analysis, presented in this chapter, were collected. the methods employed are based on participant observation, including many informal discussions during meetings with villagers (representatives of youth/notables/sages/women), with religious representatives (protestant pastors, and imams), with drivers and partners of the coordination community (e.g. doctors without borders, guinean red cross, unicef among others). some formal interviews were also conducted with key informants such as healed individuals (ebola survivors), traditional healers, pastoralists and local actors in the fight. biomedical scientific literature and reports on epidemiological data, as well as observational notes, photographs and audio recordings collected in the field, allowed me to trace the interpretations of the origin and transmission of ebola in a dual perspective: that of epidemiologists, on the one hand, and that of the population on the other. it is through the concept of explanatory models or 'cultural models of the disease' developed by arthur kleinman that i attempted to interpret the observations ( fig. . ) . this is a conceptual framework that has already been used by barry and bonnie hewlett, alain epelboin and pierre formenty in their respective interventions during the previous outbreak of ebola haemorrhagic fever in the congo in . to be able to adapt the response and interrupt transmission, it is essential to know and understand how the population perceives the introduction of a disease, especially when it is such a deadly one. explanatory or cultural models refer to the explanations of an individual or a culture and to predictions about a particular disease. these are social and cultural systems that construct the clinical reality of the disease. culture is not the only factor that shapes their forms: political, economic, social, historical and environmental factors also play an important role in disease knowledge construction. in kleinmann's model, care systems are composed of three sectors (popular, professional, and traditional) that overlap. in each healthcare system, the disease is perceived, named and interpreted, and a specific type of care is applied. the sick subject encounters different discourses about the illness as she or he moves from one sector to another. kleinman defines the existence, in each sector, of explanatory models of the disease for the sick individual, for his/her family and for the practitioner, whether professional or not. in general, only one part of an explanatory model is conscious, the other is not. although the explanatory models seek from the health district mbomo in congo in , they identified five different cultural models including a sorcery model (sorcerer sending spiritual objects into victims), a religious sect (la rose croix, a christian sect devoted to study of mystical aspects of life), an illness model (fever, vomiting, diarrhoea with blood), an epidemic model (illness that comes rapidly with the air/wind and effects many people) and a biomedical model (ebola haemorrhagic fever). interestingly, none of the integrated non-biomedical models identified a specific non-human animal as potential source and/or carrier of evd or hunting and butchering as specific health risk activities for such illness. this further supports the epistemic dissonance observed during many epidemics (including the west african evd epidemic in this case), between the public health framing of wild meat as hazardous and the practical and social significance of the activities that occasion contact with that hazard. in the case of evd, it is the biomedical cultural model that prevails among western health workers. when the alert was launched by the local health authorities on march , two and a half months after the beginning of the disease of the index case, it was virologic investigations that were conducted at first, following the many deaths that occurred during this socalled silent phase. when the zaïre ebolavirus was identified as the causative agent, retrospective epidemiological investigations of the cases took place, which are crucial during the outbreak of an infectious disease responsible for such high mortality rate. the first chains of transmission of evd are presented in the below graph adapted from baize et al. ( ) (fig. . ). these investigations are mainly based on the identification of patients and the analysis of hospital documents and reports (results of blood tests carried out in the laboratory), as well as on testimonies and interviews with the affected families, the inhabitants of the villages where the cases occurred, suspected patients and their contacts, funeral participants, public health authorities and hospital staff members. virologic analyses suggest a single introduction of the virus into the human population. but the exact origin of the infection of this two-year-old child has not yet been definitively identified, even though the role of bats as natural hosts of the ebola virus, including this time also the insectivorous species, remains one of the most probable scientific hypotheses. up to now, the precise nature of the initial zoonotic event in guinea remains undetermined and the natural reservoir of the ebola virus more generally is not yet certain, beside for three species of fruit bat and other insectivorous african bat species known to carry ebola antibodies and rna. therefore, this informational gap was from the start filled with assumptions during the west african outbreak. among these assumptions, the elusive link between bats, wild animals and humans triggered high concerns over handling, butchering and consuming wild animals, commonly referred to as 'bushmeat'. consequently, these concerns were integrated into public health messages on disease prevention and were translated into a 'bushmeat ban' by governments across the region and enforced during the entire outbreak. this raises the question of the value of focusing on zoonotic transmission, in particular by fruit bats and non-human primates, which was quickly (s ) child, years-old onset dec. dotted arrows: the epidemiological links have not been well established deemed to be of minimal risk, when the biggest threat of infection was from other humans. furthermore, it raises the question of whether there is evidence to indicate and confirm that 'bushmeat'-related information included in public health campaigns in the region actually reduced ebola transmission. first, hunting and consuming 'bushmeat' for food have long been a part of human history occurring worldwide, serving as an important source of protein, and household income, especially where the ability to raise domestic animals is limited. the term itself encompasses an extensive list of taxa that are harvested in the wild (ranging from cane rats to elephants and including duiker, squirrels, porcupine, monkeys, non-human primates, bats and hogs) for food, medicine, trophies and other traditional, cultural uses. yet, designating the consumption of wild animal meat through the use of the term 'bushmeat' for west africans instead of 'game', as is the case for europeans and americans, by the media, scientific literature and public health campaigns that prohibit this practice, participates in 'semiotics of denigration' and has the effect of perpetuating 'exotic' and 'primitive' stereotypes of africa. although involuntary, the immediate and visceral effect produced in western minds by the thought of someone eating a chimpanzee, a dog or a bat, for instance, creates a feeling of disgust which downgrades this person, his/her needs and his/her claims on us. this issue has led to calls to replace the term with 'wild meat' or 'meat from wild animals'. secondly, while the term 'bushmeat' typically refers to the practice in the forests of africa, the trade of 'bushmeat', which has expanded over the past two decades, is considered as an example of an anthropogenic factor that provides opportunities for the transmission of diseases from wildlife to humans. the unsolved reconciliation between present policies and practices and the different values at stake (ecological, nutritional, economic and intrinsic values of wildlife hunted for food) in the actual 'bushmeat crisis', have accentuated the national and global conservation, development and health (infectious disease transmission related) concerns over hunting, eating and trading wild meat. thirdly, because of the many competing interests and realities involved, the proscription of hunting and consuming certain species of wild animals-in particular fruit bats and nonhuman primates during the west africa ebolavirus outbreak-has resulted in several unintended consequences, has incurred great cost and has had only a limited effect. in addition to being vague, inconsistent with scientific research and targeted to the wrong audience, messaging that unilaterally stressed the health risk posed by wild meat and fomite consumption contradicted the experiences of target publics, who consume wild meat without incident. consequently, in addition to having a negative impact on the livelihoods of people living at the frontlines of animal contact, the ban ran the risk of eroding public confidence in the response efforts and fuelling rumours as to the cause of evd (e.g. that the government was attempting to weaken villages in areas supporting the opposition party, as wild meat is considered an important source of physical 'strength' and energy). by focusing exclusively on the risk of spillover, we are distorting and concealing aspects of the dynamics at play. what if species boundaries are not perceived in the same way by everyone? what if the transgression of this 'invisible enemy' is spotted at a different intersection, beyond the nature/society binary? the first chains of human-to-human transmission led to the conclusion that the main vector of contamination was a health professional (s ) who spread the ebola virus in macenta, nzérékoré and kissidougou in february . the fifteenth patient, a doctor (s ), would have also contaminated his relatives in the same areas. the aetiological agent of this deadly disease (the ebola virus for some, the transgression of a taboo for others) remained hidden until then and finally became apparent because of clusters of cases in the hospitals of guéckédou and macenta. indeed, even though the high risk of exposures was elucidated, the problem remained hidden for a number of months, mainly because no doctor or health official had previously witnessed a case of ebola and because its clinical presentation was similar to many other endemic diseases experienced in guinea, such as cholera, which affects the region regularly. but these signals could also have been blurred by another narrative of the causative agent of these same symptoms. this is very similar to what genese marie sodikoff has identified during the recent bubonic plague epidemic in madagascar, when scientists elicited survivors' memories of dead rats in the vicinity to reconstruct the transmission chain. not only were these clues imperceptible to most, but residents had also constructed an alternative outbreak narrative based on different evidence. indeed, the mystico-religious beliefs deeply rooted in this region, even within the medical profession, have offered a different interpretation of causality according to a cultural model other than the biomedical model used by epidemiologists. following james fairhead, it is important to note that 'cultural' model does not tend here to slip into more totalising ideas of 'culture', such as a model being a 'kissi culture' (see below) nor its strict symmetrical opposite (e.g. a model of the 'humanitarian culture' or of a 'western culture'). origin and transmission chain according to an 'animist' model at the beginning of the epidemic, for some, the first deaths in forest guinea were due to the transmission of the filovirus through contact with animals' and/or patients' body fluids; while for others, these deaths originated from the transgression of a taboo related to the touch of a fetish belonging to a sick person, a member of a secret society belonging to one of the ethnic groups of the region. as a result, susceptibility to ebola was initially perceived to be restricted to this particular ethnic group, labelling ebola as an 'ethnic disease'. i decided to name this explanatory model of evd in forest guinea, the 'animist' model, not to further racialise this epidemic, but because it refers to the genies and fetishes that constitute principal aspects of the ancient religions of west africa and also because it describes a belief in a dual existence for all things-a physical, visible body and a psychic, invisible soul. according to a young pastor from macenta who i interviewed, and as confirmed by several other sources of key informants, the population of macenta initially attributed the origin of the disease (in this region at least) to a curse that was only affecting the kissi ethnic group because the first deaths solely affected people belonging to this ethnic group. here is what was stated: … on arrival with all the rumours we heard in conakry, i really did not believe in the beginning that it [the ebola virus disease] must be true because i thought it was an issue of the kissi (…) because it had started in macenta with the kissi, the first deaths were almost only kissi. so we thought it was something related to it … and so we, as toma, it was not going to touch us, it is like that at the beginning we perceived things (…) not something genetic, we thought about the fetishism and idolatry activities that people exercised and that can influence them in one way or another … the first rumour that was there, in macenta, the first death was the doctor who was dead in front of everyone's views. people said they have an idol called 'doma' and so when a person dies of that according to the tradition and according to what is done. and those who are on the thing [those who belong to the secret society of 'doma'] have no right to touch, to manipulate the corpse, or to see it otherwise they may die (…) and that, it existed before. it is a kind of secret society, so they have told us that it can certainly be that, that it is why they [the kissi] are just dying successively. according to these discourses, a health worker from guéckédou hospital (s ), who had gone to seek treatment at his friend's house at macenta hospital (s ), belonged, like him, to a secret initiation society called 'doma' which is also the name of a very powerful fetish; so powerful that it can cause a very fast death for its owner if it has been touched by someone else belonging to the same secret society. when the guéckédou health worker's body was moved, the doctor from macenta would have touched this fetish, idol, sacred object, often hidden in the owner's boubou (traditional clothing). by touching the sacred, the fetish got upset causing the brutal death of the director of macenta's hospital very soon after this event. at that point, in order to repair this transgression and calm the anger of the fetish, six more deaths must succeed each other to reach the symbolic number of seven. if the number of sudden and rapid deaths reaches eight, it means that the fetish is very powerful, and, as a result, seven additional deaths must occur to reach deaths to restore harmony and repair sacrilege. if we reach deaths, we must go to deaths before the disturbed order is restored and moreover that the stain is 'washed', and so on. since the first deaths of this second chain were indeed members of this kissi ethnic group (fig. . ), the 'animist' explanatory model of the disease was quite consistent with people's observations and gained legitimacy among the population at the expense of the biomedical discourse of the existence of evd. as the susceptibility of dying from ebola was initially and predominantly perceived as restricted to this particular ethnic group, no preventive measures were adopted by the non-kissi population of the region. among the kissi, the consequent epistemic dissonance between the public health logic and the transgression to be restored led between june and july twenty-six kissi-speaking villages in guéckedou prefecture to isolate themselves from ebola response, cutting bridges and felling trees to prevent vehicle access, and stoning intruding vehicles. because it is a disease of the social-of those who look after and visit others, and of those who attend funerals-there are of course many reasons why the ebola phenomenon was likely to be associated with sorcery. it is also not a coincidence that the triggering event, the transgression, in this explanatory model was attributed to medical doctors. as elite africans generally educated in european ways and relatively wealthy, this social group displays many characteristics of sorcerers (they lead a secluded life, do not share their gains, exchange abrupt greetings, eat large quantities of meat and eat alone). moreover, the intense preoccupation throughout this region with 'hidden evil in the world around you that finds dramatic expression in the clandestine activities of witches and the conspiracies of enemies' is exacerbated by tiny pathogens remaining largely invisible to our routine social practices, hence attracting suspicions of sorcery (fig. . ) . following the investigation of this 'animist' model in relation to the strong community resistance manifested in forest guinea, i interviewed a member of the riposte communication unit originating from macenta about the dandano case : yes, there is the specificity of dandano. (…) [in] dandano there was a great witch doctor who had gone to greet his counterpart witch doctor where there were a lot of cases. and that is where he got infected. he returned to dandano. three days later he developed the disease and died. afterwards, as he is a great, recognised witch doctor, people said to themselves, because he died, it was not ebola that killed him but his fetish that is taking revenge on him because it is a betrayal to leave one's domain to greet one's friend. maybe he went to spy on his friend and his friend hit him … well, there have been many versions. (…) among the old people who knew the drug he had, euh… his fetish, the grigri that he had, and that if it was his grigri who killed him, it means that all those who saw him, who saw his body, must also suffer. (…) [we could] see his dead body because he was not protected, because we had to wash him and there were medicines that had to be poured to annihilate his fetishes' power before burying him. so there must have been deaths, hence it was already premeditated. then there were deaths, as it was said, and they were successive deaths. that means there were deaths, two days, three days, so people put more anathema on what happened. and that is how dandano lived things. so there were deaths, we said it is the fetish that woke up because dandano is known as a village of powerful fetishes, that is known. (…) even all the sensitisation we do, we never stop in dandano on a manager, a notable, otherwise they can do something to you … so it is well recognised (…) dandano, is not where you have to go joking. (…) at the end, with a lot of deaths, a lot of funerals, they saw that no, it is not that [the fetish anger] anymore, and with the information here and there, it is ebola. and it is like that with all the negotiations (…). notably, these explanatory models are distinct from general beliefs about diseases and care techniques in the region. we cannot argue then that 'biomedicine' and 'kissi culture' are somehow distinct and opposed. chain of transmission according to the 'animist' cultural model. s and s are the two suspect cases as presented in the 'biomedical' chain of transmission (see fig. . ); the grey blocks are the kissi people of the 'animist' transmission chain these beliefs belong to the ideology of different sectors of the care system and exist independently of the illness of a subject. explanatory models are collected in response to a particular episode of illness in a given subject in a given sector and can evolve over time, depending on how the experience, knowledge and risk exposure of the concerned individual develop. this is precisely what has been reported to us and what has been observed in forest guinea. as the number of deceased progressed, and according to the religious and/or ethnic affiliation of the deceased, a new explanatory model was put in place as stated in this conversation: yes, at first it was said, when i was in conakry, since our country is predominantly muslim, it was said that it is a matter for christians since muslims do not eat apes. muslims do not eat the bat. it's only the foresters who eat that. and that's why this disease hits only the kissi and toma who are from the forest. so it's a kaf disease. -kaf? (séverine thys) -from unbelievers, pagans who do not know god. we call kaf, all those who do not believe in the god of muslims. this last extract particularly highlights the fact that these explanatory models are not fixed in time and space and are not impervious to each other either. indeed, the first health messages communicated to the population and built on the biomedical model were intensely focused on the need to avoid the consumption of 'bushmeat', especially wild animals identified as potential primary sources of contamination, namely monkeys and bats. the content of these messages gave birth to another popular model, in which the food taboos or eating habits observed by members affiliated to a certain religion allowed them to explain why this disease was affecting certain groups and not others. this quote also perfectly illustrates how popular discourses have integrated medical interpretations or public health messages. in the study conducted by bonwitt et al. about the local impact of the wild meat ban during the outbreak, all participants, irrespective of age or gender, were aware of wild mammals acting as a source of transmission for ebola. yet a confusion remained about which species in particular could transmit the ebola virus, which may be due to the content of public health messages that were inconsistent as regards the species shown to be potentially hazardous. messages are being absorbed, but in such chaos and fear, people process information according to their own worldview, according to the sources available to them, and following their personal experiences and instincts. furthermore, the criminalisation of wild meat consumption, which fuelled fears and rumours within communities, did entrench distrust towards outbreak responders and also exacerbated pre-existing tensions within villages, ethnicities and religions. following the kissi, it seemed that it was the muslim community that was hit by sudden and numerous deaths. to cope with this new upheaval, this new incomprehension, the operated explanatory model of these deaths' origin was, consequently, first that of a 'maraboutage': it started like that until a certain moment. and then it turned upside down. there have always been upheavals. it turned upside down, and instead of being weighed at a certain moment on the toma and the kissi, it was rather on the manyas, who are entirely, %, % even muslims. and so people started saying 'ha! that only attacks muslims, why not christians?'. so there has always been upheaval in all the procedures of this disease evolution. as noted by hewlett et al., 'patients, physicists, caregivers and local people in different parts of the world have cultural patterns for different diseases. providing care and appropriate treatment for a particular disease is often based on negotiation between these different models'. to be able to negotiate, it is necessary that each one, doctor and patient, partakes in the knowledge of the explanatory model of the other. while most health professionals rarely assume that people have and construct their own interpretation of the causal chain, my ethnographic observations presented in this chapter demonstrate that the a priori on which all interventions of sensitisation are based is not only incorrect, but also a source of blockages for the adoption of prescribed behaviours. this is because, to return to hewlett et al., 'people do not just follow the continuous thread of learning; they also develop an ability to articulate adherence to prescribed behaviours with the refusal of others, to cooperate at certain times and to show reluctance to others, inviting the analysis to move towards a sociology of compromise'. through the example of funerals, wilkinson and leach have also cast light on the presumption that the knowledge needed to stop the epidemic is held by public health experts and scientists, and not by local people. this very often leads to the development of protocols and procedures that completely negate the contribution of communities. this asymmetrical reflection between caregivers and care receivers, the structural violence that has cultivated inequalities in this region, the heterogeneity of experiences seen by the populations as fundamental contradictions between words and facts, the confidence and trust crisis since the 'demystification' programme initiated during sékou touré's time, and the traumas inflicted by a transgression of usages in the name of urgency and the exceptional nature of the ebola epidemic, are all realities that have fueled community reluctance and resistance. the late involvement of traditional healers, primarily consulted by guineans when experiencing illness, in the activities of the response in macenta, is another example of this asymmetry, which too often omits to acknowledge and relate to these other categories that support the social fabric, even if since alma ata in these stakeholders should no longer be on the margins of the health system. although the concept of explanatory models is not sufficient to explain all the failures of response in the context of guinea, or the bordering regions with sierra leone and liberia, nevertheless it allows to move past linear technical discussions of 'weak health systems' as the main reason for the scale of the disaster. the use of this conceptual framework for understanding popular interpretations of the origin of the disease and its transmission reveals the complex, historically rooted and multidimensional picture of the ebola crisis. several authors agree that, 'in any case, it is not a question of archaic beliefs or outlier depictions, but good answers -which can be called rational in this context -to a vital emergency situation, interpreted in the light of past and present experiences'. a better knowledge and comparison of these discourses and different cultural models of the disease, sometimes incorporated, sometimes hermetic, could nevertheless contribute considerably to the success of the fight against the epidemic, especially when it concerns the improvement of knowledge of the chains of disease transmission, the identification and understanding of the behaviours of local populations, and of the sources of denials and rumours. explanatory models proposed by the biomedical sciences are very often in competition and in contradiction with diagnoses made by traditional healers and especially with rumours involving divine punishments, breaches of prohibitions, the misdeeds of wizards or genies, or virologic warfare. if this 'animist' model is not identified nor recognised as making sense for others at the key moment, there will also be no negotiation and no understanding of the distances and proximities existing between the thought systems present in the concerned ecosystems. an anthropological approach remains essential to adapting this response to local realities. epelboin further argues that 'local models of causation regarding misfortune, often the most predominant, involve not only the virulence of the virus and human behaviour, but the evil actions of human and non-human individuals. the virologic model is then only one explanatory model among others, leaving the field open to all social, economic and political uses of misfortune'. following the re-emergence of this infectious disease of zoonotic origin in a whole new social ecosystem, a cross-sectoral research agenda, the so-called one health integrated approach, has finally emerged in the field of viral haemorrhagic fevers, also enabling the role of anthropology to be expanded to times of epidemic outbreak. until then, anthropologists were mandated to contribute to the adaptation and improvement of immediate public health interventions in relation to human-to-human transmission. yet, the growing interest of anthropologists in the interaction between humans and non-humans has made it possible to extend their research topic to the complex dynamics of the primary and secondary transmission of the virus. in addition, this anthropological interest has provided a new cross-cultural perspective on the movement of pathogens and has therefore improved knowledge about the mechanisms of emergence, propagation and amplification of a disease located at the interface between humans and wildlife. such was the role of almudena marí saéz and colleagues who, in a multidisciplinary team, conducted an ethnographic study in the village of the ebola epidemic's origin, the index case village, to better understand local social hunting practices and the relationships between bats and humans. however, the realm of the human-animal-disease interaction has been limited to 'natural versus cultural' domains and frequently conceived as a biological phenomenon in one health studies instead of a biocultural one integrating the social and cultural dimensions generated by human-animal relations. incorporating anthropology into one health approaches should provide a more nuanced and expanded account of the fluidity of bodies, categories and boundaries as drawn up by existing ethnographies on cattle in east and southern africa for example. epelboin et al. have stressed that, 'the anthropological approach in previous epidemics has confirmed that the urgency and severity of an epidemic must not prevent people from listening to them and thinking throughout the epidemic of taking into account indigenous codes, customs, knowledge, skills and beliefs'. by taking seriously the possibility that affected people in the places where we do research or implement control measures might not see things in the same way, we have to be willing to have our categories (such as culture/nature, human/animal, mind/body, male/female, caregivers/care receivers) unsettled, and to grapple with the practical implications of this for engagement in field sites, for knowledge-sharing and for the design of interventions, in the hope that such improvements might contribute to a future prevention of ebola and to public health policies more suitable to respond to people's basic needs. it also allows the affected people themselves to have a say in the matter. as philippe descola and other anthropologists have argued, on the basis of a comparative analysis of a wide range of ethnographic work across the continents, native classificatory systems usually offer a continuum, rather than sharp divisions, among humans and other animal species. indeed, human dispositions and behaviours are attributed not only to animals but also to spirits, monsters and artefacts, contrasting to modern western models, which generally see the categories of human and non-human as clearly defined and mutually exclusive. the ability to sense and avoid harmful environmental conditions is necessary for the survival of all living organisms and, as paul slovic has argued, 'humans have an additional capability that allows them to alter their environment as well as respond to it'. as regards the emerging violence in conservation as either against nature (e.g. culling bats) or in defence of it (e.g. rearranging landscapes within an inclusive 'one health' approach), james fairhead proposes that such violence is increasingly between 'the included' and 'rogues' in ways that transcend the nature/society binary. while the 'white', and african elites were seen by the affected population as 'antisocial' intruders or rogues, suspected of sorcery and using ebola as a tool for political manipulation, those involved in the struggle to address the ebola epidemic were not fighting just against the virus but also against the natural world that harboured it: the rogues which included villainous bats but moreover habitat destroyers, namely hunters, bushmeat traders and deforesters. these were the humans casted as the ones invading the habitat of the virus. since evd will be constantly reconceptualised, and because of new scientific discoveries (e.g. on natural reservoir, or vaccine development), control interventions must listen to and take into account popular perceptions as well as the socio-cultural and political context and their respective evolution. rumours must be identified and managed on a case-by-case basis without global generalisation that could reinforce misinterpretations on the assumption that ignorance alone generates these rumours, con-flicts, lack of trust and resistance. moreover, zoonotic epidemic fighters should follow macgregor's and waldman' recommendations by starting to think differently with and about animals and about species boundaries in order to generate novel ways of addressing zoonotic diseases, allowing for closer integration with people's own cultural norms and understandings of human-animal dynamics. and medicine ( ) ebola virus disease in guinea-update (situation as of aspects épidémiologiques de la maladie à virus ebola en guinée (décembre -avril emergence of zaire ebola virus disease in guinea investigating the zoonotic origin of the west african ebola epidemic zoonosis: prospects and challenges for in this outbreak story, a disease emerges in a remote location and spreads across a world highly connected by globalisation and air travel to threaten 'us all'-read the globally powerful north: see a entre science et fiction' contagious: cultures, carriers, and the outbreak narrative: wald priscilla the global focus on wildlife as a major contributor to emerging pathogens and infectious diseases in humans and domestic animals is due to reports which are not based on field, experimental or dedicated research but rather on surveys of literature and research regarding human immunodeficiency virus (hiv) and aids, severe acute respiratory syndrome (sars) and highly pathogenic avian influenza (hpai), all of which have an indirect wildlife link: r. kock, 'drivers of disease emergence and spread: is wildlife to blame on how and why 'bushmeat' hunting leads to the emergence of novel zoonotic pathogens see bushmeat hunting, deforestation, and prediction of zoonoses emergence uncovering zoonoses awareness in an emerging disease "hotspot"'. social science attempt of the zoonotic niche of evd, see contagious: cultures, carriers, and the outbreak narrative the term 'exceptionality' is borrowed from s. l. faye, 'l' "exceptionnalité" d'ebola et les "réticences" populaires en guinée-conakry. réflexions à partir d'une approche d'anthropologie symétrique to-plague-and-beyond-how-can-anthropologistsbest-engage-past-experience-to-prepare-for-new-epidemics. for the policy relevance of anthropological expertise and a (self-)critical reflection on ebola and on anthropological (and more broadly social scientific) engagements with humanitarian response, see a. menzel and a. schroven the term 'riposte' is the french name used to designate the official national mobilisation settled to respond to the evd crisis, structured into two poles, an inter-ministerial committee and a national coordination committee grouping together the international actors and the national non-governmental organisations; see m. fribault heterogeneities in the case fatality ratio in the west african ebola outbreak challenges in controlling the ebola outbreak in two prefectures in guinea: why did communities continue to resist? comparison of social resistance to ebola response in sierra leone and guinea suggests explanations lie in political configurations not culture understanding social resistance to the ebola response in the forest region of the republic of guinea: an anthropological perspective contagious: cultures, carriers, and the outbreak narrative zoonosis: prospects and challenges for medical anthropology the good, the bad and the ugly: framing debates on nature in a one health community understanding social resistance to the ebola response in the forest region of the republic of guinea: an anthropological perspective sustainability and contemporary man-nature divide: aspects of conflict and alienation on the visual ethnographic examination of the ebola zoonotic cycle transformed into tools of public health communication by the us cdc during the outbreak of medical anthropology and ebola in congo unintended consequences of the "bushmeat ban emergence of zaire ebola virus disease in guinea maladie à virus ebola: une zoonose orpheline?'. bulletin de l'académie vétérinaire de france inclusivity and the rogue bats and the war against "the invisible enemy about the natural reservoir for ebola virus see the evolution of ebola virus: insights from the - epidemic' a review of the role of food and the food system in the transmission and spread of ebolavirus mammalian biogeography and the ebola virus in africa for information on the 'bushmeat ban', see bonwitt et al., 'unintended consequences of the "bushmeat ban ebola virus disease epidemic emergence of zaire ebola virus disease in guinea'; world health organization, 'one year into the ebola epidemic: a deadly, tenacious and unforgiving virus caring for critically ill patients with ebola virus disease ebola-myths, realities, and structural violence'; and olival and hayman the threat to primates and other mammals from the bushmeat trade in africa, and how this threat could be diminished origins of major human infectious diseases'; centers for disease control and prevention take-a-semiotician-or-what-we-talk-aboutwhen-we-talk-about-bush-meat-by-adia-benton/. the kellogg institute on the feeling of disgust as a sentiment with powerful political valences, see also j. livingston, 'disgust, bodily aesthetics and the ethic of being human in botswana the anatomy of disgust world organisation for animal health the bushmeat trade: increased opportunities for transmission of zoonotic disease bushmeat crisis' is caused by the dual threats of wildlife extinctions and declining food and livelihood security of some of the poorest people on earth and whether the hunting of bushmeat is primarily an issue of biodiversity conservation or human livelihood, or both, varies according to perspective, place and over time; see unintended consequences of the "bushmeat ban impact of the ebola virus disease outbreak on market chains and trade of agricultural products in west africa'. food and agriculture organization of the united nations sending the right message: wild game and the west africa ebola outbreak bushmeat ban" in west africa during the - ebola virus disease epidemic'; p. richards, ebola: how a people's science helped end an epidemic les errances de la communication sur la maladie à virus ebola zoonotic semiotics: plague narratives and vanishing signs in madagascar' understanding social resistance to the ebola response in the forest region of the republic of guinea: an anthropological perspective one year on: why ebola is not yet over in guinea encyclopedia of medical anthropology : health and illness in the world's cultures extracts of the individual interview conducted with the pastor on the cultural and political role of initiation societies in the forest region and the related experiences of local citizens in relation to both the manding (often islamic) world to the north, and to the 'white' (often christian) colonial and neo-colonial order, see fairhead purity and danger, an analysis of concepts of pollution and taboo communication with rebellious communities during an outbreak of ebola virus disease in guinea: an anthropological approach understanding social resistance to the ebola response in the forest region of the republic of guinea: an anthropological perspective memories of the slave trade: ritual and historical imagination in sierra leone lifeworlds: essays in existential anthropology for more information about dandano village 'surrendering their sick and dead after being battered by the virus', see a. nossiter extracts of the individual interview conducted with a voluntary of the communication unit of macenta new therapeutic landscapes in africa: parental categories and practices in seeking infant health in republic of guinea extracts of the individual interview conducted with the pastor for similar narrative about muslim communities and food taboos regarding bats, see f. batty, 'reinventing "others" in a time of ebola unintended consequences of the "bushmeat ban extracts of the individual interview conducted with the pastor medical anthropology and ebola in congo: cultural models and humanistic care ebola en guinée: violences historiques et régimes de doute briefing: ebola-myths, realities, and structural violence l' "exceptionnalité" d'ebola et les "réticences" populaires en guinée-conakry ebola en guinée: violences historiques et régimes de doute'; wilkinson and leach traiter les corps comme des fagots' production sociale de l'indifférence en contexte ebola (guinée approche anthropologique de l'épidémie de fhv ebola en guinée conakry zoonosis: prospects and challenges for medical anthropology extending the "social": anthropological contributions to the study of viral haemorrhagic fevers investigating the zoonotic origin of the west african ebola epidemic views from many worlds: unsettling categories in interdisciplinary research on endemic zoonotic diseases animal spirits and mimetic affinities: the semiotics of intimacy in african human/animal identities annexe . contribution de l'anthropologie médicale à la lutte contre les épidémies de fièvres hémorragiques à virus ebola et marburg'. in world health organisation, Épidémies de fièvres hémorragiques à virus ebola et marburg: préparation, alerte, lutte et évaluation the morning after: anthropology and the ebola hangover beyond nature and culture biosecurity and the topologies of infected life: from borderlines to borderlands nature and society: anthropological perspectives by perception of risk inclusivity and the rogue bats and the war against "the invisible enemy views from many worlds acknowledgements i would like to thank tenin traoré, a guinean sociologist and consultant to who, and joseph kovoïgui, assistant coordinator of the philafrican mission and then consultant to who, for their commitment and engagement in the fight against ebola, their generosity, their knowledge, their experience and our fruitful collaboration in many respects. i would also like to thank the coordination team and the dps (prefectural health direction) of macenta for their welcome and sincere attention; goarn/who, antwerp institute of tropical medicine, and in particular prof. marleen boelaert for emotional, financial and logistical support; dr. alain epelboin for field preparation and numerous sharing with the francophone anthropological platform; and christos lynteris for his invitation to connect and exchange with the anglophone 'anthro-zoonoses' network and contribute to this timely collection. key: cord- -zy lw authors: nakamura, g.; grammaticos, b.; badoual, m. title: confinement strategies in a simple sir model date: - - journal: nan doi: nan sha: doc_id: cord_uid: zy lw we propose a simple sir model in order to investigate the impact of various confinement strategies on a most virulent epidemic. our approach is motivated by the current covid- pandemic. the main hypothesis is the existence of two populations of susceptible persons, one which obeys confinement and for which the infection rate does not exceed , and a population which, being non confined for various imperatives, can be substantially more infective. the model, initially formulated as a differential system, is discretised following a specific procedure, the discrete system serving as an integrator for the differential one. our model is calibrated so as to correspond to what is observed in the covid- epidemic. several conclusions can be reached, despite the very simple structure of our model. first, it is not possible to pinpoint the genesis of the epidemic by just analysing data from when the epidemic is in full swing. it may well turn out that the epidemic has reached a sizeable part of the world months before it became noticeable. concerning the confinement scenarios, a universal feature of all our simulations is that relaxing the lockdown constraints leads to a rekindling of the epidemic. thus we sought the conditions for the second epidemic peak to be lower than the first one. this is possible in all the scenarios considered (abrupt, progressive or stepwise exit) but typically a progressive exit can start earlier than an abrupt one. however, by the time the progressive exit is complete, the overall confinement times are not too different. from our results, the most promising strategy is that of a stepwise exit. and in fact its implementation could be quite feasible, with the major part of the population (minus the fragile groups) exiting simultaneously but obeying rigorous distancing constraints. modelling can be a most valuable tool in the investigation of phenomena involving biological systems. this is all the more true when the phenomena in question cannot be reproduced in the laboratory, for practical or ethical reasons. prominent among the aforementioned are epidemics. considered as a sub-branch of population dynamics, epidemics lent themselves perfectly to mathematical modelling. the history of such approaches goes back to the th century and d. bernoulli who, in , presented a work [ ] on the mortality rate due to smallpox and the advantages presented by vaccination. mathematical tools for the study of epidemics have been developed decades ago and are being constantly refined since. the current pandemic sweeping the globe has rekindled the interest in epidemics. modelling is one of the approaches used in order to identify the best strategy for the mitigation of the devastating effects. the present paper is an attempt at answering, in a modelling framework, the fundamental question of the how to implement efficiently a population confinement. several works have recently addressed the same question from various perspectives. four recent papers are the product of the centre for the mathematical modelling of infectious diseases (covid- working group) of the london school of hygiene and tropical medicine. a stochastic transmission model was used first to estimate the daily reproduction number before and after confinement measures, from data obtained from the wuhan province. based on this estimate, the authors of [ ] conclude that even a small number of infections introduced in a previously unaffected area may lead to an epidemic outbreak. in the second paper [ ] , based on the same model, the authors conclude that what plays a major role in determining whether an outbreak is controllable is the delay between the onset of symptoms and the introduction of social distancing measures based on contact tracing. however the necessity of an efficient contact tracing increases with the value of the daily reproduction rate making its practical implementation particularly arduous. quantifying contacts was the object of the third paper [ ] of the team based on a largescale data collection concerning the possible (albeit self-reported) contacts of a population of volunteers. in the fourth paper [ ] the authors identify the role of the moment for the relaxation of the physical distancing measures claiming that the benefit of a somewhat delayed relaxation is the reduction of the height of the epidemic peak. their projections show that a premature lifting of the measures may lead to a secondary peak. a team of imperial college led by n. ferguson, examined the two strategies of suppression versus mitigation. while the latter aims at just slowing down the epidemic so as not to overwhelm the healthcare system, the former's objective is to reduce the number of infected to a very low level and maintain it there permanently. mitigation is a more palatable solution (although the authors consider a five month duration of the measures) but it may still lead to a staggering number of deaths and an epidemic resurgence when the interventions are relaxed. the studies [ ] of the imperial college team show that the timely adoption of measures (be they mitigation or suppression) are of the utmost importance as far as the consequences of the epidemic are concerned. any unwarranted delay may result in a huge number of additional infections and deaths. the team of stanford under e. mordecai constructed an interactive model [ ] which simulates the effects of social distancing. just as in the previous studies a resurgence of the epidemic is predicted if the controls are lifted too quickly. they also model what they call the 'light-switch' approach where confinement is turned on and off in response to the seriousness of the epidemic resurgences. a team of the university of oxford [ ] applied modelling techniques to the data collected in italy and the uk. their conclusion is that the epidemic has started at least a month before the first reported death and would have an approximate duration of - months, in the absence of any intervention. on the positive side, their analysis seems to indicate an accumulation of significant levels of herd immunity. the particularity of our modelling approach resides in the fact that we are using the simplest possible model for this, namely, an adaptation of the venerable sir. the sir model was proposed by kermack and mckendrick [ ] , inspired from the works of ross [ ] . the basic model consists in a population split into three groups: 'healthy' individuals that are susceptible to infection (s), 'infected' individuals who can transmit the disease (i), and the 'removed' (r) who either died from the disease or, having recovered, are immune to it. the differential model built on the assumption of a fully mixed population has the form with a being the infection rate and λ the removal rate of the infected individuals. the main assumption here is that the number of infected individuals increases at a rate proportional to the number of both infected and healthy. the model equations ( ) are such that the total population s + i + r is constant. by introducing the appropriate scaling of the time t it is possible to set the parameter λ to . in this case the value of a defines what is called the basic reproduction number i.e. the expected number of infections in the susceptible population resulting form a single infection. there exist a slew of versions of the sir model [ ] , introducing more subsets of the population and/or different interactions among them. hethcote [ ] presents a pedagogical review of the matter. of particular interest to our approach is the fact that the sir model can be modified so as to model vaccination. as explained clearly in [ ] , a vaccination policy presents a challenge. if a large proportion of the population is already immune then the risk, even a small one, associated with vaccination will be perceived as more significant than the risk from infection. this resonates with the perceived risks of social distancing measures, where a lockdown although offering protection from infection also entails economical and psychological downsides. in what follows we shall introduce our version of the sir model, particularly tailored for the investigation of the effect of lockdown and its eventual relaxation. we shall derive our special discrete version of the model and will use it to perform the numerical simulations. based on the latter we shall discuss the effect of lockdown and its relaxations scenarios. the classical sir model introduces three populations: susceptibles s, infective i and recovered r. given the conservation of the total population the equation for the recovered is superfluous. in view of the investigation of confinement strategies we separate the susceptible population into two sub-groups, the confined-susceptibles, c, and the unconfined-susceptibles, u . the equations become now and by scaling time we put λ = . here c and u are to be understood as percentages of the total population, with c( ) + u ( ) ≈ (no 'recovered' at the beginning of the epidemic). the condition for the number of infectives to grow is ac( ) + bu ( ) > , otherwise the epidemic fizzles out. practically, since the measures to curb the epidemic are taken once the latter has manifest itself, the initial population is unconfined. in this case the condition for an epidemic outbreak is simply b > . a fixed point of equation ( ) has necessarily i * = , but we can have c * u * = . the fixed point is attractive provided ac * + bu * < . practically this means that the epidemic stops when there are no more infective persons, while a non-infected fraction the population may exist. since we are dealing with populations the quantities c, u and i are a priori positive. given the structure of the equations ( ) positivity is guaranteed provided one starts from positive initial conditions [ ] . taking this into account we shall proceed now to the construction of a discrete version of ( ). our approach is inspired by the works of mikens [ ] . his recommendations are that 'nonlinear terms must be, in general, replaced by nonlocal discrete representations' and 'a property that holds for the differential equation should also be present in the discrete model'. our rule of thumb in this is [ ] that 'since all quantities are positive, no minus sign should appear anywhere'. we introduce thus a forward difference of the time derivative, with time step δ, and, what is more important, the staggering below solving for the points at (n + ) we obtain this system has the very same properties as the differential one. in what follows we shall use it in order to integrate the differential system ( ) . moreover ( ) is a very robust scheme which gives a realistic answer for any time step, even a very large one. let illustrate this with an example. we perform a simulation taking a time step δ = − , without distinguishing between confined and unconfined populations, a = b = . and plot the infective fraction of the population, i, as well as the fraction of infected, − (c + u ) as a function of time. next we consider a case where the time step can become large. we introduce j = δi and rewrite equation ( ) after taking the limit δ → ∞. we obtain now the system we iterate this system with the same conditions as for figure , and obtain the result shown in figure . the result is striking. while some details, like the value and position of the peak or the asymptotic value of infected population, may differ slightly, the overall behaviour of the results at infinite time step is very close to that of the small time step used in order to simulate the continuous system. this is the definite advantage of tailored integrators as compared to ready-made, black-box, routines. before proceeding to the examination of the various confinement strategies it is interesting to apply our model to a simple situation, that of hunting for the 'patient zero'. we have performed a simulation of ( ) assuming a wholly unconfined population, i.e. c( ) = , u ( ) = , with an infection rate b = . the results of the simulation with a 'reasonable' percentage of infectives i( ) = − are those shown in figure . next we performed a simulation assuming that one person on earth was infected, the patient zero. the corresponding initial condition is i( ) ≈ − . the result of the simulation is shown in figure . the comparison is quite interesting: the profile of the epidemic, i.e. the evolution of the infectives over time, is the same with both initial conditions, just shifted in time. thus by following the evolution of the epidemic one cannot go back in time and guess when the first infection took place. this has to be assessed by other methods which lie beyond the modelling approach. put in a different way, by observing the evolution of the epidemic starting at a given time one cannot be sure where the genesis of the epidemic is situated in time. in what follows we shall apply our model to situations where a population is totally or partially confined and where the lockdown is lifted progressively or abruptly. in order for our simulations to be as realistic as possible it is important that we calibrate our model, introduce the proper time scale, choose the proper parameters and initial conditions, and, finally consider the adequate confinement strategies. the time scale, given by /λ, is set to days. this is a typical time for the duration of infectiousness, according to ferguson and collaborators [ ] . in what follows, time is counted in units of /λ. the value of the basic reproduction number without confinement r = b/λ is still not known with precision. in [ ] , the r was estimated to be around . and in [ ] , r ranges from . to . . in what follows (having taken λ = ) we shall choose r = b = . . the goal of confinement is to reduce r to a value close or even below , which is the threshold for an epidemic outbreak [ ] . the infection rate for strictly confined people a = a was set to . we set the fraction of confined people to . . this value seems reasonable, since some people go to their workplace every day. these people are more exposed to the virus and belong to the category of unconfined people. in france, for example, it is estimated that around a quarter of active people still go to work. the initial value of the fraction of infected people is set to − , and the confinement is applied after a time interval, t . since we are interested here in the different strategies of ending the confinement, t is fixed in all the simulations, t = (or days). the time step used in the simulations is δ = − . we tested our choice of parameters and initial conditions by comparing the evolution of the fraction of infected people to the real evolution of active cases in italy. the confinement started in italy on march th in the north of the country, so we report here the data of the active cases from days before this date (february th ), to april th, [ ] . we divided these numbers by the population of the four most impacted regions of northern italy (lombardia, piemonte, emilia romagna, veneto), which is around millions of people, so as to get a density. in order to get a good match with the model, we had to correct the density by a factor of , which is consistent with the fact that a large fraction of cases are actually unreported or asymptomatic cases [ ] . the agreement between the real data and our model is satisfactory, we can conclude that our parameters and initial conditions are realistic. once the model is calibrated we are ready to address the question of population confinement. the first simulation is performed so as to compare the two extreme cases, one where there is no lockdown and one where the duration of the lockdown is extended till the practical disappearance of the epidemic. the results are presented in figure . they correspond in fact to the curves repeatedly shown by the media. with an absence of confinement the epidemic is of short duration but of high intensity: a sizable part of the population is infected. the positive side of such a strategy is that herd immunity of the population is reached in a short time. the downside is that the healthcare system can easily be overwhelmed by the sheer number of infected people. the prolonged confinement has the advantage of making the number of infected people (hopefully) manageable. on the downside, such a prolonged lockdown may have untenable social and financial repercussions. thus alternative strategies must be investigated. the confinement strategies we are going to investigate in what follows have to do with the lifting of lockdown measures. we shall not delve into the initial application of lockdown. the only visible strategy adopted universally is to enforce such a measure when it clear that the epidemic cannot be ignored any more. however exiting the confinement is particularly delicate and thus we are going to focus our analysis on this. three different scenarios will be examined. they correspond to an abrupt, instantaneous exit, to a progressive, continuous, one and to a progressive exit by steps. we model the effect of confinement by changing the infection rate of the confined population a during time. before the onset of confinement, this population has the same infection rate as the unconfined one, so a(t) = b. during strict confinement, a(t) = a with a < b. this period of strict confinement lasts for a period of time t . after this time interval, the lockdown starts to be lifted and a period of lighter confinement starts. the duration of this period of time is defined as t . different strategies of confinement lifting can be tested: the abrupt ending of confinement, where a(t) changes instantaneously from a to b and t = ; the progressive ending of confinement, where a(t) increases linearly during t and the step ending, where a(t) takes an intermediate value a , between a and b during t . the function a and the time intervals t , t and t are defined on figure . in our simulations, the parameters b, a and t are fixed: b = . , a = and t = . the parameters a , t and t can vary. on the other hand choosing the same moment for the relaxation of the lockdown measures but applying a progressive scenario keeps everything manageable despite a slight recurrence of the increase of the number of infected people. a second peak of infection does appear but it is lower than the first one. a stepwise exit from confinement is shown in figure , in comparison with the progressive (linear profile) exit. the stepwise strategy has the particularity to lead to a non-negligible increase in the number of infected people right after the first, partial, exit, but, on the other hand, it presents the advantage that by the time the exit is total the level of the epidemic can be considered as wholly manageable. in the case of the stepwise strategy, there are actually three peaks in the infection curve, each one corresponding to a discontinuity of function a. however, the third peak is always much smaller than the first two. thus, in what follows, we will compare only the first peak to the second one. in figure we show the variation of the (fractions of the) populations of the confined and unconfined susceptible as a function of time for two exit scenarios. as expected, an abrupt exit has as a consequence a sharp decline in the population of those who were previously confined. being now in contact with the infectives they can become infected, which explains the sharp increase observed in figure . a progressive exit, although also leading to increased infections, has a much smaller effect and a definitely smoother variation of the susceptible population. figure summarises the behaviour of the total population of infected people for the four scenarios considered here, no-confinement, confinement with abrupt exit, progressive exit and stepwise exit. as expected the number of globally infected people is larger in a no-confinement scenario. this is the one offering the most efficient 'herd-immunity' but the price to pay is a high number of infections concentrated in time. the abrupt exit scenario has a relatively smaller number of infected people, but as we saw it presents the danger of a second epidemic wave being worse than the first. the progressive strategies are the ones leading to the smallest number of infected people. while this has the advantage of keeping the epidemic manageable all along it is not optimal if what was sought to begin with was an as large as possible immunisation of the population. the dashed lines (black or grey) correspond to the absence of any measure of confinement, the dashed-dotted lines (black or grey) correspond to the abrupt exit of confinement, the dotted lines (black or grey) to the stepwise exit and the full lines (black or grey) to the linear exit. the effects of the lockdown duration as well as that of the exit strategy are better represented in a figure summarising a broad collection of values. thus in figure we show the ratio of the second to the first epidemic peak, i.e. the one reached after the exit from lockdown to the one obtained during the confinement, as a function of the duration of the strict confinement, t . the curves labelled as (a), (b) etc. correspond to increasing progressive durations of the lockdown exit t , while the dashed curve is the one obtained for an abrupt exit. clearly the latter would requite a more prolonged confinement period for the second epidemic peak not to be higher than the first. one can notice that since we study the different scenarios of ending confinement, the height of the first peak, reached during confinement, before starting to lift the constrains, is the same for all the values of the studied variables. figure . the curve represent the variation of the ratio of the second to the first peak of the infection curve as a function of the duration of the strict lockdown t . curve (a) corresponds to the duration of the progressive exit (or lighter confinement period) t = , curve (b) to t = , curve (c) to t = and curve (d) to t = . the dashed curve corresponds to the abrupt exit (equivalent to t = ). for all the curves, t = . figure concerns the stepwise strategy. in this case, the infection rate of confined people takes an intermediate value before going back to unconfined value. in figure , we show the ratio of the second to the first peak in the infection curve, as a function of the intermediate value of the infection rate of confined people. where a = a , is constant for all the curves of the figure and is equal to (since the height of the third peak is not studied, this value is not important, as long as the duration is long enough so that the third peak does not interfere with the second one). in this paper we have introduced a variant of the sir model in order to study, in the simplest possible way, without unnecessary assumptions, the effect of population confinement on the evolution of an epidemic. the motivation for this is, obviously, the current covid- epidemic, which in a matter of a few months has evolved into a pandemic. the gravity of the situation, has made mandatory the introduction, in most countries, of lockdown measures aiming at containing the epidemic, so as not to overwhelm fragile healthcare systems. our model is a classical sir one, where the population of the susceptibles is spilt into two subgroups, one which is essentially confined and one, which, due to specific duties, cannot follow strictly the social distancing directives. the infectiveness of the second population, the presence of which is crucial for the functioning of society, in sufficient in order to spread the epidemic. our model was formulated as a system of three coupled differential equations. we discussed the conditions for an epidemic to evolve, the existence of fixed points as well as their stability. a discrete form of the equations was introduced which was subsequently used as an integrator of the differential system. we have shown the extreme robustness of our difference scheme, by performing a simulation at the limit where the time step can be taken arbitrarily large. the model focused mainly on the impact of various lockdown-exit strategies on the evolution of the epidemic. however, before addressing this question, we studied the epidemic onset and its evolution in the case where a substantial nucleus of infected persons does exists compared to the case where one starts with a single infected parson. it turned out that the observed evolution was the same in the two cases. the practical implication of this is that one cannot tell when did the first infections made their appearance. this observation resonates with the speculation [ ] that there may have been covid- cases in italy as early as november . in order to apply our model in an as realistic as possible way we started by calibrating it and choosing properly initial conditions. we studied different scenarios of lifting confinement: an abrupt one, a progressive one (where the infection rate of confined people goes back to the value of the unconfined linearly), and a stepwise one (where the infection rate of confined people takes an intermediate value, between the confined and the unconfined values, before going back to the unconfined value). first, we show that an abrupt end of confinement can lead to a second peak of epidemic higher than the first one, for a confinement that lasts units of time in the model ( days). however, even with an abrupt end, the ratio between the two peaks of epidemic can be smaller than , but this requires a long confinement, longer than . units of time (which represents days), see figure . in practice, in order to be sure that the second peak is much lower than the first one, the strict lockdown should be imposed for at least . - months. practically, however, it would be difficult to impose to the population a strict lockdown during such a long time interval. a more acceptable strategy would be to alleviate the constrains progressively or stepwise. we studied both scenarios. the progressive scenario can be described by two variables: the time interval corresponding to a strict lockdown (t ) and the time of progressive exit of the lockdown (t ). it is not surprising to find that the ratio of the two peaks is smaller when the lifting of constrains starts later (large t ). for a given t , the ratio is smaller when the time of progressive exit of confinement (t ) increases (going from curve (a) to (b), (c) and (d) on a vertical line, on figure ). what is less intuitive is that the total period of confinement (including the strict and the lighter confinement) has to be longer in the case of the linear exit than for the abrupt exit, in order to get a second peak lower than the first one. on figure , for curve (d) for example (that corresponds to t = ), the time interval for strict confinement t has to be equal to units of time if we want a ratio smaller than . the total time of confinement (including the period of strict and of lighter confinement) would thus be units of time. for the abrupt exit, a duration of confinement of . units of time would suffice in order to have a ratio smaller than . figure also tells us that first, the ratios for an abrupt exit and for a progressive one tend to the same (lower than ) value, as the time of confinement t gets larger. with t = (meaning that the confinement would last days, or months), the number of infected people gets really small, but since it is not zero, the epidemics can start again when the lockdown is finally lifted, giving rise to a second, low peak, which has the same height whether the exit is progressive or not. we should point out at this point that applying a linear exit strategy in practice presents considerable difficulties. changing rules every week or even everyday to ensure the linear lifting of the lockdown is far from ideal. the stepwise strategy also allows to get ratios smaller than , if the duration of the confinement is long enough and if the intermediate infection rate a for the confined people is not too large. however, what is interesting is that this intermediate value can be larger than : this means that even if the epidemic threshold is exceeded for the confined people, the peak of the epidemics can still be controlled, if the strict confinement period is long enough. for example, suppose that the confinement lasts units of time in the model, or days, (this situation corresponds to curve (c) in figure ), then any value of a (the intermediate value of the infection rate of confined people) smaller than . would lead to a second peak lower than the first one. moreover, this strategy allows to get less infected people at the end (see figure ). this strategy seems to be easier to put into practice, as it does not necessitate a continuous change the rules. the difficult part here is to translate the parameters of the model into practical instructions. what can represent the value of . for a ? a situation between the strict confinement and a completely normal one, where, for example, everybody wears a mask, where those who can go to work do so, but work-place cafeterias are closed, where schools are still closed and where meetings of more than persons are forbidden could be a good intermediate state. a more detailed model, with a structured population would be needed to answer that question. however, in all cases one should bear in mind the words of ferguson [ ] : "models are not crystal balls. what we are building are simplified representations of reality". thus is some cases it is preferable to work with a simpler model which allows control over the various quantities in play and makes it possible to develop an intuitive grasp of the situation. essai d'une nouvelle analyse de la mortalité causée par la petite vérole, et des avantages de l'inoculation pour la prévenir early dynamics of transmission and control of covid- : a mathematical modelling study feasibility of controlling covid- outbreaks by isolation of cases and contacts contacts in context: large-scale setting-specific social mixing matrices from the bbc pandemic project the effect of control strategies to reduce social mixing on outcomes of the covid- epidemic in wuhan, china: a modelling study ferguson and the imperial college covid- response team, impact of non-pharmaceutical interventions (npis) to reduce covid- mortality and healthcare demand potential long-term intervention strategies for covid- fundamental principles of epidemic spread highlight the immediate need for large-scale serological surveys to assess the stage of the sars-cov- epidemic contributions to the mathematical theory of epidemics an application of the theory of probabilities to the study of a priori pathometry extending the sir epidemic model the mathematics of infectious diseases vaccination and the theory of games exact solutions to a finite-difference model of a nonlinear reaction-advection equation: implications for numerical analysis revisiting the human and nature dynamics model early transmission dynamics in wuhan, china, of novel coronavirusinfected pneumonia preliminary estimation of the basic reproduction number of novel coronavirus ( -ncov) in china, from to : a data-driven analysis in the early phase of the outbreak substantial undocumented infection facilitates the rapid dissemination of novel coronavirus italian scientists investigate possible earlier emergence of coronavirus from: www.reuters.com special report: the simulations driving the world's response to covid- key: cord- -khzivbzy authors: jia, peng title: understanding the epidemic course in order to improve epidemic forecasting date: - - journal: geohealth doi: . / gh sha: doc_id: cord_uid: khzivbzy the epidemic course of the severe acute respiratory syndrome (sars) has been differently divided according to its transmission pattern and the infection and mortality status. unfortunately, such efforts for the coronavirus disease (covid‐ ) have been lacking. does every epidemic have a unique epidemic course? can we coordinate two arbitrary courses into an integrated course, which could better reflect a common real‐world progression pattern of the epidemics? to what degree can such arbitrary divisions help predict future trends of the covid‐ pandemic and future epidemics? spatial lifecourse epidemiology provides a new perspective to understand the course of epidemics, especially pandemics, and a new toolkit to predict the course of future epidemics on the basis of big data. in the present data‐driven era, data should be integrated to inform us how the epidemic is transmitting at the present moment, how it will transmit at the next moment, and which interventions would be most cost‐effective to curb the epidemic. both national and international legislations are needed to facilitate the integration of relevant policies of data sharing and confidentiality protection into the current pandemic preparedness guidelines. the period of the severe acute respiratory syndrome (sars) epidemic has been divided according to its transmission pattern and the infection and mortality status. unfortunately, such efforts for the coronavirus disease (covid- ) have been lacking. does every epidemic have a unique pattern? can we find out a common real-world progression pattern of the epidemics? to what degree can such arbitrary divisions help predict future trends of the covid- pandemic and future epidemics? the advanced spatial and digital technologies provide a new perspective to understand the transmission patterns of epidemics, especially pandemics, and a new toolkit to predict the progression of future epidemics on the basis of big data. in the present data-driven era, data should be integrated to inform us how the epidemic is transmitting at the present moment, how it will transmit at the next moment, and which interventions would be most cost-effective to curb the epidemic. both national and international legislations are needed to facilitate the integration of relevant policies of data sharing and confidentiality protection into the current pandemic preparedness guidelines. the "life" course of an epidemic starts from the human-ecology interaction and can develop into a pandemic, such as coronavirus disease . think about the four periods the course of the severe acute respiratory syndrome (sars) epidemic has been divided into, according to its transmission patterns: from wildlife to humans (december to early january ), humans to humans in the epicenter (january to february ), epicenter to other regions (early february to mid-march ) , and humans to humans in other regions (mid-march to may ) . however, according to the infection and mortality status, the sars epidemic course has been differently divided into four periods: portent and incubation (december to february , outbreak and spread (february to early may), fastigium and stability (may), and recession and recovery (june) (zhong, ) . these different arbitrary divisions, while confusing us and being susceptible to the modifiable temporal unit problem (mtup) whereby the resulting epidemic trend may vary by time windows selected in the analyses (tao et al., ) , can also open a window of opportunity for reflection on is every epidemic a unique "individual" with a unique life course? can we coordinate different arbitrary courses into an integrated course, which could be less subject to mtup and better reflect a common real-world progression pattern of the epidemics? more importantly, since people are still experiencing the covid- pandemic or facing the risk for covid- reemergence in many regions, we have to ask to what degree such arbitrary divisions can help to predict the future trends of the covid- pandemic and the future epidemics? © . the authors. this is an open access article under the terms of the creative commons attribution-noncommercial-noderivs license, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made. covid- has visited many countries, and most, if not all, of them have not prepared for or even realized the risk of covid- until it landed on their territory. this could be understood to some extent. after all, any emergency response is at the economic expense of society with side effects in many aspects (nussbaumer-streit et al., ) . there is generally a lack of data-sharing mechanisms and infrastructures (e.g., datasharing protocols, intersystem interfaces, and confidentiality protection mechanisms) for most countries to make robust place-specific prediction of risk and further generate evidence-based measures of emergency response ahead (kummitha, ) . therefore, efforts of understanding the covid- epidemic course have been lacking. it has been mentioned that understanding transmissibility of the covid- epidemic is crucial for predicting the course of the epidemic and the likelihood of sustained transmission (lipsitch et al., ) . however, very few, if not none, of mathematical models that consider factors including the infection's transmissibility to predict the impact of the covid- epidemic have been useful to the real-time epidemic control on the ground (jia & yang, a ). an important reason for this uselessness is that, without the support of spatial real-time data and models, we have largely or fully lost spatial features of the epidemic and can only see a limited number of snapshots over the full, continuous spectrum of the epidemic . for example, the spatial relationships among humans and cities (i.e., the first law of geography that everything is related to everything else, but near things are more related than distant things) have been significantly downplayed in most, if not all, prediction models for covid- (shi et al., ) . the life course of an epidemic or pandemic is even more spatial than that of an endemic or hyperendemic: the accumulation of risk and infection converts an endemic into a hyperendemic, which has shown its clear "life" course; after being upgraded to an epidemics and even further pandemic, its spatial life course is just too clear to neglect. human movement at all scales, from local routine activities to global air travel, has further complicated the pandemic course, which could not be fully understood by clinical course data and mathematical models. fully understanding in order to be able to forecast the course of the covid- epidemic can be treated as elucidating the "exposome" (i.e., the totality of all exposures, originally in the context of environmental exposures and chronic diseases) of the covid- epidemic, which requires a systematic framework and a combination of advanced data and methods (bradley et al., ) . the next-generation national disease surveillance and reporting system would link a wide array of data sources together, including multiscale human movement data, to enable the construction of the epidemic course (jia & yang, b) . spatial lifecourse epidemiology is an emerging discipline that stems from chronic disease research fields for tackling the "exposome" (jia, ) and has been prospectively adapted to infectious disease and epidemic research areas to characterize the epidemiologic triad at every moment as a snapshot over a lifecourse process . a family of spatial, location-aware, big data, citizen science (i.e., crowdsourcing), and artificial intelligence tools can implement multifactorial, dynamic monitoring of one's exposure over the life course in a high dimension and resolution (jia & yang, c) . for example, remote sensing at different heights could continuously measure daily environmental conditions that may affect human behaviors and support the survival of viruses; smartphone-based applications or other location-aware services with the embedded global positioning systems could capture human movement within a day; place-specific risk can be reported by citizens through crowdsourcing users, so the risk at the next moment could be predicted by machine learning algorithms on the basis of real-time spatial data. therefore, the advanced spatial and digital technologies provide a new perspective to understand the course of epidemics, especially pandemics, and a new toolkit to predict the course of future epidemics. the risk at each moment could be predicted by the accumulated risk, exposure, infections, interventions, and responses to interventions occurring in the spatial world. transparent, anonymous reporting of travel and contact history of a relatively large number of covid- cases has been realized in china for the first time in the history of pandemics, thus opening a new avenue in the era of big data for more advanced, transdisciplinary approaches to refine results from mathematical prediction models and achieve a data-driven epidemic course of the covid- in china (kummitha, ) . however, again, the covid- pandemic is still ongoing. the worldwide spatial data are needed to be shared in a collaborative, secure way for weaving a spatial life course of the covid- across the globe, which holds unprecedented potential to further convert the current retrospective analyses into prospective forecasting. although such cross-disciplinary data sharing has been locally realized when responding to the covid- epidemic, many of them are just temporary solutions that could not be adopted for early warning. to improve pandemic response and prediction, both national and international legislation are needed to facilitate the integration of relevant policies of data sharing and confidentiality protection into the current pandemic preparedness guidelines. third-party (governmental) agencies at national and international levels should also be identified for implementation of these visions, for example, a department of big data management at municipal, provincial, and/or national levels, and the world health organization at the global level. we are now in the data-driven era, also called the fourth paradigm, where established theories are insufficient to fully guide data collection in a rapidly changing context, especially when we are facing increasingly frequent and impactful epidemics (bedford et al., ) . instead, data should be used to enrich and calibrate theories. scientific discovery is becoming increasingly impossible without the support of intensive data. it would not be sufficient and timely to arbitrarily define the periods of the epidemic on the basis of what we have observed. big data should be integrated and speak for themselves, informing us how the epidemic is transmitting at the present moment, how it will transmit at the next moment, and which interventions would be most cost-effective to curb the epidemic. rather than defining the epidemic course arbitrarily, we should be informed by data and then prepare for the epidemic proactively. a new twenty-first century science for effective epidemic response a systems approach to preventing and responding to covid- . eclinicalmedicine, spatial lifecourse epidemiology. the lancet planetary health spatial lifecourse epidemiology and infectious disease research time to spatialise epidemiology in china. the lancet global health china needs a national intelligent syndromic surveillance system are we ready for a new era of high-impact and high-frequency epidemics? smart technologies for fighting pandemics: the techno-and human-driven approaches in controlling the virus transmission defining the epidemiology of covid- -studies needed quarantine alone or in combination with other public health measures to control covid- : a rapid review forecasting covid- onset risk and evaluating spatiotemporal variations of the lockdown effect in china modifiable temporal unit problem (mtup) and its effect on space-time cluster detection sars from east to west i thank the international institute of spatial lifecourse epidemiology (isle) for the research support. the author declares no conflict of interest relevant to this study. all data are available from the cited references. no more data are used in this policy article. key: cord- -o hx i authors: carvajal, ana; argüello, héctor; martínez-lobo, f. javier; costillas, sara; miranda, rubén; g. de nova, pedro j.; rubio, pedro title: porcine epidemic diarrhoea: new insights into an old disease date: - - journal: porcine health manag doi: . /s - - - sha: doc_id: cord_uid: o hx i porcine epidemic diarrhea (ped) is an enteric disease in swine caused by an alphacoronavirus. it affects swine of all ages causing acute diarrhoea and can lead to severe dehydration and death in suckling piglets. being recognized for the first time in europe and asia during the seventies and the eighties, respectively, it has remained a relevant cause of diarrhea outbreaks in asia for years and to the present. it has become a major concern in swine production since when the virus was detected for first time in the usa and in other american countries causing a high number of pig deaths and significant economic losses. the present review aims at approaching the reader to the state of the art of ped giving answer to some of the most recent questions which have arisen related to this disease. porcine epidemic diarrhoea (ped) is a highly contagious infectious disease caused by a coronavirus, porcine epidemic diarrhoea virus (pedv). it causes acute and watery diarrhoea in pigs of all ages although the most severe signs are reported in piglets less than two weeks old, in which diarrhoea leads to severe dehydration and is associated with mortalities which can reach up to % in affected litters. the first clinical description of ped occurred in the uk and belgium in the early seventies. however, it was not until when the etiological agent of these diarrhoeal outbreaks, a new coronavirus, was identified [ , ] . soon afterwards, studies by the research group led by professor pensaert in ghent, belgium, demonstrated that there were no specific antibodies against pedv in sera collected from sows prior to , confirming that pedv was a new virus in the european swine population. up to now, there is no information available on the potential origin of this virus. distribution after its first description in uk and belgium, pedv spread throughout european countries causing diarrhoeal outbreaks in a relevant number of pig herds [ ] [ ] [ ] . pedv or specific antibodies against pedv were reported in several european countries (belgium, the uk, the netherlands, germany, hungary, bulgaria, france, switzerland and spain) in the seventies and the eighties [ ] [ ] [ ] . mortality in piglets less than two weeks old varied from to %, but it was usually lower than that described in outbreaks of diarrhoea caused by transmissible gastroenteritis virus (tgev) which is another porcine coronavirus classically recognized as a cause of diarrhoea disease in swine. however, for unknown reasons, ped outbreaks markedly decreased in the nineties and in subsequent years in europe. isolated outbreaks associated with low mortality in piglets were reported in some countries, i.e. spain [ ] , hungary [ ] , the uk [ ] or the czech republic [ , ] . the only well-documented ped epidemic over the last years in europe occurred during the winter of - in northern italy. on average, pre-weaning mortality raised from . to . %, peaking at . % in one particular farm [ ] . recent ped outbreaks have been reported in germany [ ] [ ] [ ] , italy [ , ] , the netherlands [ ] , belgium [ ] , france [ ] , the ukraine [ ] and other european countries (unpublished data). in contrast to the situation in europe, pedv has remained as a major cause of diarrhoea outbreaks on swine farms in asia for over years. viral-like diarrhoea outbreaks were reported on pig farms in shanghai, china in and despite the fact that tgev and other known enteropathogenic agents were ruled out, the aetiology could not be determined. pedv was firstly demonstrated in the area in in china [ ] and japan [ ] . in the nineties the virus spread to neighbouring countries such as korea [ ] , the philippines and thailand [ ] . later on, it was reported in taiwan in [ ] and vietnam in [ ] . due to its relevance in this area, attenuated or killed vaccines, which confer partial protection against pedv, have been used in several asian countries. these vaccines have been used in china since and also introduced in japan in , south korea in and the philippines in [ ] . it is relevant to point out that in october , a large-scale and severe ped outbreak was reported in several provinces in southern china and spread to other provinces within this country as well as to other neighbouring countries [ , ] . the outbreak caused high mortality among suckling piglets, between and % and given the fact that china was clearly not a naïve country regarding pedv infection, it was proposed that probably a new variant of pedv with a higher virulence was circulating. recently, in april , pedv was identified for the first time in the usa, on pig farms located in ohio [ ] . the virus spread quickly within the country and year after the first description, the number of ped affected farms exceeded spreading to over states. in addition, the virus spread to other countries in north, central and south america and ped outbreaks were reported for the first time on pig farms in mexico (july ), peru (october ), the dominican republic (november ), canada (january ), colombia (march ) and ecuador (july ) [ ] . based on genomic analysis, the coronaviridae family has been recently divided into four genera: alphacoronavirus, betacoronavirus, gammacoronavirus and deltacoronavirus [ ] . pedv is a member of the genus alphacoronavirus together with other coronaviruses which infect pigs (tgev and its respiratory variant, porcine respiratory coronavirus or prcv), dogs (canine coronavirus), cats (feline infectious peritonitis virus), humans (human coronavirus e or human coronavirus nl- ) or bats. there are also other swine coronaviruses (table ) . porcine hemagglutinating encephalomyelitis virus (phev) is a betacoronavirus which causes an infection associated with chronic emaciation and death in young pigs (vomiting and wasting disease) while porcine deltacoronavirus (pdcov), a member of the genus deltacoronavirus, has recently been identified as the etiological agent of an enteric disease similar to ped or tge [ ] . coronaviruses are enveloped viruses which possess a positive-sense single-stranded rna genome. they are morphologically characterized by the presence of projections or peplomers on their surface. like other members of the alphacoronavirus genus, pedv possesses four structural proteins: three membrane proteins identified as s protein or spike protein, m protein or membrane protein and e protein (previously sm or small membrane protein) and a nucleocapsid protein or n protein which encapsidates viral rna. s protein is particularly relevant among the structural proteins. it is a glycoprotein which induces neutralizing antibodies and interacts with cell receptor in the host. there are also three nonstructural proteins: two of them are encoded in open reading frames (orf) a and b and are involved in genome replication and transcription while the third, encoded in orf , has been reported to be an ionchannel protein [ ] [ ] [ ] . antigenic relationships in pedv and other coronavirus have been researched into [ ] . although some crossreactivity between pedv and tgev associated with one epitope on the n-terminal region of n protein was recently reported, pig tgev antisera do not neutralized pedv and vice versa. no cross-reactivity has been reported between pedv and any other coronavirus of the beta, gamma or delta genera. direct and indirect pedv transmission occurs mainly by faecal-oral route. viral shedding in faeces starts on postinfection day one or two and continues for a period of to days [ , ] , although it can extend up to weeks in some animals [ , ] . the transmission of the infection is facilitated by the high viral load in faeces from infected animals [ , ] as well as by the minimum infectious dose required to infect naïve pigs [ ] . moreover, the resistance of the virus in the environment facilitates the faecal-oral transmission. pedv is stable under low temperatures, while it is adversely affected by high temperatures. it survives between ph . - . at °c while only between ph . - . at °c. it can survive for at least days in slurry at °c, days in contaminated dry feed at °c or days in contaminated wet feed at °c [ ] . this fact favours the indirect transmission by different faeces-contaminated fomites such as transport vehicles [ ] , feed [ ] , clothing or footwear. genetic and phylogenetic analyses of american pedv isolates revealed a close relationship with chinese isolates and their likely chinese origin [ ] . however, how the virus might have travelled from china to the usa is a matter of speculation. the rapid spread of pedv on swine farms in the usa raised questions regarding the possibility of airborne transmission of this infection. although undoubtedly the faecal-oral route is the main source of pedv transmission, it has been suggested [ ] that pedv may travel through the air for short distances on faecal dust particles, at least under certain conditions. however, airborne transmission of pedv has only been shown under experimental conditions and up to now infectious pedv has not been demonstrated in field air samples containing pedv genetic material [ , ] . the role that vectors play in the transmission of pedv has also been investigated. so far, there has been no evidence of pedv replication in non-porcine hosts, including rodents and starlings [ ] [ ] [ ] . however, the potential role of vectors in the mechanic transmission of the virus from one farm to another cannot be ruled out, as has been described for tgev [ ] . using highly sensitive molecular assays the presence of viral rna has been reported in milk samples from infected lactating sows [ , ] as well as in semen samples [ , ] . however, infectious pedv in these samples has not been demonstrated and their contamination with faecal material in the sampling cannot be excluded. moreover, viral rna has been detected in the serum fraction of whole blood samples from infected pigs [ , ] . the role of spray-dried porcine plasma (sdpp), normally used as feed additive, as a potential vehicle of transmission of pedv has been researched into. a number of experimental studies have demonstrated that spray-drying process as well as storage conditions are sufficient to inactivate infectious pedv in sdpp [ , ] . the infectivity of commercial sdpp positive for pedv-rna has also been investigated. a research group from canada managed to reproduce pedv infection in sdpp-inoculated piglets, although they failed to reproduce the infection in animals receiving feed supplemented with the same pedv-positive sdpp [ ] . similarly, neither clinical signs nor pedv rna in faeces or pedv specific antibodies were detected in pigs which were fed a diet containing % sdpp confirmed positive for pedv, in a bioassay experiment conducted by opriessnig et al. [ ] . according to this, there is no experimental evidence of pedv transmission through pcr positive sdpp supplemented feed. this experimental data is corroborated by the fact that despite the use of large amounts of pedv positive sdpp from the usa to feed pigs in brazil or western canada, these areas remained free of pedv infection [ ] . pedv replicates in the cytoplasm of villous enterocytes of the small intestine and causes villous shortening and reduced enzymatic and absorptive capacity in the small intestine causing profuse watery diarrhoea, which lasts about a week [ , , ] . other clinical signs which are frequently associated to pedv infection include vomiting, anorexia and fever. although pigs of all ages are affected, the severity of ped is higher in suckling piglets of less than one week old which may die due to severe dehydration. the slower turnover of enterocytes in neonatal piglets ( - days) compared to three weeks-old piglets ( - days) could explain, at least partially, the higher susceptibility of these young piglets to pedv [ ] . pedv has also been detected in epithelial cells of the colon in both experimentally and naturally infected pigs, although villous atrophy has not been demonstrated in the large intestine [ ] . replication of pedv was classically circumscribed to the intestinal tract [ ] , until a recent research showed pedv replication in alveolar macrophages of day-old-colostrum-free piglets, which were experimentally inoculated with a korean wild-type pedv isolate [ ] . further studies are needed to confirm whether extra-intestinal replication also occurs with other pedv isolates as well as to determine their clinical and epidemiological relevance. two epidemiologic presentations of ped have been described on the farms. (a) epidemic ped outbreaks occur when pedv is introduced into a naïve farm (where most of the animals are pedv seronegative). the disease spreads rapidly affecting pigs of all ages with morbidity approaching %. moreover, pedv can persist and become (b) endemic on the farm affecting post-weaning piglets that have lost their lactogenic immunity as well as newly introduced seronegative gilts. mortality associated with ped outbreaks is highly dependent on the age of the infected animals. mortality can reach up to - % in suckling piglets of less than one week old, while in weaned pigs mortality rates are typically only to % [ , ] . no mortality associated with ped is usually observed among adult pigs. as has already been mentioned, differences in the severity of ped outbreaks have been reported. particularly severe ped outbreaks have been described in asia since and also in the usa. differences in the virulence of pedv isolates have been proposed to explain this variability [ , , ] . from our point of view, this is one of the most relevant questions to face regarding ped nowadays: the reason or reasons which could explain variations in the clinical outcome of an outbreak. although some reports have suggested that they could be associated with differences in the virulence of pedv isolates, exhaustive challenge studies using pig adapted virus (not cell culture adapted isolates) in suckling piglets are needed to elucidate the role of the strain. some insights have been obtained related to the virulence of different strains. in the usa, at least two main variants of pedv have been recently identified using molecular methods. the first one seems to be a highly virulent virus and similar to viruses described in several asian countries after while the second, the s indel variant, has been associated to mild clinical outbreaks [ ] . this s indel variant includes some particular insertions and deletions in the s gene and is also similar to some asian isolates, part of which were recovered before . the classical european reference strain of pedv cv is also an s indel isolate although it is located in a different cluster and well differentiated from american indel isolates ( fig. a and b) . pedv isolates recovered in european countries (germany, italy, belgium, the netherlands and france) in and have been characterized and all of them were found to be indel isolates similar to the variant described in the usa [ ] [ ] [ ] [ ] [ ] [ ] [ ] . most of these recent ped outbreaks in europe occurred in fattening farms and, as expected, no mortality was observed. however, pedv isolates recently recovered in severe outbreaks of pedv in ukraine have shown a genome nucleotide similarity reaching . % with non-indel isolates from the united states and mexico [ ] . so far, this has been the only report of pedv non-indel isolates in europe. apart from differences in the virulence of the pedv strains, many other parameters including management, immune status of the population and herd sanitary status could also explain variations in the clinical outcome of ped outbreaks [ ] . thus, the contribution of co-infections with other viruses, particularly with other enteric viruses such as porcine delta coronavirus (pdcov) or the recently described mammalian orthoreovirus (mrv ) has also been pointed out. both viruses have been detected in faecal samples collected from pedv positive farms in the usa. pdcov has been associated with mild to moderate diarrhoea in experimentally inoculated naïve suckling piglets [ ] while mrv caused severe diarrhoea with % mortality in -day-old piglets [ ] . although the rapid spread of a disease characterized by profuse watery diarrhoea affecting pigs of all ages allows the clinician to suspect that a viral agent is involved in the infection, differential diagnosis to identify pedv at the laboratory would be needed. direct detection of pedv in faecal samples by conventional or real-time pcr, are the most frequent assays used at present [ ] . pcr-assays are generally based on the amplification of fragments within the m, n or s protein genes and are associated with a high sensitivity and specificity. there are also some elisas, which are usually based on the use of monoclonal antibodies against pedv. although their analytical sensitivity is generally lower than pcr assays [ ] , they are useful under field conditions as the amount of virus in faecal samples from diseased animals in epidemic outbreaks of ped is very high. immunohistochemistry (ihc) is also a very useful tool based on the detection of pedv antigens within infected cells in formalin-fixed sections of small intestine. it is less sensitive than molecular diagnostic methods but, in contrast, it allows for the evaluation of tissue lesions [ ] . in order to increase the sensitivity of ihc assays, several sections of the small intestine of affected pigs sacrificed in the acute phase of the infection should be investigated. indirect methods are focused on the detection of antibodies. the detection of pedv specific antibodies is very useful, not for the investigation of diarrhoea outbreaks, but to determine whether an animal or a herd has previously been infected by this virus. taking this approach into account, serology is a good tool for surveillance as it provides useful information regarding viral spread in a region or a country. however, the number of tests for the detection of pedv specific antibodies is limited to elisas, indirect immunofluorescence assays (ifa), immunoperoxidase monolayer assays (ipma) and seroneutralization. most of these tests are in-house assays and information regarding their sensitivity and specificity is usually scarce. in general, the elisa tests have proven to be capable of detecting pedv specific antibodies a little earlier and for longer periods of time than ifa tests [ ] . there is no specific treatment for pedv other than supportive care and symptomatic treatment. mortality occurs in suckling piglets as a result of dehydration which should be corrected using oral electrolyte solutions. in adult pigs, dry feed should be withdrawn for a period of - h and then, carefully reintroduced while water should be kept freely available [ , ] . in order to increase passive immunity to piglets and minimize losses, sows due to farrow in at least weeks can be deliberately exposed to virulent virus by the oral route. a recent study revealed that morbidity was reduced from to % in litters exposed to virulent pedv when their sows were previously exposed to a mild virulent strain (s indel variant) of pedv [ ] . oral administration of chicken egg-yolk or cow colostrum containing pedv immunoglobulins could offer an immunoprophilactic defence [ , ] . the increase in lactogenic immunity is also the aim of pedv vaccines which are used in pregnant sows. attenuated or killed vaccines against pedv have been used in several asian countries for years [ ] . however, it has been suggested that live vaccines can revert to virulence and their use and usefulness under field conditions have been questioned [ , , ] . recently, a pedv subunit vaccine based on the s protein gene of pedv as well as a vaccine with killed virus have been licensed in the usa [ ] , although there are still no studies which prove their efficacy. however, pedv vaccines have never been used in europe as the disease was not of sufficient economic importance in this area. in general, pedv vaccines have been reported to be useful to booster antibody response in animals that have already been infected by pedv. as there are no specific treatments for the control and potential eradication of the disease from the herd, preventive measures which preclude the introduction of the virus or new pedv strains in the area, country or farm are of paramount importance. supported by the detection methods mentioned in the diagnosis, surveillance should be used to certify that trading of swine or related derivatives do not cause the spread of new strains of the virus. lorries used in transport have been highlighted as a relevant source of transmission [ ] and special attention should be paid in the effectiveness of the cleaning and disinfecting protocols to inactivate and remove the virus. at herd level, basic external biosecurity rules such as quarantine of reposition, ban the entrance of unwashed vehicles, strict visitor policies (time interval between visiting two farms, provide footwear and appropriate clothing, showers and so on) should be carried out without exception and internal biosecurity such as controlling the slurry level, carcasses disposal and carcass bin cleaning, movement of the caretakers on the farm and so on could prevent the establishment of an endemic form of the disease. finally, many virucidal disinfectants have been shown to be effective in inactivating pedv. phenol, quaternary ammonium compounds, glutaraldehyde and bleach are examples of such disinfectants. water temperature is a crucial factor and temperatures over °c help to inactivate the virus. proper cleaning and disinfecting of facilities and equipment is crucial to control pedv. the emergence and spread of pedv on us pig farms has aroused growing interest in this coronavirus. the main areas of recent research on this disease have been focused on the molecular characterization of the isolates as well as the sources of infection and means of transmission. despite the fact that relevant knowledge has increased, there are still a number of questions to be answered. on one hand, any difference in virulence among the pedv variants described needs to be clarified. on the other hand, the rapid spread of this virus in the usa has raised concerns about its transmission mechanisms. pedv is mainly spreads by the faecal-oral route either by direct or indirect contact (feed or fomites such as vehicles). other routes or sources for its transmission such as air-transmission, vectors or sdpp have been investigated although their implication has not been clearly demonstrated. the recent ped outbreak in the american continent also shows that more research is needed for the control of the disease, based on the development of useful vaccines and surveillance of the virus, standardising its detection in laboratories with the final goal being the limiting of its spread. the authors declare that they have no competing interests. all the authors helped to draft the manuscript, read and approved the final manuscript. submit your next manuscript to biomed central and take full advantage of: virus-like particles associated with porcine epidemic diarrhoea a new coronavirus-like particle associated with diarrhoea in swine update on porcine epidemic diarrhoea diseases of swine porcine epidemic diarrhoea virus infection: etiology, epidemiology, pathogenesis and immunoprophylaxis evaluation of an elisa for the detection of porcine epidemic diarrhea virus in feces of naturally infected pigs enterotoxigenic escherichia coli, 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experimental infection of pigs of different ages porcine epidemic diarrhea: a review of current epidemiology and available vaccines molecular epidemiology of porcine epidemic diarrhoea virus in china an inactivated vaccine made from a u.s. field isolate of porcine epidemic disease virus is immunogenic in pigs as demonstrated by a dose-titration we gratefully acknowledge the pig farmers and veterinarians, their organisations and the feed companies for their active cooperation in the development of our research. g.f. bayón provided excellent technical assistance. our research on pedv has been funded by the ministerio de agricultura, pesca y alimentación. key: cord- -zl txjqx authors: liu, junhua; singhal, trisha; blessing, lucienne t.m.; wood, kristin l.; lim, kwan hui title: epic m: an epidemics corpus of over million relevant tweets date: - - journal: nan doi: nan sha: doc_id: cord_uid: zl txjqx since the start of covid- , several relevant corpora from various sources are presented in the literature that contain millions of data points. while these corpora are valuable in supporting many analyses on this specific pandemic, researchers require additional benchmark corpora that contain other epidemics to facilitate cross-epidemic pattern recognition and trend analysis tasks. during our other efforts on covid- related work, we discover very little disease related corpora in the literature that are sizable and rich enough to support such cross-epidemic analysis tasks. in this paper, we present epic m, a large-scale epidemic corpus that contains millions micro-blog posts, i.e., tweets crawled from twitter, from year to . epic m contains a subset of . millions tweets related to three general diseases, namely ebola, cholera and swine flu, and another subset of . millions tweets of six global epidemic outbreaks, including h n swine flu, haiti cholera, middle-east respiratory syndrome (mers), west african ebola, yemen cholera and kivu ebola. furthermore, we explore and discuss the properties of the corpus with statistics of key terms and hashtags and trends analysis for each subset. finally, we demonstrate the value and impact that epic m could create through a discussion of multiple use cases of cross-epidemic research topics that attract growing interest in recent years. these use cases span multiple research areas, such as epidemiological modeling, pattern recognition, natural language understanding and economical modeling. the coronavirus disease has spread around the globe since the beginning of the year , affecting around countries and everyone's life. to date, the highly contagious disease has caused over . million confirmed and suspected cases and thousand deaths. in time of crisis caused by epidemics, we realize the necessity of rigorous arrangements, quick responses, credible and updated information during the premature phases of such epidemics [ ] . social media platforms, such as twitter, play an important role in informing the latest epidemic status, via the announcements of public policies in a timely manner. facilitating the posting of over half a billion tweets daily [ ] , twitter emerges as a hub for information exchange among individuals, companies, and governments, especially in time of epidemics where economies are placed in a hibernation mode, and citizens are kept isolated at home. such platforms help tremendously to raise situational awareness and provide actionable information [ ] . recently, numerous covid- related corpora from various sources are presented that contain millions of data points [ , ] . while these corpora are valuable in supporting many analyses on this specific pandemic, researchers require additional benchmark corpora that contain other epidemics to facilitate cross-epidemic pattern recognition and trend analysis tasks. during our other efforts on covid- we conduct several exploratory analyses to study the properties of the corpus, such as word cloud visualization and time series trend analysis. several interesting findings are discovered through these analyses. for instance, we find that a large quantity of topics are related to specific locations; cross-epidemic topics, i.e. one that involves more than one epidemic-related hashtag, appear frequently in several classes; and several hashtags related to non-epidemic events, such as warfare, have relatively high ranks in the list. furthermore, a time-series analysis also suggests that some of the epidemics, i.e. haiti cholera and kivu ebola, show a surge in tweets before the respective start dates of the outbreaks, which signifies the importance of leveraging social media to conduct early signal detection. we also observe that an epidemic outbreak not only leads to rapid discussion of its own, but also triggers exchanges about other diseases. epic m fills the gap in the literature where very little epidemicrelated corpora are either unavailable or not sizable enough to support cross-epidemic analysis tasks. through discussing various potential use cases, we anticipate that epic m brings great value and impact to various fast growing computer science communities, especially in natural language processing, data science and computation social science. we also foresee that epic m is able to contribute partially to cross-disciplinary research topics, such as economic modeling and humanity studies. while epic m includes tweets posted throughout the cause of each outbreak available in the corpora, we expect that epic m may serve as a timeless cross-epidemic benchmark. as of jun in this section, we discuss the existing twitter corpora for several domains, such as covid- , disasters, and others. these corpora attract a large quantity of interests and enable a large amount of research works in their respective domains, which we believe epic m generalizes to a similar level of impact in the epidemic domain. corpora of covid- . recently, the covid- pandemic spread across the globe and generated enormous economical and social impact. throughout the pandemic, numerous related corpora have been released. for instance, chen et al. [ ] released a multi-lingual corpus that consists of million tweets that include tweet ids and their timestamps, across over languages. similarly, banda et al. [ ] presented a large-scale covid- chatter corpus that consists of over m tweets with retweets and another version of million tweets without retweets. english corpora of disasters. there are several disaster-related corpora presented in the literature that are utilized for multiple works. crisislex [ ] consists of thousand tweets that are related to six natural disaster events, queried based on relevant keywords and locations during the crisis periods. the tweets are labelled as relavant or not-relevant through crowdsourcing. olteanu et al. [ ] conducts a comprehensive study of tweets to analyze crisis events from to . the paper analyzes about k tweets based on crisis and content dimensions, which include hazard type (natural or human-induced), temporal development (instantaneous or progressive), and geographic speed (focalized or diffused). the content dimensions are represented by several features such as informativeness, types and sources. imran et al. [ ] releases a collection of over million tweets, out of which thousand come with human-annotated tweets that are related to natural crisis events. the work also presents pre-trained word vec embeddings with a set of out-of-vocabulary (oov) words and their normalizations, contributing in spreading situational awareness and increasing response time for humanitarian efforts during crisis. phillips [ ] releases a set of million tweets related to hurricane harvey. littman [ ] publishes a corpus containing tweet ids of over million tweets related to hurricane irma and harvey. non-english corpora of disasters. numerous non-english crisis corpora are also found in the literature. for instance, cresci et al. [ ] released a corpus of . thousand italian tweets from to during four different disasters. the features include informativeness (damage or, no damage) and relevance (relevant or not relevant). similarly, alharbi and lee [ ] compiled a set of thousand arabic tweets, manually labelled on the relatedness and information-type for four high risk flood events in . alam et al. [ ] released a twitter corpora composed of manually-annotated thousand tweets and thousand images collected during seven natural disasters (earthquakes, hurricanes, wildfires, and floods) that occurred in . the features of the datasets include informativeness, humanitarian categories, and damage severity categories. other twitter corpora. apart from crisis-related corpora, several twitter datasets are used for analysis related to politics, news, abusive behaviour and misinformation, trolls, movie ratings, weather forecasting, etc. for instance, fraisier et al. [ ] proposes a large and complex dataset with over thousand operative twitter profiles during the french presidential campaign with their corresponding tweets, tweet ids, retweets, and mentions. the data was annotated manually based on their political party affiliation, their nature, and gender. we also find twitter corpora that are related to other domains, such as politics [ , ] , cyberbullying [ ] , and misinformation [ , , ] . this section describes the data collection process for crawling epic m. epidemic outbreaks. epic m includes six epidemic outbreaks in the st century, recorded by world health organization table . we intentionally exclude the recent covid- pandemic outbreak to avoid producing redundant work, as there are already numerous covid- datasets released by different parties with multi-million data points. search queries. for each outbreak, we initialize with a large collection of keywords used as the search queries, with the hypothesis to retrieve most relevant tweets from twitter. we use a combination of keywords for each outbreak, as listed on table , to fetch the related tweets. two types of keywords used, namely (a) general disease-related terms, such as ebola, cholera and swine flu; and (b) specific outbreak-related terms with a combination of location and disease, such as africa ebola and yemen cholera. general epidemics. besides the outbreaks set, we extend epic m by including a subset of three general diseases, namely cholera, ebola and swine flu. the tweets related to these diseases are crawled since the respective first occurrence until t h may . we expect the general epidemic subset is able to act as additional benchmarks and contribute substantially to various research topics, such as pattern recognition and trend analysis. to gain a general overview of epic m, we first conduct hashtags analysis for each epidemic and plot them on a by grid, as shown in figure . the first row (fig. a) represents three general diseases whereas the second and third rows (fig. b) represent the six outbreak classes in chronological order. each word cloud contains the top hashtags in their respective class, where the sizes represent their frequencies. through observation, we identify several interesting phenomena, such as: ( ) key terms provide semantic indication of the crises, in addition to possible cross-epidemic indicators: such as pandemic, epidemic, healthcare, vaccine, disease, sanitation, and others; ( ) location-related hashtags, such as #yemen, #haiti and #sierraleone, appear in all classes and occupy majority of the key words, which we believe to be the highest concerned feature; ( ) several classes include hashtags of other diseases, i.e., #covid in the _yemen_cholera class and #malaria in the cholera class, which implies that discussions on cross-epidemic matters are popular; and ( ) some hashtags refer to non-epidemic related events, such as # yearsofwaronyemen and #earthquake appearing in the _yemen_cholera and _haiti_cholera sets respectively. subsequently, we conduct trend analysis with an attempt to identify time-variant patterns from the corpus. for the three general classes (fig. a) , we plot each class into a line chart, where the x-axis represents the time in yearly dates and the y-axis represents the corresponding number of tweets. for the six outbreak classes (fig. b) , the x-axis of each line chart uses the number of days offset from the start date of the outbreak, whereas the y-axis represents the number of tweets normalized to between and . through the time-series line plots, we observe that some of the epidemics, i.e. haiti cholera and kivu ebola, show a surge in tweets before the respective official start dates of the outbreaks, which signifies the importance of leveraging social media to conduct early signal detection. we also observe that an epidemic outbreak not only leads to rapid discussion of its own, but also trigger exchanges of other diseases. finally, the time-series analyses also show clear dynamic properties or trends with exponential increases (shocks or spikes) in tweet type and a temporal persistence after an initial shock [ ] . other dynamic properties that may be of interest include local cycles and trends. such dynamic effects, when paired with semantic content (such as healthcare related terms), may provide potential indicators of an onset of a crisis. according to the world health organization, https://www.who.int while twitter has an enormous volume and frequency of information exchange, i.e. over half a billion tweets posted daily, such rich data potentially exposes information on epidemic events through substantial analysis. in this section, we demonstrate the value and impact that epic m could create by discussing on multiple use cases of cross-epidemic research topics that attract growing interests in recent years. these use cases span multiple research areas, such as epidemiological modeling, pattern recognition, natural language processing and economical modeling. we claim that epic m fills the gap in the literature where very little disease related corpora are sizable and rich enough to support such cross-epidemic analysis tasks. epic m supplies benchmarks of multiple epidemics to facilitate a wide range of cross-epidemic research topics. epidemiological modeling. epidemiological modeling provides various potential applications to understand the twitter dynamics during and post-outbreaks, such as compartmental modeling [ ] and misinformation detection [ ] . to name a few, jin et al. [ ] uses twitter data to detect false rumors and a susceptible-exposedinfected-skeptic (seiz) model to group users in four compartments. skaza and blais [ ] use susceptible-infectious-recovered (sir) epidemic models on twitter' hashtags to compute infectiousness of a trending topic. in the recent event of covid- , these models are repeatedly applied to predict discrete questions, such as chen et al. [ ] 's proposal of using a time-dependent sir model to estimate the total number of infected persons and the outcomes, i.e., recovery or death. trend analysis and pattern recognition. extensive prior works leverage social media data to perform trend analysis and pattern recognition tasks. for instance, kostkova et al. [ ] study the swine-flu outbreak and demonstrates the potential of twitter to act as an early warning system up-to a period of two or three weeks. similarly, joshi et al. [ ] predict alerts of western africa ebola epidemic, three months earlier than the official announcement. while early detection and warning systems for crisis events may reduce overall damage and negative impacts [ ] , epic m provides high volume and timely information that facilitate trend analysis and pattern recognition tasks for epidemic events. sentiment and opinion mining. the observation of social sentiments and public opinions plays an important part in benchmarking the effect of releasing public policy amendments or new initiatives. several prior works leverage sentimental analysis and opinion mining to extract the contextual meaning of social media content. for instance, beigi et al. [ ] provides an overview of the relationship among social media, disaster relief and situational awareness in crisis time, and neppalli et al. [ ] performs locationbased sentimental analysis on tweets for hurricane sandy in . topic detection. topic detection or modeling may enable authorities in anticipating a crisis and taking actions during the same. the technique helps in recognizing hidden patterns, understanding semantic and syntactic relations, annotating, analyzing, organizing, and summarizing the huge collections of textual information. considering the same, several researchers have implemented these approaches on crises datasets to detect and categorize the potential topics. chen et al. [ ] suggest two topic modeling prototypes to ameliorate trends estimation by seizing the underlying states of a user from a sequence of tweets and aggregating them in a geographical area. in [ ] researchers perform optimized topic modeling using community detection methods on three crises datasets [ , , ] to identify the discussion topics. natural language processing. several works leverage twitter datasets to conduct natural language processing (nlp) tasks. as a challenging downstream task of nlp, automatic text summarization techniques extract latent information from text documents where the models generates a brief, precise, and coherent summary from lengthy documents. text summarization is applicable in various real-would activities during crisis, such as generating news headlines, delivering compact instructions for rescue operations and identifying affected locations. prior works demonstrate such applications during crisis time. for instance, rudra et al. [ ] and [ ] propose two relevant methods that classify and summarize tweets fragments to derive situational information. more recently, sharma et al. [ ] proposes a system that produces highly accurate summaries from the twitter content during man-made disasters. several other works focus on nlp subtasks of social media, such as information retrieval [ , ] and text classification [ , ] . disease classification. applications of machine learning and deep learning in the healthcare sector gather growing interests in recent years. for instance, krieck et al. [ ] analyzes the relevance of twitter content for disease surveillance and activities tracking, which help alert health official regarding public health threats. lee et al. [ ] conducts text mining on twitter data and deploys a real-time disease tracking system for flu and cancer using spatial, temporal information. ashok et al. [ ] develops a disease surveillance system to cluster and visualise disease-related tweets. crisis-time economic modeling. estimating economical impact of crises, such as epidemic outbreaks, is a crucial task for policy makers and business leaders to adjust operational strategies [ ] and make right decisions for their organizations in the time of crises. several research studies in such domain. for instance, okuyama [ ] provides an overview and a critical analysis of the methodologies used for estimating the economic impact of disaster; avelino and hewings [ ] proposes the generalized dynamic input-output framework (gdio) to dynamically model higher-order economic impacts of disruptive events. such studies correlate disaster events and economy impact, which rely on disaster-related data and financial market data, respectively. we believe that epic m is able to contribute to future economic modeling studies for epidemic events. health informatics. compared to the cases above, a more general use case area is healthcare informatics , i.e., âĂIJthe integration of healthcare sciences, computer science, information science, and cognitive science to assist in the management of healthcare informa-tionâĂİ [ , , ] . while social media and online sources are used to connect with patients and provide reliable educational content in health informatics, there is growing interest in using twitter and other feeds to study and understand indicators for health trends or particular behaviors or diseases. for example, nambisan et al. [ ] utilize twitter content to study the behavior of depression. epic m contains behavioral information across various diseases and how the populace behaves with the onset and persistence of the diseases. multiple disease cases will provide such research to correlate behavioral information across instances. news and fake news. with the proliferation of news content through internet and virtual media, there is a growing interest in developing an understanding of the science of news and fake news [ ] . data mining algorithms are advancing to study news content [ ] . epic m contains real news content that grows over time from social lay-person terminology to technical and professionally based information and opinion. it likewise includes fact-based information as well as distorted or fake content. through multiple cases over time, the field will have a rich source to study news content, especially when correlating with reliable news sources for particular snapshots of time. all in all, we believe that epic m provides a set of rich benchmarks and is able to facilitate extensions of the above-mentioned works on a higher order, e.g., in cross-epidemic settings. as a result, the research findings are more robust and closer to real-world scenarios. conclusion. during our other efforts on covid- related work, we discovered very little disease related corpora in the literature that are sizable and rich enough to support such cross-epidemic analysis tasks. in this paper, we present epic m, a large-scale epidemic corpus that contains . millions tweets from to . the corpus includes a subset of tweets related to three ( ) general diseases and another subset related to six ( ) epidemic outbreaks. we conduct exploratory analysis to study the properties of the corpus and identify several phenomena, such as strong correlation between epidemics and locations, frequent cross-epidemic topics, and surge of discussion before occurrence of the outbreaks. finally, we discuss a wide range of use cases that epic m can potentially facilitate. we anticipate that epic m brings substantial value and impact to both fast growing computer science communities, such as natural language processing, data science and computation social science, and multi-disciplinary areas, such as economic modeling, health informatics and the science of news and fake news. future work. for some epidemic outbreaks, such as h n swine flu and west africa ebola, epic m includes relevant tweets posted throughout the respective duration of the epidemics. we expect the data of these few classes could serve as strong and timeless cross-epidemic and cross-disease benchmarks. on the other hand, several epidemics, such as kivu ebola and yemen cholera, are still ongoing. we intend to extend the corpus by actively or periodically crawling tweets in addition to the current version. furthermore, we plan to further develop the corpus with additional epidemic outbreak classes that happened more recently, such as the multi-national measles outbreaks in the dr congo, new zealand, philippines and malaysia, the dengue fever epidemic in asia-pacific and latin america, and the kerala nipah virus outbreak. lastly, we also intend to develop an active crawling web service that automatically update epic m, and migrate to cloudbased relational database services to ensure its availability and accessibility. the corpus is available at https://www.github.com/junhua/epic. this research is funded in part by the singapore university of technology and design under grant srg-istd- - . crisismmd: multimodal twitter datasets from natural disasters crisis detection from arabic tweets compartmental modeling and tracer kinetics a machine learning approach for disease surveillance and visualization using twitter data the challenge of estimating the impact of disasters: many approaches, many limitations and a compromise system and method for integrated learning and understanding of healthcare informatics yuning ding, and gerardo chowell. . a large-scale covid- twitter chatter dataset for open scientific research-an international collaboration an overview of sentiment analysis in social media and its applications in disaster relief analyzing discourse communities with distributional semantic models computer-aided mind map generation via crowdsourcing and machine learning covid- : the first public coronavirus twitter dataset syndromic surveillance of flu on twitter using weakly supervised temporal topic models. data mining and knowledge discovery a linguistically-driven approach to cross-event damage assessment of natural disasters from social media messages large scale crowdsourcing and characterization of twitter abusive behavior # Élysée fr: the french presidential campaign on twitter time series analysis the hoaxy misinformation and fact-checking diffusion network aidr: artificial intelligence for disaster response extracting information nuggets from disaster-related messages in social media twitter as a lifeline: human-annotated twitter corpora for nlp of crisis-related messages epidemiological modeling of news and rumors on twitter automated monitoring of tweets for early detection of the ebola epidemic # swineflu: the use of twitter as an early warning and risk communication tool in the swine flu pandemic a new age of public health: identifying disease outbreaks by analyzing tweets the science of fake news real-time disease surveillance using twitter data: demonstration on flu and cancer clustop: a clustering-based topic modelling algorithm for twitter using word networks hurricanes harvey and irma tweet ids self-evolving adaptive learning for personalized education ipod: an industrial and professional occupations dataset and its applications to occupational data mining and analysis crisisbert: a robust transformer for crisis classification and contextual crisis embedding strategic and crowd-aware itinerary recommendation understanding the perception of covid- policies by mining a multilanguage twitter dataset essentials of nursing informatics social media, big data, and public health informatics: ruminating behavior of depression revealed through twitter sentiment analysis during hurricane sandy in emergency response critical review of methodologies on disaster impact estimation crisislex: a lexicon for collecting and filtering microblogged communications in crises what to expect when the unexpected happens: social media communications across crises managing epidemics: key facts about major deadly diseases. world health organization automatic classification of disaster-related tweets why weâĂŹre sharing million russian troll tweets. fivethirtyeight summarizing situational tweets in crisis scenario extracting situational information from microblogs during disaster events: a classification-summarization approach going beyond content richness: verified information aware summarization of crisis-related microblogs fake news detection on social media: a data mining perspective mobile healthcare informatics. medical informatics and the internet in medicine modeling the infectiousness of twitter hashtags u.s. congressional election tweet ids mining misinformation in social media analysing how people orient to and spread rumours in social media by looking at conversational threads key: cord- -segffkbn authors: bonamassa, ivan; strinati, marcello calvanese; chan, adrian; gotesdyner, ouriel; gross, bnaya; havlin, shlomo; leo, mario title: geometric characterization of sars-cov- pandemic events date: - - journal: nan doi: nan sha: doc_id: cord_uid: segffkbn while the sars-cov- keeps spreading world-wide, comparing its evolution across different nations is a timely challenge of both theoretical and practical importance. the large variety of dissimilar and country-dependent epidemiological factors, in fact, makes extremely difficult to understand their influence on the epidemic trends within a unique and coherent framework. we present a geometric framework to characterize, in an integrated and low-dimensional fashion, the epidemic plume-like trajectories traced by the infection rate, $i$, and the fatality rate, $d$, in the $(i,d)$ plane. our analysis enables the definition of an epidemiometric system based on three geometric observables rating the sars-cov- pandemic events via scales analogous to those for the magnitude and the intensity of seismic events. being exquisitely geometric, our framework can be applied to classify other epidemic data and secondary waves, raising the possibility of designing epidemic alerts or early warning systems to enhance public and governmental responses to a rapidly emerging outbreak. the unprecedented amount of epidemic data collected worldwide on sars-cov- raises nowadays a unique opportunity to quantify, in a way analogous to other extreme events [ , ] , the catastrophic impact that a pandemic can have on the globalized world [ , ] . in the context of earthquakes, for example, the existence of the richter [ ] and mercalli [ ] measures, quantifying respectively the magnitude and the intensity of a local seismic event, has helped policy-makers to take informed decisions yielding better intervention strategies (e.g. by means of tsunami alerts or rapid post-earthquakes notifications [ ] [ ] [ ] [ ] ) and strong governmental actions (e.g. investments in anti-seismic infrastructures [ , ] ) to prevent their potential impact. similarly, in meteorology, the fujita [ ] and the saffir-simpson [ , ] scales have offered researchers with heuristic measures to estimate the potential damage inflicted by, respectively, tornados and hurricanes on human-build structures and vegetation, raising the opportunity of designing everincreasingly refined early warning systems and alert protocols [ ] [ ] [ ] . in the realm of pandemics, however, metric systems enabling a comprehensive classification of their types have (to the best of our knowledge) never been proposed, resulting in a fundamental gap in the human fight against this type of catastrophic events. the theoretical and practical implications of this important and timely challenge are numerous. disposing of a robust and comprehensive framework to classify the sars-cov- pandemic events reported across different countries not only can enhance early [ , ] public and governmental responses in containing the spreading and/or better absorbing the impact of a rapidly emerging epidemic outbreak, but it can further provide new information to better understand real-world epidemics and to boost the forecasting power of existing models [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] . * ivan.bms. @gmail.com a fundamental difficulty to achieve this goal relies in the large heterogeneity of epidemiological and countrydependent factors characterizing the global pandemic trends. diverse isolation [ ] and social distancing strategies [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] , age, gender impact [ , ] and demographic characteristics of different populations [ ] , local transportation systems [ ] [ ] [ ] [ ] [ ] , tracking and testing policies [ , ] , health systems' capacities [ ] and many other factors, make difficult the design of quantitative epidemiometric systems for country-to-country comparison [ ] [ ] [ ] . moreover, epidemic models or inference algorithms fine-tuned to this constellation of features, inevitably result into theoretical or semi-empirical frameworks whose complexity rapidly increases with the large number of data-driven parameters considered [ , [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] . in this work, we present a geometric, low-dimensional method to classify the impact the sars-cov- pandemic events observed across different nations. after performing a statistical best-fit of the epidemic data for the infected, i, and deceased, d, rates, we analyze the geometry of their plume-like trajectories in the (i, d) plane. moving to a polar representation, we classify the plumes' form through a set of three geometric parameters yielding two complementary rating scales for the sars-cov- pandemic types: one according to their epidemic magnitude-labeled with roman numbers from i to x for increasing strengths-and measuring the "size" of a national outbreak, and a second one according to their intensity-labeled alphabetically from a to d for increasing speed-quantifying instead the damage inflicted on the population. even though each country exhibits its own pandemic fingerprint, our geometric method unveils hidden similarities shared by their global trends emerging from an integrated representation of their evolution. we further provide a qualitative understanding of the epidemiological information contained in the developed epidemic measures, and discuss the theoretical and practical implications of our results. . comparing the pandemic trends. to set the stage arxiv: . v [physics.soc-ph] jul for a cross-comparison of the countries' pandemic trends, let us consider two widely reported epidemiological observables, i.e. the infected (i) and the fatality (d) daily rates. these quantities can vary strongly from one country to another, depending on a wide variety of factors. even within the same country, the numbers may fluctuate from one day to another due to delays in reporting, transitions to new surveillance and/or tasting systems, or simply because of weekly periodic variations in the number of daily tests performed. smoothening the data under a suitable moving average window unveils the trends of the time series, enabling a preliminary comparison. as a demonstrative example, let us consider the pandemic trends reported in italy and in germany (fig. ) . in both countries, it took approximately weeks for the outbreaks to reach their infection peaks, with similar fast-rising trends and comparable numbers of newly infected patients per day. their post-peak behaviors, however, differ noticeably: whereas germany's infection curve has decayed almost as quickly as it rose, resulting in a reduction by % of the daily infected in nearly days, it has taken almost double this time to italy to reach similar conditions. this is nicely reflected in the values of the skewnesses calculated after best-fitting the data with asymmetric gaussians (fig. , legend) , showing a decay of the italian trend roughly . times slower than the one observed in germany. slow infection rate decays similar to those reported in italy have also been observed in the united states, the united kingdom or russia and can be explained as the result of new regional outbreaks spreading throughout the country after the national lockdown, hinting at a difficulty in identifying/containing the virus since its early stages. additional information can be found by performing a similar analysis of the fatality rates. this quickly reveals that italy had to face much yellow and red arrows point respectively at the infected and fatality rate peaks, while the markers evolve on a daily rate. we calculate the largest radius, rmax ≡ ao, its inclination, θ, and the largest width, r ⊥ ≡ bc, of the plumelike trajectory traced by the epidemic evolution. these quantities define the triple (rmax, θ, ρ), with ρ ≡ r ⊥ /rmax, used to analyze classify events as described in the text. more critical conditions, counting (on average) at least times more fatalities per day than germany, with a death peak located only days after the infected one (by contrast with the weeks lag reported in germany) and a skewness roughly twice the one measured based on the german data ( fig. , legend) . by looking at these differences separately, one can heuristically conclude that both countries have experienced outbreaks with similar magnitudes though causing very different damages on the population, with germany applying a more efficient policy of containment and/or testing and with italy reaching very critical level in its health system. to extend the comparison to other countries, it proves essential to identify a suitable metric system grasping and systematically quantifying the relevant information (e.g. peak values, infected-fatality peaks lags, post-peak decay rates, etc.) enshrined in the evolution profiles of the i and d trajectories. in the spirit of dynamical systems theory [ ] , we approach this problem by departing from the representation of the dynamical observables i(t) and d(t) as functions of time, focusing instead on their mutual evolution in the (i, d) plane (fig. ) . in this way, a comprehensive portrait of the outbreak dynamics of each country can be described by an integrated plumelike trajectory (fig. ) whose geometric features, as we shall see in what below, provide an exhaustive and lowdimensional classification of the sars-cov- pandemic types according to their magnitude and intensity. . geometric parametrization. in the (i, d) plane, the daily epidemic state of each country traces a trajectory that, after departing from the healthy phase ( , ), leaves behind its own epidemic fingerprint. for reasons that will be clarified below, let us call "typical" an epidemic trajectory analogous to the one depicted in fig [ ] . countries in the scatter plot are then selected according to shells (dashed circles) of increasing radiuses, identifying six heuristic regimes, ranging from a) the ideal scenario of slow outbreaks with good tracking intervention and low fatality rates, to f ) extreme cases representing very fast outbreaks with high case-fatality rates and critical conditions of their health systems. a)-f ) sampled trajectories belonging to each heuristic group exhibit epidemic angles (notice the different extend of the y-axes) whose similarities can be better highlighted by normalizing the epidemic data of each group via the largest rmax of the country in the collection. the normalization factors are respectively: a) rmax(il) . × , b) rmax(ge) × , c) rmax(u s) × , d) rmax(sp ) × , e) rmax(u k) . × , f ) rmax(f r) ∼ . × . and characterized by a dynamics that unfolds counterclockwise in the plane, reaching first the infected peak, then the fatality peak, and finally heads back towards the axes origin. notice that during this heading back regime, new outbreaks could emerge due to e.g. premature lifting of the lockdown measures, pushing the epidemic state to trace a different plume-like trajectory (fig. a ) describing a new epidemic event. here, we focus our analysis on the epidemic data reported during the first-wave events in countries that have passed both their infected and fatality rate peaks. in the discussion section we will see how our geometric method can be naturally extended to analyze second-wave events like those observed in united states, iran or israel (see fig. b ). to quantitatively compare the countries' typical epidemic trajectories, we introduce three geometric parame-ters, (r max , θ, ρ), that we measure after transforming the epidemic observables i, d into polar coordinates. we define with r max the maximal radius of the epidemic trajectory, with θ the angle formed by r max with respect to the i-axes, and finally with ρ = r ⊥ /r max the relative width of the plume-like curve, where r ⊥ is its maximal width (fig. ) . while r max measures the largest extent of the epidemic plume-and has therefore units of population-the quantities θ and ρ have a genuine geometric nature and disclose different information about the intensity of an epidemic event. large values of θ, in fact, reflect a fast raise of the number of fatalities jointly with a rapid increase of the newly infected, which would occur in cases of a critical health system but also reflect the country's demographic features, like age and morbidity distributions, social interactions, etc. in this respect, we adopt θ as an estimator of the epidemic "speed", with large (small) angles describing fast (slow) outbreaks. the parameter ρ, on the other hand, can be written in terms of the "eccentricity", e, of the epidemic trajectory as ρ = √ − e [ ] , so that decreasing values of ρ characterize narrower plumes. this would naturally reflect situations of rapid patient identification, resulting in lower critical conditions of the country's hospitals and hence to less fatalities, i.e. lower values of the angle θ. the results in fig. support this heuristic interpretation, disclosing a linear relation between the two geometric observables θ and ρ. in light of the latter, we have selected countries according to their euclidean distance from the origin of the (θ, ρ) scatter plot, yielding a preliminary partitioning of their outbreaks according to their speed, as shown in fig. a)-f ). besides highlighting similar inclination of the epidemic trajectories, the normalization by r max adopted in fig. a)-f ) further discloses an additional degree of similarity between countries based on the time lag separating infected and fatality rate peaks. countries with low angles like e.g. germany, austria or norway ( fig. b ) feature, in fact, round plumes with well separated peaks as well as more narrow forms like those reported in e.g. israel (fig. a) , greece or finland (fig. c) . on the contrary, countries with large epidemic angles always correspond to narrow plumes with strong peak-to-peak proximity, as observed e.g. in italy (fig. d) , hungary (fig. e) or belgium (fig. f ). as we shall see in the next section, the eccentricity of the normalized epidemic plumes nicely grasps this important information, enabling to define a simple yet informative metric system characterizing the intensity of the sars-cov- types. before delving into the details of this classification, let us complete the picture by considering those epidemic plumes which have not been included in the analysis due to their non-typical evolution in the (i, d) plane. this includes epidemic data describing first-wave events whose fatality rate peak has preceded the infected one, as ob- served e.g. in brazil, mexico, united arab emirates, iran ( fig. ) and few others. such peak inversion translates into a clockwise evolution of the epidemic trajectory in the (i, d) plane, whose geometric features could, in principle, be analyzed according to our developed method but should not be similarly interpreted. fatality-rate peaks preceding the infected ones can be, in fact, only explained as the result of sparse and incomplete reporting due to e.g. limited resources at early stages of diagnostics or absence of post-mortem identification. for the sake of simplicity, in what follows we will focus only on the analysis of typical epidemic trajectories, while the classification of non-typical cases will be performed elsewhere. having introduced a geometric parametrization of the countries typical epidemic trajectories, let us now focus on defining a suitable and conventional metric system to systematically quantify their magnitude and intensity. outbreak magnitude. as we anticipated, the parameter r max yields an integrated measure in the (i, d) plane of the largest extent of an epidemic trajectory in units of population, offering the opportunity to analyze the dependence of the epidemic extent on the population size, p , of the country where it spread. by plotting the distribution of r max as a function of p (fig. ), we find an approximate power law r max = ap β , with a ∈ ( , ) a country-dependent proportionality factor and β an exponent close to one. the nearly linear relation can be explained by interpreting a as the largest fraction of daily infected and deceased reported for a given population size, suggesting a rudimentary yet informative scale to meaningfully quantify the epidemic magnitude of each country. to this aim, let us introduce the dimensionless parameter x = log r max / log p . because r max and p are linearly proportional, this relation reads as where p > , so that x ∈ (−∞, ) is a monotonically increasing function of the proportionality factor a ∈ ( , ). this fraction is bounded by two extreme cases: a → describing an extremely weak (nearly absent) outbreak with only few infected/deceased daily cases, and a → representing instead the unlikely event of a nearly full population infected/deceased in a single day. similar to the richter metric system for local seismic events, an epidemic magnitude scale can be conventionally defined by choosing a suitable, monotonically increasing function of x in eq. ( ), where x can be interpreted as the "epidemic force" of an outbreak, measuring the largest fraction of new infected and deceased reported in a single day. let us therefore define the epidemic magnitude as ), we introduce an epidemiometric system classifying epidemic events by increasing magnitudes that is described as follows: i) t ∈ [ . , . ], micro events: very weak outbreaks having strengths x < or, equivalently, r max < , i.e. an average of less than infected case per day; ii) t ∈ [ . , . ], minor events: weak outbreaks with non-negative strengths corresponding to values of r max ∈ [ , ) for small countries with p ∼ , and r max ∈ [ , ) for large countries with p ∼ ; iii) t ∈ [ . , . ], light events: epidemics featuring e.g. values of r max ∈ [ , ) if p ∼ , and r max ∈ [ , ) for large countries with p ∼ ; ix) t ≥ . , extreme epidemic events featuring e.g. values of r max ≥ for p ∼ , and r max > . × for p ∼ , i.e. outbreaks whose daily percentages of infected/deceased reach peaks respectively larger than . % and . % of the total population. similarly to the richter scale for seismic events, our epidemic magnitude scale t characterizes the local (since it depends on the population size) strength of an epidemic in an exponential fashion, so that each jump by class identifies a tenfold increase in daily reported infected/deceased among countries with similar population sizes. when applied to the available data of the sars-cov- pandemic, t yields the repartition of the epidemic events summarized in tab. i, with respect to which we filled the data points in fig. with colors ranging from dark blue to dark red for increasing magnitudes. a primary observation is that all the countries of our dataset have experienced epidemic events of magnitude equal or larger than iii [ ] , reflecting the severe and broad impact that the sars-cov- pandemic has had worldwide. we notice also that the different responses that countries with similar population sizes (e.g., p ∼ ) have had to the pandemic spread is nicely captured by t , with e.g. classification of the sars-cov- first-wave epidemic events according to their magnitude, t = x /x * , where x * ≡ − / log p represents an upper limit to the epidemic "strength" characterizing an outbreak of catastrophic proportions (see eq. ( ) and discussions therein). nations' intervention efficiency, rated with plus and minus signs, is measured according to the deviation of all countries best linear fit d = r + log(p β /r dat max ) from the ordinate r dat max of each data point (see the main text for more details). cases like greece or hungary both experiencing light outbreaks, and cases like israel or switzerland facing instead moderate to strong events (see tab. i). very strong pandemic events can be instead recognized by the orange colors in countries like italy, france or germany, and even more extreme ones by increasingly red colors describing the cases of the united states (magnitude . ) and spain (magnitude . ). surprisingly, we find that the first-wave epidemic event in spain features in fact a larger magnitude than the one reported in the united states. the linear regression analysis in fig. provides with additional information the classification by magnitude of the sars-cov- pandemic types. unlike other catastrophic events, in fact, epidemic outbreaks can be influenced at their early stages by social intervention strategies [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] , and so do their magnitude scales. while t measures the impact of the pandemic across different countries, the deviation of all countries best linear fit d = log(r max /r dat max ) from the ordinate r dat max of each data point can be adopted to rate the effectiveness of the intervention strategies adopted. values of d for the available data and reported in tab. i, are typically dispersed in the unit interval (dashed green and red lines in fig. ) around zero, suggesting the following rating system for the social intervention strategies adopted: + + +) for d ≥ as reported in countries that, despite their population size, managed to contain the outbreak very efficiently; ++) if . ≤ d ≤ . and +) if ≤ d < . for countries with efficient to good intervention; −) if − . ≤ d < and −−) if − ≤ d < − . describing instead weak or not prompt responses to the emergent outbreaks. we find (see fig. ) that highly populated countries like china or japan applied successful social intervention protocols which kept low the magnitude of the epidemic events, while other countries like ireland, belgium or spain gained less efficient results, experiencing outbreaks of larger magnitudes. outbreak intensity. in the previous section we adopted the epidemic angle θ (defined by the inclination of r max with respect to the i-axes) as an estimator of the "speed" of an epidemic event, with large values of θ reflecting highly critical conditions of the country's health system. we have also shown that θ is linearly correlated (fig. ) to the geometric parameter ρ, measuring instead the relative width of the epidemic plumes, whose values can be adopted to evaluate the quality of a country's strategies for contact tracing or patient identification. the normalization of the trajectories by r max shown in fig. a )-f ), has highlighted that a further informative quantification of the country's tracking strategies can be obtained by considering the "eccentricity", e = − ρ , of the normalized epidemic plumes. on the one hand, this operation removes all the information about the relative extend of the infected and fatality rates and hence it wipes out the classification of the epidemic events according to the angle θ. on the other hand, analyzing the eccentricity of the normalized epidemic plumes yields a more faithful comparison among their forms, clearly isolating . these categories appear to correspond to epidemic plumes with large eccentricities (class ) and small peakto-peak separation, reflecting late identification of infected patients or selection of diagnostic testing only for critically ill cases. slow pandemics (i.e. category a), on another hand, disclose a broader spectrum of forms (classes , , , ) reflecting different strategies of patient identification. narrow plumes from rounder ones. to make the best out of this trade-off of information, we have created the hybrid scatter-plot (θ, e) shown in fig. , where countries' sars-cov- events are classified according to the angle of their row epidemic data (just as in fig. ) and the eccentricity of their normalized plumes. when applied to the available data, this hybrid representation unveils something surprising. we find, in fact, that epidemic angles larger than a threshold value θ * ≡ . always correspond to narrow plumes with normalized eccentricities e ∈ ( . , ). instead, plumes with θ < θ * can correspond to a broader spectrum of forms, from the round ones reported in japan, austria or germany, to more narrow types like those of canada, portugal or turkey. to explain this surprising pattern, let us notice that the main factor decreasing the eccentricity of a normalized epidemic plume is an increasing time lag between the infected and fatality rate peaks which, in its turn, suggests that the data of reported infected and deceased are less likely correlated. the eccentricity can then be adopted for comparing the countries' strategies for patient identification, with small values of e characterizing efficient tracking protocols, and large values of e describing instead situations where the majority of the fatalities were infected patients tested positive only after arriving at the hospitals in critical conditions. this is probably best represented in fig. by cases like the united kingdom (e . ), italy (e . ) or the netherlands (e . ) which all experienced violent outbreaks with identification only of critically ill patients [ ] and highly critical conditions (θ > θ * ) of their medical system [ ] . fig. suggests therefore the following data-driven clas-sification by intensity, i.e. based on the damage produced on the population, of the sars-cov- events: a) θ < θ * , slow pandemics: low values ( . % in australia to . % in greece [ ] ) of the largest casefatality rate, well functioning health system; b) θ * ≤ θ < . , moderately-fast pandemics: higher ( . % in ireland to . % in spain) case-fatality rates, mild disruption of the medical system; similarly to the magnitude, t , the epidemic intensity scale can be accompanied by a rating system quantifying in this case the efficiency of patient identification and contact tracing strategies, suitably defined as follows: ) plumes with eccentricity e ≤ . , featured by countries that performed extensive testing and rapid patient identification, resulting in less correlated data series for infected and deceased rates as reflected by large peak-to-peak time lags; ) plumes with eccentricities . < e ≤ . , describing good patient identification; ) plumes with eccentricity . < e ≤ . , describing mildly efficient patient identification; ) plumes having eccentricity e ≥ . and strong peak-to-peak proximity, reflecting weak or not-efficient identification strategies. this classification reflects, in a quantitative fashion, a simple yet essential fact regarding the fight against the sars-cov- virus: rapid patient identification leads to functional health system and low case-fatality rates (category a ), whereas less and less efficient strategies lead more often to fast pandemics (categories b-d) depending on the country's hospital capacities. . temporal evolution of the epidemic angle. the introduction of the epidemic magnitude ( fig. and tab. i) and intensity (fig. ( ) ) enabled a preliminary yet informative classification of the sars-cov- pandemic events, highlighting the main ingredients underlying their epidemiometric fingerprints. an important byproduct of this result lies in the possibility of designing alarm protocols and other precautionary measures to dampen the societal effects of a pandemic event [ , ] . in fact, understanding the magnitude and intensity of the sars-cov- epidemic events could help policy-makers to make informative decisions not only for investing resources to strengthen a country' health system, but it can enhance the public awareness with the design of alarms platforms aiming at facilitating contact tracing or promoting responsible actions of social-distancing. unlike other catastrophic events, in fact, the magnitude and intensity of a pandemic lie entirely in the hands of the countries' governments, their preparedness to absorb the impact of a rapidly emerging outbreak, and the awareness of societies to its potential damage. in this light, quick actions at the early stages of an epidemic outbreak in tracking the infected [ ] or more efficient social intervention protocols [ , ] can help curbing down dramatically [ , ] its devastating effects. this is why an early estimation of the outbreak scales could significantly help designing epidemic alerts for enhancing the public and governmental awareness and help fighting against the virus spreading. in this context, understanding how the sars-cov- epidemic scales evolve in time could provide significant information for future design of early warning systems [ ] and risk alerts [ ] . motivated by this idea, we have analyzed in fig. the temporal evolution of the epidemic angle θ for a few representative countries of fig. . the results in fig. show that countries having experienced fast pandemics of category c or higher such as italy, spain or belgium, all crossed the critical angle θ * long before reaching their infected peaks (red filled circles), reflecting a slow responsiveness [ ] to the rapidly emerging outbreak. on the contrary, countries like germany (or austria and switzerland, not shown in fig. to simplify the exposition) succeeded in keeping θ below θ * already when they reached their infected rate peaks, suggesting efficient patient identification and well functioning medical systems. advanced knowledge of the epidemic intensity could have helped countries like italy or spain in adjusting more rapidly their policies of contact tracing and identification of seriously ill patients, offering more options of intervention to fight the epidemic crisis. . low-dimensional parametrization. our geometric analysis additionally hints at an integrated, lowdimensional parametrization for modeling the evolution of real-world epidemic trajectories. in fact, the geometric parametrization of the epidemic plumes allows (at least, on the coarse-grained level of the national trends) to curtail with a few parameters the essential information ruling the epidemic spreading [ , ] , out of a variety of epidemiological factors, from e.g. different gender-based transmission factors [ ] [ ] [ ] , to mobility patterns [ , ] and social mixing [ , ] , to cities' pollution [ ] , different quarantine [ ] or testing strategies [ ] and many others. even when adopting a well-mixed approximation among different compartments, developing a predictive framework embracing such a variety of factors easily results into mathematical or computational tour de forces [ , , ] whose complexity quickly grows with the number of realistic features included. from another viewpoint, modern epidemic models based either on detailed descriptions of the population's compartments [ , , ] or merging simplified versions of the latter with tools of bayesian inference [ ] and neural networks [ ] , typically yield predictions of a country's epidemic trend after fitting either its data for the infected rates or the ones fo the fatality rates. this separated approach leads to best-fitting epidemiological factors that, when adopted to describe the behaviors of other compartments which have not been fitted to the data, lead to results far from the real-world trends. our geometric approach offers a viable solution to circumvent both these limitations by best-fitting the synthetic epidemic plumes directly to the data-driven ones, enabling in this way an integrated and low-dimensional estimation of the epidemiological parameters best describing the outbreak evolution. as a demonstrative example, let us consider an seird epidemic model [ , ] to describe the sars-cov- dynamics. for completeness, let us recall that the seird model suitably characterizes the spreading of a viral agent featuring a latent (sometimes also referred to as cryptic [ ] ) phase where susceptible individuals (s) become exposed (e), i.e. they acquire the infection but are not yet infectious. after a characteristic incubation period /σ days (with σ ∈ ( , ]), exposed individuals become infectious (i) and start spreading the disease at a speed, λ, controlling the average number of people an infected person infects per day. infected individuals spread the disease during an average period of /γ days (with γ ∈ ( , ]), after which they either recover (r) or die (d). let /µ (with µ ∈ ( , ]) be the characteristic period of days during which an infected individual becomes critically ill and eventually dies, and α ∈ [ , ] the fatality rate characterizing instead the probability of going from infected to death (i.e., α), and from infected to recovered (i.e., − α). the parameters λ, σ, γ, µ, α define respectively the infectious, incubation, recovery, mortality and fatality rates of the seird model; to simplify the analysis, let us assume that once recovered, individuals gain immunity. the above epidemic process is summarized in the system of differential equations: where s ≡ s/n is the density of susceptible individuals and n the population size. as a last ingredient, let us include in eq. the additional information of a time dependent infectious rate λ(t), identifying the introduction of social distancing measures and quarantine strategies. these, in fact, aim at lowering the basic reproduction number r = λ/γ of the virus from a certain initial value r ,i > to a final one r ,f < . to model this decay, whose speed will depend on the efficiency of the lockdown strategy applied by a country, let us adopt a logistic function of the form where τ, κ ≥ are two "intervention" parameters ruling respectively the time of the inflection point in the profile of r (t) (i.e. the day of the country's main lockdown) and the decay rate of the reproduction number as a result of the lockdown efficacy. in particular, values of κ ∼ o( ) result into a fast decay of r (t) (signaling a rapid and efficient intervention), while κ ∼ − or smaller results into a very slow convergence towards r ,f . already at this simplistic level, the epidemiological (λ, σ, γ, µ, α, r ,i , r ,f ) and intervention (τ, κ) parameters aiming at representing the data-driven epidemic plumes, identify an -dimensional phase space for the dynamical system in eq. ( ). thanks to our geometric parametrization, it proves possible to find the functional dependences relating this variety of parameters to the three geometric factors (r max , θ, e), whose relations identify a series of data-driven parametric constraints to reduce the degrees of freedom of the problem. finding the exact dependence between the epidemiological variables and the geometric factors is beyond the scope of the present work and will be discussed elsewhere. nevertheless, it is immediate to verify that e.g. an increase of the case-fatality rate α leads to an increase of the epidemic angle (fig. a) -i.e. larger epidemic intensitieswhile increasing the infection rate λ yields larger values of r max -i.e. larger epidemic magnitudes-supporting our heuristic arguments in sec. . fig. b demonstrates this integrated, low-dimensional approach applied to the italian epidemic data. we have performed a manual search of the epidemiological parameters best fitting the data-driven values θ it . and ρ it . , selecting a suitable sub-manifold of the phase space featuring trajectories geometrically congruent to the data-driven one. even if they do not best-fit the data-driven plumes (empty markers and blue curve in fig. b) , the set of parameters we identified generates a seird plume nicely matching the epidemic data. in particular, we find that a relatively large initial reproduction number r it ,i . (in qualitative agreement to the more precise ones obtained by best fitting regional data [ ] ) and a low lockdown efficiency parameter κ it . , reflecting the slow decay already observed in fig. ( ) and therein quantified by a high infected rate skewness. the low-dimensional analysis further discloses another realistic ingredient characterizing the italian pandemic type, i.e. the high case-fatality rate σ it . % reflecting the strong intensity of the italian outbreak and the critical conditions reached by its health care system. further developing these geometric-based concepts could lead to the identification of additional parametric constraints further reducing the degrees of freedom of epidemic models, pos- . second-wave analysis. a) synthetic data (gray circles) generated by considering for both the infected and the fatality rates bimodal skewed gaussians with well resolved first-and second-wave peaks. the two trajectories, describing respectively the first (blue dot-dashed curve) and second (red dot-dashed curve) waves, are analyzed by separating the corresponding fitting plumes. both the epidemic events have same magnitude but different epidemic angles, with the first wave of category b and the second one of category a. b) epidemic data describing the evolution of the outbreak in israel (darker cyan circles) and its fitted double-plume trajectory (gray dashed curve). by separating each fitting curve as in a) we identify the first epidemic wave (blue, dot-dashed curve) of magnitude t . and category a − , and the ongoing second wave (red, dot-dashed curve). as of july , the second-wave event in israel has epidemic angle θil . (i.e. category a), and magnitude t . (i.e. class vii). sibly boosting their forecasting power. considering additional information coming e.g. from the different curvilinear velocities of the right and left lobes of the epidemic plumes, the local curvature of their traces may yield unfamiliar perspectives in achieving this task. . future directions. our study is only a preliminary step in the design of metric systems for epidemic events. we expect that the results will inspire the development of more refined epidemiometric frameworks for rating the magnitude and the impact of present and future epidemics, helping governments and other decision-makers to strengthen their policies of containment and better respond to such extreme events. in this perspective, we highlight in what follows a few important directions of future research in which respect we believe that our geometric approach could be further developed. i ) beyond first-waves. our analysis focused on typical (i.e. counter-clockwise evolving) epidemic trajectories describing the first-wave events of the sars-cov- pandemic in a selection of countries. as of july , some nations included in our analysis have entered secondary epidemic waves whose magnitude appears already to be larger than the classification in tab. i; this is the case of e.g. the united states, iran, israel or serbia. extending the geometric method to secondary waves is possible as long as the first and the second-wave peaks of the infected and deceased rates are sufficiently resolved over time (fig. a) . in this case, fitting the data by multiple (skewed) gaussians allows to trace a new epidemic trajectory in the (i, d) plane whose evolution may cross itself and disclose geometric features significantly different from those of the first wave. by isolating the fitting functions describing each lobe (fig. a) , it is possible to perform an analysis perfectly analogous to the one described above for the case of first-waves, identifying the epidemic angle θ, largest extend r max and eccentricity e of the second-wave trajectory. as most of the nations that entered the second wave have not yet reached their new infected peak, we cannot yet draw conclusive evaluation about the magnitude and intensity of their new epidemic events, but we track the evolution of the geometric parameters characterizing their new trajectories as suggested in sec. (see fig. ). in fig. b we have presented the epidemic trajectories describing the state of israel. a preliminary evaluation shows that while the new wave has already a magnitude t . , i.e. a very strong epidemic event comparable to the first-wave event of spain or us (see sec. ), its epidemic angle is still relatively low (θ il < . ) with respect to the threshold value θ * = . of the onset of a fast pandemic (fig. ). comparing the magnitude and intensity of different epidemic events in the same country could help understanding how different countries prepared themselves to absorb and dampen the impact of a new wave of epidemic events. ii ) including daily testing data. an important direction of future research for improving the epidemic measures defined in the above concerns the inclusion of the information related to the number of daily testing performed by each country. depending on their resources, in fact, different countries applied different strategies of testing or contact tracing in their fight [ ] against the spread of sars-cov- . germany or russia, for example, have been performing a tremendous amount of tests since the early stages of the pandemics and over a very broad [ ] fraction of the population, including both symptomatic and asymptomatic patients. countries like italy [ ] or spain [ ] had instead to prioritize their diagnostic capacities to test patients with more severe clinical symptoms and in need of hospitalization. including this relevant bit of information in the analysis above, e.g. by normalizing the number of new daily infected by the corresponding number of daily new tests, would possibly result into an even more meaningful comparison of the countries epidemic magnitude than the one in tab. i and, likewise, of the classification by intensity depicted in fig. . iii ) zooming-in: local characterization of countries pandemic types. our results have focused on analyzing the epidemic trends reported at national levels, offering a country-to-country comparison of their sars-cov- pandemic types. the epidemiometric system of epidemic events proposed however, can be equivalently adopted to analyze more local datasets of each country, offering a magnifying lens to determine the magnitude and the intensity of the epidemic events observed within states, regions or even on the smaller scales of provinces and towns. in the case of italy, for example, regions such as lombardia, emilia-romagna, piemonte and veneto have suffered more severe epidemic events than the rest of the country [ ] , and a similar situation has been reported in united states for the states of new york, california and (more recently) of florida [ ] . an efficient intervention at the national level could find its crucial ingredients in a rapid intervention on the level of its states, regions or provinces. combined with forecasting tools and prior epidemic risk assessments, our epidemiometric framework could provide the design of local epidemic alerts to enhance the awareness of governments and inhabitants already at local levels, helping to counter the spreading of highly infectious viruses like sars-cov- . iv ) geometry of the epidemic surfaces. as a conclusive remark, let us notice that in our developed geometric analysis, we have focused only on the projections of the epidemic trajectories in the (i, d) plane. however, other compartments (e.g. recovered, critical patients, active cases, etc) can be included in the analysis, resulting in a multi-dimensional representation of the epidemic state of each country. for instance, the addition of the compartment of daily recovered (r) yields the emergence of new information to further refine the classification of the pandemic fingerprints reported in different nations. fig. ) contains a few examples of "epidemic surfaces" in the (i, d, r) d-space observed in a selection of countries. in particular, the cases of italy (fig. a) and germany (fig. b) clearly exhibit striking differences in their dynamic evolution: italy's epidemic surface features a narrow cross-section in its projection on the (i, d) plane and a broad trajectory in the (r, d) plane, as opposed to the epidemic surface characterizing germany's outbreak. the two surfaces, in fact, appear to be roughly orthogonal with each other, a clear indication that in italy the increase of infected yielded a rapid and simultaneous increase of deceased. similar behaviors can be found in cases belonging to the same magnitude and intensity. for example, austria (fig. d) as well as norway or switzerland shares similar patterns to those observed in germany, while countries like usa, france or spain feature inclinations of their epidemic surfaces resembling the one observed in italy. the identification of the patterns shared by the outbreaks of different countries would have otherwise been impossible if we had to limit our view to the classical time evolution of the epidemic compartments as in fig. . exploring epidemic dynamics from this novel, geometricbased perspective could unveil new "hidden" features characterizing their evolution and foster new methods for their statistical analysis and mathematical modeling. we expect that our geometric framework and results will inspire alternative approaches to the study of epidemic evolution, possibly leading to longer-termed forecasting techniques or to more refined epidemiometric systems for the design of epidemic alerts and early warning systems. . discussion. we have presented a geometric framework to analyze and systematically classify the trajectories of the sars-cov- pandemic across different countries in the (i, d) plane via three geometric parameters (r max , θ, e). our geometric measures enables the design of a preliminary epidemiometric system to quantify the magnitude of a country's outbreak and its intensity, resembling respectively the richter and the mercalli measures for seismic events, and further adding information about the efficacy of lockdown strategies and of patient identification. the epidemic scale measures we defined help identifying a spectrum of sars-cov- pandemic types, ranging from weak epidemic events with slow speed, like those reported in japan, australia or south korea (magnitude t . , class ++, category a ++ ), to very extreme events with intense damage inflicted on the population, like the cases of united kingdom (magnitude t . , class −−, category d −− ) or italy (magnitude t . , class −, category c − ). however, unlike other catastrophic events, the magnitude and intensity of an epidemic event entirely depends on the responsiveness of the countries' government and the capacity of their medical systems, jointly with the awareness of their population to their potential damage. in this respect, early estimation of the epidemic scales (e.g. by merging them with forecasting models) could significantly contribute to the design of warning systems [ , ] or protocols for virus alerts to enhance the public and governmental responsiveness. we showed that, in cases like italy or spain (fig. ) , the epidemic angle θ has crossed the threshold θ * = . rad from slow to fast pandemics way before reaching the infected and fatality peaks, reflecting a slow responsiveness to the rapidly emerging crisis. from the mathematical perspective, our geometric method further raises relevant insights to improve current epidemic models. the geometric characterization of the epidemic plumes in the (i, d) plane, discloses an integrated and low-dimensional approach to modeling the epidemic trends by imposing geometric constraints relating the data-driven parameters (r max , θ, e) to the epidemiological factors entering the epidemic models adopted. this allows to lower the number of independent parameters, identifying a suitable sub-manifold of the high dimensional phase space where plumes congruent to the data-driven ones can be found. we have demonstrated this approach by manually searching, in an seird model with a time-dependent reproductive number, the best choices of the epidemiological and intervention parameters satisfying the data-driven geometric constraints for the italian trends, obtaining a realistic description of the reported behaviors. we foresee that the merging of our data-driven, low-dimensional approach with more advanced mathematical or computational methods [ , ] , could lead to predictions of the epidemiometric fingerprints of real-world epidemics with ever-increasing accuracy, possibly disclosing new directions to the identification of optimal priors for more efficient and longer-termed epidemic forecasting. handbook of disaster research at risk: natural hazards, people's vulnerability and disasters will the coronavirus end globalization as we know it? foreign affairs coronavirus and the future of globalization an instrumental earthquake magnitude scale sulle modificazioni proposte alla scala sismica de rossi-forel real-time seismology and earthquake hazard mitigation 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(covid- ), data repository nonlinear dynamics and chaos with student solutions manual: with applications to physics, biology, chemistry, and engineering theoretical statistics by definition e := − (b/a) , with a and b respectively the major and minor radiuses of a regular ellipse. in our case rmax and r ⊥ play respectively the analogous roles of a and b for the plume-like epidemic trajectories notice that the linear regression analysis yields an intercept r − . which, in turns, means a proportionality factor a − between rmax and p, meaning a magnitude of t . for p ∼ , and increasing to t case-fatality rate and characteristics of patients dying in relation to covid- in italy too many patients? a framework to guide statewide allocation of scarce mechanical ventilation during disasters social distancing measures may have reduced the estimated deaths related to covid- in brazil the italian health system and the covid- challenge nowcasting and forecasting the potential domestic and 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establishment of local transmission and the cryptic phase of the covid- assessment of the sars-cov- basic reproduction number, r , based on the early phase of covid- outbreak in italy countries test tactics in ?war?against covid- covid- : why germany?s case fatality rate seems so low covid- : how doctors and healthcare systems are tackling coronavirus worldwide update: public health response to the coronavirus disease outbreak?united states, february key: cord- -f z authors: nikitenkova, s.; kovriguine, d. a. title: it's the very time to learn a pandemic lesson: why have predictive techniques been ineffective when describing long-term events? date: - - journal: nan doi: . / . . . sha: doc_id: cord_uid: f z we have detected a regular component of the monitoring error of officially registered total cases of the spread of the current pandemic. this regular error component explains the reason for the failure of a priori mathematical modelling of probable epidemic events in different countries of the world. processing statistical data of countries that have reached an epidemic peak has shown that this regular monitoring obeys a simple analytical regularity which allows us to answer the question: is this or that country that has already passed the threshold of the epidemic close to its peak or is still far from it? people desire to know about future epidemic events in terms of where, how much and when. this information creates assurance in society, some adequate understanding and effective reaction on current events. studying the history of the pandemic in detail will undoubtedly contribute to fruitful strategic thinking. the practice of recent months has shown that well-tested and well-known mathematical methods for processing statistical data directly used to describe future events of the spread of a pandemic have been ineffective in solving such a flagrantly important and urgent problem. meanwhile, it is no secret that the aggregated dynamics of a pandemic is very simple, it is described quite fully by the solution of a well-known logistic equation, not so important whether it is discrete or differential. neither the more developed versions of this mathemati- other promising predictive technologies based on graph theory, percolation theory, and stochastic processes turned out to be too clumsy or incapable to produce a clear and concrete result on an urgent issue. in other words, the available methods for processing statistical data were found to be helpless in solving an important specific problem. the paradox is the apparent inefficiency of using the known methods of processing statistical data to obtain an adequate quantitative result, even though, it would seem, everything about the dynamics of the pandemic is known qualitatively in advance. let's try to understand the main reasons for such an unfortunate failure and try to formulate the principles for overcoming the current difficult situation. first of all, what does an epidemic look like? in the dynamics of development and spread, the epidemic is similar to a forest fire. with fire, everything is understood a little easier due to the obviousness of this phenomenon. no one is trying to delve into the physics of combustion and the nature of fire, for people the expectations of ignition of adjacent sections of the forest, threats to human settlements are obvious, the assessment of the forces . cc-by-nc-nd . international license it is made available under a is the author/funder, who has granted medrxiv a license to display the preprint in perpetuity. (which was not certified by peer review) the copyright holder for this preprint this version posted june , . . and means necessary to extinguish a fire is almost foreseeable. the epidemic does not have such striking external manifestations, so it is insidious and dangerous especially for ignorant people, in which, as a rule, there is no shortage. besides, decisive actions taken, say, to extinguish a fire, are completely inapplicable if you try to try them on to combat the epidemic. in the absence of vaccination and other effective medical countermeasures to the spread and development of the epidemic, quarantine seems to be the most effective means, like fifty years ago and earlier. self-isolation and social distancing are effective only when each member of the society realizes that any action, even if it is legitimate, borders on risk. to understand the reason for the failures of mathematical modelling, we first turn our attention to the statistical data used to make the forecast, since this forecast directly depends on them. it is not a revelation that, for completely natural reasons, statistics are not necessarily flawless. note that, in contrast to the experimental data that are dealt with, say, in physical experiments, data on the epidemic situation cannot be redundant, but only insufficient. indeed, it is difficult to imagine a situation where redundant data regularly appears in the monitoring summary of the number of newly detected cases, since the case is too delicate to allow such sloppiness. most likely, we should expect that the data will be underestimated due to a lack of information. therefore, it is natural to assume that the data contains a regular error component with a deficiency. indeed, comprehensive pandemic data can only be obtained a posteriori, but life requires reliable a priori information. to achieve this goal, it is necessary to identify, evaluate and study the mentioned regular component of the error, using the statistics of those countries that have already reached a peak -the stationary level of the epidemic dynamics. let us take a logistic pattern for the predicted result since it requires a minimum of information for modelling, i.e., the initial number of cases, the final peak number, and the number of days from the outbreak to its peak. one can use appropriate data to build these logistic curves, for example from the site is the author/funder, who has granted medrxiv a license to display the preprint in perpetuity. the copyright holder for this preprint this version posted june , . . parameters determined from the tables. the transition time from the state i n to the state i n is a day, but it does not play a significant role at large numbers. after using simple selection criteria, the obtained data appears as tables and graphs [ ] . suppose that the temporary evolution of the epidemic in countries possessing highquality statistics is adequately described by the solutions of the logistic equation let the infection rate be a specific value for each territory or country. it is easy to guess that the parameter a should tend to zero due to elementary statistical properties. thus, we can interpret the relative indicator a /n * as the quality of statistical data. always a positive parameter a determines the maximum spread of the epidemic. let it characterize the measure of social hygiene inherent in a particular country. the critical parameter determining a stable steady-state n * is this a . note that abstract theories connect this parameter with the concept of intraspecific competition, but in our case, an attempt to interpret this indicator will lead to nothing. it remains to be assumed that this negative parameter is an indicator of medical and other useful actions to counteract, spread, and develop the epidemic. now let's look at a specific example of the epidemic history in one of the countries that have reached the peak of the epidemic. let it be the most affected european country today, spain, shown in fig. . . cc-by-nc-nd . international license it is made available under a is the author/funder, who has granted medrxiv a license to display the preprint in perpetuity. the copyright holder for this preprint this version posted june , . the above graphs show that the discrepancy between real data and the forecast is most significant, starting from the early stages of the epidemic until the inflexion point of the logistic curve, which is appropriate to call a threshold. in the figures, this threshold is indicated by a dotted line. now let's try to evaluate the absolute and relative forecasting error graphically, as shown in fig. . . cc-by-nc-nd . international license it is made available under a is the author/funder, who has granted medrxiv a license to display the preprint in perpetuity. the copyright holder for this preprint this version posted june , . this illustration shows that absolute error is colossal throughout the history of the epidemic. the relative error becomes acceptable when the absolute error has passed its maximum value. fortunately, the actual data, starting from the beginning of the epidemic and almost to the point of the specified maximum, is well described by the exponential dependence shown in the left part of fig. . this fact is not a revelation: the behaviour of real data over time shown in graphs is not a specific feature of the history of the epidemic in spain alone. the authors of some works on the problem of the pandemic have noticed this pattern, but link this regular exponential component of the error with useful medical intervention in the course of the early stages of the epidemic [ ] . however, it is easier to assume that this unavoidable regular error is due only to the specifics of data monitoring. moreover, the analytical approximation of the input data set continues further, starting from the point of maximum absolute error up to the inflexion point [ ] , [ ] , [ ] . figure shows the power fit on the indicated time interval. . cc-by-nc-nd . international license it is made available under a is the author/funder, who has granted medrxiv a license to display the preprint in perpetuity. the copyright holder for this preprint this version posted june , . . https://doi.org/ . / . . . doi: medrxiv preprint these graphs show that real input data can be replaced by approximating functions without any particular error. note that beyond the inflexion point, and up to the peak of the epidemic, the predicted and real data, as a rule, practically coincide. the explanation is simple: when crossing the inflexion point, the growth rate of registered infections decreases, while the maximum effort is involved in solving the monitoring problem. if we repeat the calculation procedure using any suitable technique for processing statistical data using the indicated exponential and power-fit approximating functions, the result will be close to what is achieved using real input data. we can repeat the above arguments and calculations using other data on the history of the epidemic in other countries, for example, germany, italy, turkey, france, and many others. the pattern in the input data in question will be the same. this means that epidemic event monitoring services in many countries operate similarly, which causes the inevitable regular error component to occur. of course, there are exceptions: there are data for some countries for which the analytical analysis described in this paper cannot be used. such countries, among the most affected by the pandemic, primarily include china, whose monitoring services provided data that could not be processed in the above aspect. also, in this aspect, countries such as ecuador, japan, slovakia, guinea-bissau, kosovo are not amenable to statistical processing. in some other countries, as a rule, with a few registered cases, the causal principle is formally violated. this means that monitoring data overtakes in time the data calculated by the logistic forecast curve. since in reality this principle is never violated, it remains to be assumed that the monitoring data provided by such countries is incomplete. if desired and zealous, this error is not difficult to correct, assuming that the epidemic could have begun somewhat earlier than the officially declared date. there are some countries, also, as a rule, with some recorded cases, where the forecast data surprisingly practically coincide with the monitoring data. these countries include ireland, iceland, new zealand. we assume that the regular component of the monitoring error has a place to be. could this information have a positive effect on the reliability of predicting future epidemic events in other countries that have not yet reached the peak of the epidemic? if we take into account the evolution of the indicated regular error component in a dynamic way, that is, ad-. cc-by-nc-nd . international license it is made available under a is the author/funder, who has granted medrxiv a license to display the preprint in perpetuity. the copyright holder for this preprint this version posted june , . . just the input data appropriately, this problem will not completely disappear. the parameters of the exponential and power functions that approximate the input data are unknown a priori. the history of countries that have reached the peak of the epidemic is of fundamental value. this value is manifested in the appearance of a pattern in the so-called virtual time delay of monitoring data. the indicated delay time is determined as follows. mentally, we draw a horizontal line on the graph, which is shown on the left in fig. . we determine the intersection points of this line with the forecast logistics curve and graphs of functions that approximate the input data. the time difference at the indicated intersection points determines the virtual delay time of the monitoring data. in other words, if you move the monitoring points from right to left by the desired time interval, then all the points will be on the logistic curve, which will lead to a correct prediction, even if you do not use all the new data obtained, but only a small part of them. in fig. . replacing the real input data with approximating functions creates an error of not more than per cent; . a country has fetched its epidemic peak to the current date for at least a week ago. . cc-by-nc-nd . international license it is made available under a is the author/funder, who has granted medrxiv a license to display the preprint in perpetuity. the copyright holder for this preprint this version posted june , . . unfortunately, the above analysis cannot be applied to us monitoring data, although this country has confidently crossed the epidemic threshold. also, it is not yet possible to analyse the situation in brazil, since the epidemic in this country is at the initial stage of the exponential growth of the epidemic, despite the unprecedentedly large number of officially recorded cases in this country. . cc-by-nc-nd . international license it is made available under a is the author/funder, who has granted medrxiv a license to display the preprint in perpetuity. the copyright holder for this preprint this version posted june , . saudi arabia and russia, which have crossed the epidemic threshold but have not yet reached its peak. we have used the same illustration is as in fig. on the left as a background for visual comparison. we have found a regular component of the monitoring error of officially registered total cases of the spread of the current pandemic. this regular error component explains the reason for the failure of a priori mathematical modelling of probable epidemic events in different countries of the world. processing statistical data of countries that have reached an epidemic peak has shown that this regular monitoring obeys a simple analytical regularity. this pattern allows us to answer the question: is this or that country that has already crossed the threshold of the epidemic close to a peak or is still far from it. not far off is that happy day when the world will cope with the pandemic as a whole. monitoring data on the current pandemic, collected in its entirety, will allow us to establish valuable a posteriori patterns to significantly improve the quality of a priori dynamic modelling of epidemic events when they appear in the future. † the united kingdom has reached the epidemic peak while writing this text. . cc-by-nc-nd . international license it is made available under a is the author/funder, who has granted medrxiv a license to display the preprint in perpetuity. (which was not certified by peer review) the copyright holder for this preprint this version posted june , . . https://doi.org/ . / . . . doi: medrxiv preprint the countries of the "golden billion", despite the sometimes catastrophic situation allowed in this part of the world, judging by the dynamics of current events, are the first to pass the peak of the epidemic. the fate of the rest, most of the world remains uncertain. special attention of an enlightened society should be focused today on the most painful epidemic situation in the usa, brazil and russia. the statistics of these countries indicate the absence of a precedent in the history of the epidemic compared to other countries that are already close to recovery. a country called the world is at the beginning of the pandemic despite the truly gigantic scale of the disaster already achieved. a novel coronavirus from patients with pneumonia in china novel coronavirus and old lessons -preparing the health system for the pandemic dynamics of the covid- --comparison between the theoretical predictions and real data the covid- pandemic: growth patterns, power-law scaling, and saturation search for the trend of covid- infection following farr's law, idea model and power law strong correlations between power-law growth of covid- in four continents and the inefficiency of soft quarantine strategies key: cord- -cb u s s authors: bedford, juliet; farrar, jeremy; ihekweazu, chikwe; kang, gagandeep; koopmans, marion; nkengasong, john title: a new twenty-first century science for effective epidemic response date: - - journal: nature doi: . /s - - -y sha: doc_id: cord_uid: cb u s s with rapidly changing ecology, urbanization, climate change, increased travel and fragile public health systems, epidemics will become more frequent, more complex and harder to prevent and contain. here we argue that our concept of epidemics must evolve from crisis response during discrete outbreaks to an integrated cycle of preparation, response and recovery. this is an opportunity to combine knowledge and skills from all over the world—especially at-risk and affected communities. many disciplines need to be integrated, including not only epidemiology but also social sciences, research and development, diplomacy, logistics and crisis management. this requires a new approach to training tomorrow’s leaders in epidemic prevention and response. when nature published its first issue in , a new understanding of infectious diseases was taking shape. the work of william farr , ignaz semmelweis , louis-rené villermé and others had been published; john snow had traced the source of a cholera epidemic in london (although robert koch had not yet isolated the bacterium that caused it ). the science of epidemiology has described patterns of disease in human populations, investigated the causes of those diseases, evaluated attempts to control them and has been the foundation for public health responses to epidemic infections for over years. despite great technological progress and expansion of the field, the theories and practices of infectious disease epidemiology are struggling to keep pace with the transitional nature of epidemics in the twenty-first century and the breadth of skills needed to respond to them. epidemiological transition theory has focused mostly on the effects of demographic and socioeconomic transitions on well-known preventable infections and a shift from infectious diseases to non-communicable diseases . however, it has become clear that current demographic transitions-driven by population growth, rapid urbanization, deforestation, globalization of travel and trade, climate change and political instability-also have fundamental effects on the dynamics of infectious diseases that are more difficult to predict. the vulnerability of populations to outbreaks of zoonotic diseases such as ebola, middle east respiratory syndrome (mers) and nipah has increased, the rise and spread of drug-resistant infections, marked shifts in the ecology of known vectors (for example, the expanding range of aedes mosquitoes) and massive amplification of transmission through globally connected, high-density urban areas (particularly relevant to ebola, dengue, influenza and severe acute respiratory syndrome-related coronavirus sars-cov). these factors and effects combine and interact, fuelling more-complex epidemics. although rare compared to those diseases that cause the majority of the burden on population health, the nature of such epidemics disrupts health systems, amplifies mistrust among communities and creates high and long-lasting socioeconomic effects, especially in low-and middle-income countries. their increasing frequency demands attention. as the executive director of the health emergencies program at the world health organization (who) has said: "we are entering a very new phase of high-impact epidemics… this is a new normal, i don't expect the frequency of these events to reduce." . we have to act now but act differently: a broader foundation is required, enhancing traditional epidemiology and public health responses with knowledge and skills from a number of areas ( table ) . many of these areas have long been associated with epidemic preparedness and response, but they must now stop being seen as esoteric 'nice things to have', and instead become fully integrated into the critical planning and response to epidemics. this will require considerable changes by the global public health community in the way that we respond to epidemics today and how we prepare for and seek to prevent those of tomorrow. it will mean reshaping the global health architecture of the response to epidemics and transforming how we train new generations of researchers and practitioners for the epidemics of the future . the modern research culture-often shaped by the behaviour of funders-has required many researchers to specialize in narrow fields, with less emphasis on translation than on field-specific innovations. although this siloed landscape has brought major advances in global health, it is not fit for the transitional phase of epidemic diseases: rapidly evolving, high-impact events bring together communities, responders and researchers who do not routinely interact. different assumptions, cultures and practices, each of which may be widely accepted within a particular community, make working together in outbreak situations more challenging. fundamental to success is respect and understanding of the contribution each party brings. in a successfully integrated approach, we each have to realize that our knowledge and skills are a small part of a rapidly expanding toolkit (box ). we need to understand major trends in research and how and when they may influence the response to an epidemic, develop new research to strengthen the support that we can provide across other areas and learn to operate in multi-stakeholder situations-including, at times, as part of a critical debate to bring better practices to the fore. central to this approach must be the communities who are at risk and those affected by epidemics: local people are the first responders to any outbreak and their involvement in the preparation and response activities is essential. from communities, through local and regional health authorities, national public health institutes and international organizations-including many essential partners in sectors beyond public health-the integrated approach must be supported. the who, in particular, has a critical part to play, using its unique mandate not to lead every aspect of preparation, response and recovery, but to change its practices, facilitate integration with and among others, and ensure accountabilities are built in from the bottom to the top. a wave of cholera epidemics across europe in the s and s catalysed a new era of 'infectious disease diplomacy' globally. nations recognized that infections do not stop at borders and that therefore multilateral collaboration is essential to protecting citizens from lethal epidemics. the development of germ theory through the second half of the nineteenth century transformed ideas about the causes of infections, informing scientific research as well as clinical responses. scientific understanding translated into vaccines and antibiotics, while programmes for child health, hygiene, clean water and sanitation became common in the twentieth century. as a result, childhood diseases such as measles and mumps became rare, smallpox was eventually eradicated and polio was eliminated from all but a handful of countries . many people thought that infectious diseases would soon be history. sir frank macfarlane burnet is often cited for his remark in the s that, with the emergence of new diseases being a distant prospect, "the future of infectious diseases will be very dull" . although the focus in high-income nations turned to non-communicable diseases, which constituted a considerable and increasing burden on the health of their citizens, infectious diseases did not disappear. some endemic infections such as malaria and tuberculosis were not susceptible to elimination strategies, and new diseases with epidemic and pandemic potential emerged. ebola virus disease was first identified in the s, hiv/aids in the s, nipah virus in the s, sars and mers at the start of the twenty-first century, and many more have since been identified. far from becoming 'very dull', the field of infectious disease epidemiology has sometimes struggled to adapt: as late as , respected researchers used a nineteenth century 'law' of epidemiology to make predictions about the aids epidemic-these turned out to be vast underestimates . advances in other fields gave epidemiology the chance to evolve. in , when the editors of the international journal of epidemiology provocatively asked whether it was time to 'call it a day' given the putative power of genomics to explain diseases over the capacity of epidemiologists to describe them, their conclusion was that it had the potential to positively transform epidemiology as much as the rise of germ theory a century earlier. at least pathogens that affect humans have been identified as emerging, re-emerging or evolving since the s , while increasing rates of antimicrobial resistance threaten to make formerly controlled infections, such as malaria, untreatable -this also limits our ability to control their epidemic potential. the demographic transition is driving much of this: human society is becoming more urban than rural for the first time in our history, bringing large numbers of people (and often animals) together in densely populated areas . agricultural and forestry practices are changing the relationships between people, animals and our respective habitats . travel is more accessible around the world, advances in computer science and computing speeds have led to a number of applications of artificial intelligence across society . applications in epidemiology include tracking online searches about disease symptoms to aid early detection of epidemics, although more sophisticated methods may be required before artificial intellegence becomes a reliable detection tool . crystallography modern x-ray diffraction and electron microscopy can reveal structures of viruses and antibodies in such detail that it is possible to identify specific sites of vulnerability on the virus. a previous study showed how such techniques identified an antibody that was much more potent against respiratory syncytial virus than the only currently available intervention . developing vaccines for emerging infectious diseases has many challenges, including the time it takes, a limited market and strict regulatory requirements for products that will be given to healthy people . platform technologies use one underlying approach with standardized processes and some antigen-specific optimization to speed up both development and manufacture of vaccines. for example, vector-based platforms combine an antigen, or a gene for an antigenic protein or peptide, in a virus-like particle or liposome. such platform technologies have the potential to deliver vaccines a few months after an emerging pathogen is identified and sequenced, rather than years . review so migration, trade and tourism bring more people into contact and thus affect disease transmission . climate change has many effects on ecosystems and environments, not least in changing the habitats and migratory habits of disease vectors . states with weak health systems are far less likely to cope with or recover from multiple emergent demands without damaging routine services . inequalities , inequities and distrust in national structures and institutions compound people's vulnerabilities . conflict increases the risk of epidemics and makes responding to them close to impossible . since , there have been several outbreaks of ebola (including the two biggest in history), not to mention outbreaks of sars, mers, nipah, influenza a subtype h n , yellow fever, zika and the continued spread of dengue. epidemics overlap and run into each other, yet the world is not currently equipped to cope with this increasing burden of multiple public health emergencies. preparing for epidemics, therefore, requires global health, economic and political systems to be integrated just as much as infectious disease epidemiology, translational research and development, and community engagement. epidemics represent shared risks that cross borders and all of society. health systems, routine care, trust in governments, travel, trade, business-all are disrupted during an epidemic. with such broad risks, the preparation and response must be nationally owned and led, internationally supported and undertaken with a whole-of-society approach. some initiatives have started to build frameworks for this to happen in a coordinated way. for example, the who's pandemic influenza preparedness framework brings together nation states, industry, other stakeholders and the who to implement a global approach to pandemic preparedness and response . a focus must be building coordinated regional and country expertise, resources and capacity through national and regional public health institutions . this brings its own challenges-governance of institutions, leadership, collaborations and interventions have to be impeccable or misconduct can thrive . unwelcome in itself, misuse of funding, resources or people within efforts intended to support an epidemic response will also undermine trust in the organizations that respond to an outbreak and, in turn, prolong the outbreak. key governance components include drafting policies in advance and being willing to implement those policies for data collection and sharing during epidemics. they must be flexible enough to enable affected communities and nations to retain ownership of the response, while drawing on international expertise to find the best possible response. governance should also include processes for vaccine and therapeutic approvals during outbreaks. however, it is clear that the centre of gravity for leadership, governance and implementation must be where the need is greatest if these are to truly deliver. in , julian tudor hart proposed the inverse care law: "the availability of good medical care tends to vary inversely with the need for it in the population served." . an analogue of the inverse care law can be applied to public health and epidemiology. expertise in these fields has traditionally gravitated towards centres of excellence in europe and the united states. of course, high-income countries are not immune to the disruption associated with epidemics, especially in an era of misinformation and growing mistrust in authorities and public health initiatives. however, the centre of gravity must shift so that globally representative distributed networks of collaborating centres can jointly ensure coverage in the regions that urgently need these skills on the ground . international collaborations remain important; however, strengthening epidemiology, public health and laboratory capacity in low-and middleincome countries is essential . collaborative interventions should not be limited to when there is a major outbreak, but be integrated into regular interactions. capacity, resources, expertise and governance can be supported by the increasing role for regional and national centres of disease control. the us centers for disease control (cdc) lends its expertise all around the world in addition to protecting the us population. in , the european cdc started, followed by the china cdc in and by the africa cdc in . although more can be done to improve data sharing and access to laboratories, the networks and connections between these centres have strengthened all of their work, as well as having a positive effect on public health systems in low-and middle-income countries. during the pan-european wave of cholera in the s, there were riots across the continent: doctors, nurses and pharmacists were murdered, hospitals and medical equipment destroyed . similar reports today usually come from communities that have not had positive prior interactions with public health initiatives, and thus the encounter with national or international teams who arrive only in response to a 'new' disease means that trust can never be assumed and has to be earned on both sides. engagement needs to start before an outbreak-ensuring that patients, their families and their communities are at the centre of all public health is essential for the successful prevention and response to epidemics. there is no public health without the support of the community. for example, the early detection of disease events will be improved if more national and regional public health institutions establish community event-based surveillance systems. communities are the first to know when something unusual happens -therefore training and mobilizing community volunteers to report such occurrences is a costeffective way to rapidly detect diseases and contain them at the source. this will also help to sustain engagement between communities and the organizations that respond to outbreaks. furthermore, improved information flow between the community and the public health system should provide a better understanding of local social networks to complement other means of tracking chains of transmission between individuals and places. this can be the community themselves, or it might be veterinarians who see clusters of sick animals, or nurses and doctors who care for patients in primary care-or it may be teams that are often forgotten in public health initiatives, such as those working in critical care facilities; it is striking how the first cases of nipah, sars, mers and influenza a subtype h n were all first identified by clinical teams in critical care facilities. an inclusive, whole-of-society approach is challenging, and the challenges may be magnified in a conflict or post-conflict zone. wars and conflicts not only increase the risk of epidemics as people move to escape violence and health services become harder to maintain , but also make public health responses vulnerable to interruption, thus making them less effective. then, miscommunication, mistrust, disease and violence can fuel each other in a vicious cycle. engaging local communities remains the highest priority, even in unstable contexts such as north kivu and ituri provinces of the democratic republic of the congo (drc) , where an ebola epidemic started in august . it seems inevitable that responding to epidemics in politically unstable environments will become more common, and skilled negotiators and peacekeepers will have to be better integrated in response teams. equally essential, therefore, will be an improved understanding of these challenging operational contexts among affected communities and external responders alike. social scientists have long applied their skills and knowledge in epidemic responses, although their roles have become more visible in recent years . by focusing on communities, social science humanizes the epidemic response , helps to increase understanding of context and may uncover associations between the context or local practices and the risk of transmission. the social science in humanitarian action platform has successfully produced rapid reports and briefings on regions in which an epidemic has been identified, and the global research collaboration for infectious disease preparedness includes a social science research funders' forum to 'propel research in this area' , acknowledging that its integration in the preparation and response to outbreaks is often missing or added as an afterthought to solve a problem that could have been forseen. there is still much to learn about how epidemic responders and social scientists can make the most of each other's expertise and how data from social science can fit into the wider information architecture of epidemic response. as an example, behavioural surveillance will be critical in twenty-first century responses to disease outbreaks . just as behavioural surveillance to improve the understanding of hiv was crucial in identifying high-risk groups for hiv infection, so human behaviours will continue to be important as we respond to future infectious diseases. for instance, the ebola virus outbreak in west africa probably began before december , but it took several months before hospital transmission and traditional burial practices were found to be the leading causes of its rapid spread. the increasing prevalence of mobile phones, wireless internet connectivity and social media activity raises the possibility of using these tools to gather data for epidemiological studies, diagnostics , population mobility during an ebola epidemic or influenza incidence in real time . future developments in predictive technology, machine learning and artificial intelligence will bring more opportunities to move towards 'precision public health' (box ). the use of data from people is becoming strictly controlled, however, and it will be a challenge to persuade countries to invest in a new surveillance system, for example, before its general effectiveness has been demonstrated at a country level . even then, technology-based solutions should be integrated with community-based programmes and other existing epidemic preparedness and response systems because surveillance is more effective when standardized among different countries, districts and communities. to this end, suites of guidance and open-access standardized tools are being developed for reporting cases of disease, as well as consent forms, standard operating procedures and training materials , properly validated diagnostic assays and access to quality-assurance panels in public and veterinary health. the rising trend of engaging citizens in data gathering is also welcome-the use of mosquito-recognition apps enables the collection of data far beyond the capacity of routine mosquito surveillance . this way, citizens feed information into the public health system and the feedback loop offers a fast and direct way to provide citizens with details of potential actions that they can take. as well as potentially supporting diagnosis and surveillance , the fast-developing field of genomic epidemiology can yield information to track the evolution of a virus such as ebola during an epidemic , . there will be times when it can detect outbreaks better than traditional epidemiology, illustrating the need to have these tools available in the same toolbox. during the large lassa fever outbreak in nigeria in , real-time genomic sequencing provided clear evidence that the rapid increase was not due to a single lassa virus variant, nor attributable to sustained human-to-human transmission. rather, the outbreak was characterized by vast viral diversity defined by geography, with major rivers acting as barriers to migration of the rodent reservoir . these findings were crucial in containing the outbreak. developing and sustaining the capacity to conduct real-time sequencing with adequate bioinformatics analyses at regional and national levels will be challenging in low-and middle-income countries. moreover, investments in relatively high-tech capacity (such as real-time sequencing) are competing with other, arguably more fundamental needs, such as equipment and training in primary laboratories. political engagement must be nurtured between epidemics: it is not enough to offer technological and laboratory support during a crisis, even with the promise of building capacity, if the political will is not there. however, with proper preparation, and accessible and trusted data sharing and governance mechanisms, laboratories with limited resources may be able to leap-frog into the twenty-first century , . vaccination is one of the most effective public health interventions and innovative strategies for research and development of vaccines, such as using ring vaccination as a trial design during ebola epidemics since - , must be encouraged. at the start of the - epidemic in west africa, vaccine candidates were already in development, based on a long history of preclinical research, although a lot of work was still required to get clinical trials underway in time to be useful . in , when zika was first internationally recognized as a pathogen that could cause birth defects , there was hardly any research and no vaccines in late-stage development. two-and-a-half years later, results from three phase i clinical trials had been reported , although challenges remained for further development. the lack of a profitable market for such products means that pharmaceutical companies lack the incentives to push this work between epidemics. initiatives such as the coalition for epidemic preparedness innovations are attempting to positively disrupt financing models for vaccines against epidemic diseases , and stockpiles of meningococcal vaccine, yellow fever vaccine and oral cholera vaccine are maintained by the international coordinating group to minimize potential delays due to limited manufacturing capacity . similarly, if investigational treatments or vaccines are to be used as part of the response to an epidemic, ethical protocols for managing informed consent and introducing them in clinical settings must be planned in advance with at-risk communities (box ). trial designs precision medicine refers to the use of genomic sequencing to retrace the specific course of a disease in individual patients, with the aim of being able to choose the best treatment option for each person. in public health, the analogous idea of precisely directing the right intervention to the right population is equally appealing. the potential of such an approach has been illustrated by the identification of two areas in the united states in that were at risk of zika transmission . rather than the whole country, or even only florida, being declared at risk, these two areas each measured less than km , and the response focused only on these specific neighbourhoods. by contrast, a campaign against yellow fever, also in , defined risk 'at the level of entire nations'. a broad interpretation of precision public health incorporates many different types of data to increase the power of epidemiology . such data would not only include genomic information, but also satellite imaging, mobile phone data, social media use data and so on. for example, a study published in combined epidemiological surveillance data, travel surveys, parasite genetics and anonymized mobile phone data to measure the spread of malaria parasites in southeast bangladesh . a retrospective analysis of mobile phone call data in sierra leone from showed how it might have been used to assess the impact of travel restrictions on mobility during the ebola epidemic . the principle of selecting the most relevant information from all available data seems within the scope of good epidemiological practice already. the challenge is recognizing and incorporating new types of data when they become available. should be created as soon as the option becomes viable. the essential consideration is how the resulting data can add to previous trials and influence the approach to trials in future epidemics. for example, research during the - ebola epidemic enabled progress on therapeutic agents that are now being trialled in the ongoing outbreak in drc . scientific progress during and between epidemics must be matched by other workstreams, such as the preparation of supply chain logistics and communication with at-risk populations. plans have to be made for a series of future outbreaks, enabling adaptive, multi-year, multi-country studies . similar plans are needed for continual preclinical research to ensure that future vaccine and therapeutic pipelines will be filled. the term 'one health' is used to acknowledge that human, animal and ecosystem health are tightly interconnected and need to be studied in the context of each other (fig. ) . changes in the environment-whether natural or anthropogenic-affect interactions between pathogens, vectors and hosts in multiple and complex ways, making the emergence or decline of endemic, epidemic and zoonotic diseases difficult to predict, while epidemics of animal diseases can challenge a community's access to food. the fact that pools of viruses, bacteria and parasites are maintained in wild and domesticated animals makes surveillance of potentially zoonotic diseases an intrinsic part of one health epidemic planning. many agencies and nations around the world now use prioritization tools such as those developed by the us cdc or the united nations (un) food and agriculture organization (fao) to identify and prioritize zoonotic diseases of concern. an early precedent was a joint consultation on emerging zoonotic diseases by the who, the fao and the world organisation for animal health in . understanding disease ecology in the zoonotic reservoir could potentially lead to ways to predict the risk of human disease, thus providing the basis for smart early-warning surveillance systems. individual countries with limited resources for epidemiological studies and epidemic preparation and response must decide their own priorities. however, infectious diseases do not respect borders. similarly, the interdisciplinary nature of one health means there are several different lenses through which different sectors assess risks and priorities. for one health approaches to work, these multiple perspectives must be taken into account, whether human health or animal health, ecology or social sciences . epidemics do more than cause death and debilitation: they increase pressure on healthcare systems and healthcare workers and draw resources from services not directly linked to the epidemic. this can leave a legacy of distrust between people, governments and health systems, although more-positive outcomes have been found to strengthen relations between communities and public authorities. the full social and economic costs of the ebola outbreak in west africa have been estimated to be as high as us$ billion when including the effect on health workers, long-term conditions suffered by , ebola survivors, and costs of treatment, infection control, screening and deployment of personnel beyond west africa. as healthcare resources became increasingly allocated to the ebola response, hospital admissions fell and deaths from other diseases rose markedly, adding us$ . billion to the estimated cost. such pressure can be withstood in high-income countries with strong health systems, but in low-income countries the pressure can quickly reach a breaking point. ebola killed almost . % of doctors, nurses and midwives in guinea, . % in sierra leone and just over % in liberia . this is compared to mortality between . % and . % of the whole population of these countries. estimates of the effect of this loss on maternal mortality suggest that thousands more women may have died in childbirth each year since the epidemic ended. beyond the tragic deaths of so many healthcare workers, people were less likely to use health services for children or adults during the epidemic, suggesting decreased trust or even fear of healthcare settings . more recently, in some areas affected by the ebola outbreak in drc, the introduction of free non-ebola healthcare led to unprecedented demand. however, healthcare facilities box in , the prevent project received wellcome funding to provide ethics guidance "at the intersection of pregnancy, vaccines, and emerging and re-emerging epidemic threats" . this was in response to the newly recognized association between infection with zika virus during pregnancy and microcephaly in the newborn. developing a vaccine was an obvious route to explore, but many researchers felt that they could not conduct clinical trials with pregnant women because it is generally assumed that the risk to the woman, the fetus or both outweighs any potential benefit. however, as heyrana et al. argue: "preventing pregnant women from participating in clinical trials is well intentioned but misguided." . prevent rapidly developed guidance for including pregnant women and their babies in zika vaccine research , and has since extended their scope to "a roadmap for the ethically responsible, socially just, and respectful inclusion of the interests of pregnant women in the development and deployment of vaccines against emerging pathogens." . integrating ethics in the preparation and response to epidemics does not close off avenues of research; it opens up possibilities and expedites progress. were not given sufficient additional resources to care for the number of people, which may have contributed to nosocomial infections. survivors, too, need to be cared for long after the epidemic is declared over. a cohort of more than , children is growing up in brazil after being born with microcephaly because their mothers were infected with zika during pregnancy. tracking the development of these children increases understanding of the effects of zika infection and helps to define what medical and social support the affected families may need as many of the children will grow up with severe developmental delays . the challenges posed by twenty-first century epidemics are real and changing: future epidemics will be fuelled by conflict, poverty, climate change, urbanization and the broader demographic transition. in our response we must consider epidemics not as discrete events, but rather as connected cycles for which we can prepare, even if we cannot predict specific outbreaks. the challenge is then to choose the right response at the right scale in the right area at the right time. there needs to be a greater emphasis on absorbing and using positive lessons from each episode and avoiding those that led to negative outcomes . the way that we train practitioners and researchers working in all fields relevant to today's epidemic landscape has to change. a modern approach that is capable of characterizing epidemics and the best ways to control them must go beyond a narrow definition of epidemiology that sustains artificial barriers between disciplines. instead, it must be able to integrate tools and practices from a diverse range of established and emerging scientific, humanistic, political, diplomatic and security fields. we believe that such an approach needs to become the norm for the curriculums of schools of public health around the world. as well as training new generations of epidemiologists so that they have the skills, knowledge and networks to recognize and make use of every tool available to help them to do their work effectively, the entire architecture of the response to epidemics has to be adapted. only then will we be able to maintain the comprehensive and effective response-including prevention and research-needed to stop epidemics and protect people's lives, no matter what the circumstances. celebration: william farr ( - )-an appreciation on the th anniversary of his birth rediscovering ignaz philipp semmelweis ( - ) louis-rene villerme ( - ), a pioneer in social epidemiology: re-analysis of his data on comparative mortality in paris in the early th century john snow's legacy: epidemiology without borders this is a wide-ranging meeting report that places modern epidemiology in the context of the past two hundred years and highlights the importance of bringing in new disciplines, remaining open-minded and using those skills across a wider range of societal issues than are traditionally considered public health robert koch and the cholera vibrio: a centenary epidemiology for the uninitiated the epidemiologic transition. a theory of the epidemiology of population change large ebola outbreaks new normal, says who applied epidemiology and public health: are we training the future generations appropriately? managing epidemics: key facts about major deadly diseases ignaz semmelweis, carl mayrhofer, and the rise of germ theory history of vaccination the global eradication of smallpox from emergence to eradication: the epidemiology of poliomyelitis deconstructed natural history of infectious disease p farr's law applied to aids projections epidemiology-is it time to call it a day? global rise in human infectious disease outbreaks pandemics, public health emergencies and antimicrobial resistance -putting the threat in an epidemiologic and risk analysis context how urbanization affects the epidemiology of emerging infectious diseases microbial evolution and co-adaptation: a tribute to the life and scientific legacies of joshua lederberg travel, migration and emerging infectious diseases understanding the link between malaria risk and climate the ebola outbreak, fragile health systems, and quality as a cure health inequalities and infectious disease epidemics: a challenge for global health security historical parallels, ebola virus disease and cholera: understanding community distrust and social violence with epidemics war and infectious diseases: challenges of the syrian civil war pandemic influenza preparedness framework for the sharing of influenza viruses and access to vaccines and other benefits (who how africa can quell the next disease outbreaks the ability to prevent, detect and respond to any health issues will always depend on the local capacity and although international partners can bring complementary expertise and resources, it is the local capacity that is critical; in this article, the authors argue for national investment in public health, health systems, science and local leadership un health chief orders probe into misconduct the inverse care law agenda setting, research questions and funding for biomedical research has historically been led from northern hemisphere countries in an unequal northern-southern hemisphere relationship science granting councils in sub-saharan africa: trends and tensions international federation of red cross and red crescent societies. community-based surveillance: guiding principles conflict and emerging infectious diseases institutional trust and misinformation in the response to the - ebola outbreak in north kivu, dr congo: a population-based survey application of social science in the response to ebola towards people-centred epidemic preparedness and response: from knowledge to action anthropology in public health emergencies: what is anthropology good for? launching a new era for behavioural surveillance integrated biological-behavioural surveillance in pandemic-threat warning systems taking connected mobile-health diagnostics of infectious diseases to the field population mobility reductions associated with travel restrictions during the ebola epidemic in sierra leone: use of mobile phone data national and local influenza surveillance through twitter: an analysis of the - influenza epidemic social media and internet-based data in global systems for public health surveillance: a systematic review isaric. protocols & data tools enhancing early warning capabilities and capacities for food safety real-time, portable genome sequencing for ebola surveillance infection control in the new age of genomic epidemiology genomic surveillance elucidates ebola virus origin and transmission during the outbreak genetic diversity and evolutionary dynamics of ebola virus in sierra leone genomic analysis of lassa virus during an increase in cases in nigeria the integration of genomics and other types of data into the surveillance, prevention and response of epidemics is critical and can help to transform the ability to enhance public health; although the tools are now available, it will be key to ensure that these new approaches are fully integrated and not seen as esoteric ivory tower research, but instead as an essential component of twenty-first century epidemiology, public health and epidemics-the next generation of leaders need to be efficacy and effectiveness of an rvsv-vectored vaccine in preventing ebola virus disease: final results from the guinea ring vaccination, open-label, cluster-randomised trial (ebola Ça suffit!) a seminal study that shows that ring vaccination could be used in the midst of a devastating ebola epidemic and, furthermore, that innovation research can be conducted in an epidemic, trial designs can be adapted without compromising scientific integrity and that ebola can be prevented through vaccination ethical rationale for the ebola "ring vaccination" trial design ebola vaccination in the democratic republic of the congo insights from clinical research completed during the west africa ebola virus disease epidemic gone or forgotten? the rise and fall of zika virus current status of zika vaccine development: zika vaccines advance into clinical evaluation cepi: preparing for the worst the development of global vaccine stockpiles the ebola clinical trials: a precedent for research ethics in disasters it is an ethical imperative to consider and implement research in an epidemic setting as, for many epidemic diseases, it is the only time at which to conduct the research that will inform and improve the lives of the individuals affected during epidemic and to ensure that future generations are better prepared; however, such research is challenging at many levels and it is critical to have an ethical framework that guides the research, places individuals and communites at the heart of the research and facilitates the maximum benefit for the maximum number of people improving vaccine trials in infectious disease emergencies progression of ebola therapeutics during the - outbreak ebola therapies: an unconventionally calculated risk performance of different clinical trial designs to evaluate treatments during an epidemic the one health concept: years old and a long road ahead surveillance of zoonotic infectious disease transmitted by small companion animals prioritizing zoonoses: a proposed one health tool for collaborative decision-making evaluation of the emergency prevention system (empres) programme in food chain crises report of the who/fao/oie joint consultation on emerging zoonotic diseases (who european centre for disease prevention and control. towards one health preparedness the economic and social burden of the ebola outbreak in west africa epidemics cause enormous disruption to countries, regions and the world; however, the focus is often on the epidemic itself, the pathogen and its immediate effect rather than the much broader effect that the epidemic has not only on the healthcare system-which lasts long after the epidemic itself-as routine vaccination programmes often collapse, maternal-child health suffers, and malaria, hiv and tuberculosis clinics and surgery-all aspects of healthcare-are disrupted, but also on the wider society, as mistrust and tension occurs between citizens, authorities and governments, and education, investments, businesses, trade and tourism inevitablely suffer leading to an economic impact that can health-care worker mortality and the legacy of the ebola epidemic patterns of demand for non-ebola health services during and after the ebola outbreak: panel survey evidence from further pieces of evidence in the zika virus and microcephaly puzzle responding to the ebola virus disease outbreak in dr congo: when will we learn from sierra leone? artificial intelligence in medical practice: the question to the answer? artificial intelligence and big data in public health structure of rsv fusion glycoprotein trimer bound to a prefusionspecific neutralizing antibody vaccine platforms: state of the field and looming challenges platform technologies for modern vaccine manufacturing four steps to precision public health precision" public health -between novelty and hype offline: in defence of precision public health mapping imported malaria in bangladesh using parasite genetic and human mobility data pregnant women & vaccines against emerging epidemic threats: ethics guidance for preparedness, research, and response increasing the participation of pregnant women in clinical trials the ethics working group on zikv research & pregnancy. pregnant women & the zika virus vaccine research agenda: ethics guidance on priorities, inclusion, and evidence generation acknowledgements we thank m. regnier at wellcome for editing the manuscript.author contributions all authors developed the scope and focus of the review and contributed to the writing of the manuscript. the authors declare no competing interests. correspondence and requests for materials should be addressed to j.f. reviewer information nature thanks peter byass, sharon peacock and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. reprints and permissions information is available at http://www.nature.com/reprints. publisher's note springer nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. key: cord- -nzh aux authors: caley, peter; becker, niels g.; philp, david j. title: the waiting time for inter-country spread of pandemic influenza date: - - journal: plos one doi: . /journal.pone. sha: doc_id: cord_uid: nzh aux background: the time delay between the start of an influenza pandemic and its subsequent initiation in other countries is highly relevant to preparedness planning. we quantify the distribution of this random time in terms of the separate components of this delay, and assess how the delay may be extended by non-pharmaceutical interventions. methods and findings: the model constructed for this time delay accounts for: (i) epidemic growth in the source region, (ii) the delay until an infected individual from the source region seeks to travel to an at-risk country, (iii) the chance that infected travelers are detected by screening at exit and entry borders, (iv) the possibility of in-flight transmission, (v) the chance that an infected arrival might not initiate an epidemic, and (vi) the delay until infection in the at-risk country gathers momentum. efforts that reduce the disease reproduction number in the source region below two and severe travel restrictions are most effective for delaying a local epidemic, and under favourable circumstances, could add several months to the delay. on the other hand, the model predicts that border screening for symptomatic infection, wearing a protective mask during travel, promoting early presentation of cases arising among arriving passengers and moderate reduction in travel volumes increase the delay only by a matter of days or weeks. elevated in-flight transmission reduces the delay only minimally. conclusions: the delay until an epidemic of pandemic strain influenza is imported into an at-risk country is largely determined by the course of the epidemic in the source region and the number of travelers attempting to enter the at-risk country, and is little affected by non-pharmaceutical interventions targeting these travelers. short of preventing international travel altogether, eradicating a nascent pandemic in the source region appears to be the only reliable method of preventing country-to-country spread of a pandemic strain of influenza. the emergence of a pandemic strain of influenza is considered inevitable [ ] . provided the emerged strain is not too virulent, it may be possible to eliminate a nascent influenza pandemic in the source region via various combinations of targeted antiviral prophylaxis, pre-vaccination, social distancing and quarantine [ , ] . if early elimination in the source region is not achieved, then any delay in a local epidemic that a country can effect will be highly valued. to this end, countries may consider introducing non-pharmaceutical interventions such as border screening, promoting early presentation of cases among arriving passengers, requiring the use of personal protective equipment during travels (e.g. the wearing of masks), and reducing traveler numbers. while the case for believing that measures such as these can not stop the importation of an epidemic from overseas has been argued strongly, whether it be sars or influenza [ ] [ ] [ ] , the extent to which such interventions delay a local epidemic is currently not well quantified, and hence of considerable interest. in this paper we demonstrate how the delay to importation of an epidemic of pandemic strain influenza may be quantified in terms of the growing infection incidence in the source region, traveler volumes, border screening measures, travel duration, inflight transmission and the delay until an infected arrival initiates a chain of transmission that gathers momentum. we also investigate how the delay is affected by the reproduction number of the emerged strain, early presentation of cases among arriving passengers, and reducing traveler numbers. as noted in previous simulation modeling [ ] , many aspects of this delay have a significant chance component, making the delay a random variable. therefore, the way to quantify the delay is to specify its probability distribution, which we call the delay-distribution. some issues of the delay distribution, such as the natural delay arising in the absence of intervention and the effect that reducing traveler numbers has on this delay has been studied previously [ ] [ ] [ ] . specifically, if the originating source is not specified, and homogeneous mixing of the worlds population is assumed, then the most likely time to the initial cases arising in the united states is about days assuming r = . [ ] . the additional delay arising from travel restrictions appears minimal until a. % reduction in traveler numbers [ ] [ ] [ ] . this paper adds to previous work [ ] [ ] [ ] [ ] by simultaneously including a wider range of epidemiological factors and possible interventions, such as elevated in-flight transmission, flight duration, the effect of wearing of mask during flight, early presentation of cases among travelers, and quarantining all passengers from a flight with a detected case at arrival. consider a region in which a new pandemic strain of influenza has emerged, and a region currently free from the infection. we refer to these as the source region and the at-risk country, respectively. travel between these countries is predominantly via commercial air travel and/or rapid transport which could potentially be subject to border screening and other interventions. we restrict our discussion to air travel. the aim is to assess the effects that a variety of non-pharmaceutical border control measures have, individually and in combination, on the time it takes before the epidemic takes off in the at-risk country. an epidemic is said to have ''taken off'' when it reaches current infectious cases, after which its growth is highly predictable (i.e. nearly deterministic) and the probability of fade-out by chance is very low, if intervention is not enhanced. the source country of origin will undoubtedly have a large impact on the natural delay until importation of an epidemic, although this is difficult to quantify [ ] . an alternative is to fix the originating city, for example a highly connected city such as hong kong [ ] , with the obvious effect that results are highly dependent on the choice. we adopt no specific source region, but assume that the number of international travelers originating from it is reasonably small (see methods), suggestive of a rural or semirural source region [ ] . it is further assumed that the current heightened surveillance for pandemic influenza is continued and that a nascent pandemic with human-to-human transmission is identified and the pandemic is declared when there are concurrent cases in the source region. for an epidemic to take off in an at-risk country, a series of events need to occur. first, the epidemic needs to get underway in the source region. second, an intending traveler needs to be infected shortly before departure. third, the infected traveler must actually travel and successfully disembark in the at-risk country. fourth, the infected traveler, or fellow travelers infected during the flight, must initiate an epidemic in the at-risk country with the infectiousness that remains upon arrival. finally, the epidemic needs to reach a sufficient number of cases to begin predictable exponential growth. international spread of the emerged pandemic strain of influenza may occur when a recently infected person travels. by 'recently infected' we mean that their travel is scheduled to occur within ten days of being infected. we assume that the number of individuals traveling from the source region to the at-risk country each day is known. the probability that a randomly selected traveler is a recently-infected person is taken to be equal to the prevalence of recently-infected people in the source region on that day. the incidence of infection in the source region is assumed to grow exponentially initially, with the rate of exponential growth determined by the disease reproduction number (the mean number of cases a single infective generates by direct contact) and the serial interval (the average interval from infection of one individual to when their contacts are infected) ( figure a) . the time since infection of a recently-infected traveler is a key component of the calculations, because it affects the chance of positive border screening, the chance of in-flight transmission and the infectivity remaining upon arrival in the at-risk country. the time since infection at the time of scheduled departure is random and the dependence of its probability distribution on the exponential growth rate of infection is illustrated by figure b (see also supporting information). the higher the epidemic growth rate in the source region, the greater the probability than an infected traveler will have been infected more recently. it is assumed that individuals detected by departure screening are prevented from traveling. to be detected by screening an infected traveler must be symptomatic and positively screened. an individual is assumed to become symptomatic hours after being infected (cf. [ ] who use . days). the probability of being symptomatic when presenting for departure screening is computed from the curve in figure b . the distribution of the time since infection immediately after departure screening, given that the infected traveler was not detected, is given by the curve in figure c . it contains an adjustment for the probability of being detected at departure. the instantaneous rate at which susceptible contacts are infected depends on the time since infection, and is described by an infectiousness function ( [ ] , page ). we use a peaked infectiousness function, motivated by viral shedding and household transmission data [ ] , which has a serial interval of . days. the basic reproduction number (r ), namely the reproduction number when there is no intervention in place and every contacted individual is susceptible, is given by the area under the infectiousness function. however, our concern is with the effective reproduction number r that holds when various interventions are in place. we obtain any r by simply multiplying the infectiousness function by the appropriate constant (to make the area under the curve equal to r). this keeps the serial interval the same. in the absence of suitable data we assume for most scenarios that the aircrafts ventilation and filtration systems are functioning properly, and that infected travelers transmit the infection at the same rate during a flight as they would while mixing in the community. we examine the sensitivity of this assumption by increasing the inflight transmission by as much as -fold (as could potentially happen if air-circulation and filtration systems malfunction, e.g. see [ ] ). the in-flight transmission rate is set to zero under the optimistic scenario that all travelers wear % effective masks during transit. in terms of a sensitivity analysis this illustrates what would be achievable in a best-case scenario. the number of offspring that an infected traveler infects during a flight is a random variable, taken to have a poisson distribution with a mean equal to the area under the infectiousness function over to the flight duration. travelers infected during flights of less than hours duration are asymptomatic at arrival and will not be detected by screening. the probability that an arriving traveler who was infected in the source region is detected on arrival is computed from the distribution of the time since infection on arrival. this distribution is obtained from the curve in figure c by shifting it to the right by an amount equal to the duration of the flight. the distribution of the time since infection for an individual infected in the source region, who passes through arrival screening undetected has a further adjustment for the chance of being detected at arrival ( figure d ). this curve shows that an infected traveler who escapes detection at departure and arrival is highly likely to enter the at-risk country with most, or all, of their infectious period remaining. authorities are assumed to implement one of two control options when detecting an infected traveler by arrival screening. under option one (individual-based removal), all passengers who test negative are released immediately and only passengers who test positive are isolated. under the second option (flight-based quarantining), authorities prevent all passengers from dispersing into the community until the last person has been screened from that flight. should any one passenger be detected as infected then all passengers will be quarantined, as previously recommended [ ] . transmission chains can be initiated in the at-risk country by infected travelers who mix within the community upon arrival. suppose now that a flight arrives with one, or more, infected passengers who mix within the community. we classify these infected arrivals into those who are 'pre-symptomatic' and those who are 'symptomatic' at entry. it is assumed that the 'symptomatic' infected arrivals do not recognize their symptoms as pandemic influenza and will not present to medical authorities. in other words, they spend the remainder of their infectious period mixing in the community. on the other hand, the 'presymptomatic' infected arrivals, including all individuals infected during flight, are assumed to mix freely in the community only from entry until they present to medical authorities after some delay following the onset of symptoms. not all infected travelers entering the community initiate a 'major' epidemic, even when the reproduction number (r) exceeds one. quite generally, the distribution of the size of an epidemic initiated by an infected arrival is bimodal, with distinct peaks corresponding to a major epidemic and a minor outbreak ( figure e ). in the latter event the outbreak simply fades out by chance despite there being ample susceptibles in the population for ongoing trans- in (b), the step illustrates the probabilistic removal of travelers who have completed their incubation period. in (d), the distribution of time since infection in (c) will have shifted to the right by an amount equal to the flight duration, and cases incubated in-flight may be detected by symptomatic screening, as will those symptomatic cases that were not detected previously. screening sensitivity for this illustration is % on both departure and arrival. (e) upon entering the community undetected, an infected traveler may initiate a minor (inconsequential) or major epidemic, depending on the characteristics of the disease and public health policy. doi: . /journal.pone. .g mission [ ] . the number of cases in an outbreak that fades out is typically very small compared to an epidemic. the probability that a typical infective generates a local epidemic is computed by using a branching process approximation [ ] for the initial stages of the epidemic, and equating 'epidemic' with the event that the branching process does not become extinct. this calculation is well known (e.g. [ ] , page ), but is modified here to allow for the fact that the process is initiated by a random number of infected arrivals and some of them have spent a random part of their infectious period before arriving in the at-risk country. the distribution for the random number of individuals infected by an infected individual when all their contacts are with susceptible individuals is needed for the calculation. the lack of data prevents a definitive conclusion for the most appropriate offspring distribution for influenza transmission [ ] , and we use a poisson distribution with a mean equal to r, discounted for individuals who spent only some of their infectious period mixing in the at-risk country. a poisson offspring distribution is appropriate when the area under the infectiousness function is non-random (i.e. all individuals have the same infection 'potential'). we assume that r is the same in the source region and the at-risk country. for an undetected infected traveler and all their in-flight offspring to fail to initiate an epidemic on arrival, all of the chains of transmission they initiate must fail to become large epidemics (see supporting information). we calculate the probability distribution of d, the total delay until an epidemic gathers momentum by noting that it is given by d = d +d , where d is the time until an epidemic is first initiated and d is the time from initiation until the local epidemic gathers momentum. for an epidemic to be first initiated in the at-risk country on day d, it must have not been initiated on all previous days. hence the probability distribution of the time delay (d ) until the epidemic is first initiated in the at-risk country following identification in the source region is described by: pr (d ~d )~ p p p p p p ::: p p d{ p d where p d denotes the probability that the epidemic is initiated on day d , and p p d~ {p d denotes the probability that the epidemic is not initiated on day d (see supporting information for calculation of p d ). once successfully initiated, an epidemic may initially hover around a handful of cases before reaching a sufficient number of cases for its growth to become essentially predictable. as mentioned, concurrent cases is our criterion for an epidemic to have gathered momentum. we determine the distribution of d , the time to this occurrence, from , stochastic simulations and approximate this empirical distribution by a shifted gamma distribution. our criterion of concurrent cases is conservatively high, as results from the theory of branching processes shows that the probability of a minor epidemic (and hence no take-off) starting from concurrent cases is about when r = . , and even smaller for higher values of r. finally, the distribution of the total delay (d = d +d ) from the pandemic being identified in the source region until cases in the at-risk country was calculated by the convolution of the distributions of d and d . for the illustrative purposes, we chose values of . , . and . for r, which encompass estimates proposed for previous pandemics [ , , ] . the number of people within the infected source region was assumed reasonably small ( million), and there was one flight per day traveling from the source region to the at-risk country carrying , or passengers. a higher number of travelers affects the delay only marginally, assuming the epidemic takes off in the source region (see results). we assume a typical travel duration between attempted departure and possible arrival of hours, but also examine the effect of varying this from - hours. the time to presentation following symptom onset is varied from 'immediately' to 'never presenting', with a time of hours considered likely in the presence of an education campaign. the sensitivity of symptomatic screening is varied from - %, with results presented for , and % sensitivity. the probability that a recently infected traveler evades screening is substantial even if screening reliably detects symptomatic travelers (figure a) , because the typical travel duration is shorter than the -day incubation period. in addition, during the early stages of the epidemic a high r in the source region acts to increase the probability that an infected traveler has been infected quite recently and hence will escape detection due to being asymptomatic during their travels (figure a ). for example, assuming % sensitivity for detecting symptomatic infection, we calculate that during the early stages of the epidemic the proportion of infected travelers that evade both departure and arrival screening after hours of travel is . , . and . for disease reproduction numbers . , . and . , respectively. as the duration of travel approaches the disease incubation period, effective symptomatic screening substantially reduces the likelihood that a traveler evades screening and initiates an epidemic ( figure b ). reducing the time from the onset of symptoms to presentation (and subsequent isolation) for each infected arrival also reduces the probability that a major epidemic is initiated, however the best case scenario of infected travelers and all their in-flight offspring presenting immediately following the onset of symptoms still poses a substantial risk of epidemic initiation arising from pre-symptomatic transmission ( figure c ). the delay contains a fairly substantial natural component, primarily due to the time it takes to increase the number of infectives in the source region sufficiently to make the chance of a recently infected traveler appreciable ( figure a ), and the time (d ) it takes for a local epidemic in the at-risk country to gather momentum following successful seeding ( figure a ). in the absence of any interventions, the number of infected individuals who successfully enter the community of the at-risk country initially increases exponentially ( figure a ). with individual-based removal of infected travelers, the number of individuals entering the at-risk country undetected by screening is proportionately reduced over the course of the epidemic ( figure a ). with flightbased quarantining, the number of infected individuals entering the at-risk country undetected is dramatically reduced over the course of the epidemic, even for relatively insensitive screening ( figure a ). with flight-based quarantining, the number of infected passengers slipping through undetected is bimodal, with the first peak occurring when the number of infected travelers attempting to travel is still in single figures. without screening, the daily probability that an epidemic is initiated (p d ) increases, and becomes near certain once the number of infected travelers arriving undetected exceeds about ( figure b, solid line) . with screening and individual-based removal of infected individuals, p d follows a similar pattern only reduced somewhat. with screening in combination with flightbased quarantining, this probability is changed dramatically. after an initial rise it dips, to become essentially zero during the height of the epidemic in the source region ( figure b , dotted line). this arises because once a flight has several infected travelers, the probability that at least one is detected approaches one (even if screening is imperfect), and all passengers on such a flight are quarantined. once the epidemic starts to wane in the source region (assuming the unlikely event of the pandemic strain is restricted to the source region), the probability of initiation rises once again. the corresponding distribution of d , the delay until the effects of r and the time from symptom onset to presentation on the probability that an infected traveler, having entered the wider community following arrival, will initiate an epidemic. there is no screening. doi: . /journal.pone. .g the epidemic is first initiated in the at-risk country, is bi-modal in the presence of screening ( figure c) . although flight-based quarantining is effective in preventing the entry of infected travelers during the height of the epidemic, a substantial cumulative risk of initiation has already occurred before this from the handful of infectives that have slipped through undetected ( figure b ). hence, whilst the effect of border screening, particularly in conjunction with flight-based quarantining, on the daily probability of initiation is dramatic, its effect on the delay to initiation is much less pronounced ( figure c ). border screening, even with perfect sensitivity for detecting symptomatic cases, tends to increase d , the time to an epidemic being initiated, by a matter of days to weeks. the time (d ) from initiation (the arrival of the index case) to an epidemic reaching concurrent cases within the at-risk country is adequately modeled using a shifted gamma distribution ( figure a ). the convolution of this right-skewed gamma distribution with the left-skewed delaydistribution of d (figure c ) yields the distribution for d, the total delay until the epidemic reaches cases in the at-risk country ( figure b ). the distribution of d is approximately symmetrical. the effect of border screening on the total delay d is quite modest, though sensitive to how screening is implemented. for example, with r = . and travelers per day, % sensitive screening with individual-based removal increases the median delay from to days ( figure b ). flight-based quarantining would extend the median delay to days. in general, the added delay arising from flight-based quarantining is about four-fold that arising from individual-based removal. the natural component of the delay is highly sensitive to the disease reproduction number ( figure a ). for example, with passengers per day departing the source country and in the absence of any interventions, the median delay ranges from a low of days for r = . to days for r = . ( table ). the delay is less sensitive to the number of intending travelers, with little appreciable increase in the median delay occurring until traveler numbers become very low ( figure b ). for example, if r = . , with no other border control measures, decreasing the number of intending travelers departing the source region from to per day increases the median total delay d from to days. a further decrease in the number of intending travelers to per day increases the median delay to days ( table ) . the delay is quite insensitive to the rate of transmission in-flight. for example, with r = . , a -hour flight, travelers per day and no other interventions, preventing in-flight transmission altogether increases the median delay from to days. conversely, doubling the rate of in-flight transmission reduces the median delay from to days. a -fold increase in the rate of transmission in-flight only decreases the median delay from to days. encouraging the early presentation of cases among travelers following the onset of symptoms has a limited effect on the delay distribution ( figure c ). for example, for r = . , intending travelers per day and no other interventions, reducing the time to presentation from 'never presenting' to hours increases the median delay from to days. immediate presentation at symptom onset only increases the median delay a further day in this scenario. in general, the additional delay achieved by introducing nonpharmaceutical border control measures is generally small in comparison with the natural delay ( figure d ). for the scenario with r = . and intending travelers per day, a combination of % flight-based quarantining, % compliance with mask wearing during travel and immediate presentation at symptom onset extends the estimated median delay from to days ( figure d ). this added delay diminishes in absolute terms as r increases. for example, if the same interventions are applied with r = . , the median delay is extended from to just days ( figure d ). the one exception to this generalisation is when travel numbers are reduced dramatically. the added delay achieved when a drastic reduction in travel numbers is combined with other border control measures appears to be greater than adding the delays each achieves on its own. for example, if r = . , and we reduce the number of intending travelers from to per day, implement % flight-based quarantining, implement compulsory mask wearing during travel and presentation at hours following symptom onset then there is a substantial probability ( . ) that the pandemic strain will never be imported (assuming the epidemic is confined to the source country). the estimated quartile delay (the median in this case is undefined) to the start of a major epidemic in an at-risk country is extended from to days. again, the added delay decreases rapidly as r increases, and if the above interventions were applied with r = . , the estimated median delay is extended from to days, and the importation of the epidemic is certain ( figure d ). we have formulated a model of the importation of an infectious disease from a source region to an at-risk country that permits a comprehensive analysis of the effect of border control measures. our results are most relevant to the early stage of a pandemic when most cases are contained within a single source region. once the pandemic has spread to several countries, models with greater complexity and ability to more realistically model global mixing patterns [ ] [ ] [ ] are required. our model is developed with a pandemic-strain of influenza in mind, but could apply to any emerging infectious disease that is transmitted from person to person. we have assumed a poisson distribution for the number of secondary infections, which a natural choice when each infected individual has the same infectivity profile. a distribution with a larger variance is appropriate when individuals vary substantially in their infectiousness. our results are conservative in the sense that they give an upper bound for the probability that an infected traveler manages to initiate an epidemic, compared to an offspring distribution with a greater variance but the same reproduction number [ ] . the nature of the next pandemic influenza virus, and particularly its reproduction number, is uncertain. if its reproduction number is low (r, . ), our results indicate that at-risk countries receiving a reasonably small number of travelers (say per day) from the infected source region can expect a natural delay until importing an epidemic of the order of months. this is quite variable and under favourable conditions it could be months. however, the natural delay decreases rapidly as r increases. the additional delay from isolating individuals detected by border screening is merely a few days under most plausible scenarios, even if both departure and arrival screening is introduced and screening detects every symptomatic traveler. while the extra delay is more than quadrupled if flights with a detected case(s) are quarantined, the effect remains modest (weeks at most) and it is questionable whether the extra delay achieved warrants the disruption created by such a large number of quarantined passengers. in-flight transmission is a commonly raised concern in discussions about the importation of an infection, so inclusion of in-flight transmission is an attractive feature of our model. events of substantial in-flight transmission of influenza have been documented [ , ] and modeling of indoor airborne infection risks in the absence of air filtration predicts that in-flight transmission risks are elevated [ ] . however, it difficult to estimate the infectiousness of influenza in a confined cabin space, as there is undoubtedly substantial under-reporting of influenza cases who travel and fail to generate any offspring during flight. provided the aircraft ventilation system (including filtration) is operational, it is considered that the actual risk of in-flight transmission is much lower than the perceived risk [ ] . our results indicate that the delay is relatively insensitive to the rate of in-flight transmission, making in-flight transmission less of an issue than commonly believed. a highly elevated transmission rate inflight will hasten the importation of an epidemic only marginally. consistent with this, eliminating in-flight transmission by wearing protective masks increases the delay only marginally. early presentation by infected arrivals not detected at the borders was found to add only a few days to the delay. to some extent this arises due to our assumption that pre-symptomatic transmission can occur, for which there is some evidence. in contrast, ferguson et al. [ ] assume that the incubation and latent periods are equal, with a mean of . days. in their model presymptomatic transmission is excluded and infectiousness is estimated to spike dramatically immediately following symptom onset and declining rapidly soon afterwards. under their model assumptions, immediate presentation at onset of symptoms would reduce transmission effectively. however, as presentation occurs some time after onset of symptoms and the bulk of infectivity occurs immediately after onset of symptoms the results on the effect of early presentation of cases are likely, in practical terms, to be similar to those found here. given the variable nature of influenza symptoms, there is likely to be a difference between the onset of the first symptoms as measured in a clinical trial (e.g. [ ] ) and the time that a person in the field first suspects that they may be infected with influenza virus. to fully resolve the issue of how effective very early presentation of infected travelers is in delaying a local epidemic we need better knowledge about the infectiousness of individuals before and just after the onset of symptoms. it is assumed that the pandemic is identified and declared when there are concurrent cases in the source region attributed to human-to-human transmission, and that screening is applied at both departure and arrival. the time between screening events is assumed to be hours and infected travelers are not isolated following the onset of symptoms. of the border control measures available, reducing traveler numbers has the biggest effect on the delay and even then it is necessary to get the number of travelers down to a very low number. an equivalent control measure is to quarantine all arriving passengers with near perfect compliance. our results indicate that short of virtually eliminating international travel, border control measures add little to avoiding, or delaying, a local epidemic if an influenza pandemic takes off in a source region. all forms of border control are eventually overwhelmed by the cumulative number of infected travelers that attempt to enter the country. the only way to prevent a local epidemic is to rapidly implement local control measures that bring the effective reproduction number in the local area down below , or to achieve rapid elimination in the source region, in agreement with other recent studies [ ] [ ] [ ] . preventing the exponential growth phase of an epidemic in the source region appears to be the only method able to prevent a nascent influenza pandemic reaching atrisk countries. text s estimating the daily probability of epidemic initiation found at: doi: . /journal.pone. .s ( . mb pdf) mitigation strategies for pandemic influenza in the united states strategies for containing an emerging influenza pandemic in southeast asia containing pandemic influenza at the source border screening for sars entry screening for severe acute respiratory syndrome (sars) or influenza: policy evaluation delaying the international spread of pandemic influenza strategies for mitigating an influenza pandemic will travel restrictions control the international spread of pandemic influenza analysis of infectious disease data an outbreak of influenza aboard a commercial airline should be expect population thresholds for wildlife disease? the theory of branching processes matrix population models: construction, analysis, and interpretation superspreading and the effect of individual variation on disease emergence transmissibility of pandemic influenza influenza outbreak related to air travel a probabilistic transmission dynamic model to assess indoor airborne infection risks transmission of infectious diseases during commercial air travel use of the oral neuraminidase inhibitor oseltamivir in experimental human influenza we thank james wood, katie glass and belinda barnes and an anonymous reviewer for helpful comments. conceived and designed the experiments: nb pc. performed the experiments: pc dp. analyzed the data: nb pc dp. contributed reagents/materials/analysis tools: pc dp. wrote the paper: nb pc. key: cord- - q zwc authors: aiello, luca maria; quercia, daniele; zhou, ke; constantinides, marios; vs'cepanovi'c, sanja; joglekar, sagar title: how epidemic psychology works on social media: evolution of responses to the covid- pandemic date: - - journal: nan doi: nan sha: doc_id: cord_uid: q zwc disruptions resulting from an epidemic might often appear to amount to chaos but, in reality, can be understood in a systematic way through the lens of"epidemic psychology". according to the father of this research field, philip strong, not only is the epidemic biological; there is also the potential for three social epidemics: of fear, moralization, and action. this work is the first study to empirically test strong's model at scale. it does so by studying the use of language on m social media posts in us about the covid- pandemic, which is the first pandemic to spread this quickly not only on a global scale but also online. we identified three distinct phases, which parallel kuebler-ross's stages of grief. each of them is characterized by different regimes of the three social epidemics: in the refusal phase, people refused to accept reality despite the increasing numbers of deaths in other countries; in the suspended reality phase (started after the announcement of the first death in the country), people's fear translated into anger about the looming feeling that things were about to change; finally, in the acceptance phase (started after the authorities imposed physical-distancing measures), people found a"new normal"for their daily activities. our real-time operationalization of strong's model makes it possible to embed epidemic psychology in any real-time model (e.g., epidemiological and mobility models). in our daily lives, our dominant perception is of order. but every now and then chaos threats that order: epidemics dramatically break out, revolutions erupt, empires suddenly fall, and stock markets crash. epidemics, in particular, present not only collective health hazards but also special challenges to mental health and public order that need to be addressed by social and behavioral sciences . almost years ago, in the wake of the aids epidemic, philip strong, the founder of the sociological study of epidemic infectious diseases, reflected: "the human origin of epidemic psychology lies not so much in our unruly passions as in the threat of epidemic disease to our everyday assumptions." in the recent covid- pandemic (an ongoing pandemic of a coronavirus disease), it has been shown that the main source of uncertainty and anxiety has indeed come from the disruption of what alfred shutz called the "routines and recipes" of daily life (e.g., every simple act, from eating at work to visiting our parents, takes on new meanings). yet, the chaos resulting from an epidemic turns out to be more predictable than what one would initially expect. philip strong observed that any new health epidemic resulted into three social epidemics: of fear, moralization, and action. the epidemic of fear represents the fear of catching the disease, which comes with the suspicion against alleged disease carriers, which, in turn, may spark panic and irrational behavior. the epidemic of moralization is characterized by moral responses both to the viral epidemic itself and to the epidemic of fear, which may result in either positive reactions (e.g., cooperation) or negative ones (e.g., stigmatization). the epidemic of action accounts for the rational or irrational changes of daily habits that people make in response to the disease or as a result of the two other social epidemics. strong was writing in the wake of the aids/hiv crisis, but he based his model on studies that went back to europe's black death in the th century. importantly, he showed that these three social epidemics are created by language and incrementally fed through it: language transmits the fear that the infection is an existential threat to humanity and that we are all going to die; language depicts the epidemic as a verdict on human failings and as a divine moral judgment on minorities; and language shapes the means through which people collectively intend to, however pointless, act against the threat. hitherto, there has never been any large-scale empirical study of whether the use of language during an epidemic reflects strong's model, not least because of lack of data. covid- has recently changed that: it has been the first epidemic in history in which people around the world have been collectively expressing their thoughts and concerns on social media. as such, researchers have had an unprecedented opportunity to study this epidemic in new ways: social media posts have been analyzed in terms of content and behavioral markers , , and of tracking the diffusion of covid-related information coding strong's model back in the s, philip strong was able not only to describe the psychological impact of epidemics on social order but also to model it. he observed that the early reaction to major fatal epidemics is a distinctive psycho-social form and can be modeled along three main dimensions: fear, morality, and action. during a large-scale epidemic, basic assumptions about social interaction and, more generally, about social order are disrupted, and, more specifically, they are so by: the fear of others, competing moralities, and the responses to the epidemic. crucially, all these three elements are created, transmitted, and mediated by language: language transmits fears, elaborates on the stigmatization of minorities, and shapes the means through which people collectively respond to the epidemic , , . we operationalized strong's epidemic psychology theoretical framework in two steps. first, three authors hand-coded strong's seminal paper using line-by-line coding to identify keywords that characterize the three social epidemics. for each of the three social epidemics, the three authors generated independent lists of keywords that were conservatively combined by intersecting them. the words that were left out by the intersection were mostly synonyms (e.g., "catching disease" as a synonym for "contagion"), so we did not discard any important concept. according to strong, the three social epidemics are intertwined and, as such, the concepts that define one specific social epidemic might be relevant to the remaining two as well. for example, suspicion is an element of the epidemic of fear but is tightly related to stigmatization as well, a phenomenon that strong describes as typical of the epidemic of moralization. in our coding exercise, we adhered as much as possible to the description in strong's paper and obtained a strict partition of keywords across social epidemics. in the second step, the same three authors mapped each of these keywords to language categories, namely sets of words that reflect how these concepts are expressed in natural language (e.g., words expressing anger or trust). we took these categories from existing language lexicons widely used in psychometric studies: the linguistic inquiry word count (liwc) , emolex , the moral foundation lexicon , and the prosocial behavior lexicon . the three authors grouped similar keywords together and mapped groups of keywords to one or more language categories. this grouping and mapping procedure was informed by previous studies that investigated how these keywords are expressed through language. these studies are listed in table daily habits concern mainly people's experience of home, work, leisure, and movement between them leisure (liwc) . . . table . operationalization of the strong's epidemic psychology theoretical framework. from strong's paper, three annotators extracted keywords that characterize the three social epidemics and mapped them to relevant language categories from existing language lexicons used in psychometric studies. category names are followed by the name of their corresponding lexicon in parenthesis. we support the association between keywords and language categories with examples of supporting literature. to summarize how the use of the language categories varies across the three temporal states, we computed the peak values of the different language categories (days when their standardized fractions reached the maximum), and reported the percentage increase at peak compared to the average over the whole time period; in each row, the maximum value is highlighted in bold. to find occurrences of these language categories in our twitter data, we matched them against the text in each tweet. we considered that a tweet contains a language category c, if at least one of the tweet's words (or word stems) belonged to that / category. for each day, we computed the fraction of users who posted at least one tweet containing a given language category over the total number of users who tweeted during that day. we experimentally checked that each day had a number of data points sufficient to obtain valid metrics (i.e., the minimum number of distinct users per day is above k across the whole period of study). to allow for a fair comparison across categories, we z-standardized each fraction by computing the number of standard deviations from the fraction's whole-period average. figure (a-c) shows how the standardized fractions of all the language categories changed over time. the cell color encodes values higher than the average in red, and lower in blue. we partitioned the language categories according to the three social epidemics. to identify phases characterized by different combinations of the language categories, we determined change-points-periods in which the standardized fractions considerably vary across all categories at once. to quantify such variations, we computed the daily average squared gradient of the standardized fractions of all the language categories. the squared gradient is a measure of the rate of instantaneous change (increase or decrease) of a given point in a time series . figure d shows the value of the average squared gradient over time; peaks in the curve represent the days of high local variation. we marked the peaks above one standard deviation from the mean as change-points. we found two change-points that coincide with two key events: february th , the day of the announcement of the first infection in the country; and march th , the day of the announcement of the 'stay at home' orders. these change-points identify three phases, which are described next by dwelling on the peaks of the different language categories (days when their standardized fractions reached the maximum) and reporting the percentage increase at peak (the increase is compared to the average over the whole period of study, and its peak is denoted by 'max peak' in table ). the first phase (refusal phase) was characterized by anxiety and fear. death was frequently mentioned, with a peak on february of + % compared to its average during the whole time period. the pronoun they was used in this temporal state more than average; this suggests that the focus of discussion was on the implications of the viral epidemic on 'others', as this was when no infection had been discovered in us yet. all other language categories exhibited no significant variations, which reflected an overall situation of 'business-as-usual. ' the second phase (suspended reality phase) began on february th with an outburst of negative emotions (predominantly anger), right after the first covid- contagion in us was announced. the abstract fear of death was replaced by expressions of concrete health concerns, such as words expressing risk, and mentions of how body parts did feel. on march th , the federal government announced the state of national emergency, followed by the enforcement of state-level 'stay at home' orders. during those days, we observed a sharp increase of the use of the pronoun i and of swear words (with a peak of + % on march th ), which hints at a climate of discussion characterized by conflict and polarization. at the same time, we observed an increase in the use of words related to the daily habits affected by the impending restriction policies, such as motion, social activities, and leisure. the mentions of words related to home peaked on march th (+ %), the day when the federal government announced social distancing guidelines to be in place for at least two weeks. the third phase (acceptance phase) started on march th , the day after the first physically-distancing measures were imposed by law. the increased use of words of power and authority likely reflected the emergence of discussion around the new policies enforced by government officials and public agencies. as the death toll raised steadily-hitting the mark of , people on march th -expressions of conflict faded away, and words of sadness became predominant. in those days of hardship, a sentiment of care for others and expressions of prosocial behavior became more frequent (+ % and + %, respectively). last, mentions of work-related activities peaked as many people either lost their job, or were compelled to work from home as result of the lockdown. the language categories capture broad concepts related to strong's epidemic psychology theory, but they do not allow for an analysis of the fine-grained topics within each category. to study them, for each of the combinations of language category and phase ( language categories, for phases), we listed the most retweeted tweets (e.g., most popular tweets containing anxiety posted in the refusal phase). to identify overarching themes, we followed two steps that are commonly adopted in thematic analysis , . we first applied open coding to identify key concepts that emerged across multiple tweets; specifically, one of the authors read all the tweets and marked them with keywords that reflected the key concepts expressed in the text. we then used axial coding to identify relationships between the most frequent keywords to summarize them in semantically cohesive themes. themes were reviewed in a recursive manner rather than linear, by re-evaluating and adjusting them as new tweets were parsed. table summarizes the most recurring themes, together with some of their representative tweets. the thematic analysis revealed that the topics discussed in the three phases resemble the five stages of grief : the refusal phase was characterized by denial, the suspended reality phase by anger mixed with bargaining, and the acceptance phase by sadness together with forbearance. more specifically, in the refusal phase, statements of skepticism were re-tweeted widely ( table , row ). the epidemic was frequently depicted as a "foreign" problem (r. ) and all activities kept business as usual (r. ). in the suspended reality phase, the discussion was characterized by outrage against three main categories: foreigners (r. ), political opponents (r. ), and people who adopted different behavioral responses to the outbreak (r. ). this level of conflict each row in the heatmaps represents a language category (e.g., words expressing anxiety) that our manual coding associated with one of the three social epidemics. the cell color represents the daily standardized fraction of people who used words related to that category: values that are higher than the average are red and those that are lower are blue. categories are partitioned in three groups according to the type of social epidemics they model: fear, morality, and action. (d) average gradient (i.e., instantaneous variation) of all the language categories; the peaks of gradient identify change-pointsdates around which a considerable change in the use of multiple language categories happened at once. the dashed vertical lines that cross all the plots represent these change-points. (e-h) temporal evolution of four families of indicators we used to corroborate the validity of the trends identified by the language categories. we checked internal validity by comparing the language categories with a custom keyword-search approach and two deep-learning nlp tools that extract types of social interactions and mentions of medical symptoms. we checked external validity by looking at mobility patterns in different venue categories as estimated by the gps geo-localization service of the foursquare mobile app. the timeline at the bottom of the figure marks some of the key events of the covid- pandemic in us such as the announcements of the first infection of covid- recorded. corroborates strong's postulate of the "war against each other". science and religion were two prominent topics of discussion. a lively debate raged around the validity of scientists' recommendations (r. ). some social groups put their hopes on god theme example tweets the acceptance phase sadness "we deeply mourn the new yorkers we lost yesterday to covid- . new york is not numb. we know this is not just a number-it is real lives lost forever." we-focus, hope "we are thankful for japan's friendship and cooperation as we stand together to defeat the #covid pandemic.", "during tough times, real friends stick together. the u.s. is thankful to #taiwan for donating million face masks to support our healthcare ", "now more than ever, we need to choose hope over fear. we will beat covid- . we will overcome this. together." authority "you can't go to church, buy seeds or paint, operate your business, run on a beach, or take your kids to the park. you do have to obey all new 'laws', wear face masks in public, pay your taxes. hopefully this is over by the th of july so we can celebrate our freedom. resuming work "we need to help as many working families and small businesses as possible. workers who have lost their jobs or seen their hours slashed and families who are struggling to pay rent and put food on the table need help immediately. there's no time to waste." table . recurring themes in the three phases, found by the means of thematic analysis of tweets. themes are paired with examples of popular tweets. rather than on science (r. ). mentions of people self-isolating at home became very frequent, and highlighted the contrast between judicious individuals and careless crowds (r. ). finally, during the acceptance phase, the outburst of anger gave in to the sorrow caused by the mourning of thousands of people (r. ). by accepting the real threat of the virus, people were more open to find collective solutions to the problem and overcome fear with hope (r. ). although the positive attitude towards the authorities seemed prevalent, some people expressed disappointment against the restrictions imposed (r. ). those who were isolated at home started imagining a life beyond the isolation, especially in relation to reopening businesses (r. ). to assess the validity of our approach, we compared the previous results with the output of alternative text-mining techniques applied to the same data (internal validity), and with people's mobility in the real world (external validity). we processed the very same social media posts with three alternative text-mining techniques (figure e-g). in table , we reported the three language categories with the strongest correlations with each behavioral marker. first, to allow for interpretable and explainable results, we applied a simple word-matching method that relies on a custom lexicon containing three categories of words reflecting consumption of alcohol, physical exercising, and economic concerns, as those aspects have been found to characterize the covid- pandemic . we measured the daily fraction of users mentioning words in each of those categories (figure e) . in the refusal phase, the frequency of any of these words did not significantly increase. in the suspended reality phase, the frequency of words related to economy peaked, and that related to alcohol consumption peaked shortly after that. table shows that economy-related words were highly correlated with the use of anxiety words (r = . ), which is in line with studies indicating that the degree of apprehension for the declining economy was comparable to that of health-hazard concerns , . words of alcohol consumption were most correlated with the language dimensions of body (r = . ), feel (r = . ), home (r = . ); in the period were health concerns were at their peak, home isolation caused a rising tide of alcohol use , . finally, in the acceptance phase, the frequency of words related to physical exercise was significant; this happened at the same time when the use of positive words expressing togetherness was at its highest-affiliation (r = . ), posemo (r = . ), we (r = . ). all these results match our previous interpretations of the peaks for our language categories. second, since it is unclear whether using a standard word count analytic system would allow for the distinction among the three different types of social epidemics, we used a deep-learning natural language processing tool that mines conversations according to how humans understand them in the real world . the tool can classify any textual message according to types of interaction that are close to human-level understanding. in particular, we studied over time the three types most frequently found: expressions of conflict (expressions of contrast or diverging views), social support (emotional aid and companionship), and power (expressions that denote or describe person's power over the behavior and outcomes of another). figure f shows the min-max normalized scores of the fraction of people posting tweets labeled with each of these three interaction types. in refusal phase, conflict increased-this is when anxiety and blaming foreigners were recurring themes in twitter. in the suspended reality phase, conflict peaked (similar to anxiety words, r = . ), yet, since this when the first lock-down measures were announced, initial expressions of power and of social support gradually increased as well. finally, in the acceptance phase, social support peaked. support was most correlated with the categories of affiliation (r = . ), positive emotions (r = . ), and we (r = . ) ( table ) ; power was most correlated with prosocial (r = . ), care (r = . ), and authority (r = . ). again, our previous interpretations concerning the existence of a phase of conflict followed by a phase of social support were further confirmed by the deep-learning tool, which, as opposed to our dictionary-based approaches, does not rely on word matching. third, we used a deep-learning tool that extracts mentions of medical entities from text . when applied to a tweet, the tool accurately extracts medical symptoms in the form of n-grams extracted from the tweet's text (e.g., "cough", "feeling sick"). out of all the entities extracted, we focused on the most frequently mentioned and grouped them into two families of symptoms, respectively, those related to physical health (e.g., "fever", "cough", "sick") and those related to mental health (e.g., "depression", "stress") . the min-max normalized fractions of people posting tweets containing mentions of these symptoms are shown in figure g. in refusal phase, the frequency of symptom mentions did not change. in the suspended reality phase, instead, physical symptoms started to be mentioned, and they were correlated with the language categories expressing panic and physical health concerns-swear (r = . ), feel (r = . ), and negate (r = . ). in the acceptance phase, mentions of mental symptoms became most frequent. interestingly, mental symptoms peaked when the twitter discourse was characterized by positive feelings and prosocial interactions-affiliation (r = . ), we (r = . ), and posemo (r = . ); this is in line with recent studies that found that the psychological toll of covid- has similar traits to post-traumatic stress disorders and its symptoms might lag several weeks from the period of initial panic and forced isolation [ ] [ ] [ ] . to test for the external validity of our language categories, we compared their temporal trends with mobility data. we used the data collection that foursquare made publicly available in response to the covid- crisis through the visitdata.org website. the data consists of the daily number of people in us visiting each of venue types, as estimated by the gps geo-localization service of the foursquare mobile app. we picked three venue categories: grocery shops, travel & transport, and outdoors & recreation to reflect three different types of fundamental human needs : the primary need of getting food supplies, the secondary need of moving around freely (or to limit mobility for safety), and the higher-level need of being entertained. in figure h, we show the min-max normalized number of visits over time. the periods of higher variations of the normalized number of visits match the transitions between the three phases. in the refusal phase, people's mobility did not change. in the suspended reality phase, instead, travel started to drop, and grocery shopping peaked, supporting the interpretation of a phase characterized by a wave of panic-induced stockpiling and a compulsion to save oneself-it co-occurred with the peak of use of the pronoun i (r = . )-rather than helping others. finally, in the acceptance phase, the panic around grocery shopping faded away, and the number of visits to parks and outdoor spaces increased. to embed our operationalization of epidemic psychology into real-time models (e.g., epidemiological models, urban mobility models), our measures need to work at any point in time during a new pandemic, yet, given their current definitions, they do not: that is because they are normalized values over the whole period of study (figure a-c) . to fix that, we designed a new composite measure that does not rely on full temporal knowledge, and a corresponding detection method that determines which of the three phases one is in at any given point in time. for each phase, this parsimonious measure is composed of the language dimensions that positively and negatively characterize the phase. more specifically, it is composed of two dimensions: the dimension most positively associated with the phase (expressed in percent change) minus that most negatively associated with it (e.g., (death -i) for the refusal phase). to identify such dimensions, we trained three logistic regression binary classifiers (one per phase) that use the percent changes of all the language dimensions at time t to estimate the probability that t belongs to phase i (p phase i (t)). the on average, the classifiers were able to identify the correct phase for % of the days. the regressions coefficients were then used to rank the language category by their predictive power. table shows the top three positive beta coefficients and bottom three negative ones for each of the three phases. for each phase, we subtracted the top category from the bottom category without considering their beta coefficients, as these would require, again, full temporal knowledge. the top and bottom categories of all phases belong to the liwc lexicon. the resulting composite measure has change-points ( figure ) similar to the full-knowledge measure's ( figure ) , suggesting that the real-time and parsimonious computation does not compromise the original trends. in a real-time scenario, transition between phases are captured changes of the dominant measure; for example, when the refusal curve is overtaken by the suspended reality curve. in addition, we correlated the composite measures with each of the behavioral markers we used for validation (figure e-h) to find which are the markers that are most typical of each of the phases. we reported the correlations in table . during the refusal phase, conflictual interactions were frequent (r = . ) and long-range mobility was common (r = . ); during the suspended reality phase, as mobility reduced , , people hoarded groceries and alcohol , and expressed concerns for their physical health (r = . ) and for the economy , ; last, during the acceptance phase, people ventured outdoors, started exercising more, and expressed a stronger will to support each other (r = . ), in the wake of a rising tide of deaths and mental health symptoms (r = . ) - . new infectious diseases break out abruptly, and public health agencies try to rely on detailed planning yet often find themselves to improvise around their playbook. they are constantly confronting not only the health epidemic but also the three social epidemics. measuring the effects of epidemics on societal dynamics and population mental health has been an open research table . top three positive and bottom negative beta coefficients of the logistic regression models for the three phases. the categories in bold are those included in our composite temporal score. problem for long, and multidisciplinary approaches have been called for . as our method is easy to use, and can be applied to any public stream of data, it has a direct practical implication on improving the ability to monitor whether people's behavior and perceptions align with or divert from the expectations and recommendations of governments and experts, thus informing the design of more effective interventions . since our language categories are not tailored to a specific epidemic (e.g., they do not reflect any specific symptom an epidemic is associated with), our approach can be applied to a future epidemic, provided that the set of relevant hash-tags associated with the epidemic is known; this is a reasonable assumption to make though, considering that the consensus on twitter hash-tags is reached quickly , and that several epidemics that occurred in the last decade sparked discussions on twitter since their early days [ ] [ ] [ ] . our method could complement the numerous cross-sectional studies on the negative psychological impact of health epidemics , . those studies are usually conducted on a small to medium scale and are costly to carry out; our approach could integrate them with real-time insights from large-scale data. for computer science researchers, our method could provide a starting point for developing more sophisticated tools for monitoring social epidemics. furthermore, from the theoretical standpoint, our work provides the first operationalization of strong's theoretical model of the epidemic psychology and shows its applicability to social media data. furthermore, starting from strong's epidemic psychology, our analysis showed the emergence of phases that parallel kuebler-ross's stages of grief. this demonstrates the centrality of the psychological responses to major life trauma in parallel with any potential physical danger. thus, future research could integrate and apply the two perspectives not just to pandemics, but to large scale disasters and other tragedies. finally, and more importantly, our real-time operationalization of strong's model makes it possible to embed epidemic psychology in any real-time models for the first time. future work could improve our work in five main aspects. first, we focused only on one viral epidemic, without being able to compare it to others. that is mainly because no other epidemic had an online scale comparable to covid- . yet, if one were to obtain past social media data during the outbreaks of diseases like zika , ebola , and the h n influenza , one could apply our methodology in those contexts as well, and identify similarities and differences. for example, one could study how mortality rates or speed of spreading influence the representation of strong's epidemic psychology on social media. second, our geographical focus was the entire united states and, as such, was coarse and limited in scope. our collected data did not provide a sufficient coverage for each individual state in the us. if we were to obtain such high-coverage data, we could relate differences between states to large-scale events (e.g., a governor's decisions, prevalence of cases, media landscape, and residents' cultural traits). in particular, recent studies suggested that the public reaction to covid- varied across us states depending on their political leaning , . one could also apply our methodology to other english-speaking countries, to investigate how cultural dimensions and cross-cultural personality trait variations might influence the three social epidemics. third, the period of study is limited yet proved to be sufficient to discover a clear sequence of collective psychological / phases. future work could explore longer periods to ultimately assess the social epidemics' long-term effects. fourth, our study is limited to twitter, mainly because twitter is the largest open stream of real-time social media data. the practice of using twitter as a way of modeling the psychological state of a country carries its own limitations. despite having a rather high penetration in the us (around % of adults, according to the latest estimates ), its user base is not representative of the general population . additionally, twitter is notoriously populated by bots , , automated accounts that are often used to amplify specific topics or view points. bots played an important role to steer the discussion on several events of broad public interest , , and it is reasonable to expect that they have a role in covid-related discussions too, as some recent studies seem to suggest . to partly discount their impact, since they tend to have anomalous levels of activity (especially retweeting ), we performed two tests. first, we computed all our measures at user-level rather than tweet-level, which counter anomalous levels of activity. second, we replicated our temporal analysis excluding retweets, and obtained very similar results. in the future, one could attempt to adapt our framework to different sources of online data, for example to web search queries-which have proven useful to identify different phases of the public reactions to the covid- pandemic . last, as strong himself acknowledged in his seminal paper: "any sharp separation between different types of epidemic psychology is a dubious business." our work has operationalized each social epidemic independently. in the future, modeling the relationships among the three epidemics might identify hitherto hidden emergent properties. we collected tweets related to covid- from two sources. first, from an existing dataset of , , covid-related tweets , we gathered , , english tweets posted between february st up to april th by , , unique users. we augmented this dataset with our own collection of tweets obtained by querying the twitter streaming api continuously from march th until april th using a list of keywords aligned with the previous data collection : coronavirus, covid , covid , coronaviruslockdown, coronavirusoutbreak, herd immunity, herdimmunity. the streaming api returns a sample of up to % of all tweets. this second crawl got us , , english tweets. by combining the two collections, we obtained , , unique english tweets posted by , , users. as we shall discuss in the remainder of this section, we normalized all our measures so that they are not influenced by the fluctuating volume of tweets over time. we focused our analysis on the united states, the country where twitter penetration is highest. to identify twitter users living in it, we parsed the free-text location description of their user profile (e.g., "san francisco, ca"). we did so by using a set of custom regular expressions that match variations for the expression "united states of america", as well as the names of us cities, and us states (and their combinations). albeit not always accurate, matching location strings against known location names is a tested approach that yields good results for a coarse-grained localization at state or country-level . overall, we located , , unique users in us who posted , , tweets; this is the final dataset we used for the analysis. the number of active users per day varies from a minimum of k on february nd to a maximum of . m on march th , with and average of k. the median number of tweets per user during the whole period is . a small number of accounts tweeted a disproportionately high number of times, reaching a maximum of , tweets; those were clearly automated accounts, which were discarded by our approach. we selected our language categories from four lexicons: linguistic inquiry word count (liwc) . a lexicon of words and word stems grouped into over categories reflecting emotions, social processes, and basic functions, among others. the liwc lexicon is based on the premise that the words people use to communicate can provide clues to their psychological states . it allows written passages to be analyzed syntactically (how the words are used together to form phrases or sentences) and semantically (an analysis of the meaning of the words or phrases). emolex . a lexicon that classifies k+ words and stems into the eight primary emotions of plutchik's psychoevolutionary theory . moral foundation lexicon . a lexicon of words and stems, which are grouped into categories of moral foundations : harm, fairness, in-group, authority, and purity. each of which is further split into expressions of virtue or vice. pro-social behavior . a lexicon of pro-social words and stems, which have been found to be frequently used when people describe pro-social goals . we considered that a tweet contained a language category c if at least one of the tweet's words or stems belonged to that category. the tweet-category association is binary and disregards the number of matching words within the same tweet. that is mainly because, in short snippets of text (tweets are limited to characters), multiple occurrences are rare and do not necessarily reflect the intensity of a category . for each language category c, we counted the number of users u c (t) who posted at least one tweet at time t containing that category. we then obtained the fraction of users who mentioned category c by dividing u c (t) by the total number of users u(t) who tweeted at time t: computing the fraction of users rather than the fraction of tweets prevents biases introduced by exceptionally active users, thus capturing more faithfully the prevalence of different language categories in our twitter population. this also helps discounting the impact of social bots, which tend to have anomalous levels of activity (especially retweeting ). different categories might be verbalized with considerably different frequencies. for example, the language category "i" (first-person pronoun) from the liwc lexicon naturally occurred much more frequently than the category "death" from the same lexicon. to enable a comparison across categories, we standardized all the fractions: where µ( f c ) and σ ( f c ) represent the mean and standard deviation of the f c (t) scores over the whole time period, from t = (february st ) to t = t (april th ). these z-scores ease also the interpretation of the results as they represent the relative variation of a category's prevalence compared to its average: they take on values higher (lower) than zero when the original value is higher (lower) than the average. we compared the results obtained via word-matching with a state-of-the-art deep learning tool for natural language processing designed to capture fundamental types of social interactions from conversational language . this tool uses long short-term memory neural networks (lstms) that take in input a -dimensional glove representation of words out of the ten interaction types that the tool can classify , only three were detected frequently with likelihood > . in our twitter data: conflict (expressions of contrast or diverging views ), social support (giving emotional or practical aid and companionship ) , and power (expressions that mark a person's power over the behavior and outcomes of another ) . given a tweet's textual message m and an interaction type i, we used the classifier to compute the likelihood score l i (m) that the message contains that interaction type. we then binarized the confidence scores using a threshold-based indicator function: following the original approach , we used a different threshold for each interaction type, as the distributions of their likelihood scores tend to vary considerably. we thus picked conservatively θ i as the value of the th percentile of the distribution of the confidence scores l i , thus favoring precision over recall. last, similar to how we constructed temporal signals for the language categories, we counted the number of users u i (t) who posted at least one tweet at time t that contains interaction type i. we then obtained the fraction of users who mentioned interaction type i by dividing u i (t) by the total number of users u(t) who tweeted at time t: last, we min-max normalized these fractions, considering the minimum and maximum values during the whole time period [ , t ]: . to identify medical symptoms on twitter in relation to covid- , we resorted to a state-of-the-art deep learning method for medical entity extraction . when applied to tweets, the method extracts n-grams representing medical symptoms (e.g., "feeling sick"). this method is based on the bi-lstm sequence-tagging architecture introduced by huang et al. in combination with glove word embeddings and roberta contextual embeddings . to optimize the entity extraction performance on noisy textual data from social media, we trained its sequence-tagging architecture on the micromed database , a collection of tweets manually labeled with medical entities. the hyper-parameters we used are: hidden units, a batch size of , and a learning rate of . which we gradually halved whenever there was no performance improvement after epochs. we trained for a maximum of epochs or before the learning rate became too small (≤ . ). the final model achieved an f -score of . on micromed. the f -score is a performance measure that combines precision (the fraction of extracted entities that are actually medical entities) and recall (the fraction of medical entities present in the text that the method is able to retrieve). we based our implementation on flair and pytorch , two popular deep learning libraries in python. for each unique medical entity e we counted the number of users u e (t) who posted at least one tweet at time t that mentioned that entity. we then obtained the fraction of users who mentioned medical entity e by dividing u e (t) by the total number of users u(t) who tweeted at time t: last, we min-max normalize these fractions, considering the minimum and maximum values during the whole time period [ , t ]: comparison with mobility traces foursquare is a local search and discovery mobile application that relies on the users' past mobility records to recommend places user might may like. the application uses gps geo-localization to estimate the user position and to infer the places they visited. in response to the covid- crisis, foursquare made publicly available the data gathered from a pool of million us users. these users were "always-on" during the period of data collection, meaning that they allowed the application to gather geo-location data at all times, even when the application was not in use. the data (published through the visitdata.org . we then averaged the values across all states: where s is the total number of states. by weighting each state equally, we obtained a measure that is more representative of the whole us territory, rather than being biased towards high-density regions. all our temporal indicators are affected by large day-to-day fluctuations. to extract more consistent trends out of our time series, we applied a smoothing function-a common practice when analyzing temporal data extracted from social media . given a time-varying signal x(t), we apply a "boxcar" moving average over a window of the previous k days: x * (t) = ∑ t i=t−k x(i) k ; we selected a window of one week (k = ). weekly time windows are typically used to smooth out both day-to-day variations as well as weekly periodicities . we applied the smoothing to all the time series: the language categories (z * c (t)), the mentions of medical entities ( f * e (t)), the interaction types ( f * i (t)), and the foursquare visits (v * j (t)). to identify phases characterized by different combinations of the language categories, we identified change-points-periods in which the values of all categories varied considerably at once. to quantify such variations, for each language category c, we computed ∇(z * c (t)), namely the daily average squared gradient of the smoothed standardized fractions of that category . to calculate the gradient, we used the python function numpy.gradient. the gradient provides a measure of the rate of increase or decrease of the signal; we consider the absolute value of the gradient, to account for the magnitude of change rather than the direction of change. to identify periods of consistent change as opposed to quick instantaneous shifts, we apply temporal smoothing (equation. ) also to the time-series of gradients, and we denote the smoothed squared gradients with ∇ * . last, we average the gradients of all language categories to obtain the overall gradient over time: peaks in the time series ∇(t) represent the days of highest variation, and we marked them as change-points. using the python function scipy.signal.find peaks, we identified peaks as the local maxima whose values is higher than the average plus one standard deviation, as it is common practice . for each language category c, we first computed the average value of f c during the first day of the epidemic, specifically µ [ , ] ( f c ). during the first day, k users tweeted. we experimented with longer periods (up to a week and . m users), and obtained qualitatively similar results. we used the averages computed on this initial period as reference values for later measurements. the assumption behind this approach is that the modeler would know the set of relevant hashtags in the initial stages of the pandemic, which is reasonable considering that this was the case for all the major pandemics occurred in the last decade [ ] [ ] [ ] . starting from the second day, we then calculated the percent change of the f c values compared to the historical average: finally, we combined the ∆% c values of the selected categories to create measures that capture the average relative change of the prevalence of verbal expressions typical of each of the three temporal phases: ∆% re f usal = ∆% death − ∆% i ∆% suspended reality = ∆% swear − ∆% death ( ) ∆% acceptance = ∆% sad − ∆% anxiety those categories were selected among those that proved 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about the covid- pandemic: development of a public coronavirus twitter data set a twitter geolocation system with applications to public health the emotions moral foundations theory: the pragmatic validity of moral pluralism mining the social web: data mining facebook long short-term memory glove: global vectors for word representation coloring in the links: capturing social ties as they are perceived an integrative theory of intergroup conflict universal dimensions of social cognition: warmth and competence exchange and power in social life bidirectional lstm-crf models for sequence tagging a robustly optimized bert pretraining approach identifying diseases, drugs, and symptoms in twitter flair: an easy-to-use framework for state-of-the-art nlp automatic differentiation in pytorch from tweets to polls: linking text sentiment to public opinion time series new introduction to multiple time series analysis simple algorithms for peak detection in time-series we thank sarah konrath, rosta farzan, and licia capra for their useful feedback on the manuscript. key: cord- -heg h l authors: ahmad, munir; iram, khadeeja; jabeen, gul title: perception-based influence factors of intention to adopt covid- epidemic prevention in china date: - - journal: environ res doi: . /j.envres. . sha: doc_id: cord_uid: heg h l background: the researches investigating the influence factors of epidemic prevention are not only scarce, but also provide a gap in the domain of perception-based influence factors of intention to adopt covid- epidemic prevention. objective: this work has attempted to examine the perception-based influence factors of individuals’ intention to adopt covid- epidemic prevention in a modified behavioral framework. theoretical framework: a behavioral framework composed of the theory of reasoned action and the theory of planned behavior is developed to incorporate some additional perception-based influence factors. methods: a partial least square-based path analysis has been employed to estimate the path coefficients of those factors in terms of drivers, barriers, and neutral factors based on questionnaire data of respondents from six universities and two hospitals in china. results: among the perception-based influence factors, governments’ guidelines on epidemic prevention is found to be the most important and influential factor, which was followed by risk perception. finally, attitude towards epidemic prevention exhibited the least degree of impact on individuals’ intention to adopt epidemic prevention. moral norms did not show any contribution to individuals’ intention to adopt epidemic prevention. conclusion: concerning importance ranking, the governments’ guidelines on epidemic prevention, risk perception, and epidemic knowledge are revealed as the top three drivers of individuals’ intention to adopt epidemic prevention, while the perceived feasibility to adopt epidemic prevention is found to be a barrier. moreover, moral norms is identified to have an insignificant influence on individuals’ intention to adopt epidemic prevention. given the empirical results, dissemination of governments’ guidelines on epidemic prevention, proper risk perception, and knowledge about epidemic would help prevent the covid- pandemic outbreak within china and worldwide. results: among the perception-based influence factors, governments' guidelines on epidemic prevention is found to be the most important and influential factor, which was followed by risk perception. finally, attitude towards epidemic prevention exhibited the least degree of impact on individuals' intention to adopt epidemic prevention. moral norms did not show any contribution to individuals' intention to adopt epidemic prevention. conclusion: concerning importance ranking, the governments' guidelines on epidemic prevention, risk perception, and epidemic knowledge are revealed as the top three drivers of individuals' intention to adopt epidemic prevention, while the perceived feasibility to adopt epidemic prevention is found to be a barrier. moreover, moral norms is identified to have an insignificant influence on individuals' intention to adopt epidemic prevention. given the empirical results, dissemination of governments' guidelines on epidemic prevention, proper risk perception, and knowledge about epidemic would help prevent the covid- pandemic outbreak within china and worldwide. keywords: modified behavioral framework; risk perception; epidemic knowledge; risk aversion; governments' guidelines on epidemic prevention. since the global epidemics are increasing day by day due to a lack of the prevention and control of such epidemics, therefore the involvement of all stakeholders, including vaccine companies, medical health officers, governments, and the public is essential (yang et al., ) . coronavirus" (mers-cov) infected people and took lives of people worldwide (who, ) . though all the three viruses belonged to the coronavirus family, covid- is a novel coronavirus that is both highly contagious and extremely fatal (who, ). given the transmission of covid- is highly efficient due to its contagion characteristic (yang et al., ) , the mitigation of the outbreak may involve social distancing, home quarantine, isolation testing of suspected cases, and treatment of the patients, among others (who, ). though the identification and treatment of infected cases are of utmost importance for the containment of the outbreak, however, the social distancing and home quarantine also play a crucial role. the covid- epidemic outbreak and the resulting economic shutdowns have brought chaos to all the sectors of the world economies-namely, the primary sectors that involve the extraction of raw materials, the secondary sectors that produce the finished commodities, and the tertiary sectors which provide services (nicola et al., ) . despite these economic repercussions, as per the mode of transmission of the epidemic, its human to human spread may only be contained through the adoption of epidemic prevention. therefore, there is a clear scope of identifying perception-based influence factors (pifs) of individuals' intention to adopt epidemic prevention (iaep) during the outbreak of the covid- epidemic. to begin with, the previous studies fundamentally focussed on the prevention and control of diseases such as malaria, aids , west nile, dengue, zika, and chikungunya (cui et al., ; omodior et al., ; przybyla et al., ; raude et al., ; xiaoliang et al., ) . the first group of researches focussed on the epidemiology of diseases like malaria, dengue, and aids (bryant-davis et al., ; cui et al., ) . the second group of researches was based on surveys and their interpretation through the response rate of certain variables on epidemic prevention (baghbanzadeh et al., ; sued et al., ) . the third group of the studies was based on the situation analysis of the disease profiles in terms of explaining their prevention and control measures (elmahdawy et al., ; kiviniemi et al., ; raude et al., ) . finally, the fourth group of studies focussed the epidemics like sars-cov of , mers-cov of , and covid- nishiura et al., ; you et al., guidelines on epidemic prevention. second, to carry out analysis, the survey-based data collection has been done for six universities and two hospitals in china. the data based on respondents are examined using a partial least square (pls)-based path analysis. to sum up, first, governments' guidelines on epidemic prevention, risk perception, epidemic knowledge, risk aversion, perceived behavioral control, subjective norms, and attitude towards epidemic prevention are suspected to be the drivers of individuals' iaep. secondly, the perceived feasibility to adopt epidemic prevention may be a barrier to individuals' iaep. lastly, the moral norms played a neutral role in shaping individuals' iaep. the rest of the research is structured as follows: section is based on a modified behavioral framework. section documents the materials and methods. section describes the results. section is based on the discussion. finally, section concludes this work. a modified odified odified odified behavioral behavioral behavioral behavioral framework framework framework framework the fundamentals of the tora stated that individuals' behavior is in accordance with their intention (fishbein and ajzen, ) . it substantiated that individuals ponder over the perceived consequence of behaviors instead of performing immediate actual behavior. in this way, individuals choose to perform actual behaviors that they think would lead to desired results. based on this, the intention-based behavior to adopt epidemic prevention depends on subjective norms and attitudes towards epidemic prevention (ajzen, ) . besides, subjective norms may be considered as a set of perceptions of the ways other people judge the individuals' behavior and their motive to deal with intention-based behavior (ajzen and fishbein, ) . later on, ajzen ( ) introduced an extended version of tora by incorporating a vital component of perceived behavioral control and called it topb (as can be seen in fig. ). according to ajzen ( ) , the perceived behavioral control is described as the control which individuals perceived to own in order to perform any behavior. the tora and topb are widely used in behavioral sciences to describe diversified intention-based behavioral scenarios (elyasi et al., ; msn and kang, ) . this work has advanced the behavioral framework of tora and topb through integrating some additional pifs of individuals' iaep (see fig. ). a modified behavioral framework depicting the influence factors of individuals' intention to adopt epidemic prevention. the data are compiled from academic as well as technical channels to examine the proposed hypotheses. in this respect, an online questionnaire survey was undertaken from a scholarly channel, which involved chinese universities. among those universities, guangdong medical university is located in the seaport city of zhanjiang, and southern medical university is located in guangzhou city of guangdong province. next, xinxiang medical university is located in xinxiang city of henan province, zhejiang university is located in hangzhou city, and north china electric power university and peking university are located in the capital city of beijing. further, the survey was also administered at a technical platform, including tianjin first central hospital located in tianjin city, and shanghai united family hospital in shanghai city, which is located near to the first epicenter of the epidemic outbreak called wuhan city of hubei province. the fundamental rationale to include two universities of beijing as a study location was that the persons to be surveyed in the capital city contained heterogeneous communities belonging to diverse provinces of china. moreover, other locations were opted, first, based on their proximity to the province of hubei being the epicenter of the covid- outbreak. secondly, those locations were selected based on the feasibility of the conduction of the survey. a questionnaire was planned and sent for evaluation and pre-testing to professors of psychology and medicine, and researchers for their expert opinions. those professors and researchers belonged to various universities. in this regard, the profiles of the participants are provided in table . moreover, expert medical technicians from two hospitals also commented on the planned questionnaire. finally, a few health advisors from the chinese centre for disease control and prevention located in beijing were contacted to comment on the structured questionnaire for further refinement. all of the conversations with those experts were regulated through emails (see table ). a bilingual questionnaire involving both english and chinese versions was floated to eliminate the language barrier and to obtain unbiased responses. the survey was conducted through a chinese multipurpose cell phone application called "wechat" in chinese "微信 (weixin)." to this end, the questionnaire was floated in different wechat-based groups of students, instructors, and researchers belonging to chinese universities. additionally, the questionnaires were also circulated in the wechat-based group of medical practitioners from the two chinese hospitals. on the whole, respondents completed the questionnaire survey. after examination, questionnaires were confirmed valid for analysis purposes. besides, the harman single-factor diagnostic test was made use of to deal with the problem of common-method-bias to verify the presence of the possible bias from collected evidence. although the data was obtained from respondents responding based on their previous activities correlated with their internal environments, this may influence the empirical performance. thus, variation in the method may extend the spotted associations between predicted and observed variables (lindell and whitney, ) . this method is one of the most common and easiest methods in this regard, using the likelihood of particular device variance (podsakoff et al., ) . the check confirmed the absence of any possible inclination in the findings. the factors influencing the individuals' iaep explored by making use of content analysis are empirically analyzed through the pls-based path modeling technique. a five-point likert scale is employed, which involved " =strong agreement," " =agreement," " =neutral," " =disagreement," and " =strong disagreement." in order to estimate the measurement and structural models, the statistical package called stata is employed. in order to estimate the influence factors of individuals' iaep, this work has employed partial least square (pls) based path analysis. to this end, for the assessment of whether the constructs are reliable as well as valid, confirmatory factor analysis is performed. in this connection, at the outset, the evaluation of outer loadings is done in table a . (see appendix a). in this context, it has been argued that outer loading of equal to or more than . denotes approximately more than percent of the explained variance (hair et al., ) . it implicates that the measured factor accomplished an admissible extent of reliability. as a consequence, the values of outer loadings exceeding . indicate the retention of the loading (hair et al., ) . bortoleto et al. ( ) suggested that the internal consistency of a construct determines its reliability. for appraisal purposes of reliability, ρ-a, cronbach-α, and composite reliability (cmpr) are employed. the values between . and . are considered within an acceptable degree of reliability (elmustapha et al., ) . the cronbach-α explains the reliability of the opted scales that how precisely they measure the latent construct. however, the range of its values (usually . to . ) does not implicate the degree of strength of reliability; it rather tells that beyond that range of values, the opted scales are not reliable. bearing in mind the possibility that cronbach-α is a customary measure and thus may have the possibility to underplay the reliability in case of a relatively small sample, there comes suggestion to consider the additional measure of cmpr (hair et al., ) . the cmpr can be explained as the variance of the total true score relative to the variance of the total scale score (netemeyer et al., ) . like cronbach-α, the cmpr is also a measure of scale reliability, and it has a threshold level value to indicate whether the opted scales of a construct are reliable. though its threshold value is reported as . by hair et al. ( ) and . by bagozzi and heartherton ( ) , the number of items taken for a construct is important for deciding whether the construct is internally reliable (netemeyer et al., ) . it has been further envisaged that the value of ρ-a between cmpr and cronbach-α is suggested reliable (lopes et al., ) , which implies that the selected items are considered reliable for the value of ρ-a within the stated range. table results of path analysis and post-analysis model criteria. to be below the square roots of ave, which proved the existence of the discriminant validity. it means the difference between each of the ltvs is stronger (hair et al., ) . these findings are documented in table a . (appendix a). following the critical benchmarks of the t-statistic and probability score, the path coefficients for all the pifs are found relevant, except for moral norms (see table ). this is because the tstatistic are documented to be more than or were equal to the threshold level of . , and the probability score is below or equal to . . it means that, except moral norms, all of the pifs significantly contribute to individuals' iaep. in the structural model, given the estimated path coefficients' magnitudes, the relative importance of the pifs of individuals' iaep is depicted in fig. . considering the relative importance of the pifs, governments' guidelines on epidemic prevention, risk perception, and epidemic knowledge are exposed to be the top three pifs having path coefficient values of . , . , and . , accordingly. on the other hand, attitude towards epidemic prevention remained the least contributor ( . ), while moral norms revealed no contribution to individuals' iaep. taking the nature of the pifs of individuals' iaep into consideration, the perceived feasibility to adopt epidemic prevention is revealed as the only barrier to individuals' iaep. whereas the remaining pifs are exposed as the drivers of individuals' iaep, while the moral norms is exposed to be the neutral factor. among the drivers of individuals' iaep, governments' guidelines on epidemic prevention is unveiled to be the strongest driver (see fig. ). for the role of strategic leadership is emphasized by carrel ( ) in switzerland concerning the future epidemic outbreaks. another most recent research showed a significant mediating role of government on epidemic prevention (yasir et al., ) . in this way, governments' role would be central in shaping the behaviors of individuals for adopting epidemic prevention. risk perception is found to have a positive contribution to shaping individuals' intention to adopt epidemic prevention. it implicates that if people perceive the severity, susceptibility, and fatality of the infection, then it will enhance their intention to adopt epidemic prevention. in brief, better epidemic knowledge is found to drive individuals' intention to adopt epidemic prevention. it entails that without knowing about some infection, it is unrealistic to have its precautions. in this regard, the knowledge of how an infection can be transmitted, and to which degree it is contagious is likely to be proved the fundamental breakthroughs to motivate the individuals to argued that knowledge gaps in health risks play an essential role in the prevention of aids (kiviniemi et al., ) . in light of this, epidemic knowledge may play an integral role in shaping the epidemic prevention behaviors of individuals. some limitations should be considered while conducting future work in this domain of this work. first, this is a perception-based work, and therefore the intention of individuals to adopt covid- epidemic prevention might change for pre and post-adoption scenarios. hence, it would be useful to consider the data from adopters and non-adopters of epidemic prevention for drawing even better implications. second, the sample compiled from individuals was just enough to conduct a single estimation to yield homogeneous findings. in the future, the conduction of an extensive and large-scale questionnaire survey is advisable to compile large samples enough to perform regional estimations to yield heterogeneous findings. it would provide deep insights into heterogeneity concerning the individuals' adoption behavior of epidemic prevention across regional disparities. thirdly, the selection of a specific class of people, particularly highly educated people holding at least a master's degree, may fault our generalization for china. therefore, future research should select a good representative sample of the entire population in china, in terms of the level of education, income, and type of employment, for a more generalized and informed understanding. . conclusions . conclusions . the core focus of this work was to examine the perception-based factors influencing the individuals' intention to adopt covid- epidemic prevention in a modified behavioral framework in terms of estimating the relevance as well as the relative importance of those factors. first, governments' guidelines on epidemic prevention, risk perception, epidemic knowledge, risk aversion, perceived behavioral control, subjective norms, and attitude towards epidemic prevention are revealed to be drivers of individuals' intention to adopt epidemic prevention. second, perceived feasibility to adopt epidemic prevention measures was exposed to be the barrier to individuals' intention to adopt epidemic prevention. third, moral norms was identified to perform a neutral role in shaping individuals' intentions to adopt epidemic prevention. fourth, concerning the relative importance of perception-based influence factors, governments' guidelines on epidemic prevention is found to be the most important and influential factor which is followed by the risk perception. finally, attitude towards epidemic prevention showed least contributed in shaping the individuals' intention to adopt epidemic prevention. notes: the level of agreement is categorized as: = "strong agreement", = "agreement", = "neutral", = "disagreement", = "strong disagreement." after the measurement model is proven accurate and effective, the structural model is tested. as a key requirement, the r score of the construct is manipulated. the r score calculates the variance accounted by every endogenously found construct. this measure has the function of validating the prediction capability of the structural model. in other words, it demonstrates the explanatory power of the model. it has been suggested that its score values exceeding the threshold level of . would be an average score. however, its score of about . would not be a very appropriate one in the behavioral sciences. on the other hand, its score less than or equal to . is absolutely a weak score (davison and hinkley, ) . as can be seen from the table , the r score is . , which is way greater than . and thus satisfying the first requirement. it implicates that the eight significant pifs collectively explain . % of the variations in the individuals' iaep. it means that the model has reasonably high statistical power to present the explained variations. as a further requirement q score by stone-geisser is tested. its score exceeding zero (positive number) demonstrates the accuracy and the prediction significance of the construct under consideration (ringle et al., ) . in the same vein, the extent of impact estimated by the q score provides the relative impact of the predictive relevance. to this end, the q score exceeding . means that an exogenously found construct supplied enough amount of predictive relevance for the corresponding endogenously found construct of a variable (hair et al., ) . based on the calculated score of q (i.e., . ), the precision and accuracy of the structural model are verified. it implies that the predictive relevance of the pifs on individuals' iaep is acceptable. the measure of explained variation (i.e., r ) as well as the measure of predictive relevance (q ) yields a single value for each model. in present scenario, a model is estimated involving path modeling from nine pifs to individuals' iaep, therefore it estimated single value for each of the measures including r and q . the diagonal values reported in brackets ( ) are square root of aves. as a further requirement, the path coefficients are taken under advisement. in this regard, it is suggested that the estimated scores of path coefficients above . demonstrate effective impact within a structural model (hair et al., ) . additionally, f is manipulated as a further requirement. its score shows the impact size to describe the contributing capacity of a construct, through which the explained variations in endogenously determined ltvs are found by exogenous constructs (davison and hinkley, ) . in the case of this work, governments' guidelines on epidemic prevention has depicted the greatest score in terms of its impact size. similarly, risk perception has exposed the second greatest score, which is preceded by the impact size of epidemic knowledge. on the contrary, the moral norms demonstrated the slightest impact size from the set of all influence factors. thus, the impact size determines the relative contribution of each of the pifs to individuals' iaep. any value of variance inflation factor (vif) below demonstrates the presence of acceptable level of multicollinearity issue, while vif more than is considered high level of multicollinearity. in present case the vif values remained below , which showed its acceptable level. the pls-based path analysis is free of normality assumption applied to the parameter-based bootstrap procedure, which serves to determine the significance of outer loading and path coefficients. the bootstrap procedure considers contemplation of about x sampling units derived and extracted based on the original sampling unit through making use of the 'with swap' choice to get each sampling unit estimated. a bootstrap-based distribution originates, which is served to manipulate estimates' standard errors and the standard deviation. in this regard, the student's t-statistic is manipulated. for hypothesis testing, the null hypothesis for each established path is given as h i = for i = , , ,…, . while the alternative hypothesis for each established path is given as h i ≠ for i = , , ,…, . the path coefficients are taken to be relevant for any score of t-statistic equal to or exceeding the threshold level of . (ringle et al., ) . as for its equivalent, the path coefficients are considered significant at a % level for any probability score below ore equal to . 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outbreak : a multi-mediation approach estimation of the time-varying reproduction number of covid- outbreak in china the authors have no conflict of interest to disclose. the authors are highly thankful to the editor, and the two anonymous reviewers as their suggestions have extensively improved this work. supplemental l l l m m m materials aterials aterials aterials key: cord- -zb wxt authors: hardiman, david title: the influenza epidemic of and the adivasis of western india date: - - journal: soc hist med doi: . /shm/hks sha: doc_id: cord_uid: zb wxt the influenza epidemic of was the single worst outbreak of this disease known in history. this article examines an area of western india that was affected very badly—that of a tract inhabited by impoverished indigenous peoples, who are known in india as adivasis. the reasons for this are discussed. some oral accounts help to bring out the enduring memory of that terrible time. the general health of the adivasis and the existing medical facilities in this area are examined. attempts to check and treat the disease by the colonial government and its doctors, as well as missionary doctors and other non-governmental agencies, are considered to see why they had so little overall impact. some comparisons are made with the fate of indigenous people in other parts of the world during the epidemic, in particular with the inuits of alaska. in the usa, for example, african americans had lower mortality rates during the pandemic than whites, even though they generally suffered much higher death rates from respiratory and other such diseases. native americans, however, suffered worst of all. the reasons for these mortality patterns are still not well understood, though various propositions have been put forward. although there is considerable contemporary documentation of the epidemic, for many years afterwards it was not studied in any depth by historians. compared to other great epidemics, such as the black death, and to events that were contemporary with it, such as the mass slaughter and traumas of the first world war and the revolutions and displacements that followed in its wake, the influenza epidemic received little attention. this began to change in the wake of new epidemiological discoveries from the s onwards. in particular, robert webster and graeme laver's discovery of the way in which the influenza virus migrated from birds, mutating into a human form, transformed understanding of the epidemiology of the disease. they argued that this process was an ongoing one, producing new strains of the virus through 'antigenetic drift'. although most such mutations proved relatively mild, virologists warned that this was not always going to be the case. a future epidemic on a par with that of -or perhaps worse-was predicted to be almost certain at some time or other. these findings provided a wake-up call for historians. the first of a new wave of studies appeared in , with richard collier's the plague of the spanish lady. this was based mainly on interviews with survivors from different countries, and although anecdotal, brought out how people experienced the epidemic. it failed, however, to analyse the dissonance between such graphic memories and the official and academic silence on the pandemic. a more scholarly study followed in by alfred w. crosby, epidemic and peace. it was republished in as america's forgotten pandemic: the influenza of . in his preface to this new edition, crosby noted how the hubris surrounding the supposed triumphs of medical science had ensured that until the s the epidemic of was regarded-when it was at all-as an aberration that was largely irrelevant to our present condition. this had all changed as people began to understand how 'pathogens .ˆ.ˆ. seem to the general public to have become nastier faster than scientists have become smarter'. now, it seemed a harbinger of a dark future rather than an oddity from the past. by the s, the trickle of studies on the epidemic became a firm flow, with the current becoming ever stronger in the subsequent decade. despite this, the area that suffered the highest mortality of all in -india-has hardly been examined at all. indeed, there are only a couple of articles, by i. d. mills little or nothing about the epidemic. both mills and ramanna focus on bombay presidency, making widespread use of an excellent source for the epidemic in this regionthe annual report of the sanitary commissioner for the government of bombay for the year . this contained a detailed survey of the outbreak, along with extensive statistics on mortality. together, this report and the two articles show that the disease appears to have entered india through bombay port at the end of may , becoming epidemic in bombay presidency in june. at this juncture-as elsewhere-it was relatively mild, with most victims recovering. it spread to other parts of india by august . the second, and much more virulent wave, began again in bombay presidency, and was well established by september. official figures at that time put the death rate at . per cent of the population of the presidency, although mills estimated that about half the twenty million people of the presidency were infected, and that , , , or . per cent of the population died. he based this estimate not on recorded deaths (which were usually much under-reported in india) but on his own projections relating to population growths based on the census reports of and . mortality rates were particularly high in certain pockets of the interior of the presidency. the coastal districts were in general less hard-hit. urban areas were badly affected; in bombay presidency the urban death rate for was . per cent of the population, as compared to the rural death rate of . per cent. in normal years, there was no great difference between urban and rural death rates. as elsewhere, a feature of this phase of the epidemic was the high incidence of death among those aged to . unlike in the west, however, women in india suffered more. in bombay presidency, for example, . per cent of all women in the - age range died, compared to . per cent of all men. also, in contrast to the west, the poor suffered disproportionately. in bombay city, for example, low caste hindus had a death rate of . per cent in , in contrast to death rates of . per cent for europeans, . per cent for parsis, . per cent for anglo-indians, . per cent for indian christians, . per cent for high caste hindus, and . per cent for muslims. the millworkers, who were mostly low caste hindus, were badly affectedand this was said to be because they tended to be poorly-fed, and lived in badly-ventilated rooms with a smoky atmosphere filled with coal and dust. disproportionately-between and their population in india as a whole fell from , , to , , , or by . per cent-while the overall population of india increased during the same period by . per cent. the decline in the adivasi population was caused chiefly by the influenza epidemic of . in her study of the epidemic in bombay presidency, ramanna describes the way that the disease spread rapidly through western india in , and the measures adopted by colonial medical officials to try to contain it-largely without success. she points out that good nursing provided the best hope for a cure, but that there was a paucity of trained nurses in bombay presidency. she examines the response by voluntary groups, arguing that such public relief work was confined mainly to the larger cities. she states there was an 'absolute lack of any public health organisation in rural areas', so that the rural population was left helpless in the face of the epidemic. she does not, however, provide much detail on exactly how the rural population fared, or explain why some rural areas were harder-hit than others. my own experience from research in the mountain tracts that run between southern gujarat and maharashtra suggest that there are many histories yet to be written of the epidemic in india. when conducting interviews in villages in the early s, some older adivasis had told me about a fearsome epidemic that devastated their society when they were young. it was known as 'mā nmodi'. large numbers, i was told, had died suddenly. never before or since then had so many died in such a short space of time. in some households, everyone was wiped out. the bhagats (diviners, exorcists and herbalists) had tried to counter it by bringing out the spirit that was causing the sickness. for the most part they failed in this, and many lost their confidence in the bhagats at that time. i was told that 'mā nmodi' had occurred not long before the coming of the goddess, or devi, known as salabai. this was the topic that i was researching at the time, and later wrote about in a book. the coming of the devi is dated in the colonial and other records as occurring in - . this convinced me that 'mā nmodi'-which according to the adivasis occurred just a few years earlier-was the great influenza epidemic of . navsubahi patel of chankal village in the dangs said that people would be sitting, and they would start shaking all over and die. some went mad, and fell into water and died. some jumped up and down on the ground very vigorously. some died of fever. he, a youth of about fifteen at that time, helped to dispose of the dead. at first they had buried them, but soon were overwhelmed, and began throwing the bodies over cliffs. he had helped dispose of bodies in these ways. no home escaped. this was the case all over the dangs. govinda karbhari of saputara in the dangs said that of the inhabitants of his villages, had died in mā nmodi. in some villages, half the population had died, in others three-quarters. the bhagat was helpless, and they were so scared that they had fled the place. this went on for about one-and-a-half to two months. memories of the epidemic remained alive in these villages even in the twenty-first century. when my colleague gauri raje carried out research in some adivasi villages in eastern surat district in , she was told of an epidemic that they knew as 'dhani pani'. as with 'mā nmodi', it was said to have occurred just before the coming of the devi. they considered it a landmark in their history as so many had died. their parents had told them about it, as family members had succumbed. the symptoms were head thrown back, rigid limbs, high fever and delusions, and death came in a day or two. people who recovered were immune to any disease thereafter. large numbers died in each village, and whole villages were evacuated. it affected the entire region. oral histories such as these, collected many years after the event are valuable for the way they bring to life the intense emotions stirred at such a time, such as the sensation of dread and social threat, helplessness in the face of the unknown, and the desperate means employed to try to deal with the danger, such as fleeing a village. they provide what joann mcgregor and terence ranger have called an 'alternative narrative' that enriches the existing medical history and which also can be set against and contrasted with the official and other narratives that come down to us through the archives. as lucy taksa has shown in her admirable oral history of the epidemic in sydney, australia, such accounts bring out the multiple ways in which the epidemic was experienced, described and understood. they reveal the partiality of the official historical account, allowing us to reach toward different interpretations of the event. no such oral histories have, however, been attempted for india-a lacuna that the present article will attempt to rectify for one region at least. my aim is to focus on the epidemic of in the areas of southern gujarat and the immediately adjoining parts of maharashtra that have large adivasi populations. as i have indicated already, the topic first came to my attention through the interviews that i conducted there in the early s. at the time, i knew very little about the epidemic, and as it was not a part of my wider research agenda, i put it aside as a subject that i could return to at a later date. once i did this many years later, i began to discover that the adivasis appeared to have suffered particularly badly in comparison with other peoples of the plains of southern gujarat. i wondered why this was the case. what made the difference at such a time of extreme medical crisis? what was the state of medical facilities in these tracts, and could better facilities have saved lives? starting from the oral histories, i sought to answer these questions by examining the written evidence from that time-as produced by both official and non-officials agencies (notably missionaries). who were the 'adivasis' of india? they tended to inhabit the hilly and forested regions of the subcontinent. many lived from hunting and gathering combined with shifting agriculture. some were found in adjoining plains regions, where they practised a more settled peasant agriculture-sometimes independently, sometimes as tenants or labourers for non-adivasi landlords and usurers. such peoples were described by the british as 'aboriginals' or 'early tribes', being characterised, so it was said, by their 'clan'-based systems of kinship and their 'animistic' religious beliefs. sometimes, they were defined in terms of their habitat, as 'jungle tribes'. by classifying them in these ways, the british created a conceptual unity that such peoples had not hitherto possessed. from the s onwards they claimed, assertively, to be the 'original inhabitants' of their tracts, calling themselves by the hindi term that expresses such an idea-that of adivasi. i have used this term in this paper for the sake of convenience, even though it was not yet in currency during the epidemic of . in india, the largest concentrations of such people were in the northeast. elsewhere, many were found in the central-eastern region, in what is now the state of jharkhand and areas adjoining to it in bengal, orissa and bastar, and in a section of western india that spans the border regions between the four modern indian states of rajasthan, gujarat, madhya pradesh and maharashtra. the adivasis that form the subject of this article inhabited a belt that stretches nearly as far as the city of bombay in the south, to the narmada river in the north, to the districts of west khandesh (now dhule) and nasik in the east, and to the arabian sea in the west (see map). in terms of terrain, they inhabited the hills and forests of the sahyadri and satpuda mountain ranges and the immediately adjoining plains areas. in the past, they were classed by non-adivasi indians as belonging to two main groups-the 'kaliparaj' ('black people') and the bhils. the former were generally considered to be less aggressive than the latter. the 'kaliparaj' were divided in turn into a number of separate communities, such as the chaudhrys, dhodiyas, gamits, konkanas and varlis. before examining the epidemic in this adivasi region, i shall say something about the nature of the epidemic, how it was understood and treated at the time, and look briefly at a well-documented case in which indigenous people were severely hit by the pandemic-that of the inuit in alaska-to help to draw out some lessons about the response to the crisis more widely. although the symptoms of influenza in differed throughout the world, its most frequently reported indicators were severe headaches, body pains and fever; with coughing of blood and bleeding from the nose. death was often caused when the disease affected the lungs, causing massive pulmonary oedema or haemorrhage, turning the lungs into sacks of fluid and thus effectively drowning the sufferer. a particular feature of the malady was the 'heliotrope cyanosis' (a term coined at the time), in which the face of victims turned blue as they in effect drowned in the fluids that accumulated in their lungs. an attack normally lasted - days. however, death could be sudden, even within a few hours. in , the epidemiology of influenza was poorly understood. since the s, it had been held that influenza was caused by a bacillus, identified as pfeiffer's bacillus. little was then known about viruses, and much of the research into the disease in was focused in the wrong direction. the influenza virus was in fact only identified in , and it was found that its surface antigens change from epidemic to epidemic. this made it hard to classify the virus retrospectively. later research on the corpses of victims frozen in the arctic tundra suggest that it was most likely a particularly lethal form of the h n -subtype influenza a virus that had mutated from an aggressive bird flu. it is not yet known precisely why it caused such high mortality among those in the prime of their life. in bombay, the medical establishment tried to establish that pfeiffer's influenza bacillus was the cause of the disease. investigators at the bombay bacterial laboratory had difficulty in isolating the bacillus, but they believed that it was 'one of the most constant elements in the bacteriology of the disease and it appears to thrive best in symbiosis with other organisms such as the pneumococcus and streptococcus.' a combination of the three was held to account for the particular virulence of the outbreak in september-october . in particular, the pneumonia that generally occurred on the second or third day of the illness frequently proved life-threatening, and it was believed that it was likely to be especially fatal in the case in patients who failed to take proper rest as soon as they fell ill. despite the epidemiological uncertainty, it was felt that a vaccine was needed, and one was prepared and used for the military for preventive purposes only. the constitution of the vaccine was only decided on at a conference in delhi in december , and it was then manufactured and provided free of charge-after the most lethal phase of the epidemic had passed. although many medics knew at the time that there was no effective drug-remedy for influenza, others were not short of recommendations-often conflicting. thus, while many indian doctors advised daily doses of the wonder-drug of the day, quinine, the surgeon-general of bombay warned against it. particular doctors advocated a wide range of remedies, such as belladonna, laudanum, camphor, creosote, a mixture of iodine and chloroform and the like. many indian medics, as well as ayurvedic practitioners, dispensed indigenous medication, such as powdered long pepper, mixed with ginger juice and honey. to prevent congestion and bronchitis, they prescribed tulsi and turmeric in milk. the bombay government itself disparaged the use of such indigenous remedies. people were also advised to take preventive measures, particularly the wearing of face masks, irrigating their noses with warm salt water, disinfecting their houses, avoiding congregation in crowds, and refraining from smoking tobacco and consuming alcohol. in practice, many resorted to prayer and patent medicines. in fact, probably the most effective treatment for sufferers at that time was the prescription of aspirin to lower the body temperature, complete bed-rest and good nursing care. the sanitary commissioner's report for bombay noted that a previous bout of influenza did not appear to confer immunity in . it was argued that certain individuals were by their nature more susceptible to the infection, but that this was aggravated by 'overwork, lack of food, bad housing and overcrowding'. the poor monsoon of that year had also meant that people were malnourished and had less resistance. the report also noted the fact that in general, regions lying close to the arabian sea had lower mortality than those inland. the reason for this was not however clear. the report also mentioned that female mortality was in general considerably higher than male mortality. this gender difference was not found to be the case in all age categories, as more male babies under one year and more males in the - age group had died. the report argued that women who had domestic responsibilities had been unable to take the necessary rest when ill, having to cook and tend to other members of the family who were ill. this was compounded by 'their continued indoor existence in the average ill-ventilated house', which made them more vulnerable to the pneumonia that was such a killer. the reports did not take note of the fact that women from poor families tended to be malnourished-more so in a year of crop failure-and also more likely to suffer from anaemia and other debilitating conditions. a different report of noted that pregnant women were particularly at risk, and that in almost all cases those who contracted influenza aborted and died of post-partum haemorrhage. the high female mortality was a feature of the epidemic in india-elsewhere, male mortality tended to be strikingly higher. the particularly high mortality rates from influenza suffered by indigenous and aboriginal peoples throughout the world in has been brought out in a number of studies. this was the case of native americans and the inuits of northern canada and alaska, and in new zealand the epidemic killed more maoris than people of european origin. it had a devastating effect in many pacific islands; in fiji about per cent of the population died, in tonga per cent and in western samoa per cent. in alaska, some isolated inuit villages had death rates of up to per cent of the adult population. in some cases, the relative isolation of indigenous people made them more vulnerable to such infection; this was not however the case with most, as there had been widespread contact with outsiders for many years. crosby's study of the alaskan case brings out just how important the reaction to the crisis by the authorities and concerned and well-informed citizens could be. the epidemic began in alaska in october, just before the winter freeze cut off the interior, so that it spread rapidly from seaports up the rivers that provided the main means of access to the interior. the us authorities put a lot of resources into providing health care, establishing emergency hospitals and hiring extra physicians and nurses, who were sent to places where they were needed most. in the more remote areas that lacked such care, death rates proved to be much higher. the epidemic arrived in many interior settlements just as winter was closing in, isolating them almost completely as it raged. cases were reported of people panicking and wandering about spreading the disease. there was nobody to perform the life-saving tasks, such as cutting firewood, and providing food (the people were too weak to hunt the moose). cabins became dirty, and vermin increased. people became demoralised and merely sat in their cabins waiting for death. they no longer lit fires, and many froze to death. when a number were rounded up and placed in a single large, heated building where they could be cared for better, several responded to what they saw as incarceration in a deathhouse by hanging themselves. crosby notes that where there was strong leadership in an inuit village by people such as schoolteachers, survival rates were much better. meetings were held to explain what was happening and ways in which people might avoid infection, and arrangements were made to provide food and firewood for infected families. the lesson here was that although the cause of the pandemic was not understood, and although there was no wonder-cure, infection-rates could be kept down through quarantine, and there was a better chance of survival if the sufferer had complete bed-rest and good-quality nursing. as i shall argue, these conditions were lacking for the most part in the more remote adivasi tracts of western india. if we compare mortality rates for districts, as given in the annual report of the sanitary commissioner for bombay presidency, , there does not appear to be any obvious statistical correlation between high mortality and the districts with larger numbers of adivasis. sholapur district was recorded as having the highest mortality rate of all districts in the presidency- . per cent of the population. nasik followed, with . per cent, then west khandesh with . per cent. other districts had mortality rates under per cent. while nasik and west khandesh had sizeable adivasi populations in their western regions, sholapur-with the highest of all mortality rates-did not. also, some districts with large adivasi populations had below average figures-such as the districts of thana ( . per cent), panchmahals ( . per cent), and surat ( . per cent). such averages concealed, however, variations within each part of a district. the annual report of the sanitary commissioner for also provides breakdowns for sub-districts (talukas), and these can be used to pinpoint the areas with highest mortality with greater precision. the highest mortality rates of all were found in sakri and baglan talukas, where respectively . per cent and . per cent of the populations died; per cent of the population of sakri were adivasis, while the figure for baglan was per cent. these two talukas were in the sahyadri mountains adjoining the dangs-the area where i had first encountered a strong and abiding popular memory of the epidemic of . kalwan, which bordered both the dangs and surgana state had a mortality rate of . per cent, and peint, which adjoined dharampur state, had a mortality rate of . per cent. in the report, there are no mortality figures for the princely states, but in the dangs the population dropped by . per cent and in dharampur by . per cent between and , and in both cases the main cause was said to be the epidemic of . mortality rates in the british-ruled talukas of surat district were lower, with an average rate of . per cent for its rural areas and . per cent for its three largest towns. the highest rates were found in the talukas that adjoined the forests and hills of dharampur, namely chikhli ( . per cent mortality and per cent of the population adivasi), valsad ( . per cent mortality and per cent adivasi), and pardi ( . per cent mortality and per cent adivasi). besides chikhli and pardi, the only other talukas of surat district with adivasi populations over per cent were mandvi and valod, and they had mortality rates that were in line with the district rural average. significantly, i did not come if we accept mills' argument, we may double this and the other mortality figures that follow in this section to give more likely realistic mortality rates. it is beyond the scope of this article to try to explain the reasons for the large differences in mortality rates within bombay presidency as a whole. the worst-affected areas were all in the interior plateau regions of maharashtra-the deccan and khandesh-while the coastal regions of the konkan and the gujarat plains had considerably lower mortality rates. there may have been a mutation that appeared first in the area around pune in september and caused particularly high mortality in the adjoining areas of the deccan and khandesh in october, thereafter subsiding in virulence. this is merely a conjecture that requires further investigation, as no convincing explanation has been provided either in the official reports or by subsequent historians, such as mills. my general argument in this paper is, nonetheless, that varying degrees of virulence could be compounded-sometimes dramatically-by the underlying health profile of different social groups and their access to medical knowledge and care. i have been unable to find mortality rates during the epidemic for the talukas of navsari district of baroda state. all we have are the census figures. if we examine the baroda state census report for , we find that the population of songadh taluka had declined by . per cent since , mangrol and vajpur (the two were counted together) by . per cent, while vyara recorded a small increase of . per cent. mahuva, another largely adivasi taluka recorded a decline of . per cent. in the other four talukas of navsari district, which had a far lower concentration of adivasi in their population, the population increased by . per cent between and . this points to relatively high mortality in the adivasi areas of navsari district-and, significantly, these lay for the most part close to the foothills of the sahyadri mountains. the taluka figures for navsari are however significantly lower than the rates found in the more mountainous adivasi regions to the east. continuing in a southerly direction, we find that in thane district there were two talukas with high adivasi populations-umargam ( . per cent mortality rate and per cent adivasis) and dahanu ( . per cent mortality rate and per cent adivasis). in addition there was jawhar, a princely state in the mountainous interior of the region that was largely surrounded by dahanu taluka, in which per cent of the population was adivasi and the mortality rate was a higher . per cent. these statistics, taken together, suggest that mortality rates were generally lower in the adivasi areas of south gujarat and thane district that lay in the coastal plains. pardi taluka was an exception to this rule, although it had a considerable amount of its territory in the interior on the borders with dharampur, and this region may have accounted for the higher mortality rate of this taluka as a whole. to the immediate south of pardi, umargam taluka, which lay mostly in the coastal plain, had a relatively low mortality rate ( . per cent) that was comparable to the adivasi-dominated talukas of the plains of surat district. the general finding is thus that the worst-affected adivasi areas were located in a broad line that stretched from northeast to southwest along the spine of the sahyadri range and its adjoining foothills in gujarat and maharashtra. in this area the particularly virulent strain of the disease that swept inland maharashtra affected the adivasis of the mountain villages worst of all. i shall now go on to say something about the social, economic and medical history of the adivasis of this region in order to try to understand why some of them suffered so badly in . using census data to suggest mortality rates is open to the problem that it might show out-migration from the region-caused perhaps by an agricultural crisis such as rain failure-rather than mortality from influenza as such. the census reports do not put forward any such suggestion. discussing the period - , the baroda census commissioner, s. v. mukerjea, argued that although the rains had failed in , there was little distress or human starvation due to the implementation of more effective famine relief measures than in earlier years. in the past, the adivasis of southern gujarat were known as the 'kaliparaj', or 'black people'. this was a disparaging term given to them by the high castes, who were known locally by contrast as the 'ujliparaj', or 'white people'. the kaliparaj were for the most part poor subsistence farmers. in the more fertile plains regions of southern gujarat they lived in settled villages and cultivated fixed plots of land, while in the forested and hilly tracts in the east crops were grown both in fields in the valleys and through shifting slash-and-burn cultivation on the hilly slopes. the adivasis of the hilly tracts tended to move their places of settlement in periodic cycles, finding fresh land to cultivate. they had in general suffered badly from colonial rule. the british had appropriated large tracts of the forests that the adivasis had previously controlled so that state foresters and timber merchants could exploit the natural wealth of the woodlands. those so displaced were encouraged to settle down as full-time farmers. the commodification of farmland by the colonial state had in turn allowed landlords, usurers and liquor dealers to move in and expropriate large areas of their land, leaving them as tenants or agricultural labourers. their hard conditions of life reflected on their health. this was remarked on by colonial officials, missionaries and indian outsiders alike. writing in , e. maconochie of the indian civil service noted that the health of the 'kaliparaj' was in general poor as compared to the high caste people who lived in the same area. this was due to their 'coarse and scanty food, bad water and insufficient clothing'. they were 'generally of inferior physique' to members of the higher castes, probably because of the malaria that they more than others suffered from. the focus on malaria-or 'fever'-was a longstanding trope in colonial commentary on the health of the kaliparaj. in the nineteenth century, this was believed to be caused by what a colonial official described in as 'the pestilential vapours of this unsettled land'. a british official, writing in , noted the 'inferior and wretched' sanitary condition of the villages of mandvi taluka, stating that: 'the inhabitants are generally dull looking with their pale faces, enlarged abdomen and emaciated limbs and their health on the whole giving proof of it being below par.' women, he said, were generally in worse health than men. the connection between malaria, an enlarged spleen and anaemia was pointed out by missionary doctors working in the tract in . they called this 'malarial anaemia', but more recent investigations in this area have discovered that there is widespread sickle cell anaemia amongst the adivasis. while providing some protection against malaria, it is also very debilitating. there is also a close connection between female nutritional anaemia and maternal and fetal morbidity and mortality. an indian anthropologist who carried out research in the area in the late s remarked on the very high infant mortality rate in the adivasi village that he studied-with . per cent of all deaths there being of children under five. . per cent of all children failed to survive to their fifth birthday. in all this, there was a clear link between the material poverty of the adivasis and their poor health. this was a fate suffered by such people elsewhere in india. p. o. bodding, a missionary ethnographer whose wife was a doctor carried out a detailed study of the health and therapeutic practices of the santal adivasis of eastern india in the early twentieth century. he noted that they suffered from most diseases found in india at that time. he was told by his santal informants that they had not suffered from syphilis, tuberculosis or leprosy before the middle of the nineteenth century. although he felt that this was perhaps an exaggeration, he suggested that their former isolation may have protected them from many infections. by the twentieth century, however, all of the three abovementioned diseases had become widespread in the community. the most prevalent maladies of all were malaria, then skin diseases, bowel complaints such as dysentery, eye diseases, pneumonia, and rheumatism. they also suffered badly in epidemics, fearing cholera and smallpox in particular. government officials commonly argued that this could all be remedied through forest clearance and agricultural development in adivasi villages. a senior tax officer employed by the baroda state government (which ruled a large tract of territory in this region, often interspersed with the british-held areas) stated in that the poor social and economic conditions of the adivasi tracts was caused by poor health, and particularly malaria, as mosquitoes thrived in the dense vegetation. he held that if the jungle and scrub was cleared, their health would improve dramatically. the unhealthy nature of this area was also said to deter non-adivasi settlers who might have developed the land more productively. the drawback with this argument was that even in the supposedly 'healthy' tracts of the areas of south gujarat that adjoined the arabian sea and had no forestswhich was an area in which high caste landowners carried on commercial agriculture with adivasis making up most of the agricultural labour force (working either as bonded labourers or indebted tenants)-the health of the adivasis was not noticeably better than that of their counterparts in the forest zones. poverty, rather than terrain, ) . it may be noted that modern irrigation projects have in the past four decades allowed intensive cultivation of sugarcane in large swathes of the plains regions of south gujarat. the cane is cut largely by adivasi migrant labourers, who live in appears to have been the more likely cause of their ill health. non-official high caste commentators, on the other hand, tended to blame the generally poor health of the adivasis throughout south gujarat on their high consumption of alcohol, contrasting this with the more 'healthy' high castes-who were said to generally abstain from taking liquor. because their health was generally poor, the south gujarat adivasis suffered particularly badly in epidemics. reports from the dangs speak of whole villages becoming deserted after outbreaks of cholera. there was a particularly deadly cholera epidemic during the time of the great famine of - in which large numbers of adivasis died. there was an influenza pandemic in that affected the whole region, but while in general in india it was relatively mild compared to the later epidemic of - , it killed about , out of a total population in the dangs of , -that is per cent of the population. all of this suggests that the adivasis of the region were particularly vulnerable in epidemics, and this was certainly the case in . indeed, the effects of poor general health and malnourishment were compounded in that year by a severe economic crisis and rain-failure. there was soaring inflation during the first world war, making the cost of imported essential commodities extremely high. there was only about one-third the normal rainfall in the region that we are focusing on here during the monsoon of , with widespread crop failure just at the time that the particularly lethal form of influenza swept the area in september-october. due to illness, many were unable to harvest the little crop that remained. despite all this, it was widely observed in - that good medical information and care could make a big difference. biomedical facilities were not, however, available for a large majority of the adivasis. during the nineteenth century, the british colonial and princely state governments provided minimal health care for these people, with small town dispensaries mainly serving local officials and high caste people. this situation began to change in the first decade of the twentieth century as government establishments expanded and missionaries started to provide care for the rural poor. the missionary organisation that worked in the interior of south gujarat was that of the church of the brethren mission, based in illinois, usa. its first missionaries arrived in the area in , established a base at valsad-which was on the main railway from bombay to delhi, and on the border with the adivasi tracts-with new mission stations being opened as and when fresh mission workers arrived from america. however, only a small number of qualified doctors were employed by the mission, as at valsad, where they ran a mission hospital. in most of the mission stations, missionaries without medical temporary camps next to irrigation canals. they suffer very badly from malaria. the prediction that agricultural development would protect all of the people from malaria has not therefore been fulfilled. qualifications provided basic health care. for example, in the dangs in the year ending march , the medically-unqualified missionaries treated , cases in a population of about , . on top of this, medically unqualified teachers in the five mission schools situated in different parts of the dangs gave out basic remedies to local people. there was also a government-run dispensary at ahwa in the dangs, where, in , , patients were treated. in general therefore, only a fairly small minority of the adivasis of the area were able to avail themselves of either government or mission medical facilities. as already pointed out, the chance of survival from an attack of this strain of influenza depended significantly on whether or not the patient obtained plenty of rest, light but nourishing food-preferably in liquid form-and good nursing. as medical facilities were so inadequate, few were able to benefit from such care in a hospital. at that time, the training of nurses was in its infancy, and there was no nucleus of trained nurses outside the city of bombay. the hospitals and health workers of the church of the brethren mission provided this to some extent in the adivasi tracts, but in they were quickly overwhelmed by the disease. their reports stated that the epidemic started in their area in september , and that by october many people in both towns and rural areas were falling ill and dying. both dr laura cottrell and her husband dr a. raymond cottrell, the mission doctors at valsad, went down with the disease at the moment that they were most needed, and the hospital had to be closed for a time. fortunately for them and the mission, both survived. dr barbara nickey, who ran the clinic at dahanu, was also kept very busy there treating cases of influenza. after the cottrells fell ill, nickey went to valsad and reopened the hospital there. others of the american missionaries also fell ill. the missionaries who were not affected did their best to alleviate the suffering. this was the case in the dangs, where the medically unqualified missionaries worked in very difficult circumstances. they reported that the epidemic was at its worst there in october, with a mortality in some villages, they reported, of from - per cent. of the twelve teachers employed in the mission schools of the dangs, two died. adam ebey reported that although there was a government dispensary at ahwa, the sick preferred to come to the missionaries for treatment. he said: 'people have more faith in an un-medical missionary than in a non-missionary medical man.' nonetheless, however hard the missionaries tried, there was little they could do to prevent the high mortality. in particular, those who developed pneumonia had little chance of survival. when all the members of a family had died, the ebeys had to bury their bodies. other christians helped them in this sombre task. they wore masks over their faces, kept damp with eucalyptus oil, to ward off possible infection. the missionaries thus tried to provide medical aid and well-informed leadership during the pandemic, but they were in general overwhelmed, and were only able to have a minimal impact. was there any comparable effort from philanthropically minded indians at that time? a notable feature of the epidemic that was observed in the major cities of bombay presidency was the mobilisation of voluntary organisations to provide relief. they raised funds, distributed medicines, set up temporary hospitals and propagated the vaccine when it was available. according to ramanna, such 'relief was not extended to the villages, because there was neither the infrastructure nor the resources.' this was not, however, the case in south gujarat, where a caste association called the patidar yuvak mandal (patidar youth association) formed a 'mitra mandal' (association of friends) to fight the epidemic. volunteers, who were largely young patidars who were studying in surat city, travelled around the rural areas distributing ayurvedic medicine free of charge. the patidar yuvak mandal was a very dynamic organisation with strong links with the nationalist movement, and the young men were both idealistic and energetic in their work. they opened over distribution centres in thirteen talukas of the region, including ones under baroda rule, and medicine was provided for over , people. there were such centres in bardoli taluka, and in mandvi taluka-a predominantly adivasi area. this provided the first occasion on which these young nationalists made contact with the adivasis of the interior-and they gained an experience that they were able to turn to political advantage in later years. nonetheless, on this occasion they found that the adivasis were suspicious of them as outsiders from a caste that they had hitherto considered their exploiters. many adivasis rejected their medicines, telling them that it was of no use and that all they could do was to propitiate their deities. only a few were persuaded to take the ayurvedic remedies. although these young nationalists were, during the s, able to gradually win the confidence of the adivasis, with gandhian projects being established in their villages, in there was no time during the brief span of the epidemic to build such contacts and trust. later, in the s, gandhian workers were able to provide extremely effective leadership in areas in which they had influence during a recurrence of plague. in , this sort of civil society response was still embryonic in the rural areas, and could not be expected to have a significant impact. in most cases, the adivasi were left to their own resources in the face of the pandemic. this can be brought out through the use of oral evidence, as collected in interviews. such testimonies are, in the case of memories of epidemics, valuable mainly for the way they bring to life the intense emotions stirred at such a time, such as the sensation of dread and social threat, helplessness in the face of the unknown, and the desperate means employed to try to deal with the danger, such as fleeing a village. they cannot be expected to provide a clear description of the symptoms, causes or extent of a disease that would stand up to the scrutiny of medical science. indeed, the statements are by such standards often confusing, and all we can do is record them without necessarily trying to explain them in unconvincing ways. dhuliya powar, who lived in what was then surgana state, said that older people were particularly hard hit, though in some households all had died. this contradicts the wider picture of mortality-by-age, although it might have been a peculiarity of this particular locality. others gave the symptoms, variously, as diarrhoea and vomiting, high fever and delusions, violent shakes and fits, and the throwing back of the head. the latter was seen to be so characteristic that the disease itself was called 'mā nmodi', or 'the breaking of the neck' ailment. the term 'mā nmodi' does not appear in any of the records on the influenza epidemic of . it is a marathi word, and all of the references to it in interviews were either from villages that are now situated in the state of maharashtra, or the dangs, where the local dialect is heavily influenced by the marathi language. there is in fact a village called mā nmodi in the dangs-and there is a local legend that the village was so called after a man had his neck (mā n) severed after he had angered the god baramdev. the man's head was replaced after a sacrifice to the deity. d. d. kosambi has also mentioned a 'unique and primitive goddess mā nmodi' who is worshipped in a cave in the mā nmodi hills near junnar, in pune district of maharashtra, which is nearly kilometres from the dangs. he says that the literal meaning of the word is 'neck-breaker', and in this is reminiscent of the goddess kavada-dara ('skull-splitter') that is worshipped in an adjoining valley kilometres away. he says that the goddess mā nmodi 'is not found elsewhere, in any context'. the caves at junnar were nonetheless located at a place where several ancient trade routes met, and the caves became a location for a buddhist monastery called manamakuda. after the decline of buddhism, they were used for local forms of worship, and he believes that the earlier name evolved in time into mā nmodi. traces of the buddhist origin, he believes, have continued in the custom that no blood sacrifice is ever offered to the goddess, which is most unusual for such a deity. the fact that the cave was on a trade route, and that the dangi village of mā nmodi lies close to the old route from maharashtra to gujarat via saputara (the one that shivaji is said to have used in his raid on surat in -in which he assembled his force first at junnar ) suggests that the term might have travelled. why the term is used for what clearly was influenza is not so obvious, as influenza does not, as such, 'break the neck'. the villagers of vansda state who knew the epidemic by a different name, that of 'dhani pani', spoke of the head being thrown back, as well as high fever, rigid limbs, and 'delusions'-and the 'neck-breaking' might have referred to the way that people threw their heads back while in a very high fever and suffering the resulting hallucinations. it could be the case that the disease was considered to be a visitation of a goddess who was either called 'mā nmodi', or linked in some way to the word. it was commonly believed that epidemic disease was caused by such visitations; sitala, the smallpox goddess, was the best known, and cholera was known in those parts as 'marakhi', after a goddess of cholera called mari mata. in the interviews, nonetheless, informants referred to the 'neck-breaking' qualities of the disease, and did not link the use of the term 'mā nmodi' to the goddess of that name. there are, however, some references from outside the dangs to a belief that the disease was caused by the visitation of a goddess, as we shall see below. the way in which the popular name for the epidemic differed from area-to-area is also significant. lucy taksa, in her oral history of the epidemic in sydney, recounts how most people there remembered it as 'the plague'. for them, the seriousness of the crisis required it to be described in terms of what was popularly believed to be the most fearsome epidemic disease, that of bubonic plague. even those who accepted that it was in fact influenza still talked of the great 'plague' of that year. she also notes how the epidemic was known by many different names throughout the world, whether the 'spanish influenza', 'the pneumonic flu', 'bronchial pneumonia', 'singapore fever', and even the 'bolshevik disease'. in iran, it was known as 'the disease of the wind'. in the dangs, where there were no local words for 'influenza', 'plague', and the like, 'mā nmodi'-the neck-breakerappears to have provided an appropriate metaphor for this fearsome, seemingly supernatural force that spread through the villages with such terrifying speed. as for 'dhani pani'; no explication of the term was provided for raje when she conducted her interviews, and although the meaning of 'pani' ('water') is quite clear, 'dhani' has more than one meaning in gujarati, and so it is not possible to hazard any guesses in this case. in some of the interviews, old adivasis recounted how they and their families had fled their villages to escape the epidemic. whole villages became deserted at this time. this is borne out by the mission evidence. adam ebey of the church of the brethren mission, who was based at ahwa in the dangs, reported that many people of the tract had fled from their villages to ahwa during the epidemic, trying desperately to escape the disease, generally to no avail. indeed, in that forest region where people lived in huts in small settlements, it was very common for them to desert a locality whenever an epidemic struck, as it was believed that the place was then haunted by the spirits of the dead. the downside to this practice was that it ensured that the infection was disseminated quickly through the area. this was almost certainly a contributing element to the exceptional severity of the epidemic in this hilly region. the adivasis of the south gujarat plains generally lived in villages in more substantial houses on fixed sites, and were less likely to flee their villages at such a time. this would in part explain the lower mortality rates there. from interviews, it appears that the adivasis resorted to remedies that they knew. in the villages of eastern vansda state, the bhagats had sought to treat the disease by catching a particular type of crab from the rivers and streams, roasting it on a fire with some grain, and then making the patient inhale the smoke. no spices or oils were to be consumed. this latter prescription is found also with measles, chickenpox and other diseases believed to be caused by the visitation of a goddess. more commonly, however, they sought to exorcise and drive away the spirit or deity that was causing the outbreak. in unbarthan in surgana, as we have seen, the diviners and exorcists-the bhagats-made a figure of a man from a mixture of ground flour and water. they passed the figure over those who were ill, exhorting the spirit to pass from the sick person into the figurine. a few of those so treated were said to have survived, but most did not, and the people lost their confidence in the bhagats at that time. vedu powar of chankapur in kalvan takuka said that nine or ten had died there in the mā nmodi epidemic, and the bhagat of the village could save only one or two. the failure of the bhagats at that time is brought out also in accounts collected by a. n. solanki, an anthropologist who carried out a study of the dhodiya adivasi community in the s. he was based at khergam, a village in the interior of chikhli takula. he found that there were still many vivid memories of that time. his informants believed that the epidemic was caused by a goddess. a ceremony was performed to entice the goddess into a pot called a khapru, which was then placed on a small cart-a rath-and drawn beyond the boundaries of the village. this did not, he was told, stop the disease, and people died in great numbers, including the bhagats whom they had looked to save them. the failure of the bhagats appears to have caused some loss of confidence in them at this time. this was compounded by the devi movement of - , when many new-style reformed bhagats emerged who denounced the older bhagats, whose demands were often extravagant, and instead asked for offerings in coconuts rather than live animals, liquor or sexual favours. another feature that comes out from the mission record was that was that the epidemic broke out once more in a virulent form in the interior villages of this region in the early months of . in the dangs, the ebeys took over the mission from the bloughs at the end of january . soon after they arrived, in early february, influenza struck again. though they, like the bloughs, lacked medical training, they dealt with this as best they could. they reported that the new cases were mainly in villages that had not been affected in october and november. in chankal, for example, where the headman, his family, and six other families had been converted to christianity, the headman died, along with nineteen other of the christians. when i visited chankal in , i was told that the influenza lingered on in the village for five years. in homes in which no one had died in the first year, people often died in the second. no home escaped altogether in those years. the sanitary commissioner's report for bombay described only the second phase of the epidemic that peaked in october, and provided mortality statistics only up to the end of december . it acknowledged that deaths from the disease continued into january , but says that this was mainly the case in sindh, where the course of the epidemic ran a month later than in the rest of the presidency. examining wider mortality rates for bombay presidency, mills notes that the death rate remained elevated up until march . by april it was back to normal. he also notes that the epidemic had a profound influence on fertility, as many survivors lost their partners, and even if they remarried, women took time to conceive. the ongoing dearth and, in some areas, famine of - , would have contributed to this effect. studies of the effects of the epidemic in other parts of the world have brought out a common 'post-flu fatigue characterised by mental apathy, depression, subnormal body temperatures and low blood pressure, which could last for weeks or months'. the lack of proper funerals for the dead was also considered highly inauspicious, causing widespread demoralisation. recent studies have also suggested that those who survive severe bouts of influenza are prone subsequently to diseases of the central nervous system, and it has been suggested that there was a close connection between the epidemic of and the widespread incidence of the sleepy sickness encephalitis lethargic (el) that killed around five million globally during the s. the statement by navsubahi patel of chankal village that people in his village continued to suffer for five years afterwards appears to conform to these recent findings. in the adivasi villages, the bhagats provided the main leadership in times of epidemiological crisis. faith in their remedies soon failed as their remedies proved of no avail. an educated middle-class leadership of the sort found quite widely in alaska was not available for the vast majority of the adivasis. there were few schoolteachers, and officials tended to be aloof and uninterested in the so-called 'primitive' classes whose destiny-so they saw itwas to either acculturate to high caste values or perish. although some idealistic young nationalists tried to provide ayurvedic remedies for the adivasis of south gujarat, they had no previous connection with the villages, and they were unable to have much impact at the time. other nationalists adopted a moralistic stance, holding that the adivasis suffered disproportionately because of their moral deficiencies and in particular their alleged drunkenness. in the words of the congress leader of surat, haribhai desai: 'those addicted to drink paid a frightful toll to the epidemic of influenza in . whole villages were devastated in forest areas and those parts of the district inhabited by kaliparaj.' in this region, christian missionaries provided almost the only wellinformed and sympathetic leadership, as well as biomedical health care, but taken as a whole, they were few and far between, so that their overall impact was fairly minimal. this all left the adivasis of this region particularly vulnerable to epidemic disease. their poverty, poor sanitation, diet and water supply, and the chronic malaria that sapped their energy and undermined their immune system, along with-at that time-an undiagnosed sickle-cell anaemia, all made them particularly susceptible when influenza swept their villages in . to compound this, the colonial state failed to provide any welfare for these people, and in particular any meaningful health care or guidance and leadership, and aid and help from civil society organisations was poorly developed and only able to have a small impact. the adivasis were largely left alone to suffer, and so traumatic was their experience that to this day they still, in those hill and forest villages, remember that terrible time of mā nmodi. sanitary commissioner for government of bombay to secretary to government one year's visiting with our missionaries in india: a story thirty-fifth annual report of the church of the brethren mission for year ending the aborigines of south gujarat myth and reality: studies in the formation of indian culture the masked disease shuttleworth to bombay government the dhodias: a tribe of south gujarat area on this, see hardiman, the coming of the devi thirty-fifth annual report of the church of the brethren mission for year ending the - influenza pandemic death in india a fierce hunger": tracing impacts of the - influenza epidemic in southwest tanzania the spanish influenza pandemic of - , xvii-xix report of the excise committee appointed by the government of bombay key: cord- -j q pcfa authors: zhan, xiu-xiu; liu, chuang; zhou, ge; zhang, zi-ke; sun, gui-quan; zhu, jonathan j.h.; jin, zhen title: coupling dynamics of epidemic spreading and information diffusion on complex networks date: - - journal: appl math comput doi: . /j.amc. . . sha: doc_id: cord_uid: j q pcfa the interaction between disease and disease information on complex networks has facilitated an interdisciplinary research area. when a disease begins to spread in the population, the corresponding information would also be transmitted among individuals, which in turn influence the spreading pattern of the disease. in this paper, firstly, we analyze the propagation of two representative diseases (h n and dengue fever) in the real-world population and their corresponding information on internet, suggesting the high correlation of the two-type dynamical processes. secondly, inspired by empirical analyses, we propose a nonlinear model to further interpret the coupling effect based on the sis (susceptible-infected-susceptible) model. both simulation results and theoretical analysis show that a high prevalence of epidemic will lead to a slow information decay, consequently resulting in a high infected level, which shall in turn prevent the epidemic spreading. finally, further theoretical analysis demonstrates that a multi-outbreak phenomenon emerges via the effect of coupling dynamics, which finds good agreement with empirical results. this work may shed light on the in-depth understanding of the interplay between the dynamics of epidemic spreading and information diffusion. the interaction between disease and disease information on complex networks has facilitated an interdisciplinary research area. when a disease begins to spread in the population, the corresponding information would also be transmitted among individuals, which in turn influence the spreading pattern of the disease. in this paper, firstly, we analyze the propagation of two representative diseases ( h n and dengue fever ) in the real-world population and their corresponding information on internet, suggesting the high correlation of the two-type dynamical processes. secondly, inspired by empirical analyses, we propose a nonlinear model to further interpret the coupling effect based on the sis (susceptible-infected-susceptible) model. both simulation results and theoretical analysis show that a high prevalence of epidemic will lead to a slow information decay, consequently resulting in a high infected level, which shall in turn prevent the epidemic spreading. finally, further theoretical analysis demonstrates that a multi-outbreak phenomenon emerges via the effect of coupling dynamics, which finds good agreement with empirical results. this work may shed light on the in-depth understanding of the interplay between the dynamics of epidemic spreading and information diffusion. recently, understanding how diseases spread among individuals has been an increasing hot research area of nonlinear studies [ ] . generally, epidemic spreading is considered to be a dynamic process in which the disease is transmitted from one individual to another via physical contact in peer-to-peer networks. to date, there is a vast amount of research tries to understand the epidemic spreading phenomenon, which could be mainly categorized into three types: (i) epidemic spreading on various types of networks [ ] , such as the scale-free network [ , ] , the small-world network [ , ] and the interdependent network [ , ] ; (ii) propagation mechanisms that describe the dynamic spreading process, such as the table illustration of parameters used in the spreading processes. susceptible-infected-recovered (sir) model for influenza [ , ] , the susceptible-infected-susceptible (sis) model for sexually transmitted disease [ , ] and the susceptible-exposed-infected-recovered (seir) model for rabies [ , ] ; (iii) data-driven modeling approaches that tackle the epidemic transmission [ ] by analyzing the available real datasets, such as the scaling laws in human mobility [ , ] , individual interactions [ , ] , and contact patterns [ , ] . the majority of the aforementioned studies focused on epidemic spreading independently, ignoring the fact that information diffusion of the diseases themselves may also have significant impact on epidemic outbreaks [ ] . for example, the outbreak of a contagious disease may lead to quick spreading of disease information, through either medias or friends. conversely, the information shall also drive people to take corresponding protective measures, such as staying at home, wearing face masks, and getting vaccinated [ ] . such behavioral responses may further impact epidemic outbreak in large population [ ] . therefore, studies on the coupling effect between epidemic spreading and information diffusion have attracted much attention from various disciplines. theoretical models have been proposed to explain how both disease and information simultaneously spread in the same population [ ] [ ] [ ] [ ] [ ] . in particular, the nonlinear influence of coupling parameters on the basic reproductive number ( r ) is studied to show the interplay between the two spreading processes [ ] . theoretical results indicate that the coupling interaction could decrease epidemic outbreak size in a well-mixed population [ ] . in some cases, enough behavioral changes would emerge in response to the diffusion of a great deal of disease information so that the severe epidemic would vanish completely, even the epidemic transmission rate was higher than the classical threshold initially [ ] [ ] [ ] [ ] [ ] . in addition, the interplay between information diffusion and epidemic spreading is elucidated on multiplex networks, where each type of dynamics diffuses on respective layers (e.g., information diffusion on communication layer versus epidemic spreading on physical layer) [ ] [ ] [ ] . as a consequence, the epidemic threshold, as related to the physical contact layer, can be increased by enhancing the diffusion rate of information on the communication layer. therefore, the effect of behavioral changes arises in three aspects [ ] : (i) disease state of the individuals, e.g., vaccination [ ] [ ] [ ] [ ] [ ] ; (ii) epidemic transmission and recovery rate [ , ] ; (iii) topological structure of contact network, e.g., the adaptive process [ ] [ ] [ ] [ ] . besides researches from physical discipline, scholars from mass communication share similar views on the causal linkages of the two diffusion processes. the outbreak of severe diseases usually attracts heavy media coverage, subsequently resulting in massive responses from the public: (i) cognitive responses, such as the attention to the information and increased awareness of the situation [ ] ; (ii) affective responses, such as anxiety, fear, or even panic [ ] ; (iii) behavioral responses, such as the adoption of new practices in order to replace undesirable habits [ ] . however, those assumptions are just theoretical hypotheses rather than empirical facts as it is difficult to find relevant data of one-to-one relationship in the spreading process. even when the data is available, it is also difficult to separate the unique effect of information on the control of epidemics from interference factors, such as variation of virus, seasonal factors and improved medical treatments, etc. present studies on the coupling dynamics mainly focus on the suppression effect of epidemic spreading by information diffusion. the occurrence of a disease prompts the sharing of corresponding information, leading to preventive measures that inhibit further epidemic spreading [ , ] . researchers have also pointed out that when the epidemic outbreak is under control, people shall not be very vigilant in discussing or sharing relevant information. it will lead to a consequent decrease in protection actions and may result in a recurrence of epidemics in future. for example, the spread of sars (severe acute respiratory syndromes) is alleviated in early march , however, a sudden increase appear later that month (as indicated in the evolution curve of the probable cases of sars, see fig. in ref. [ ] ). in this work, firstly, we demonstrate a similar outbreak pattern using data on the spread of two representative diseases, i.e., avian influenza a ( h n ) [ ] [ ] [ ] and dengue fever [ , ] , along with the diffusion of respective disease information. secondly, a nonlinear mathematical model is proposed to describe the coupled spreading dynamics as an sis spreading model. results show that information diffusion can significantly inhibit epidemic spreading. finally, both empirical analysis and the proposed model find good agreements in revealing a multi-outbreak phenomenon in the coupled spreading dynamics. to better illustrate this work, we collected data of two representative diseases, h n and dengue fever. each disease has two time series datasets: (i) daily number of individuals infected by the corresponding disease in china, which are collected from the chinese center for disease control and prevention ; (ii) online diffusion messages discussing or forwarding the information of the corresponding disease during the same period of epidemic spreading. the message diffusion data was crawled from the largest micro-blogging system in china [ ] , sina weibo ( http://www.weibo.com/ ). we have essentially obtained one-year data for the disease h n from the year to , and two-year data for dengue from the year to . we assume that individuals who post or retweet messages about the observed diseases are considered to be aware of the disease. empirical analysis of h n : fig. (a) shows the spreading processes of both disease and disease information of h n . it can be seen that the evolutionary trend of two processes are highly correlated, with pearson correlation coefficient of . . when the epidemic broke out in apr. and feb. ( fig. (a) ), it shows that many people were discussing it online simultaneously. actually, public responses to h n , such as staying at home or wearing face masks, can also affect the spread of the epidemic. the peaks of the disease spreading and the information diffusion shown in fig. (a) suggest that the mutual influence of these two spreading processes could be significant. interestingly, the size of the first epidemic peak (apr. ) is smaller than the second one (feb. ), which is inversely correlated with the information amount. that is to say, the number of individuals discussing the disease during the first outbreak is much greater than that of the second one. this might imply that the awareness of epidemics and the physical epidemics could influence each other. empirical analysis of dengue fever: fig. (b) describes the spreading processes of both disease and disease information of dengue. similar to the analysis of h n , the evolution trend of the two processes is also consistent with each other, with even much higher correlation coefficient of . . according to the two largest peaks (in sept. and sept. , respectively) of disease spreading, we find that the first epidemic peak is also smaller than the second one, while the corresponding information peaks show a contrary trend. considering the two small peaks of information in fig. (b ) and (b ), we can also find the same relationship between the the two dynamic processes as that of two largest peaks, suggesting also the possible coupling effect of the awareness of epidemics and the infected cases of dengue. in the aforementioned section, we empirically showed that the spread of disease and disease information has a coupling effect with each other by analyzing the data from two contagious diseases. inspired by the empirical results, we propose a network based nonlinear model to describe the interaction between epidemic spreading and information diffusion in this section. in this model, we assume there are two states for disease spreading: susceptible ( s ) and infected ( i ), and two states of information diffusion: aware (+) and unaware (-). as a consequence, each individual will be at one of the four states during the model evolution: • initially, one arbitrary individual is randomly picked from the given network as the spreading seed ( i + state). the rest individuals are set to be s − state. • at each time step, the infected individuals ( i + and i − states) will spread epidemics to their susceptible network neighbors ( s + and s − states) with given spreading probability. the infected individuals ( i + and i − states) could recover to the susceptible state with given recovery probability. • at each time step, individuals that are aware of the disease ( i + and s + states) will transmit the information to their unaware neighbors ( i − and s − states) with probability α. in addition, the informed individuals ( i + and s + ) could become unaware of the disease with the probabilities of λ and δλ, respectively. beyond the parameters given in table , we define σ as the probability of individuals taking protective measures. thus, σ s < is defined as that a susceptible aware individual ( s + ) will take protective measures to avoid becoming infected, and σ i < is defined as infected aware individuals ( i + state) will reduce contact with their susceptible neighbors or adopt medical treatments. in addition, we assume the infected probabilities for these two different populations are independent with each other, hence σ si = σ s σ i is defined as the probability of the i + state individuals infecting the s + state ones. when an i + individual is aware of the epidemic, s/he will take positive measures, leading to an increased recovery rate, which is represented by the factor ε > . furthermore, i + state individuals, which could be assumed to better understand the seriousness of epidemics, would be less likely to neglect relevant information, leading to δ < . in this work, since the spreading processes of information and disease are primarily determined by the corresponding transmission probabilities, we fix other parameters and mainly investigate the effects of α and β. in the following analysis, we set σ s = . , σ i = . , δ = . , ε = . , λ = . and γ = . . table . subsequently, the proposed model is performed on an er network with a total population n = , and average degree k = . to measure the spreading effects, we denote the infected level ( i ) as the fraction of infected individuals (both i + and i − ), and the informed level ( info ) as the fraction of individuals who are aware of the disease (both s + and i + ). fig. shows the simulation results by fixing the infection probability β = . . in this model, the parameter α can be considered as the information diffusion capability, hence larger α indicates that information diffuses much easier, resulting in a monotonically increase in the number of informed individuals (see the inset of fig. ). in fig. , it also shows that the increase in α will inversely hamper the speed of epidemic spreading, hence diminish the overall epidemic outbreak size. as a consequence, appropriate publicity might be an effective strategy to inhibit further spreading of epidemics, which is also consistent with the empirical analysis shown in fig. . in fig. , the model also indicates that there is mutual influence between information diffusion and epidemic spreading. a high prevalence of epidemic would lead to a small information fading probability δ, consequently resulting in a high infected level i . it in turn inhibits the epidemic spreading ( σ { i , s , si } < ). this coupling effect can be clearly described by the full set of differential equations (see appendix ). in addition, the equations are solved by mean-field and pairwise approaches, respectively. fig. shows the results of simulation, theoretical analysis of both mean-field and pairwise analysis. we find that the pairwise approach can better fit the model than the mean-field method. therefore, we use pairwise approach to perform further studies in the following analysis. in order to investigate the effect of the mutual interaction between α and β on the spreading process, we explore the phase diagram showing the fraction of infected individuals caused by combination of such coupling effects (see fig. ). the . that is to say, epidemic outbreak will occur if the parameter combination is larger than the critical value, otherwise the epidemic will die out. the results also clearly show that more individuals will be infected with large β and small α, suggesting that the information diffusion can impede the disease spreading. it is noted that the process degenerates to the standard sis model if α = , where there is no information diffusion in the system. thus, the epidemic outbreak threshold is β c = γ k = . [ ] , which is also consistent with the results of pairwise analysis and simulation shown in fig. . in addition, fig. (c) shows a detailed view of pairwise analysis for α, β ∈ [ , . ] in order to better observe the threshold changes. the threshold value of β is around . when α → , as the epidemic information cannot spread out in this case according to the inset of fig. . when α > , the epidemic threshold can be significantly increased because of the effect of information diffusion. on the contrary, fig. shows that the informed level only slightly ascends when α is large enough (e.g., α > . ), which leads to an obscure change in the epidemic threshold. this result additionally indicates that abundant information would not always work for obstructing epidemic spreading. for example, in the case that a disease with a strong infectiveness (corresponds to large β in fig. ), enhancing the public awareness alone is insufficient to control the large outbreak of epidemics. in order to obtain better understanding of dynamics of the critical phenomenon, we observe the evolution of infection density for various values of β in fig. . from the differential equation, di dt we can obtain i ∝ t − at the critical point, which shows a power-law decay. in addition, the inset of fig. also presents a power-law decay of the infection density when β ≈ . . by contrast, the infection turns to break out as an endemic, namely steady state, for β > . ( β = . in fig. ), otherwise the epidemic will be eliminated, so-called healthy state for β < . ( β = . in fig. ). therefore, it can be inferred that β c is approximately . in this case, which is consistent with the results in fig. , where β c is around . for α = . . interestingly, the empirical analysis also demonstrates that a multi-outbreak phenomenon emerges for both epidemic spreading [ , [ ] [ ] [ ] and information diffusion [ ] , in which there are several outbreaks during the dynamic process of epidemic spreading. generally, there are many complicated factors that might contribute to this phenomenon, including seasonal influence, climate change, and incubation period, etc. in this model, the periodic outbreaks can be interpreted by the influence of information diffusion. as discussed above, there is a mutual interaction as the two dynamics are coupled with each other during the process. on one hand, a larger proportion of infected individuals should result in an increase in preventive behavioral responses [ ] due to the increased awareness of the disease, consequently leading to a steady decrease of further infected cases. on the other hand, when the spread of epidemic tends to be under control, people shall become less sensitive to discuss or share relevant messages, which leads to dissemination of information and simultaneously raises the possibility of a second outbreak. notably, there are also some cases where the size of the second outbreak is smaller than the first one. for example, the eight dengue outbreaks in thailand over years from to [ ] , and there are also some cases that the second outbreak is larger than the previous one, as in the case of sars in [ ] and dengue in taiwan in - [ ] . in order to better understand the underlying mechanism that drives the multi-outbreak phenomenon of the coupled dynamics, we set two thresholds, i high and i low , to represent different infected levels. that is to say, when the fraction of infected individuals is larger than i high , the information diffusion parameter α will be set as high as α = . so that the information will diffuse even more quickly. accordingly, when it is smaller than i low , the parameter will directly decay to α = . to represent the corresponding response to abatement effect of information. fig. shows the simulation results. it can be seen that the epidemic spreads very quickly at the beginning as there are very few people aware of it, and soon reaches the threshold i high and triggers the designed high information transmission probability α = . . as a consequence, as the information bursts out, the high informed level has a significant impact on inhibiting epidemic spreading (the decay period of the epidemic), which will be completely suppressed if the high informed level remains. however, when the epidemic spreading is notably controlled from the first outbreak (i.e. the infected density is smaller than i low ), people are less likely to consider the epidemic as a threat, hence ignore relevant information and no longer actively engage in taking protective measures, which will in turn lead to a subsequent epidemic outbreak in the future. two representative outbreak patterns are shown in fig. , where the first outbreak is smaller than the second one ( fig. (a) ) and vice versa ( fig. (b) ). moreover, fig. , where the size of the first epidemic outbreak is smaller than that of the second one, while the informed level shows to the contrary. it should be noted that, due to the difficulty in collecting data of patient-to-fans to precisely quantify the informed level in the empirical analysis, the number of messages that discuss the epidemic is alternatively used in fig. . different from the trend shown in fig. , a high informed level( info > . ) must be maintained during the period when the infected level decreases shown in fig. . based on the model analysis, it could be concluded that it is important to raise public awareness of epidemic occurrence, especially during when the epidemic seems to be under control, otherwise, there is a likelihood of subsequent outbreak in the foreseeable future. furthermore, we explore the evolution of the informed and infected density with different values of β in fig. . in fig. (a) , it shows that the infected density firstly achieves a small peak and then rapidly vanishes, resulting in a evolution pattern known as healthy , which means there is approximately no disease. in fig. (b) , an oscillatory pattern is revealed for . < beta ≤ . . similarly, for large β ∈ ( . , ], the infected density firstly achieves a large peak (almost close to one), then rapidly decrease to a low level (nearly zero) and gradually raised to a steady state, showing a unimodal pattern [ ] . in this paper, we have studied the coupling dynamics between epidemic spreading and relevant information diffusion. empirical analyses from representative diseases ( h n and dengue fever ) show that the two kinds of dynamics could significantly influence each other. in addition, we propose a nonlinear model to describe such coupling dynamics based on the sis (susceptible-infected-susceptible) process. both simulation results and theoretical analyses show the underlying coupling phenomenon. that is to say, a high prevalence of epidemic will lead to a slow information decay, consequently resulting in a high infected level, which shall in turn prevent the epidemic spreading. further theoretical analysis demonstrates that a multi-outbreak phenomenon emerges via the effect of coupling dynamics, which finds good agreement with empirical results. the findings of this work may have various applications of network dynamics. for example, as it has been proved that preventive behaviors introduced by disease information can significantly inhibit the epidemic spreading, and information diffusion can be utilized as a complementary measure to efficiently control epidemics. therefore, the government should make an effort to maintain the public awareness, especially during the harmonious periods when the epidemic seems to be under control. in addition, in this work, we only consider the general preventive behavioral response of crowd. however, the dynamics of an epidemic may be very different due to the behavioral responses of people, such as adaptive process [ ] , migration [ ] , vaccination [ ] , and immunity [ ] . this work just provides a starting point to understand the coupling effect between the two spreading processes, a more comprehensive and in-depth study of personalized preventive behavioral responses shall need further effort s to discover. mean-field analysis: according to fig. , we adopt mean-field analysis for the spread of epidemic and information in a homogeneous network as follows: where n is the number of individuals in the system, k is the average degree of the network and the other parameters are illustrated in table . pairwise analysis: pairwise models have recently been widely used to illustrate the dynamic process of epidemics on networks, as those models take into account of the edges of the networks [ ] [ ] [ ] . in this study, we consider a set of evolution equations which are comprised of four types of individuals and types of edges. using the well-known closure, (assuming the neighbors of each individual obey poisson distribution) [ ] , we can get a set of differential equations as follows: ( ) epidemic processes in complex networks 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mobility responses to the large-scale spreading of infectious diseases modeling human dynamics of face-to-face interaction networks small but slow world: how network topology and burstiness slow down spreading temporal networks how human location-specific contact patterns impact spatial transmission between populations? dynamics of information diffusion and its applications on complex networks epidemic spreading with information-driven vaccination world health organization. consensus document on the epidemiology of severe acute respiratory syndrome (sars) the spread of awareness and its impact on epidemic outbreaks endemic disease, awareness, and local behavioural response modelling the influence of human behaviour on the spread of infectious diseases: a review interacting epidemics on overlay networks epidemic dynamics on information-driven adaptive networks on the existence of a threshold for preventive behavioral responses to suppress epidemic spreading the impact of awareness on epidemic spreading in networks imitation dynamics predict vaccinating behaviour social contact networks and disease eradicability under voluntary vaccination imitation dynamics of vaccination behaviour on social networks dynamical interplay between awareness and epidemic spreading in multiplex networks competing spreading processes on multiplex networks: awareness and epidemics asymmetrically interacting spreading dynamics on complex layered networks vaccination and the theory of games effects of behavioral response and vaccination policy on epidemic spreading-an approach based on evolutionary-game dynamics vaccination and epidemics in networked populationsan introduction information cascades in complex networks statistical physics of vaccination the impact of information transmission on epidemic outbreaks epidemic dynamics on an adaptive network adaptive human behavior in epidemiological models information spreading on dynamic social networks roles of edge weights on epidemic spreading dynamics issue competition and attention distraction: a zero-sum theory of agenda-setting moral threats and dangerous desires: aids in the news media diffusion of innovations h n is a virus worth worrying about determination of original infection source of h n avian influenza by dynamical model global concerns regarding novel influenza a (h n ) virus infections controlling dengue with vaccines in thailand impact of human mobility on the emergence of dengue epidemics in pakistan how events determine spreading patterns: information transmission via internal and external influences on social networks mapping spread and risk of avian influenza a (h n ) in china transmission characteristics of different students during a school outbreak of (h n ) pdm influenza in china the effect of antibody-dependent enhancement, cross immunity, and vector population on the dynamics of dengue fever spatial behavior of an epidemic model with migration epidemic enhancement in partially immune populations representing spatial interactions in simple ecological models the effects of local spatial structure on epidemiological invasions pair approximation of the stochastic susceptible-infected-recovered-susceptible epidemic model on the hypercubic lattice key: cord- - oqv jom authors: rguig, ahmed; cherkaoui, imad; mccarron, margaret; oumzil, hicham; triki, soumia; elmbarki, houria; bimouhen, abderrahman; el falaki, fatima; regragui, zakia; ihazmad, hassan; nejjari, chakib; youbi, mohammed title: establishing seasonal and alert influenza thresholds in morocco date: - - journal: bmc public health doi: . /s - - -y sha: doc_id: cord_uid: oqv jom background: several statistical methods of variable complexity have been developed to establish thresholds for influenza activity that may be used to inform public health guidance. we compared the results of two methods and explored how they worked to characterize the influenza season performance– season. methods: historical data from the / to / influenza season performance seasons were provided by a network of primary health centers in charge of influenza like illness (ili) sentinel surveillance. we used the who averages and the moving epidemic method (mem) to evaluate the proportion of ili visits among all outpatient consultations (ili%) as a proxy for influenza activity. we also used the mem method to evaluate three seasons of composite data (ili% multiplied by percent of ili with laboratory-confirmed influenza) as recommended by who. results: the who method estimated the seasonal ili% threshold at . %. the annual epidemic period began on average at week and lasted an average of weeks. the mem model estimated the epidemic threshold (corresponding to the who seasonal threshold) at . % of ili visits among all outpatient consultations. the annual epidemic period began on week and lasted on average weeks. intensity thresholds were similar using both methods. when using the composite measure, the mem method showed a clearer estimate of the beginning of the influenza epidemic, which was coincident with a sharp increase in confirmed ili cases. conclusions: we found that the threshold methodology presented in the who manual is simple to implement and easy to adopt for use by the moroccan influenza surveillance system. the mem method is more statistically sophisticated and may allow a better detection of the start of seasonal epidemics. incorporation of virologic data into the composite parameter as recommended by who has the potential to increase the accuracy of seasonal threshold estimation. seasonal influenza epidemics result in considerable annual morbidity and mortality, with an estimated , to , deaths per year globally [ ] . associated with these seasonal epidemics are substantial economic losses due to absenteeism, lost wages and increased utilization of health care services [ ] . the influenza-associated respiratory annual mortality rate for people aged and older in morocco has been recently estimated by the us centers for disease control and prevention (us cdc) at . per , ( % credible interval of . - . ) [ ] . the risk of hospitalization due to influenza is to times greater in high-risk populations in morocco (e.g., the elderly and people with chronic disease) than in the general population [ ] . the most effective ways to prevent or mitigate these effects are through vaccination combined with appropriate clinical management of persons infected with influenza. optimal impact of vaccination campaigns is achieved by timing them prior to the beginning of the influenza season to ensure maximum coverage and protection among the population. likewise, a timely signal to healthcare providers that the influenza season is underway helps to guide their patient management decisions and to mitigate the effects of illness in the individual and in the community. local patterns of influenza virus circulation and seasonality may differ geographically, necessitating national estimates of seasonal influenza activity to inform public health guidance. national surveillance data is essential for understanding those patterns and establishing signals for the beginning of the influenza season and epidemic periods. establishing baseline activity, epidemic and alert thresholds is a useful tool to inform recommendations for timely influenza vaccination to lessen the burden of seasonal epidemics [ ] . while several statistical methods are commonly used, there is no gold standard for calculating influenza epidemic thresholds. the methods developed to date vary in their complexity and calculate either time-varying or fixed thresholds. the simplest ones use visual inspection of historical data to create a fixed threshold indicating the expected level of activity throughout the year [ , ] . statistical methods include regression models [ ] [ ] [ ] [ ] , time series methods [ ] , adaptation of industrial control processes such as shewart charts [ ] , cumulative sum (cusum) [ ] and rate difference models [ ] . methods that involve calculation of means and medians are of medium complexity but are practical as they may be simple to implement. the objective of this study was to evaluate the performance of two methods using means and medians to establish thresholds using data from the moroccan national influenza-like illness (ili) syndromic surveillance system. we compare the results of the world health organization averages method (who method) with the moving epidemics method (mem) which is recommended by both the who and the european centre for disease prevention and control (ecdc). as a complement to the thresholds using syndromic data, we also calculated a threshold using a composite parameter integrating both syndromic and virologic surveillance data. following these direct comparisons of the methodologies, we explored the best method for characterizing the / influenza activity. in , the epidemiology department of the ministry of health of morocco launched a year-round public sector syndromic surveillance system for ili comprised of primary health centers, with a catchment population of almost million people. sites report weekly ili activity to the regional and central levels, where health officials aggregate the surveillance data. a case definition similar to the who ili case definition recommended for public health surveillance, defined as "a sudden onset of fever, a temperature > °c and cough or sore throat in the absence of another diagnosis" was used from to [ , ] . in , morocco adopted the updated who standard ili case definition [ ] developed in as "an acute respiratory illness with a measured temperature of ≥ °c and cough, with onset within the past days" [ ] . reporting includes the total number of ili consultations aggregated by gender and age group, as well as total outpatient consultations. the proportion of ili visits among all outpatient consultations is used as a proxy for influenza activity. in , the moroccan national influenza center (nic) began a virologic surveillance system in both ambulatory and hospital sites to complement the syndromic system and provide data on laboratory-confirmed influenza activity [ ] . after an interruption in data collection beginning in , virologic surveillance was resumed in sentinel sites in . specimens were collected and characterized between september and june. enrolling patients from both out-and in-patient facilities allowed the integration of epidemiologic and virologic data representing the spectrum of illness from mild (ili) to severe (e.g. severe acute respiratory infection or sari) [ ] . we used seasons of syndromic surveillance data ( / to / , excluding the / pandemic year from analysis as influenza activity was not reflective of a typical season); this was described elsewhere [ ] . we compared two methodologies for establishing seasonal baseline activity and epidemic thresholds. we also compared the calculated thresholds with the observed weeks for the start and end of the / season. using three seasons of virologic ili surveillance data ( / to / ), we used the mem method to make calculations using the composite parameter recommended by who [ ] ; this method estimates the proportion of laboratory-confirmed influenza ili consultations among all outpatient consultations, or the product of weekly ili consultations of total outpatient visits and weekly percentage of influenzapositive specimens among respiratory tests. the methods discussed in order to standardize country information on influenza activity, have raised basic concepts summarized in table . the who global epidemiological surveillance standards for influenza (who manual) [ ] included a simple method to establish an average epidemic curve to identify the beginning of the influenza season using national influenza surveillance data. this method characterizes the intensity of influenza activity each year and may be used to describe the seasonality of influenza virus circulation. using ili as a proxy for influenza virologic activity [ , ] , we used weekly proportion of ili among all outpatient consultations as our indicator of influenza activity. with this method, we were able to produce an average epidemic curve. using data from the average epidemic curve, we used statistical measures of variance to establish an alert threshold. we determined the flat baseline for expected influenza activity throughout the year in order to develop an indicator for the onset of influenza season (seasonal threshold). sustained influenza activity (i.e., three consecutive weeks) above this baseline indicated the start of the influenza season or the epidemic period [ ] . in the final step, moderate, high, and extraordinary intensity thresholds were estimated as described in the who pandemic influenza severity assessment manual [ ] , (fig. ) . the moving epidemic method (mem) [ ] [ ] [ ] [ ] [ ] [ ] is an alternative tool developed to help model influenza epidemics also using retrospective national surveillance data. it may be described as a combination ratedifference model that uses cumulative differences in mem software produces an average curve, lower interval, and higher interval. calculate the mean and standard deviation (sd) of the average epidemic curve. for each week, the alert threshold is . sd above the weekly ili% mean. ili% > . sd indicates high ili activity or outbreaks and may be used to characterize a severe season. a graph consisting of the alert thresholds for each epidemic week. median weekly ili% over all weeks (i.e., the average epidemic curve is not used). indicates the level of influenza activity that signals the start and end of the annual influenza season(s). for prospective surveillance: upper limit of the % onesided confidence interval of the arithmetic mean of the highest pre-epidemic weekly ili% values. parameter value which marks the start of the epidemic period. for prospective surveillance: upper limit of the % onesided confidence interval of the arithmetic mean of the highest post-epidemic weekly ili% values. the third of three consecutive weeks with ili% above seasonal threshold. indicates that influenza activity occurs consistently. for retrospective analysis of individual season data: see "length of epidemic period". the third of three consecutive weeks with ili% below seasonal threshold for retrospective analysis of individual season data: see "length of epidemic period". weeks from epidemic start to end. for retrospective analysis of individual season data: mem software uses a "maximum accumulated proportions percentage (map)" algorithm to split the season into three periods: a pre-epidemic, an epidemic, and a post-epidemic period. proportion of total cases that occurred during the epidemic period upper % limit of -sided ci of mean of all peak values. upper % limit of the one-sided confidence interval of the geometric mean of the highest epidemic weekly ili% values. upper % limit of -sided ci of mean of all peak values. upper % limit of the one-sided confidence interval of the geometric mean of the highest epidemic weekly ili% values. upper . % limit of -sided ci of mean of all peak values. upper % limit of the one-sided confidence interval of the geometric mean of the highest epidemic weekly ili% values. rates to determine epidemic periods and intensity of activity [ , ] . using the free software r for statistical computing and graphics [ ] and its open source user interface rstudio [ ] , we uploaded our surveillance data via the mem application [ ] , and fit the model using three steps. we first visually compared activity over the seasons in order to compare the timing of peak activity and activity trends across seasons. the mem procedure has three main steps: first, the length, start and the end of the annual epidemics are determined, splitting the season in three periods: a pre-epidemic, an epidemic and a postepidemic period [ , ] . in the second step, we built the model by using retrospective data from all seasons. the mem app calculated the pre-epidemic threshold that marks the start of the epidemic period (analogous to the seasonal threshold in the who method). in the third step, medium, high, and very high intensity thresholds were estimated ( table ) . using the app, we produced graphs of each season showing the preepidemic, epidemic and post-epidemic periods (fig. ). in addition, as the assumption that ili activity is reflecting influenza virus circulation has limitations, we created a second seasonal threshold with this methodology using the composite parameter recommended by who for three seasons of virologic ili surveillance (fig. ) . lastly, we calculated indicators of performance of the app to detect epidemics, using values from the model for sensitivity, specificity, positive predictive value, negative predictive value, percent agreement and the matthew correlation coefficient ( table ). the application allowed us to optimize the model by searching the optimum slope of the map curve to optimize the goodness-of-fit of the model for detecting epidemics. the mem app calculates goodness-of-fit indicators in an iterative process using a cross-validation procedure [ ] . true positives (tp) were then defined as values of epidemic period above the threshold, true negatives (tn) as values of the non-epidemic period below the threshold, false positives (fp) as values of the non-epidemic period above the threshold and false negatives (fn) as values of epidemic period below the threshold. the process was repeated for each season in the dataset and all tp, tn, fp and fn were pooled. to measure the performance of the threshold, the following statistics and definitions were used [ ] : . sensitivity: the number of epidemic weeks above the pre-epidemic threshold and above the postepidemic threshold divided by the number of epidemic weeks (epidemic length). . specificity: the number of non-epidemic weeks below the pre-epidemic threshold and below the post-epidemic threshold divided by the number of non-epidemic weeks. . positive predictive value (ppv): the number of epidemic weeks above the threshold divided by the number of weeks above the threshold. the ili sentinel surveillance system is a public health activity organized by the ministry of health of morocco. personally identifiable data is excluded from this surveillance system; as a result, no request for authorization from the national ethics committees was required. indeed, the royal dahir n° - - dated august , , promulgating the law n° - relating to the protection of persons participating in biomedical research, provides for special provisions for non-interventional or observational researches as stipulated in its articles and . when applying the who method to our years of surveillance data, we estimated that the seasonal threshold was the point at which more than . % of outpatient consultations were due to ili (table ) . influenza activity crossed this threshold on average at week and the beginning of the epidemic period would be declared after three consecutive weeks of activity above this threshold, on average at week . the typical epidemic period lasted weeks, finishing at week , when activity was below the seasonal threshold for three consecutive weeks. the average peak activity occurred during week . seasons where ili activity regularly crossed the alert threshold may be characterized as severe ( fig. and table ). intensity thresholds were ili% of . , . and . % for moderate, high and extraordinary intensity thresholds) ( fig. and table ). the mem model produced an estimate that the average annual influenza epidemic period began on week , and that the epidemic period lasted on average weeks. the epidemic threshold (corresponding to the who seasonal threshold) was higher, at . % of ili patients among all outpatients. the average peak activity occurred during week , consistent with the estimate using the who method. intensity thresholds were of . , . and . % of ili patients among all outpatients for respectively medium, high and very high intensity thresholds ( fig. and table ). indicators related to the goodness-of-fit of the mem model for detecting the epidemics, using these retrospective data showed that the sensitivity of the mem epidemic threshold was . whereas the specificity was . . positive predictive value was . and negative predictive value was . (table ) . using three seasons of virologic data, we established a third seasonal baseline based on the composite parameter recommended by who, which integrated both laboratory-confirmed influenza and syndromic ili reporting (fig. ) . this method allowed us to compare the results of characterizing seasonality using these data types to identify the beginning of the influenza season. applying the mem methodology to our combined data, we determined that the average epidemic began at week , average peak activity occurred at week and the average epidemic period lasted weeks. using this method, medium, high and very high intensity thresholds were set at . , . and . % of laboratory-confirmed ili patients among all outpatients ( fig. and table ). goodness-offit indicators showed a sensitivity of %, specificity of %, positive predictive value of % and negative predictive value of % (table ) . ili data with the who/ ili data with the who thresholds, the curve overlapped the average epidemic curve and activity crossed the seasonal threshold during week of and was sustained after this time, confirming that this was the start of the epidemic period (fig. ) . the season peaked during the second week of , week earlier than the average identified by the who methodology (week ); we observed peak activity of . % of ili patients among all outpatients (fig. ) . when using the mem method with ili proportions, the epidemic period began at week , or the end of november . this finding indicated an early season, beginning weeks before the average epidemic start week of . the season peaked at week of (beginning of january), week before the average peak week determined by mem (week ), with peak activity above % of ili patients among all outpatients. this season was characterized as one of medium intensity (fig. ) . when considering the composite parameter, the mem method showed that the epidemic period began at week , or the end of november , with a sharp increase of the epidemic curve weeks prior to the average start (week ). the seasonal peak occurred at week of , week before the average peak week (week ), with peak activity above . % of confirmed ili patients among all outpatients. this season almost reached the threshold for high intensity (fig. ). the occurrence of the h n pandemic highlighted the need for a robust and standardized method to make timely assessments of the severity of influenza activity that may be used as an indicator of an unusual event. who developed and began implementing a framework on pandemic influenza severity assessment (pisa) [ ] in march . member states are encouraged to establish influenza baseline and epidemic alert thresholds from surveillance data and to monitor and describe the severity of each influenza season (seasonal, epidemic or pandemic influenza) using these thresholds. for this purpose, a simple method proposed by the who was used [ , , ] . who is now recommending mem, which is a more sophisticated method of reporting influenza activity adopted by the european centre for disease prevention and control [ ] [ ] [ ] [ ] and adopted by several countries from other regions [ , ] . the analysis using the mem application with seasons of syndromic surveillance data showed clear seasonality to ili activity and visual inspection of graphed data revealed a single seasonal peak per year. the data show seasonal peaks between december and march, varying by year, as described by barakat et al. based on visual analysis [ ] , matching trends observed in other northern hemisphere countries [ ] . the average seasonal peak in morocco occurs at week (mid-january) using either method. the seasonal threshold established using the method described in the who influenza surveillance guidelines was lower than the epidemic threshold calculated by the mem method when ili proportions are considered ( . % versus . % of ili patients among all outpatients). the average epidemic start week was estimated to be earlier when using the who method, with an average start at week versus week or by using respectively ili proportions or the composite parameter with the mem method. there is a three-to four-week difference between these methods when describing the typical start to a season; the optimal timing of a seasonal influenza vaccination campaign might vary accordingly. public health officials must weigh the costs and benefits of the optimal campaign period. influenza vaccine administration is ideally timed at least several weeks prior to influenza virus circulation as antibody response is achieved on average weeks post vaccination [ ] . the average epidemic period estimated by the who method was longer compared with the mem method ( weeks vs. or weeks respectively). there are few publications with estimates of the typical duration of an influenza season [ ] . according to the available evidence, the duration of the influenza season in the temperate zone of the northern hemisphere, ranges - weeks in europe [ ] . the goodness-of-fit calculations from the mem application indicate that the mem capacity for detecting epidemic activity had a sensitivity of % and a specificity of % when using ili proportions, implying that it is better for eliminating false signals than it is for detecting a true signal. our finding is similar to that of vega et al., who also found the sensitivity to be significantly lower than the specificity [ ] . using cambodian surveillance data, ly et al. [ ] also found that the who methodology appeared to have a higher sensitivity for detecting early epidemic activity, but a lower specificity than mem, implying a greater risk of signalling false starts to the season. timely detection of the start of seasonal epidemics may be important to alert health services and to mitigate morbidity, mortality and economic costs by allowing resource allocation and adjusting response measures to face the seasonal overload in the healthcare system. the public health implications for this difference between methodologies are that using the mem method without applying the seasonal threshold established using the who method, there is a risk of missing the beginning of the epidemic period and not providing timely guidance to clinicians to indicate influenza season has begun, and to manage patient treatment accordingly. using the lower who threshold for public health messaging regarding the beginning of the influenza season may pose the risk of a false alert and perhaps overprescribing antiviral medications. from another point of view, using a low seasonal threshold could influence decision-makers to recommend earlier vaccination. as our results showed that the seasonal threshold typically occurs between mid-november and mid-december in morocco, appropriate timing for vaccination could be about month before this date. of note, the us advisory committee on immunization practices (acip) recommends that vaccination should be offered by the end of october, considering the unpredictability of timing of onset of the influenza season and concerns that vaccineinduced immunity might wane over the course of a season [ ] . low seasonal thresholds may be crossed multiple times as was the case in our application of the who threshold for several seasons ( / , / , / , / and / [not shown]), due perhaps to variability in reporting by the surveillance sites. because of this variability, it is possible that declaring the start of the influenza season after two or three sustained weeks of activity above the threshold as recommended by who, is a prudent option for considering influenza transmission as epidemic. the mem methodology, however, calculates the length of the epidemic period during each season separately in order to determine the average length. thus, the epidemic threshold calculated with the mem method could be preferable to that established with the who method. mem was first used in in the who european region to estimate epidemic period and intensity using a minimum of five historical seasons for the calculations and the target season [ ] . despite the availability of only years of virologic data in morocco, we followed a who recommendation to use the composite parameter with mem [ ] . this allowed a clearer cut estimation of the beginning of the influenza epidemic period, characterized by a sharp increase in influenza-confirmed ili cases. when ili proportions are used, the two methods produce similar values for each intensity threshold considered in the pisa assessment of seasonal transmissibility; who has adopted the mem for this purpose. when comparing the highest weekly activity per season (the seasonal peak) to the intensity thresholds established by who and mem procedures, the / season was of moderate intensity ( figs. and ) . using the composite parameter, the / seasonal peak nearly reached the high intensity threshold, whereas this curve didnot cross the medium intensity threshold when using only ili proportions. our study has several limitations. first, the assumption that ili activity reflects influenza virus circulation is limited because of possible concurrent circulation of other respiratory viruses (e.g., rsv) [ , ] . who recommends using a composite parameter defined as the product of the ili or ari proportion and the percentage positive for the transmissibility indicator of the pisa tools [ ] . unfortunately, virologic data collected prior to was not consistently available for the period of our study as virologic surveillance was disrupted between and . despite this limitation, our laboratory-confirmed data showed something different than the syndromic data as the start of the virologic activity occurs suddenly and is therefore clearly identified. it is obvious that the inclusion of virologic data increases the specificity of seasonal threshold estimation. according to the who guidelines [ ] , "a combination of parameters may be preferable. for example, a seasonal threshold could be defined as the week in which the ili rate crosses a certain value and the percentage of specimens testing positive reaches a certain point". given the long life of our surveillance system, our data were limited by changes in data collection practices, inconsistency of reporting by surveillance sites, and variable access to primary health care. these problems are not unique to the morocco ili surveillance system, and we believe they are the nature of routine, sentinel surveillance. another limitation was the adoption of a new case definition in , at which point we also relaunched our surveillance system using a new protocol. these changes may have affected the trends that we observed in ili activity from that year forward. since both methods we used to establish thresholds recommend using a minimum of three to five seasons of data, we would not have enough data to run the models if we used only data from onward. determining a gold standard for influenza epidemic and intensity thresholds has been a long-standing research question for both international organizations and country-level public health authorities, and there is no consensus on the best method [ , , , , [ ] [ ] [ ] . both the who method and the moving epidemic method translate quantitative trend data into standardized qualitative intensity levels, which permit countries to determine if the current season is atypical or to assess country or regional differences in activity and intensity. both methods identified that the / season was the most active in morocco, excluding the / pandemic season according to non-published observations. both methods are coherent to identify excess activity or high intensity thresholds even though with adequate laboratory data mem with the use of the composite parameter, gives a theoretically better qualitative measure of the level of activity. this comparative study has shown that the threshold methodology presented in the who manual is simple to implement and easy to adopt for use by the influenza surveillance system in morocco or the national surveillance systems of other similar countries. mem is more statistically sophisticated and may provide a more accurate detection of the start of seasonal epidemics in temperate countries with clear seasonal circulation of influenza viruses, especially if virologic data are considered. whichever method is used, analysis of surveillance data will provide information about seasonal thresholds and epidemic curves 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and other respiratory viruses in hong kong establishing thresholds for influenza surveillance in victoria european centre for disease prevention and control. indicators of influenza activity detecting the start of an influenza outbreak using exponentially weighted moving average charts publisher's note springer nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations we would like to thank dr. amgad elkholy and dr. mohamed elhakim from infectious hazard management (ihm)/emro at world health organization and dr. henry laurenson-schafer for organizing training sessions on statistical methods for analyzing data provided by influenza surveillance systems as well as pr. abderrahmane maaroufi, former director of epidemiology at the ministry of health of morocco. a pilot study to assess the historical surveillance data of influenza in morocco and to compare the who method authors' contributions ar and ic designed the study. ic performed data analysis, interpretation of results and drafted the manuscript. mmc helped with study design, data analysis, interpretation of results, and drafting of the manuscript. ar and my assisted with study implementation and provided oversight of study personnel. ho, ab, fef, zr and hi assisted with access to and interpretation of laboratory testing results. st and he helped with data collection and study design and implementation. cn read and approved the final manuscript. all authors have read and approved the manuscript. none.availability of data and materials datasets were collected by each participating site including the national influenza center and gathered on a pooled database at the direction of epidemiology and disease control of the ministry of health of morocco. data cannot be publicly shared due to internal regulations of the ministry of health of morocco. the datasets analyzed during the current study could be available from the corresponding author on reasonable request and with special authorization of the ministry of health of morocco. the ili sentinel surveillance system is a public health activity organized by the ministry of health of morocco. personally identifiable data is excluded from this surveillance system; as a result, no request for authorization from the national ethics committees was required. indeed, the royal dahir n° - - dated august , , promulgating the law n° - relating to the protection of persons participating in biomedical research, provides for special provisions for non-interventional or observational researches as stipulated in its articles and . not applicable. the findings and conclusions in this report are those of the authors and do not necessarily represent the official position of the us centers for disease control and prevention. the authors declare that they have no competing interests. key: cord- - b o ccp authors: saakian, david b. title: a simple statistical physics model for the epidemic with incubation period date: - - journal: nan doi: nan sha: doc_id: cord_uid: b o ccp based on the classical sir model, we derive a simple modification for the dynamics of epidemics with a known incubation period of infection. the model is described by a system of integro-differential equations. parameters of our model directly related to epidemiological data. we derive some analytical results, as well as perform numerical simulations. we use the proposed model to analyze covid- epidemic data in armenia. we propose a strategy: organize a quarantine, and then conduct extensive testing of risk groups during the quarantine, evaluating the percentage of the population among risk groups and people with symptoms. mathematical modeling for epidemiology has a rather long history, dating back to the studies by d. bernoulli [ ] . later, kermack and mckendrick [ ] proposed their prominent theory for infectious disease dynamics, which influenced the following sir and related models. by the end of the last century, significant progress in the field was made (a systematic literature review for this period is presented in anderson and may's book [ ] ). the covid- pandemic has drawn the attention of researchers from all over the world and different areas to epidemic modeling. one of the simplest sir models for the virus spread in northern italy was introduced in [ ] . another research group used the logistic equation to analyze empirical data on the epidemic in different states [ ] . here, we mainly focus on mean-field models that discard the spatial dependence of the epidemic process. therefore, we avoid network models of epidemics. moreover, it is crucial to consider the final incubation period of the disease to construct a correct model for the covid- case. taking into account this distinctive feature, we consider the dynamics of the aged-structured population, which a well-known problem in evolutionary research [ ] - [ ] . generally, epidemic models have a higher order of non-linearity than evolutionary models, although there are some similarities between these two classes. in this study, we derive a system of integro-differential equations based on the rigorous master equation that adequately describes infection dynamics with an incubation period, e.g., covid- . first, we discuss the sir model. then, we move on to its modification and apply it to the data on the covid- epidemic in armenia. consider the sir model where the parameter s stands for the number of susceptible people, i for the number of infected people, and r for the number of people who have recovered and developed immunity to the infection. we assume that s, i, r satisfy the constraint s + i + r = n . where /b is the period when the infected people are contagious. the parameter a can be obtained from the empirical data on infection rate: thus, we assume that a healthy person is infected with a probability proportional to the fraction of infection in the population. probability is also proportional to the population density. one of the most widely discussed and crucial parameters in epidemiological data is the basic reproduction number of the infection: for the covid- , it has been estimated as [ ] : in fact, the real data allows us to measure three main parameters: the exponential growth coefficient at the beginning of the epidemic; the minimum period of time, in which an infected person can transmit the infection; and the maximum period, when an infected person ceases to transmit the infection. the most important objectives of the investigation are the maximal possible proportion of the infected population, and then the period before the peak of the epidemic. consider the spread of infectious diseases with a recovery period up to t days. at the t-th moment of time, we have s(t) for the size of the susceptible population, r(t) for the recovered population. we divide the infected population according to the age of infection, looking at time intervals δ and defining i l (t) as the number of infected people with the age of infection in (lδ, (l+ )δ). we assume that the incubation period for a random infected person is l and the infection spreads from l to t days. below, we take δ → for the continuous mode of time limit. assuming that the spread of infection has a rate a, we obtain the following system of equations: where the coefficient a is expressed via the infection rate we suggested that after t days a person recovers and the patients are not isolated from the rest of the population between days l and t . eq. ( ) describes the dynamics of the population over discrete time, which is the right choice for numerical simulation. consider now the continuous-time version of the model. in the limit of small δ, we introduce the continuous function i l (t) = i(x, t), where δi(x, t) is the size of the infected population with age x, x + δ. the continuous time versions for the first three equations are: the solution of the second equation in eq. ( ) is where we denote j(x) = i( , t) let us look at the difference using the latter expressions, we get the following full system of equations: at the start, when substituting an ansatz j(t) = e kt , we get: at k → , we get: for increasing α, we get an increasing value of k as well. in the sir model the epidemic threshold is at r = or a = b, so our model is similar to sir with b = /(t − l). in fig . , we analyze the epidemiological data for covid- in armenia using our model. we examine the dynamics of infected population in armenia from march , when the quarantine in the country has been introduced by the government, until april . let us consider the case, when the infectivity (the ability to transfer the infection to susceptible individuals) of infected individuals depends on the age of infection (via a kernel f (x)), also the population with the age x is diluted with the rate g(x). the latter seems to be a reasonable assumption, since an infected individual with a large age reveals some symptoms of infection, therefore, has chances to be isolated. now eq. ( ) is modified: the continuous time limit gives the following system of equations: consider now the asymptotic solution: then, we get the following equations: and thus, we derive for the epidemics threshold: a. the specific functions g(x) let us analyze our eq. ( ). if we are trying to reduce the growth rate k, it can be done in two ways: . reducing the number of contacts, a, let us introduce non-zero reduction, just after days, g(x) = g. hence, we get the following result: we should estimate the value of g that stops the epidemics. we now apply the generalized version of the model to the epidemics in armenia. we look at two periods of epidemics: the first period from march to april and the later (second period), when quarantine starts to work efficiently. a. the choice g= in the model. let us first take g = for the first period, see table . the parameter a in our model is proportional to the number of human contacts during the day. in the first time period, we have had a = . , k = . . after the quarantine in armenia, k decreased from the value . till the value . , with a = . . the critical value of a to eliminate the epidemics is a = . . we reduced % of human contacts. the reducing further % of remaining contacts, we can eliminate the epidemics. let's evaluate what degree of g we need to eliminate the epidemic at given values ofa, if we attribute the current situation to g = . for the case of quarantine, we take the current value k = . , then we see that g = . eliminates epidemics. the parameter a in our model is proportional to the number of human contacts during the day. in the first period of epidemics, we had a = . , k = . . after quarantine in armenia, k decreased from . to . , with a = . . the critical value of a for the elimination of epidemics is a = . . we have reduced % of human contacts. a further reduction of % of the remaining contacts, we can eliminate the epidemic. for the case without quarantine, k = . , we need g = . to eliminate the epidemics, much more efforts compared to the previous considered case. . let us take g = . for the first period (we identify the % of infected individuals during a week), see table ii . then, we apply a = . for the first period, a = . during the second period and we need a = . to eliminate the epidemic. due to the quarantine, we reduced % of contacts, we now needs in reducing of % of existing contacts. holding current values of contacts, we need rising the value of g from . to . . we verified that taking g = . before the quarantine does not give adequate results. how can we increase g in practice? testing the % per week in high risk groups of the population, we can eliminate the epidemics. in this paper, we introduced a version of sir model for infection spreading with known incubation period. this model was applied to analyze the covid- epidemic data in armenia. we constructed the simplest version of population dynamics of age-structured population. close work has been done in [ ] , which is related to sir model. in [ ] , a temporal kernel f (t) has been introduced that modulates the infectivity of each infected individual. compared to such model, we introduced the distribution of infected population at given moment of time via an age of infection, instead of looking just long history of focus populations. in other works related to the population dynamics of age-structured population, the differential equations with time delay usually have been considered. instead, we use integro-differential system of equations, which seems to be an adequate approach to the current situation with covid- epidemic. from our perspective, the proposed approach significantly changes the epidemiological picture (compare to classical sir models), since the virus is active for about two weeks. next, we introduced two functions: f (x), which describes the distribution of infectivity by age, and g(x), which describes the content measures. in the normal sir model, we have two parameters for the rate of infection and the removal of infections. in our integrodifferential model, mapping to elementary processes is straightforward: we just need the velocity parameter a and two periods: the incubation period l and recovery period t with symptoms after the carrier is separated from society. we derive an analytical result for exponential growth in the early stages of epidemics, as well as for the epidemic threshold. it will be very interesting to investigate the transitional situation near the threshold. we suggest simply making numbers and choosing a parameter value to match the correct exponential growth. we applied our model to understand the situation with epidemics in armenia. what is advantageous in our model, that we can clearly separate two aspects of the epidemic: contact strength (through coefficient a) and deterrence measures through parameter g. we check that in fact we need to make minimal efforts to stop the epidemics, and testing is much cheaper during quarantine. currently, if we detect only . % of the infected population per day, strictly monitoring the symptoms, we can stop the epidemic. this is much more complicated without quarantine. i thank armen allahverdyan, pavel krapivsky, ruben poghosyan, didier sornette, and tatiana yakushkina for useful discussions. the work is supported by the russian science foundation under grant - - from russian university of transport infectious diseases in humans data analysis for the covid- early dynamics in northern italy evolution in age-structured populations rdoes good mutation help you live longer? different fitnesses for in vivo and in vitro evolutions due to the finite generation-time effect db saakian, as martirosyan generalized logistic growth modeling of the covid- outbreak in provinces in china and in the rest of the world ke wu, didier darcet epidemic processes in complex networks epidemics with containment measures key: cord- - ubyveyt authors: szymkowiak, andrzej; kulawik, piotr; jeganathan, kishokanth; guzik, paulina title: in-store epidemic behavior: scale development and validation date: - - journal: nan doi: nan sha: doc_id: cord_uid: ubyveyt epidemics of infectious diseases have accompanied humans for a long time and, depending on the scale, cause various undesirable social and economic consequences. during the ongoing covid- pandemic, governments of many countries impose restrictions to inhibit spreading of infection. isolation and limiting interpersonal contacts are particularly recommended actions. adhering to the rule of isolation may involve restrictions in freedom during daily activities, such as shopping. the aim of the study was to develop a scale of in-store pandemic behavior. the whole process involved stages: qualitative inquiry, scale purification and scale validation, which were based on studies: qualitative ( in-depth interviews) two quantitative ( and respondents, respectively), and allowed to identify factors. following, a theoretical model was created to investigate the impact of in-store infection threat on identified variables. all identified factors significantly correlated with the in-store infection threat which reiterates the importance of providing information revealing the true scale of the pandemic and not leaving space for individuals to create subjective probability judgments. the developed scale can help counteract disinformation and assess consumer behavior compliance and understanding of the official recommendations imposed by governments, enabling more efficient educational efforts. viral infections and epidemics have plagued humanity for generations, with many researchers indicating their occurrence as inevitable (funk, salathé, & jansen, ; kuiken, fouchier, rimmelzwaan, & osterhaus, ) . since , approximately emerging infectious diseases have been identified, with most of them being zoonotic (morse et al., ) . these, in turn, cause many undesirable effects such as an increased mortality rate and economic impact on society (heymann, ; salathé et al., ) . the majority of zoonotic diseases require direct contact with an infected animal as was the case with malaria, yellow fever or zika, which are transmitted through mosquito bites (abeku et al., ; ahmed ali, nyla, mashael, salvatore, & mohammed, ; briand et al., ; carey, wang, su, zwiebel, & carlson, ; ferguson et al., ; lucey & gostin, ; wanjala, waitumbi, zhou, & githeko, ; wasserman, tambyah, & lim, ) , or avian flu (h n ), in which the main vectors are poultry and wild birds (lewis, ; peiris, de jong, & guan, ; woo, lau, & yuen, ) . in the absence of a vaccine, the best means of prevention against such diseases is avoidance and protection against potentially infected individuals (craft, ; yousaf et al., ) .another possible transmission route is through the consumption of infected feces, mainly through oral means. examples of such transmitted diseases include rotavirus, norovirus or hepatitis a. the key to protecting oneself, apart from being vaccinated, is to maintain proper hygienic practices, especially related to hand and food hygiene (de graaf, van beek, & koopmans, ; dennehy, ; fitzsimons, hendrickx, vorsters, & van damme, ) . droplet transmitted viral infections exhibit the highest potential for rapid pandemic spread in large clusters of people (heeney, ; salathé et al., ) . this is rather worrying as the percentage of the world population living in cities is estimated to have increased from % in to % in due to population growth, migration and opportune climate conditions. the spread of a possible pandemic in such urban areas may be hastened by the deterioration of sanitation often encountered in the case of overpopulation (bell et al., ). pandemic cases of diseases which have spread through droplets in recent years include: severe acute respiratory syndrome (sars) in - (tan, li, wang, chen, & wu, , influenza h n in - (kanadiya & sallar, ), ebola (aylward et al., dudas et al., ) and the ongoing covid- pandemic (ge, yang, xia, fu, & zhang, ; j. wang & du, ) . for droplet transmitted infections, the steps that can be applied to reduce spreading of the epidemic include testing and detection, patient isolation, contact tracing and encouraging society to take specific actions including altering behavior regarding hygiene (fung & cairncross, ; tan et al., ) . such behavior are of paramount importance when dealing with pandemics as they can often be transmitted before any symptoms occur (wilder-smith & freedman, ). however, to achieve self-isolation or government mandated quarantine to prevent the spread, one has to be in possession of a sufficient supply of food. despite hampered logistics and problems related to supply chain and storage, grocery stores have to be open because they represent public access to the purchase of food products that are necessary to survive. nonetheless, one must also bear in mind that grocery stores are a place for possible transmission of many bacterial and viral pathogens (bell et al., ; dalton, new, & health, ; sinclair, fahnestock, feliz, patel, & perry, ) , causing consumers to undertake various behavioral changes in their approach to shopping. the latest pandemic case is the emergence of severe acute respiratory syndrome coronavirus (covid- ). the scale of infection of the new virus is very serious in the public health sector and has a basic reproduction number of . - . , whereas the sars virus from was at the level of . - . (lai, shih, ko, tang, & hsueh, ; massad, burattini, lopez, & coutinho, ; mccloskey et al., ) . as of april th , who confirmed , , cases of covid- with a total death toll of , victims (who, a). in the authors' analysis of literature on the behavioral changes caused by pandemics on individuals who frequent stationary stores for their shopping, one overarching phenomenon stands out: a distinct lack of research on this topic, despite there being extensive research on the economic havoc that can be caused by such mass behavioral changes. such a dearth of research on the behavioral changes undertaken by consumers in response to the perceived threat of contagion during epidemics and pandemics is worrying, as it displays a lack of preparedness for the crisis that is to follow. this further indicates a more sophisticated need to measure what areas of consumer behaviors at stores are affected by the epidemic and therefore, the aim of the present study was an attempt to create such a measure. the cdc ( ), along with many governments around the world, are encouraging citizens to practice social distancing and undergo quarantine as greatly as it possible in order to limit the spread and exposure of covid- . such advisories and regulations disrupt normal routines, create anxiety and cause what (forster & tang, ) call a crisis of fear. the results of a survey examining the level of anxiety among students during a swine flu pandemic showed that . % of respondents felt some kind of anxiety, with . % feeling severely worried (alnajjar, attar, farahat, & althaqafi, ; funk et al., ; jones & salathé, ) . sometimes, the chaos and pressure of information concerning the high mortality risk of pandemic causes misunderstandings and improper behavior, such as refusing vaccination or avoiding public health facilities. the results of a survey submitted by jones and salathé ( ) showed that the level of anxiety and preventive actions decreased with the perception of the seriousness of the outbreak and the high level of belief in avoiding infection. however, in most cases, it was been possible to introduce changes and increase public awareness related to personal and environmental hygiene as well as frequent disinfection (balkhy, abolfotouh, al-hathlool, & al-jumah, ; jones & salathé, ; little et al., ; zhang, gu, & kavanaugh, ) . the higher level of anxiety, the greater was the implementation of preventive actions. the results of many studies indicated that more than half of the pandemic population was more likely to wash and disinfect their hands as an effective infection control intervention. wearing face masks has also became common. in addition, house spaces are more frequently ventilated (balkhy et al., ; fleischman et al., ; kanadiya & sallar, ; kantele et al., ; steelfisher et al., ; tan et al., ) . depending on nationality, respondents started to more often cough or sneeze into their elbow or shoulder ( - %) and covered their mouth and nose with a tissue when coughing or sneezing ( - %) (steelfisher et al., ) . during the covid- epidemic in china, due to the high risk of infection, . % of respondents spent - hours a day at home, and . % of subjects rated the psychological impact of the outbreak as moderate or severe (c. . a survey was conducted in several countries in response to the h n pandemic. results showed that respondents most often avoided places where larger group of people could gather, such as shopping centers or sports events (steelfisher et al., ) . according to other studies performed during epidemic, . % of respondents limited all outdoor activities (tan et al., ) , and . % believed avoiding crowded places is an effective preventive action (kanadiya & sallar, ) . the perceived fear during the pandemic, however, may be separate from the real threat posed by the disease in question, creating disproportionate behavioral changes among individuals. for example, during sars epidemic in hong kong, % of respondents considered themselves "very likely" or "somewhat likely" to become infected with sars at the peak of the epidemic, when the post-infection rate was only . % (leung et al., ) . such exaggerated perceptions were also recorded in taipei where % of surveyed respondents rated themselves as " " or " " on a -point scale to measure the chances of contracting sars, leading to their death, when the actual mortality rate was % (liu, hammitt, wang, & tsou, ) . such individual subjective probability judgments about the risk of contraction cause mass avoidance of other individuals (brahmbhatt & dutta, ) , initiating major economic disruptions (noy & shields, ) . a sector in which consumers maintained relatively persistent expenditures during times of an epidemic such as mers in korea, concerned groceries. such an aspect cannot be postponed unlike discretionary spending (jung, park, hong, & hyun, ) . however, the epidemic causes shopping behaviors of consumers to change. according to (forster & tang, ) , the peak of sars in hong kong drew an increasing number of consumers to online shopping for their staples such as canned goods and rice. similar findings have been obtained by jung et al. ( ) who discovered that the spread of mers in korea made consumers shift their spending to online portals and away from physical retail stores due to the risk of contagion. in a recent study focused on us household spending patterns amidst the covid- pandemic, it was discovered that consumer spending dramatically increased in order to stockpile goods in anticipation of an inability to shop at retailers (baker, farrokhnia, meyer, pagel, & yannelis, ) . another interesting observation from south korea, provided by nielson ( a) , was that the spread of covid- is prompting consumers to reduce their visits to large supermarkets, and shift their shopping tendencies more towards neighborhood stores where they have little interaction with other consumers whilst only travelling short distances. the same author reports that a korean family affair such as shopping has now become the responsibility of an adult member of the family in order to minimize the exposure of the remaining family members to potential threats. a survey conducted in germany showed that . % of respondents did not do shopping daily with at least % of the german population having stockpiled food to last for to days (gerhold, ). based on the analysis of this limited quantity of research related to consumer behavioral changes in response to epidemics, it is clear that there is a gap in research on how the fear of contagion and not budgetary limitations can impact consumer willingness to shop at stationery stores. a number of activities were performed to develop a tool for measuring the dimensions of covid- impact on the in-store behavior of consumers. this study was conducted in accordance with the guidelines for building scales (churchill, ; peter, ) and takes into account the proposal of rossiter ( ) and its limitations (bergkvist & zhou, ; lee & cadogan, ; salzberger, sarstedt, & diamantopoulos, ) . the whole process involved stages: qualitative inquiry, scale purification and scale validation, which were based on studies: qualitative and quantitative. qualitative data was used to prepare the first list of statements. on the basis of data from the first qualitative study, exploratory and then confirmatory factor analysis was conducted. the final part of the research included carrying out the study on a larger sample and on this basis, re-conducting confirmatory analysis. in quantitative research, the r programming environment and the gpa rotation, psych, lavaan packages were used as well as r-based programs: jamovi and jasp. qualitative methodology was applied due to the exploratory nature of this research. the research team was particularly interested in developing a deeper understanding of how consumers behave at stores and choose the place of food purchase. individual interviews were conducted in the study. the trial was semi-structured and included nearly questions in total, except for the initial and demographic questions, which were intended to create an open atmosphere between the researcher and the participant. these questions were grouped into areas: questions about the person doing grocery shopping, about the place of shopping, behavior at the store and questions regarding preferred products. interviews were conducted remotely using the zoom application and the entire conversations were recorded. the study was carried out among respondents and each interview lasted on average of approx. - min. the subjects were diversified according to age, education, sex and place of residence. in the study, many differences were revealed in the approach to shopping during an epidemic emergency. all enquiries indicated that the epidemic has affected the way the respondents' shop. for some respondents, the change in behavior was due to the top-down restrictions rather than their own beliefs, while for some, these alterations related to changes in the place, time, frequency of purchase, and behavior in the store itself. importantly, more attention was paid to the person or people shopping. in the case of some participants, not all the areas of possible epidemic impact and sense of threat were affected in the same way. what is more, opposing phrases appeared, e.g. regarding the size of the preferred store or its distance from place of residence. the form of the open interview allowed exploring motives for individual behaviors, which translated into the possibility of generating items. the original statement list, which was prepared for analysis of qualitative data, was linguistically modified. this modification included the elimination of negative forms in sentences, as well as complex and difficult formulations. furthermore, a normative nature of the scale was adopted. the list of items was prepared as statements to which the respondent could refer. in connection with the implementation of the quantitative study among us residents, the original version of the questionnaire was prepared in english and verified by an american-english native speaker. the basis for the first stage of quantitative research was a list of items which were created on the basis of qualitative analysis. data collection was preceded by a pilot study among respondents to verify command clarity and eliminate possible restrictions. as a result, minor corrections were made. the respondents were recruited for the main study using the amazon mturk platform. the study involved people, of whom persons were included in the analysis on the basis of passing control questions that verified attention. the average age was (sd = ), participants were women ( . %), men ( . ), person did not answer the questions. the respondents were diverse due to education, income and professional status (table ) . items except for one statement (shop at the same store more frequently -. ) were above . . the next element of analysis was to determine the number of factors. parallel analysis was carried out, based on which factors were established. then, exploratory factor analyzes with oblique rotation were proposed because of the presumed correlations among the construct's dimensions. items that had a saturation below . , and when they considered communities below . , were eliminated from further research. in addition, items with a load of several factors were also excluded (hair, black, babin, anderson, & tatham, ). some of the items were characterized by high residual covariances, which was due to their synonymous nature, also being the basis for elimination. as a result of purification, a more complex pattern of consumer purchasing behaviors at the store emerged than that assumed at the stage of qualitative research. in addition, the procedure resulted in the elimination of some of the variables identified during in-depth interviews. an example of such an area is the use of personal protective equipment such as masks or gloves. this may be due to the determinants of certain behaviors through pre-defined rules that form the foundation of store security. moreover, the introduction of restrictions on the number of customers or rules prevailing in the store eliminate the importance of store size. as a result, factors were identified relating to the shopping process, including the choice of place and time as well as to the selection and preferences of products. the total number of factors was identified. contact limitation (cl) factor include behaviors that are supposed to reduce the risk of coming across other people while shopping for food products. it should also be noted that the cdc (burke, ) estimates the contamination risk from an infected individual to be approx. . % for close contact with someone infected and . % for household members. in light of this, the cl factor also includes limiting the indicator regarding the number of household members who do shopping. this indicator of shopping alone is also important, since family co-shopping is a strong socializing agent (keller & ruus, ) and changes in attitude related to co-shopping may affect inter-family relations. food supply security (fss) is the second identified factor. it involves behaviors related to purchase of non-easily perishable food products and their stockpiling. this considers indicators which include purchase of frozen, preserved or, in general, food products with long expiration dates. this may be caused by main reasons: in the case that something happens to the global food chain, and to reduce the number of times an individual has to leave home for shopping and thus, risk getting infected. it should be noted that up until now, there has been no evidence that the covid- outbreak has affected the global food safety and security at any rate (fereidoon, ) . factor identified as food product familiarity (pf) involves the purchase of recognized/trusted products and brands. this includes the purchase of products which are familiar to the consumer but also the purchase of trusted food brands. this might be due to desire to shorten shopping time to a minimum or due to the attitude that the time of epidemic is no time for experimenting with unfamiliar food products. shopping time optimization (sto) is a factor involving the reduction of time spent in a shop and is related to limiting the time an individual is exposed to contamination by strangers. this regards not only shopping quickly but also the reluctance to have any direct conversation with other individuals present in shop as indicated by the "move smoothly without stopping other" indicator. this is an important factor since shopping is often used as means to socialize and meet new people (dawson, bloch, & ridgway, ). the keeping distance (kd) factor is indicated by attitudes related to maintaining a space between individuals within the shop, to ensure that even if there is an infected person present at the moment of shopping, distance will reduce the risk of contamination. this involves not only keeping one's distance in the line, but also directly in the shop when someone else is choosing products from the shelves. this factor is similar to the contact limit aspect, with the difference that it includes indicators of in-shop behaviors, while the contact limitation factor is more related to general avoidance of other individuals. information about maintaining physical distance, usually of at least one meter between individuals, is widely spread by the media and governmental organizations (who, b). the next identified factor is product packaging (pp), which is related to attitudes towards packed and unpacked foods. these indicators are related to the most common food products that are often purchased unpacked, such as vegetables, bread and various ready-to-eat products, including unpacked nuts, confectionery, dried fruits, etc. the change in attitudes towards this factor during an epidemic may be relevant due to recent ambivalence in relation to food packages. on the one hand, there was a growing trend of so called zero-packaging, which shopping. this factor includes indicators related to how many shops a person chooses during shopping, but also if s/he avoids shopping at unfamiliar stores. this is related to time optimization since going to unfamiliar shops usually increases the time spent on shopping. the consumer then requires more time to find desired products. the last identified factor is related to personal security (ps) during shopping and includes the implementation of protective gear such as gloves or masks and the use of disinfectants. one indicator of this factor is the use of disinfectants to sanitize handles after touching, for instance, freezer doors. this factor also regards the use of contactless payment methods as a protective measure, which is related to the warnings that physical money may be a source of virus transmission (who, c) next, confirmatory factor analysis was performed. the indices show an acceptable fit to the data (rmsea = . , tli = . , cfi . , smrm = . , rni = . ) (hu & bentler, the authors re-examined the -dimensional scale of in-store consumer behaviors during a pandemic. recruitment, as before, was carried out using amazon mturk among americans who did not answer the previous questionnaire. the questionnaire containeds questions verifying attention, the answers involved included duplicated reversed questions. the study included responses from all answers. the questionnaire included women ( . %) and men ( . %), and the average age of the respondents was almost years (sd = . ). this question was not answered by respondents. as in the first study, consumers were diversified based on education, income and employment status ( table ). the study included questions from the original . a pandemic can cause individuals to undertake behavioral changes that are far from those truly required in accordance with pandemic severity. such exaggerated perceptions of ones chances of being infected with virus was recorded in taipei, where % of survey respondents rated their likelihood of contracting sars, leading to their death, as very probable (liu et al., ) . the same was discovered in research from hong kong during the sars epidemic, as % of respondents considered themselves "very likely" or "somewhat likely" to become infected when the post-infection rate was only . % (leung et al., ) . such individual subjective probability judgments about the risk of contraction cause mass avoidance from other individuals (brahmbhatt & dutta, ) , as was observed in south korea during the spread of the covid- , where shopping has now become the responsibility of a single adult in the family (nielson, a) . such shopping, as per the same report, was also centered in neighborhood stores where the chance of interaction with other consumers is small, which is why we posit that: -h . perceived in-store infection threat has positive impact on contact limitation. another change in behavior induced by an epidemic is re-assessment of the preferences and the importance of food attributes. such changes was clearly observed during the sars crisis in hong kong as there was a spike in the demand for rice, cooking oil, canned and consumable goods, frozen foods, cleaning products and toiletries (forster & tang, ) . this beans, canned meat, chickpeas, rice, tuna, black beans, biscuit mix, water and pasta was also evident during the current covid- epidemic in the us (nielson, b) . the same situation could be observed in canada where the majority of items in consumer stockpiles consisted of canned, frozen, and fresh foods, along with toilet paper and hand sanitizers (deloitte, ) . with this past evidence the authors suggest the following hypotheses: -h . perceived in-store infection threat has positive impact on food supply securing behaviors. -h . perceived in-store infection threat has positive impact on the tendency to consume familiar products. in a study by balkhy et al. ( ) concerning statements and self-reported precautionary measures against h n influenza in saudi arabia, it was discovered that . % of respondents preferred to stay at home during its duration. this aversion to conducting shopping in stores can find its justification in the research by sadique et al. ( ) , who discovered that venturing out to shops was considered the third riskiest setting in which one could acquire pandemic influenza, after places of entertainment and shops. in the same study, it was also concluded that % of respondents were partial towards doing only shopping that was considered essential. in the research conducted by nielson ( a) on south korean consumers, analogous observations were noted, as the author were found that consumers reduced their visits to large supermarkets, and shifted more towards neighborhood stores where there is little interaction with other consumers. this interaction aversion behavior and dislike of instances where one can be exposed to the virus allow the authors to erect the following hypotheses: -h . perceived in-store infection threat has positive impact on how consumers optimize their shopping time. -h . perceived in-store infection threat has positive impact on in-store social distancing. -h . perceived in-store infection threat has positive impact on the consumption of products without packaging. -h . perceived in-store infection threat has positive impact on the number of stores frequented by the consumer. -h . perceived in-store infection threat has positive impact on in-store behavioral changes taken to ensure one's personal safety. in order to test the above hypotheses, in-store infection threat was measured using items on a -point scale (there is a fear of becoming infected with the covid- virus while shopping (sit ), one can become infected with covid- at the grocery store (sit ), shopping during the covid- epidemic is a risk to health (sit ), there is a risk of infection with the covid- virus while at the store (sit ), when shopping, one is at risk of becoming infected with covid- (sit )) among respondents participating in the second quantitative survey. load values exceeded . (table ) and reached recommended values for the factor. a structural model was created to measure the impact of in-store infection threat on all identified dimensions of behavior in a store during an epidemic. the analyzes relied on a bootstrap procedure to ensure stability of the results across the whole sample. the model fit is very satisfactory (χ / ddl = . ; tli = . ; cfi = . ; gfi = . , rmsea = . , srmr = . ). the results of the analysis indicate that sit positively affects all identified variables within the range from . for the pf factor to . for cl and the same for the sto factor (table ). this is the first study ever to design a scale of in-store behavior during an epidemic, which resulted in obtaining a validated scale with high confidence degree. the process of developing the scale included qualitative and quantitative methods. the resulting scale contains items, with dimensions of in-store behaviors. all identified factors correlate with the in-store infection threat which reiterates the importance of providing information that reveals the true scale of the pandemic and not leaving space for individuals to create subjective probability judgments. this is all the more important in order to support the april call from the who ( b) to fight the so called "infodemic" that is flooding the average consumer. since a great deal of this information is false or unreliable, it causes a serious problem for the consumers to recognize "true" recommendations. the fight against an infodemic such as the one experienced at present with covid- and any future pandemics cannot be won without assessing consumers' attitudes and behaviors during an epidemic. the scale that has been developed in this study can be useful for assessing consumer compliance with official recommendations and may be a valuable tool in targeting gaps in consumer education and knowledge. the authors expect that the provision of information revealing the true severity of the pandemic to the general public will also reduce panic-buying associated with the onsets of pandemics, reducing the strain on supply chains. doing so will allow citizens to go about their shopping in a rational manner, without the worry of any impending inability to do their shopping to feed their families. this research also has important implications for stationary store outlets as they could initiate changes in store layout to accommodate any pandemic induced precautionary behaviors from their consumers. other changes that stationary shops could undertake to accommodate pandemic-induced consumer behavioral changes include the provision of disinfections, disposable gloves, covering fresh produce such as bread, fruits and vegetables with protective covering, encouraging customers to make payments by cards, limiting the number of patrons in the store, marking distances at which consumers waiting in line should adhere to and increasing the stock of staple goods with long shelf-life. the authors hope that the implications of this research provide governments and policymakers with an understanding of how the timely provision of correct information using the right mediums can prevent consumers from making their own probability judgements about the threat of infection, which, in turn, leads to a climate of distrust, panic-purchasing and mass avoidance of stationary stores. this is all the more important as urbanization is at an all-time high with a majority of consumers depending on supermarkets for their shopping needs. this research, as previously mentioned, may also prove to be useful for manufacturers and stationery stores to adjust their supply of products to the demand shocks that are to be expected with the onset of a crisis such as the covid- pandemic. although the study was designed in a way to be as precise as possible, some limitations exist. the main limitation is that the study was performed on only consumers from the usa and although the study included large number of participants with different metrics, it may still be difficult to apply this scale to consumers from countries with a different cultural background. therefore, in future research, the questionnaire should be translated into different languages and performed among consumers from other countries affected by the epidemic. moreover, the questionnaire was performed during the outbreak of the covid- pandemic which limits the possibility of comparing the results for in-shop behaviors with a time from before the epidemic. moreover, some responses may have been affected by government-imposed restrictions. the data and findings obtained in this study raise several interesting avenues for future research. the first is honing in on the demographics of the research sample in order to identify whether factors such as education, income and employment status reveal discrepancies in the degree to which the threat of the virus is considered. further research into this could then disclose their correlations with the factors proposed in this article. another area of research that could prove to be interesting, in order to discover the information medium upon which consumers' subjective opinions about the probability of contracting the virus are founded, is the amalgamation of data on where consumers receive their information on pandemics and its spread with a model such as the one presented by the authors of this study. there is also the possibility of extending this model to find out whether variables such as preexisting health conditions, the number of family members and the possibility of remote work has impact on how the threat of the virus is perceived and how behavioral changes influence in-store shopping. malaria epidemic early warning and detection in african highlands business continuity management and pandemic influenza shopping motives, emotional states, and human norovirus transmission and evolution in a changing world covid- : voice of canadians and impact to 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( b). coronavirus disease (covid- ): situation report retrieved from isolation, quarantine, social distancing and community containment: pivotal role for old-style public health measures in the novel coronavirus ( -ncov) outbreak infectious diseases emerging from chinese wet-markets: zoonotic origins of severe respiratory viral infections rabies molecular virology, diagnosis, prevention and treatment the impacts of sars on the consumer behaviour of chinese domestic tourists key: cord- -xit najq authors: van damme, wim; dahake, ritwik; delamou, alexandre; ingelbeen, brecht; wouters, edwin; vanham, guido; van de pas, remco; dossou, jean-paul; ir, por; abimbola, seye; van der borght, stefaan; narayanan, devadasan; bloom, gerald; van engelgem, ian; ag ahmed, mohamed ali; kiendrébéogo, joël arthur; verdonck, kristien; de brouwere, vincent; bello, kéfilath; kloos, helmut; aaby, peter; kalk, andreas; al-awlaqi, sameh; prashanth, ns; muyembe-tamfum, jean-jacques; mbala, placide; ahuka-mundeke, steve; assefa, yibeltal title: the covid- pandemic: diverse contexts; different epidemics—how and why? date: - - journal: bmj glob health doi: . /bmjgh- - sha: doc_id: cord_uid: xit najq it is very exceptional that a new disease becomes a true pandemic. since its emergence in wuhan, china, in late , severe acute respiratory syndrome coronavirus (sars-cov- ), the virus that causes covid- , has spread to nearly all countries of the world in only a few months. however, in different countries, the covid- epidemic takes variable shapes and forms in how it affects communities. until now, the insights gained on covid- have been largely dominated by the covid- epidemics and the lockdowns in china, europe and the usa. but this variety of global trajectories is little described, analysed or understood. in only a few months, an enormous amount of scientific evidence on sars-cov- and covid- has been uncovered (knowns). but important knowledge gaps remain (unknowns). learning from the variety of ways the covid- epidemic is unfolding across the globe can potentially contribute to solving the covid- puzzle. this paper tries to make sense of this variability—by exploring the important role that context plays in these different covid- epidemics; by comparing covid- epidemics with other respiratory diseases, including other coronaviruses that circulate continuously; and by highlighting the critical unknowns and uncertainties that remain. these unknowns and uncertainties require a deeper understanding of the variable trajectories of covid- . unravelling them will be important for discerning potential future scenarios, such as the first wave in virgin territories still untouched by covid- and for future waves elsewhere. late in , a cluster of acute respiratory disease in wuhan, china, was attributed to a new coronavirus, - later named severe acute respiratory syndrome coronavirus (sars-cov- ). it was soon discovered that the virus is easily transmitted, can cause summary box ► severe acute respiratory syndrome coronavirus (sars-cov- ), the virus that causes covid- , has spread to nearly all countries of the world in only a few months. it is unique that an emerging respiratory virus becomes a pandemic, and can continue human-to-human transmission unabated, probably permanently. ► depending on the context, the trajectory and the impact of the covid- epidemic vary widely across affected countries. this is in fact the case with most infectious diseases. ► despite limited initial knowledge on covid- , most societies have deployed draconian measures, including lockdowns, to contain the virus and mitigate its impact. this had variable success, but invariably with profound socioeconomic collateral effects. ► through research and rapid sharing of its findings, progressively more insights on sars-cov- and covid- have been uncovered (knowns), mainly based on evidence from china, europe and the usa; however, important knowledge gaps remain (unknowns). ► the different covid- epidemics and the responses unfolding in the global south are little described, analysed or understood. insights from these less researched contexts are important for discerning potential future scenarios, not only for the first wave in virgin territories still untouched by covid- , but also for future waves. ► more understanding of lived experiences of people in a variety of contexts is necessary to get a full global picture and allow learning from this variety. ► bmj global health and emerging voices for global health have launched a call for such on-the-ground narratives and analyses on the epidemics of, and responses to, covid- . severe disease and can be quite lethal especially in the elderly and those with comorbidities. [ ] [ ] [ ] [ ] the new human disease is called covid- . soon it became clear that its global spread was unstoppable. even with draconian containment measures, such as strict movement restrictions, the so-called lockdown, it spread, and within a few months reached almost all countries and was declared a pandemic by the who. table summarises key events in the unfolding of the covid- pandemic, from december to may . this progression is quite unique. new human pathogens emerge frequently from an animal host, but most cause only a local outbreak. human-to-human transmission stops at some point, and the virus can only re-emerge as a human pathogen from its animal host. only very rarely does an emerging pathogen become a pandemic. over the past decades, a totally new pathogen emerged, caused serious disease, and spread around the globe continuously only once before: the hiv. it seems increasingly likely that sars-cov- transmission will be continuing. all countries are now facing their own 'covid- epidemic'. in only a few months, the scientific community has started to learn the virus's characteristics and its manifestations in different contexts. but we fail to understand fully why the virus spreads at different speeds and affects populations differently. our main objective is to make sense of those different expressions of the covid- pandemic, to understand why covid- follows variable trajectories in ways that are often quite different from the collective image created by the mediatisation of the dramatic covid- epidemics in densely populated areas. we start by exploring the role of context, followed by a brief summary of what is already known at the time of writing about sars-cov- and covid- . we then bmj global health compare these knowns with what is known of some other viral respiratory pathogens and identify the critical unknowns. we also discuss the coping strategies and collective strategies implemented to contain and mitigate the effect of the epidemic. we finally look ahead to potential future scenarios. the unfolding covid- pandemic: importance of context initially, human-to-human transmission was documented in family/friends clusters. [ ] [ ] [ ] [ ] [ ] [ ] progressively, it became clear that superspreading events, typically during social gatherings such as parties, religious services, weddings, sports events and carnival celebrations, have played an important role. [ ] [ ] [ ] [ ] dense transmission has also been documented in hospitals and nursing homes possibly through aerosols. sars-cov- has spread around the world through international travellers. the timing of the introduction of sars-cov- has largely depended on the intensity of connections with locations with ongoing covid- epidemics; thus, it reached big urban centres first and, within these, often the most affluent groups. from there, the virus has spread at variable speeds to other population groups. as of may , the most explosive covid- epidemics observed have been in densely populated areas in temperate climates in relatively affluent countries. the covid- pandemic and the lockdowns have been covered intensively in the media and have shaped our collective image of the covid- epidemic, both in the general public and in the scientific community. the covid- epidemic has spread more slowly and less intensively in rural areas, in africa and the indian subcontinent, and the rural areas of low and lower-middle income countries (lics/lmics). not only the media but also the scientific community has paid much less attention to these realities, emerging later and spreading more slowly. the dominant thinking has been that it is only a question of time before dramatic epidemics occur everywhere. this thinking, spread globally by international public health networks, has been substantiated by predictive mathematical models based largely on data from the epidemics of the global north. however, what has been observed elsewhere is quite different although not necessarily less consequential. the effects of the covid- epidemic manifest in peculiar ways in each context. in the early stages of the covid- epidemic in sub-saharan africa, the virus first affected the urban elites with international connections. from there, it was seeded to other sections of the society more slowly. in contrast, the collateral effects of a lockdown, even partial in many cases, are mostly felt by the urban poor, as 'stay home' orders abruptly intensify hardship for those earning their daily living in the informal urban economy. governments of lics/lmics lack the budgetary space to grant generous benefit packages to counter the socioeconomic consequences. international agencies are very thinly spread, as the pandemic has been concurrent everywhere. donor countries have focused mainly on their own covid- epidemics. the epidemic is thus playing out differently in different contexts. many factors might explain sars-cov- transmission dynamics. climate, population structure, social practices, pre-existing immunity and many other variables that have been explored are summarised in table . although all these variables probably play some role, many uncertainties remain. it is difficult to assess how much these variables influence transmission in different contexts. it is even more difficult to assess how they interact and change over time and influence transmission among different social groups, resulting in the peculiar covid- epidemic in any particular context. we do not attempt to give a complete overview of viruses but select only those viruses that emerged recently and caused epidemics such as ebola, that have obvious similarities in transmission patterns such as influenza and measles, or that are closely related such as other coronaviruses. respiratory viruses such as severe acute respiratory syndrome coronavirus (sars-cov), middle east respiratory syndrome coronavirus (mers-cov) and avian influenza a and also ebola have originated from animal hosts and caused human diseases (table ) . these viruses do not continuously circulate from human to human. they create an outbreak only when there is interspecies cross-over transmission, most frequently from bats to another animal host. the first human case of a disease from an emerging viral pathogen, the 'index case' or 'patient zero', is invariably someone in close contact with the originating animal host or an intermediary animal host. if this contact occurs in a remote rural community, the spread is usually slow, at low intensity, and could fade out before the pathogen gets a chance to spread to another community. the spread can suddenly intensify if seeded in a densely populated community, frequently in a particular context such as a hospital or during a social event, often referred to as a superspreading event. when the spread reaches a city, it can become a major outbreak, from where it can spread further; this happened with sars-cov in hong kong in and with ebola in conakry, freetown and monrovia in - . but at some stage human-to-human transmission is interrupted and the outbreak stops. only very exceptionally can a new viral pathogen sustain continuous human-to-human transmission. other viral diseases such as measles and influenza are 'old' diseases; they have been studied in great depth. what can we learn from them? measles and influenza: the importance of context it is thought that measles emerged thousands of years ago in the middle east. it is assumed that a cross-over occurred from the rinderpest virus, to become the human measles virus. measles has since spread around the globe in continuous human-to-human transmission. when measles, along with other viruses such as smallpox and influenza, was introduced in the americas by european conquerors, it contributed to a massive die-off of up to % of the original population. the transmission dynamics of sars-cov- can be compared with influenza. influenza typically causes yearly epidemics in temperate climates during winter with less seasonal patterns in tropical or subtropical regions. in hotter climates, such as in sub-saharan africa or south and southeast asia, it is transmitted year round, often not identified as influenza. such different epidemic patterns of influenza are still incompletely understood but thought to be associated with temperature and humidity and human behavioural factors such as indoor crowding. but, in contrast to sars-cov- , the influenza virus is not new. influenza is a very old disease, certainly circulating for several centuries. it has infected most human beings living on the planet already, many of them several times, leaving some immunity but no durable protection. the virus also mutates, giving rise to a new dominant strain every influenza season. influenza is every year a slightly different virus (due to antigenic drift as a result of progressive mutations) with major differences every few decades (antigenic shift as a result of recombination with novel strains). one such antigenic shift resulted in the h n 'spanish' influenza pandemic, which had an estimated case fatality rate (cfr) of %- %, killing millions. box summarises some key facts about h n , including factors thought to be associated with its high cfr. a major difference between covid- and influenza is that sars-cov- is a new pathogen and influenza is not. at the time of writing (may ), sars-cov- has triggered an immune response in over million confirmed infections (and probably in many more), definitely too few to create anything close to herd immunity. calculations using an estimated reproductive number (r ) for sars-cov- suggest that herd immunity would require at least % of the population to have protective immunity (see box ). like covid- , measles and influenza have different epidemic patterns in different contexts. this also is the case for cholera, tuberculosis, hiv/aids and most infectious diseases. the difference in patterns is most pronounced and so is easily understood with vectorborne and water-borne diseases. epidemic patterns are also different for air-borne infections, although they are less easily understood. transmission of respiratory viruses is influenced by factors related to the virus and box pandemic h n influenza, - ► the h n virus probably infected one-third of the world's population at that time (or ~ million people). ► the pandemic had three waves in quick succession; the second wave, in , was worse than the first wave. ► high mortality, especially in younger persons ( - years; ~ % of total deaths) in the pandemic, may have been due to antibody-dependent enhancement and 'cytokine storms'. another possible explanation is that older persons had some protective cross-immunity from previous influenza outbreaks while younger persons did not. ► h n continued to circulate along with seasonal influenza viruses, often recombining to produce more severe local outbreaks, including other pandemics between and , giving it the nickname 'mother of all pandemics'. ► the original h n strain was replaced by a(h n )pdm virus that resulted from an antigenic shift and caused the h n influenza pandemic. ► the h n virus originated in pigs in central mexico in march and was responsible for an estimated deaths worldwide with an estimated cfr< . %. ► during the pandemic, mortality was much lower than in the pandemic. higher mortality in persons younger than years was related to cytokine storms. a role of protective crossimmunity from previous influenza strains in older persons has been suggested. ► after august , the a(h n )pdm virus appeared to have integrated with circulating strains of influenza and continues to cause localised seasonal influenza outbreaks worldwide. box on the use of mathematical models during epidemics a dominant way of studying the transmission dynamics of an infectious disease such as covid- , and predicting the amplitude and peak of the epidemic in a population (city, province, country) and analysing the effect of control measures is using mathematical models. based on available data and several assumptions, a model attempts to predict the course of the epidemic, the expected number of infections, clinical cases and deaths over time. critical is the effective reproductive number (rt). when rt > , the number of cases in a population increases; when rt < , the number of cases decreases. a relatively simple and widely used model is the susceptible-exposed-infectious-recovered model, as used in the two papers recently published in bmj global health on covid- in africa. there are many more types of models, with varying degrees of complexity. the use of such models has strengths and limitations. building a mathematical model implies trade-offs between accuracy, transparency, flexibility and timeliness. a difficulty, in general, is that the parameters on which the model is based, the so-called assumptions are frequently uncertain (table ) and predictions can vary widely if any of the parameters are modestly different. this uncertainty is captured in a sensitivity analysis, leading to various possible quantitative outcomes, usually expressed as a range of plausible possibilities, between 'worst-case' and 'best-case' scenarios. with a new disease such as covid- , certainly at the start of the outbreak, the parameters had to be based on very limited data from a particular context. however, many variables can widely differ across communities as they critically depend on contextual factors (table ) . in mathematical models, all such uncertainties and unknowns are somehow hidden in the complex formulae of the model, as a quasi 'black box'. few people have the knowledge and skill to 'open up the black box'. as uncertainties in covid- are large, the range of possibilities produced by a model is wide, with the worst-case scenario typically predicting catastrophic numbers of cases and deaths. such predictions are often misunderstood by journalists, practitioners and policy-makers, with worst-case estimates getting the most attention, not specifying the huge uncertainties. bmj global health the human host but also by factors related to the natural and human environment (table ) . however, we are quite unable to explain fully which factor has which influence, how these factors vary among different social groups and how interdependent or isolated they are. we are certainly unable to fully model all these variables mathematically to explain the epidemic pattern across a variety of different contexts. too many variables and their interrelations are difficult to quantify, and when all these factors change over time while the pathogen continues to spread in diverse societies, the complexity becomes daunting. understanding transmission dynamics is a bit less daunting for measles, as several variables are well known and rather constant across individuals and contexts. the natural transmission pattern of measles, before the introduction of vaccines, has been well described. measles is mostly a childhood disease, but this is not the case in very remote communities, where measles transmission had been interrupted for extended periods (such as the faroe islands). measles affected all age groups when reaching new territories, causing dramatic first-wave epidemics, a phenomenon called 'virgin soil epidemic'. the latest stages of the global dissemination of measles have been well documented, including in australia, the fiji islands and the arctic countries, where such virgin soil epidemics occurred in the th and the mid- th centuries. fortunately, measles infection creates robust protective immunity and after a first wave becomes a typical childhood disease, affecting only those without any prior immunity. human-to-human transmission of measles virus in a community stops when the virus cannot find new susceptible human hosts and the so-called herd immunity is reached. but transmission of measles continues elsewhere on the planet from where it can be reintroduced a few years later when the population without protective immunity has grown large enough to allow human-to-human transmission again. the epidemic patterns of measles are easily understood as measles is highly infectious, creates disease in almost every infected person and leaves lifelong natural immunity. measles circulation, prior to vaccination, was continuous only in large urban areas with high birth rates. everywhere else reintroduction occurred typically every - ► genetic stability or variability (affecting the potential of long-lasting immunity). ► viral load determines the incubation period with the formula high load ->short incubation period ->high severity. human host ► human susceptibility to the virus; transfer of parental immunity to newborns. ► route and efficiency of human-to-human transmission. ► presence and capacity of asymptomatic carriers to transmit the virus. ► immunity created after infection, its robustness and how long-lasting it is. ► severity and duration of the disease: proportion symptomatic, lethality (cfr). ► pathogenicity and disease spectrum; disease pattern according to age and comorbidities, and related potential to spread. natural environment ► temperature, humidity and seasonal changes in climate affecting the stability and transmission potential of the virus and human susceptibility. ► increasing extreme weather conditions such as droughts and severe storms, as well as global climate change may also affect transmission patterns. ► air pollution may also play a role in the transmission and stability of the virus. human environment/social geography ► demographic variables such as population density, age structure and household composition. ► mixing patterns within households, including bed sleeping patterns, related to housing conditions and hygiene practices. ► house construction with solid walls or permeable walls (thatched walls, straw mats). ► mixing patterns among households related to settlement patterns: social networks, urban-rural differences, working conditions, religious practices and commuting patterns. ► variables related to built environments, road infrastructure and socioeconomic conditions. ► mobility between communities, including international travel. ► crowding institutions: for example, elderly homes, extended families, boarding schools, child institutions, seclusion during tribal ceremonies, hospitals, nursing homes, military barracks and prisons. cfr, case fatality rate. years but sometimes only after or years in isolated rural communities (such as among nomadic groups in the sahel), causing epidemics among all those without acquired immunity and having lost maternal antibodies. these diverse patterns of measles epidemics have been fundamentally changed by variable coverage of measles vaccination. they can still help us make sense of the diversity of covid- epidemics being observed in . measles illustrates convincingly that the transmission pattern of a respiratory virus is strongly influenced by the demographic composition, density and mixing pattern of the population and the connectedness to big urban centres. measles transmission is continuous only in some large urban areas. it presents in short epidemics everywhere else with variable periodicity. this transmission pattern may well be a bit similar for covid- . but it took thousands of years for measles to reach all human communities while sars-cov- spread to all countries in only a few months, despite measles being much more transmissible than sars-cov- . factors such as increased air travel and more dense community structures play bigger roles for sars-cov- than they did for measles. comparison with other pathogenic coronaviruses sars-cov- has many close relatives. six other human coronaviruses (hcovs) are known to infect humans. sars-cov and mers-cov (causing sars and mers, respectively) are very rare and do not continuously circulate among humans. the other four (hcov- e, hcov-oc , hcov-hku and hcov-nl ) cause the common cold or diarrhoea and continuously circulate and mutate frequently. they can cause disease in the same person repeatedly. the typical coronavirus remains localised to the epithelium of the upper respiratory tract, causes mild disease and elicits a poor immune response, hence the high rate of reinfection (in contrast to sars-cov and mers-cov, which go deeper into the lungs and hence are relatively less contagious). there is no cross-immunity between hcov- e and hcov-oc , and new strains arise continually by mutation selection. coping strategies and collective strategies how a virus spreads and its disease progresses depend not only on the variables described above (table ) but also on the human reactions deployed when people are confronted with a disease outbreak or the threat of an outbreak. all these variables combined result in what unfolds as 'the epidemic' and the diverse ways it affects communities. what a population experiences during an epidemic is not fully characterised by the numbers of known infections and deaths at the scale of a country. such numbers hide regional and local differences, especially in large and diverse countries. the epidemic reaches the different geographical areas of a country at different moments and with different intensities. it affects different communities in variable ways, influencing how these communities perceive it and react to it. what constitutes a local covid- epidemic is thus also characterised by the perceptions and the reactions it triggers in the different sections of the society. even before the virus reaches a community, the threat of an epidemic already causes fear, stress and anxiety. consequently, the threat or arrival of the epidemic also triggers responses, early or late, with various degrees of intensity and effectiveness. the response to an epidemic can be divided into individual and household actions (coping strategies), and collectively organised strategies (collective strategies). coping strategies are the actions people and families take when disease threatens and sickness occurs, including the ways they try to protect themselves from contagion. collective strategies are voluntary or mandated measures deployed by organised communities and public authorities in response to an epidemic. these include, among others, isolation of the sick or the healthy, implementation of hygiene practices and physical distancing measures. they can also include mobility restrictions such as quarantine and cordon sanitaire. coping strategies and collective strategies also include treatment of the sick, which critically depends on the availability and effectiveness of diagnostic and therapeutic tools, and performance of the health system. collective strategies also include research being deployed to further scientific insight and the development of diagnostic and therapeutic tools, potentially including a vaccine. implementation of these measures depends not only on resources available but also on the understanding and interpretation of the disease by both the scientific community and the community at large, influenced by the information people receive from scientists, public authorities and the media. this information is interpreted within belief systems and influenced by rumours, increasingly so over social media, including waves of fake news, recently labelled 'infodemics'. coping strategies and collective strategies start immediately, while there are still many unknowns and uncertainties. progressively, as the pandemic unfolds and scientists interpret observations in the laboratory, in the clinic, and in society, more insights are gained and inform the response. table lists measures recommended by the who for preventing transmission and slowing down the covid- epidemic. - 'lockdown' first employed in early in wuhan, china, is the label often given to the bundle of containment and mitigation measures promoted or imposed by public authorities, although the specific measures may vary greatly between countries. in china, lockdown was very strictly applied and enforced. it clearly had an impact, resulting in total interruption of transmission locally. this list or catalogue of measures is quite comprehensive; it includes all measures that at first sight seem to reduce transmission opportunities for a respiratory virus. however, knowledge is lacking about the effectiveness of each measure in different contexts. as a global health bmj global health agency, the who recommends a 'generic catalogue' of measures from which all countries can select an appropriate mix at any one time depending on the phase of the epidemic, categorised in four transmission scenarios (no cases, first cases, first clusters, and community transmission). however, under pressure to act and with little time to consider variable options, public authorities often adopted as 'blueprint' with limited consideration for the socioeconomic context. the initial lockdown in china thus much inspired the collective strategies elsewhere. this has been referred to as 'global mimicry', : the response is somehow partly 'copy/paste' from measures observed previously (strong path dependency). some epidemiologists in northern europe (including the uk, sweden and the netherlands ) pleaded against strict containment measures and proposed that building up herd immunity against sars-cov- might be wiser. towards early april , it became increasingly clear that reaching herd immunity in the short term was illusive. most countries thus backed off from the herd immunity approach to combating covid- and implemented lockdowns. the intensity of the lockdowns has been variable, ranging from very strict ('chinese, wuhan style'), over intermediary ('french/italian/new york city style' and 'hong kong style'), to relaxed ('swedish style'), or piecemeal. the effectiveness of lockdowns largely depends on at what stage of the epidemic they are started, and how intensively they are applied. this is quite variable across countries, depending on the understanding and motivation of the population and their perceived risk ('willingness to adhere'), on the trust they have in government advice ('willingness to comply'), and on the degree of enforcement by public authorities. the feasibility for different population groups to follow these measures depends largely on their socioeconomic and living conditions. it is obviously more difficult for people living in crowded shacks in urban slums to practise physical distancing measures and strict hand hygiene when water is scarce than for people living in wealthier parts of a city. collateral effects of the response every intervention against the covid- epidemic has a certain degree of effect and comes at a cost with collateral effects. each collective strategy ( ) has intended and unintended consequences (some are more or less desirable); ( ) is more or less feasible and/or acceptable in a given context and for certain subgroups in that society; ( ) has a cost, not only in financial terms but in many other ways, such as restrictions on movement and behaviour, stress, uncertainty and others. these costs are more or less acceptable, depending on the perception of the risk and many societal factors; ( ) can be implemented with more or less intensity; and ( ) can be enforced more or less vigorously. the balance between benefit and cost is crucial in judging whether measures are appropriate, which is very context specific. furthermore, benefits and costs are also related to the positionality from which they are analysed: benefits for whom and costs borne by whom? more wealthy societies with strong social safety nets can afford increased temporary unemployment. this is much more consequential in poorer countries, where large proportions of the population live precarious lives and where public authorities cannot implement generous mitigation measures at scale. the adherence to hygiene and distancing measures depends not only on living conditions but also on risk perception and cultural norms. mass masking has been readily accepted in some asian countries, where it was already broadly practised even before the covid- bmj global health epidemic. it remains more controversial in western societies, some of which even have legal bans on veiling in public places. lockdowns are unprecedented and have triggered intensive public debate. not surprisingly, the impact of lighter lockdowns on the transmission is much less impressive; they decrease transmission but do not stop it. quite rapidly, the justification for lockdowns shifted from stopping transmission to 'flattening the curve'. also, once a lockdown is started, rationalised, explained and enforced, it is difficult to decide when to stop it. exit scenarios, usually some form of progressive relaxation, are implemented with the knowledge that transmission will be facilitated again. what we already know the available information on sars-cov- and the spectrum of covid- disease is summarised in tables and . it is increasingly becoming clear that most transmission happens indoors and that superspreading events trigger intensive dissemination. the virology and immunology of sars-cov- / covid- are being studied intensively. this is critical not only to understand what will potentially happen in future waves but also for the development of a vaccine. some scientists and companies are very upbeat about the possibility of producing a vaccine in record time. having a vaccine is one thing, but how effective it is, is quite another. as acquired immunity after a natural infection is probably not very robust (table ), it will also be challenging to trigger robust immunity with a vaccine, but perhaps it is not impossible. many questions remain, some of which are summarised in table . regarding the severity of covid- , initial fears of very high mortality have also lessened. it has progressively become clear that many infections remain asymptomatic, that severe disease is rare in children and young adults, and that mortality is heavily concentrated in the very old and those with comorbidities. table summarises a fuller overview of the present state of knowledge regarding covid- . with covid- epidemics unfolding rapidly, several of the variables in the transmission of sars-cov- and the disease spectrum of covid- could be quantified. this allows for mathematical modelling. several models have been quickly developed, leading to predictions of the speed of transmission and the burden of covid- (box ). predictive models developed by the imperial college ; the center for disease dynamics, economics & policy and johns hopkins university ; the institute for health metrics and evaluation ; harvard university ; and the who, including an 'african model', are a few that are influencing containment strategies around the world. although the covid- pandemic triggered unprecedented research efforts globally, with over scientific papers published between january and april , there are still critical unknowns and many uncertainties. tables and summarise many of the knowns, but their relative importance or weight is not clear. for instance, the virus can spread via droplets, hands, aerosols, fomites and possibly through the environment. however, the relative importance of these in various contexts is much less clear. these factors undoubtedly vary between settings, whether in hospitals, in elderly homes, or at mass events. the weight of the variables also probably differs between the seeding and initial spread in a community and the spread when it suddenly amplifies and intensifies. the importance of each variable probably also depends on climatic conditions, not only outdoors, but also on microclimates indoors, influenced by ventilation and air conditioning and built environments. we summarise the critical unknowns in table along some elements to consider in addressing the unknowns and thoughts on their importance. uncertainty remains, leading to controversy and directly influencing the choice of containment measures. controversy continues regarding when and where lockdown or more selective measures are equally effective with lower societal effects. relationship between the dose of the initial infectious inoculum, transmission dynamics and severity of the covid- disease new evidence is being discovered rapidly. some evidence comes from field observations and ecological studies; other evidence results from scientific experiments or observations in the laboratory and the clinic. sense-making by combining insights from different observations and through the lens of various disciplines can lead to hypotheses that can be tested and verified or refuted. one such hypothesis is that there is a relationship between the dose of virus in the infectious inoculum and the severity of covid- disease. several intriguing observations in the current pandemic could be (partially) explained by such a relationship. we develop this hypothesis in box , as an example of possible further research, to create new insight which may influence control strategies. this viral inoculum theory is consistent with many observations from the early stages of the covid- pandemic, but it is not easy to test scientifically. as covid- is a new disease, we should make a distinction between ( ) the current - 'virgin soil pandemic' caused by sars-cov- , specifically in how it will further spread around the globe in the first wave, and ( ) the potential future transmission in subsequent waves. in some countries, transmission will continue at lower levels. in other countries, such as china, the virus bmj global health may have been eliminated but can be reintroduced in identical or mutated form. for the current first wave, using influenza and the common cold as reasonable comparisons, it is possible that the major epidemics, as witnessed in wuhan, northern italy, or new york, will typically occur in temperate climates in the winter season. some predict that such epidemics will last between and weeks (but this is just a plausible and reasonable comparison in analogy with seasonal influenza). it is possible that in hotter climates the transmission may become continuous, year round at lower levels. it is increasingly clear that hot climate does not exclude superspreading events as observed in guayaquil, ecuador and in various cities in brazil. ventilation, air-conditioning and crowded places may still create favourable environments for intensive transmission. it is also quite possible that the more difficult spread of sars-cov- in such climates may, in certain table knowns, uncertainties and unknowns about severe acute respiratory syndrome coronavirus (sars-cov- ), as of may origin of sars-cov- ► most probably from bats via intermediate animal hosts to index case. all subsequent cases resulted from human-to-human transmission. transmission ► mainly through respiratory droplets from infected persons ; by hands, after contamination at nose, mouth or eyes; also through air on exposure to sneezing or coughing from an infected person at close distance. ► through aerosols, while singing/talking loudly in congregations, groups, parties, karaoke, and so on, especially in poorly ventilated spaces. ► through fomites. ► possibly via faecal-oral route ; detection in sewage. [ ] [ ] [ ] ► related to peak in upper respiratory tract viral load prior to symptom onset in presymptomatic (paucisymptomatic) persons. ► transmission dynamics in asymptomatic persons not fully elucidated although viral shedding occurs. influence of climate and/or air pollution on transmission ► influence of climate on the capacity of the virus to survive outside human body (in air, in droplets, on surfaces, etc.) and to spread has been speculative. ► may spread more readily in milder/colder climate ; although variability of the reproductive number could not be explained by temperature or humidity. ► existing levels of air pollution may play a role; air pollutants, such as particulate matter, nitrogen dioxide and carbon monoxide, are likely a factor facilitating longevity of virus particles. ► elevated exposure to common particulate matter can alter host immunity to respiratory viral infections. immunity-protective antibodies ► igm and iga antibody response - days after onset of symptoms, does not depend on clinical severity, correlates with virus neutralisation; igg is observed ~ days after onset of symptoms, may or may not correspond to protective immunity. whether antibody response is long lasting has remained unclear. ► rechallenge in rhesus macaques showed immunity post primary infection. how protective immunity after first infection is against subsequent infection with an identical or mutated strain has been uncertain. ► incidental reports showed recovered persons positive by real-time pcr, later attributed to testing errors. seroprevalence to sars-cov- ► reported estimates for seroprevalence range between . % and . % ; differences in timing of the serosurvey, the use of assay kits with varying sensitivity/specificity, and different methods for detection may contribute to this large variation. ► seemingly high seroprevalence may be due to cross-reactive epitopes between sars-cov- and other hcovs. ► whether seroprevalence implies immune protection is unclear, yet, some countries have considered use of 'immunity passports'. ► for herd immunity to be effectively achieved, an estimated seroprevalence of % of the population will be required. other studies estimate between . % and % seroprevalence in different countries. communities, be compensated for by human factors such as higher population density, closer human contacts and lesser hygiene (as, for instance, exist in urban slums in mega cities in low income countries). how all this plays out in sub-saharan africa, in its slums and remote areas, is still largely unknown. with sars-cov- , transmission scenarios are mainly based on mathematical models despite their serious limitations (box ). as the virus continues to circulate, it will progressively be less of a 'new disease' during subsequent waves. the immunity caused by the first epidemic will influence how the virus spreads and causes disease. whether later waves will become progressively milder or worse, as observed in the - spanish influenza, is a matter of intense speculation. both views seem plausible and the two are not necessarily mutually exclusive. indeed, immunity should be defined on two levels: individual immunity and herd immunity. individual immunity will dictate how mild or severe the disease will be in subsequent infections. herd immunity could be defined in different communities/regions/ disease spectrum ► many different estimates: ► initially, it was estimated that among infected, % remained asymptomatic, %- % had mild/moderate disease, %- % had severe disease, and %- % became critically ill. - ► very variable estimates for remaining totally asymptomatic (estimated %- % [ ] [ ] [ ] [ ] ). ► what determines that an infection remains asymptomatic? ► quasi-absence of disease in children: why? case fatality rate (cfr) ► initial estimates cfr: %- %; comparisons: influenza . %; common cold: %; sars: %- %; mers: %. ► calculated infection fatality rates (cifr) and calculated cfr (ccfr) on the princess diamond were . % and . %, respectively (for all ages combined), and projected cifr and ccfr for china were between . %- . % and . %- . %, respectively. in gangelt, germany: ccfr of . %. ► cfr is influenced significantly by age; male sex; comorbidities; body mass index and/or fitness; and adequacy of supportive treatment, mainly oxygen therapy. if a vaccine is developed? ► what type of vaccine will it be (live/non-live, classic killed, dna, or recombinant)? ► will it need special manufacture and transport conditions (such as cold chain)? ► how robust will be vaccine-acquired immunity? after how many doses? ► how protective will it be against infection? ► for how long will vaccine-acquired immunity last? and hence: how often will the vaccine have to be administered? only once? or yearly? ► will there be any adverse effects? acquired immunity is not very strong; hence, what is the consequence regarding herd immunity? ► to achieve herd immunity, how efficient will the vaccine need to be? ► what proportion of the population (critical population) will need to be vaccinated? ► how long will it take to effectively vaccinate the critical population? ► will vaccination be acceptable in the population? or will vaccine hesitancy reduce uptake? what are the socioeconomic implications? ► which countries will get the vaccine first (implications for lics/lmics)? ► how expensive will the vaccine be? ► will vaccination be made mandatory, especially for international travel? the various degrees of societal disruption and the collateral effects on other essential health services (eg, reluctance to use health services for other health problems, because of 'corona fear'). our growing knowledge may enable us to progressively improve our response. learning from the variety of ways the covid- epidemic is unfolding across the globe provides important 'ecological evidence' and creates insights into its epidemiology and impacts. until now, the insights gained on covid- have been largely dominated by the covid- epidemics in the global north. more understanding of lived experiences of people in a variety of contexts, where the epidemic is spreading more slowly and with different impacts, is necessary to get a full global picture and allow learning from this variety. this is an important missing piece of the covid- puzzle. bmj global health and emerging voices for global health have launched a call (https:// blogs. bmj. com/ bmjgh/ / / / from-models-to-narratives-andback-a-call-for-on-the-ground-analyses-of-covid- spread-and-response-in-africa/) for such on-the-ground narratives and analyses of the spread of and response to covid- , local narratives and analyses that will hopefully help to further enrich our understanding of how and why the covid- pandemic continues to unfold in multiple local epidemics along diverse trajectories around the globe. table some critical unknowns in sars-cov- transmission which transmission patterns will occur and will human-to-human transmission continue permanently? ► seasonal transmission in temperate climate? ► continuous tides, with ups and downs? ► the experience from china and some other countries showed that 'local elimination' is possible but risk of reintroduction remains. ► increasingly unlikely that elimination everywhere is possible. this will strongly depend on: how strong will the acquired immunity after a first infection with sars-cov- be and how long will it last? ► evidence of acquired immunity against subsequent infections has been limited. ► measurable antibodies have been observed in most persons who have recovered from covid- , and research in animal models has suggested limited possibility of reinfection. ► it is still unclear as to how robust the immunity is and how long it will last. ► debate on use, practicality and ethics of 'immunity passports' for those recovered from covid- has been ongoing. how stable is the virus (mutation) and do the different clades seen worldwide have any effect on the transmission potential/severity of the disease? ► if the virus mutates quickly and different strains develop, then antibodydependent enhancement might be an important risk, as in dengue with its four different strains. if so, then in subsequent waves progressively more severe cases could occur. ► this has been reported for the spanish influenza, where the second and third waves were characterised by a more severe disease pattern. what is the role of children in transmission? ► children have quasi-universally presented less severe disease. however, their susceptibility to infection remains unclear, with large heterogeneity reported between studies. ► their role in transmission has remained unclear, but evidence points to a more modest role in transmission than adults. how significant are asymptomatic carriers in transmission? ► there have been several reports of asymptomatic transmission and estimates based on modelling. ► increasing consensus that asymptomatic carriers play an important role in transmission. box relationship between the dose of the initial infectious inoculum, transmission dynamics and severity of the covid- disease hypothesis: the dose of the virus in the initial inoculum may be a missing link between the variation observed in the transmission dynamics and the spectrum of the covid- disease. it is plausible that: ► viral dose in inoculum is related to severity of disease. ► severity of disease is related to viral shedding and transmission potential. this hypothesis plays out potentially at three levels: ► at individual level: a person infected with a small dose of viral inoculum will on average develop milder disease than a person infected with a high viral inoculum and vice versa. ► at cluster level: a person with asymptomatic infection or mild disease will on average spread lower doses of virus in droplets and aerosols and is less likely to transmit disease; when the person transmits, the newly infected person is more likely to have milder disease than if infected by a severely ill person, who spreads on an average higher doses of virus. this causes clusters and chains of milder cases or of more severe cases. ► at community level: in certain contexts, such as dense urban centres in moderate climates during the season when people live mostly indoors, the potential for intensive transmission and explosive outbreaks is high, especially during indoor superspreading events. in other contexts, such as in rural areas or in regions with hot and humid climate where people live mostly outdoors, intensive transmission and explosive outbreaks are less likely. outbreak of pneumonia of unknown etiology in wuhan, china: the mystery and the miracle new-type coronavirus causes pneumonia in wuhan: expert a novel coronavirus from patients with pneumonia in china coronaviridae study group of the international committee on taxonomy of viruses. the species severe acute respiratory syndrome-related coronavirus: classifying -ncov and 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isn't mutating quickly, suggesting a vaccine would offer lasting protection. the washington post genomic epidemiology of novel coronavirus implications of test characteristics and population seroprevalence on 'immune passport' strategies systematic review of covid- in children shows milder cases and a better prognosis than adults susceptibility to and transmission of covid- amongst children and adolescents compared with adults: a systematic review and meta-analysis presumed asymptomatic carrier transmission of covid- transmission of -ncov infection from an asymptomatic contact in germany acknowledgements we would like to thank johan leeuwenburg, piet kager, and luc bonneux for useful comments on a previous draft, the teams of the riposte corona, inrb, kinshasa and the belgian embassy in kinshasa for welcoming and hosting wvd during his unscheduled extended stay in kinshasa during the lockdown, march-june . we are thankful to mrs. ann byers for editing the manuscript at short notice. funding the authors have not declared a specific grant for this research from any funding agency in the public, commercial or not-for-profit sectors.competing interests none declared. provenance and peer review not commissioned; externally peer reviewed. open access this is an open access article distributed in accordance with the creative commons attribution non commercial (cc by-nc . ) license, which permits others to distribute, remix, adapt, build upon this work non-commercially, and license their derivative works on different terms, provided the original work is properly cited, appropriate credit is given, any changes made indicated, and the use is non-commercial. see: http:// creativecommons. org/ licenses/ by-nc/ . /. key: cord- -ecuex m authors: fong, simon james; li, gloria; dey, nilanjan; crespo, ruben gonzalez; herrera-viedma, enrique title: composite monte carlo decision making under high uncertainty of novel coronavirus epidemic using hybridized deep learning and fuzzy rule induction date: - - journal: nan doi: nan sha: doc_id: cord_uid: ecuex m in the advent of the novel coronavirus epidemic since december , governments and authorities have been struggling to make critical decisions under high uncertainty at their best efforts. composite monte-carlo (cmc) simulation is a forecasting method which extrapolates available data which are broken down from multiple correlated/casual micro-data sources into many possible future outcomes by drawing random samples from some probability distributions. for instance, the overall trend and propagation of the infested cases in china are influenced by the temporal-spatial data of the nearby cities around the wuhan city (where the virus is originated from), in terms of the population density, travel mobility, medical resources such as hospital beds and the timeliness of quarantine control in each city etc. hence a cmc is reliable only up to the closeness of the underlying statistical distribution of a cmc, that is supposed to represent the behaviour of the future events, and the correctness of the composite data relationships. in this paper, a case study of using cmc that is enhanced by deep learning network and fuzzy rule induction for gaining better stochastic insights about the epidemic development is experimented. instead of applying simplistic and uniform assumptions for a mc which is a common practice, a deep learning-based cmc is used in conjunction of fuzzy rule induction techniques. as a result, decision makers are benefited from a better fitted mc outputs complemented by min-max rules that foretell about the extreme ranges of future possibilities with respect to the epidemic. on top of devastating health effects, epidemic impacted hugely on world economy. in the ebola outbreak between - where more than , and cases were suspected and , deaths in west africa [ ], $ . billion was lost [ ] . on the other hand, sars took over lives from china including hong kong and lives worldwide between and [ ] . its losses on global economy are up to a huge $ billion, % and . % dips of gdps in chinese and asian domestic markets respectively [ ] . although the current coronavirus (codename: ncp or covid- ) epidemic is not over yet, its economy impact is anticipated by economists from ihs markit to be far worse than that of sars outbreak in [ ] . the impact is so profound that will lead to factories shut down, enterprises bankruptcy especially those in tourism, retail and f&b industries, and suspensions or withdrawals in longterm investment, if the outbreak cannot be contained in time. since the first case in december , the suspected cases and deaths around the world skyrocketed to over confirmed cases and deaths, mostly in china, by the time of writing this article. an early intervention measure in public health to thwart the outbreak of covid- is absolutely imperative. according to a latest mathematical model that was reported in research article by the lancet [ ] , the growth of the epidemic spreading rate will ease down if the transmission rate of the new contagious disease can be lowered by . . knowing that the early ending the virus epidemic or even the reduction in the transmission rate between human to human, all governments especially china where wuhan is the epicenter are taking up all the necessary preventive measures and all the national efforts to halt the spread. how much input is really necessary? many decision makers take references from sars which is by far the most similar virus to covid- . however, it is difficult as the characteristics of the virus are not fully known, it details and about how it spreads are gradually unfolded from day to day. given the limited information on hand about the new virus, and the ever evolving of the epidemic situations both geographically and temporally, it boils down to grand data analytics challenge this analysis question: how much resources shall be enough to slow down the transmission? this is a composite problem that requires cooperation from multi-prong measures such as medical provision, suspension of schools, factories and office, minimizing human gathering, limiting travel, strict city surveillance and enforced quarantines and isolations in large scales. there is no easy single equation that could tell the amount of resources in terms of monetary values, manpower and other intangible usage of infrastructure; at the same time there exist too many uncertain variables from both societal factors and the new development of the virus itself. for example, the effective incubation period of the new virus was found to be longer than a week, only some time later after the outbreak. time is an essence in stopping the epidemic so to reduce its damages as soon as possible. however, uncertainties are the largest obstacle to obtain an accurate model for forecasting the future behaviours of the epidemic should intervention apply. in general, there is a choice of using deterministic or stochastic modelling for data scientists; the former technique based solely on past events which are already known for sure, e.g. if we know the height and weight of a person, we know his body mass index. should any updates on the two dependent variables, the bmi will be changed to a new value which remains the same for sure no matter how many times the calculation is repeated. the latter is called probabilistic or stochastic model -instead of generating a single and absolute result, a stochastic model outputs a collection of possible outcomes which may happen under some probabilities and conditions. deterministic model is useful when the conditions of the experiment are assumed rigid. it is useful to obtain direct forecasting result from a relatively simple and stable situation in which its variables are unlikely to deviate in the future. otherwise, for a non-deterministic model, which is sometimes referred as probabilistic or stochastic, the conditions of a future situation under which the experiment will be observed, are simulated to some probabilistic behaviour of the future observable outcome. for an example of epidemic, we want to determine how many lives could be saved from people who are infected by a new virus as a composite result of multi-prong efforts that are put into the medical resources, logistics, infrastructure, spread prevention, and others; at the same time, other contributing factors also matter, such as the percentage of high-risk patients who are residing in that particular city, the population and its mobility, as well as the severity and efficacy of the virus itself and its vaccine respectively. real-time tools like cdc data reporting and national big data centers are available with which any latest case that occurs can be recorded. however, behind all these records are sequences of factors associated with high uncertainty. for example, the disease transmission rate depends on uncertain variables ranging from macro-scale of weather and economy of the city in a particular season, to the individual's personal hygiene and the social interaction of commuters as a whole. they are dynamic in nature that change quickly from time to time, person to person, culture to culture and place to place. the phenomena can hardly converge to a deterministic model. rather, a probabilistic model can capture more accurately the behaviours of the phenomena. so for epidemic forecast, a deterministic model such as trending is often used to the physical considerations to predict an almost accurate outcome, whereas in a non-deterministic model we use those considerations to predict more of a probable outcome that is probability distribution oriented. in order to capture and model such dynamic epidemic recovery behaviours, stochastic methods ingest a collection of input variables that have complex dependencies on multiple risk factors. the epidemic recovery can be viewed in abstract as a bipolar force between the number of populations who has contracted the disease and the number of patients who are cured from the disease. each group of the newly infested and eventually cured (or unfortunately deceased) individuals are depending on complex societal and physiological factors as well as preventive measures and contagious control. each of these factors have their underlying and dependent factors carrying uncertain levels of risks. a popular probabilistic approach for modeling the complex conditions is known as monte carlo (mc) simulation which provides a means of estimating the outcome of complex functions by simulating multiple random paths of the underlying risk factors. rather than deterministic analytic computation, mc uses random number generation to generate random samples of input trials to explore the behaviour of a complex epidemic situation for decision support. mc is particularly suitable for modeling epidemic especially new and unknown disease like covid- because the data about the epidemic collected on hand in the early stage are bound to change. in mc, data distributions are entered as input, since precise values are either unknown or uncertain. output of mc is also in a form of distribution specifying a range of possible values (or outcome) each of which has its own probability at which it may occur. compared to deterministic approach where precise numbers are loaded as input and precise number is computed to be output, mc simulates a broad spectrum of possible outcomes for subsequent expert evaluation in a decision-making process. recently as epidemic is drawing global concern and costing hugely on public health and world economy, the use of mc in epidemic modeling forecast has become popular. it offers decision makers an extra dimension of probability information so called risk factors for analyzing the possibilities and their associated risk as a whole. decades ago, there has been a growing research interest in using mc for quantitatively modelling epidemic behaviours. since , bailey et al was among the pioneers in formulating mathematical theory of epidemics. subsequently in millennium, andersson and britton [ ] adopted mc simulation techniques to study the behaviour of stochastic epidemic models, observing their statistical characteristics. in , house et al, attempted to estimate how big the final size of an epidemic is likely to be, by using mc to simulate the course of a stochastic epidemic. as a result, the probability mass function of the final number of infections is calculated by drawing random samples over small homogeneous and large heterogeneous populations. yashima and sasaki in extended the mc epidemic model from over a population to a particular commute network model, for studying the epidemic spread of an infectious disease within a metropolitan area -tokoyo train station. mc is used to simulate the spread of infectious disease by considering the commuters flow dynamics, the population sizes and other factors, the proceeding size of the epidemic and the timing of the epidemic peak. it is claimed that the mc model is able to serve as a pre-warning system forecasting the incoming spread of infection prior to its actual arrival. narrowing from the mc model which can capture the temporal-spatial dynamics of the epidemic spread, a more specific mc model is constructed by fitzgerald et al [ ] in for simulating queuing behaviour of an emergency department. the model incorporates queuing theory and buffer occupancy which mimic the demand and nursing resource in the emergency department respectively. it was found that adding a separate fast track helps relieving the burden on handling of patient and cutting down the overall median wait times during an emergency virus outbreak and the operation hours are at peak. mielczarek and zabawa [ ] adopted a similar mc model to investigate how erratic the population is, hence the changes in the number of infested patients affect the fluctuations in emergency medical services, assuming there are epidemiological changes such as call-for-services, urgent admission to hospital and icu usages. based on some empirical data obtained from ems center at lower silesia region in poland, the ems events and changes in demographic information are simulated as random variables. due to the randomness of the changes (in population sizes as people migrate out, and infested cases increase) in both demand and supply of an ems, the less-structured model cannot be easily examined by deterministic analytic means. however, mc model allows decision makers to predict by studying the probabilities of possible outcomes on how the changes impact the effectiveness of the polish ems system. there are similar works which tap on the stochastic nature of mc model for finding the most effective escape route during emergency evacuation [ ] and modelling emergency responses [ ] . overall, the above-mentioned related works have several features in common: their studies are centered on using a probabilistic approach to model complex real-life phenomena, where a deterministic model may fall short in precisely finding the right parameters to cater for every detail. the mc model is parsimonious that means the model can achieve a satisfactory level of explanation or insights by requiring as few predictor variables as possible. the model which uses minimum predictor variables and offers good explanation is selected by some goodness of fit as bic model selection criterion. the input or predictor variables are often dynamic in nature whose values change over some spatial-temporal distribution. finally, the situation in question, which is simulated by mc model, is not only complex but a prior in nature. just like the new covid- pandemic, nobody can tell when or whether it will end in the near future, as it depends on too many dynamic variables. while the challenges of establishing an effective mc model is acknowledged for modelling a completely new epidemic behaviour, the model reported in [ ] inspires us to design the mc model by decomposing it into several sub-problems. therefore, we proposed a new mc model called composite mc or cmc in short which accepts predictor variables from multi-prong data sources that have either correlations or some kind of dependencies from one another. the challenge here is to ensure that the input variables though they may come from random distribution, their underlying inference patterns must contribute to the final outcome in question. considering multi-prong data sources widen the spectrum of possibly related input data, thereby enhancing the performance of monte carlo simulation. however, naive mc by default does not have any function to decide on the importance of input variables. it is known that what matters for the underlying inference engine of mc is the historical data distribution which tells none or little information about the input variables prior to the running of mc simulation. to this end, we propose a pre-processor, in the form of optimized neural network namely bfgs-polynomial neural network is used at the front of mc simulator. bfgs-pnn serves as both a filter for selecting important variables and forecaster which generates future time-series as parts of the input variables to the mc model. traditionally all the input variables to the mc are distributions that are drawn from the past data which are usually random, uniform or some customized distribution of sophisticated shape. in our proposed model here, a hybrid input that is composed of both deterministic type and non-deterministic type of variables. deterministic variables come from the forecasted time-series which are the outputs of the bfgs-pnn. non-deterministic variables are the usual random samples that are drawn from data distributions. in the case of covid- , the future forecasts of the time-series are the predictions of the number of confirmed infection cases and the number of cured cases. observing from the historical records, nevertheless, these two variables display very erratic trends, one of them contains extreme outliers. they are difficult to be closely modelled by any probability density function; intuitively imposing any standard data distribution will not be helpful to delivering accurate outcomes from the mc model. therefore in our proposal, it is needed to use a polynomial style of self-evolving neural network that was found to be one of the most suited machine learning algorithm in our prior work [ ] , to render a most likely future curve that is unique to that particular data variable. the composition of the multiple data sources is of those relevant to the development (rise-and-decline) of the covid- epidemic. specifically, a case of how much daily monetary budget that is required to struggle against the infection spread is to be modelled by mc. the data sources of these factors are publicly available from the chinese government websites. more details follow in section below. the rationale behind using a composite model is that what appears to be an important figure, e.g. the number of suspected cases are directly and indirectly related to a number of sub-problems which of each carries different levels of uncertainty: how a person gets infested, depends on ) the intensity of travel (within a community, suburb, inter-city, or oversea) ) preventive measures ) trail tracking of the suspected and quarantining them ) medical resources (isolation beds) available, and ) eventual cured or dead. some of these data sources are in opposing influences to one another. for example, the tracking and quarantine measures gets tighten up, the number of infested drops, and vice-versa. in theory, more relevant data are available, the better the performance and more accurate outcomes of the mc can provide. mc plays an important role here as the simulation is founded on probabilistic basis, the situation and its factors are nothing but uncertainty. given the available data is scare as the epidemic is new, any deterministic model is prone to high-errors under such high uncertainty about the future. the contribution of this work has been twofold. firstly, a composite mc model, called cmcm is proposed which advocates using non-deterministic data distributions along with future predictions from a deterministic model. the deterministic model in use should be one that is selected from a collection of machine learning models that is capable to minimize the prediction error with its model parameters appropriately optimized. the advantage of using both fits into the mc model is the flexibility that embraces some input variables which are solely comprised of historical data, e.g. trends of people infested. and those that underlying elements which contribute to the high uncertainty, e.g. the chances of people gather, are best represented in probabilistic distribution as non-deterministic variables to the mc model. by this approach, a better-quality mc model can be established, the outcomes from the mc model become more trustworthy. secondly, the sensitivity chart obtained from the mc simulation is used as corrective feedback to rules that are generated from a fuzzy rule induction (fri) model. it is known that fri outputs decision rules with probabilities/certainty for each individual rule. a rule consists of a series of testing nodes without any priority weights. by referencing the feedbacks from the sensitivity chart, decision makers can relate the priority of the variables which are the tests along each sequence of decision rules. combining the twofold advantages, even under the conditions of high uncertainty, decision makers are benefited with a better-quality mc model which embraces considerations of composite input variables, and fuzzy decision rules with tests ranked in priority. this tool offers a comprehensive decision support at its best effort under high uncertainty. the remaining paper is structured as follow. section describes the proposed methodology called grooms+cmcm, followed by introduction of two key soft computing algorithms -bfgs-pnn and fri which is adopted for forecasting some particular future trends as inputs to the mc model and generating fuzzy decision rules respectively. section presents some preliminary results from the proposed model followed by discussion. section concludes this paper. mc has been applied for estimating epidemic characteristics by researchers over the year, because the nature of epidemic itself and its influences are full of uncertainty. an application that is relatively less looked at but important is the direct cost of fighting the virus. the direct cost is critical to keep the virus at bay when it is still early before becoming a pandemic. but often it is hard to estimate during the early days because of too many unknown factors. jiang et al [ ] have modelled the shape of a typical epidemic concluding that the curve is almost exponential; it took only less than a week from the first case growing to its peak. if appropriate and urgent preventive measure was applied early to have it stopped in time, the virus would probably not escalate into an epidemic then pandemic. ironically, during the first few days (some call it the golden critical hours), most of the time within this critical window was spent on observation, study, even debating for funding allocation and strategies to apply. if a effective simulation tool such as the one that is proposed here, decision makers can be better informed the costs involved and the corresponding uncertainty and risks. therefore, the methodology would have to be designed in mind that the available data is limited, each functional component of the methodology in the form of soft computing model should be made as accurate as possible. being able to work with limited data, flexible in simulating input variables (hybrid deterministic and its counterpart), and informative outcomes coupled with fuzzy rules and risks, would be useful for experts making sound decision at the critical time. our novel methodology is based on group of optimized and multisource selection, (grooms) methodology [ ] which is made for choosing a machine learning method which has the highest level of accuracy. grooms as a standalone optimizing process is in aid of assuring the deterministic model that is to be used as input variable for the subsequent mc simulation to have the most accurate data source input. by default, mc model at its naive form accepts only input variable from a limited range of standard data distributions (uniform, normal, bernoulli, pareto, etc.); best fitting curve technique is applied should the historical data shape falls out of the common data distribution types. however, this limitation is expanded in our composite mc model, so-called cmcm in such a way that all relevant data sources are embraced, both direct and indirect types. an enhanced version of neural network is used to firstly capture the non-linearity (often with high irregularity and lack of apparent trends and seasonality) of the historical data. out of the full spectrum of data sources, direct and indirect, the selected data sources through feature selection by correlation, that are filtered by the neural network, whose data distributions would be taken as input variables to the mc model. the combined methodology, grooms+cmcm is shown in figure . according to the methodology, a machine learning algorithm candidate called bgfs-pnn which is basically pnn as selected as the winning algorithm in [ ] enhanced with further parameter optimization function. the given timeseries data fluctuated more than the same that were collected earlier. as a data pre-processor, bfgs-pnn has two functions. firstly, for the non-deterministic data, using a classifierbasedfilter function in a wrapper approach, salient features could be found in feature selection. the selected salient features are those very relevant to the forecast target in the mc. in this case, it is composite mc model or cmcm as the simulation engine intakes multiple data sources from types of deterministic and non-deterministic. the second function is to forecast a future time-series as a type of deterministic input variable for the cmcm. the formulation of bfgs-pnn is shown as follow. the naïve version of pnn is identical to the one reported in [ ] . bfgs-pnn uses bfgs (broyden-fletcher-goldfarb-shanno) algorithm to optimize the parameters and network structure size in an iterative manner using hill-climbing technique. bfgs theory is basically for solving non-linear optimization problem iteratively by finding a stationary equilibrium through quasi-newton method [ ] and secant method [ ] . let pnn [ ] take the form of kolmogorov-gabor polynomial as a functional series in eqn. ( ). the polynomial is capable to take form of any function which is generalized as y=f( ̅ ). the induction process is a matter of finding all the values for the coefficient vector ̅ . as the process iterates, the variables from ̅ arrive in sequence fitting into the polynomial via regression and minimizing the error. the complexity grows incrementally by trying to add a neuron at a time while the forecasting error is being monitored [ ] . when the number of neurons reach a pre-set level, the hidden layer increases. this continues until there is no further performance gain observed, the growth of the polynomial stops and taken as the final equation for the pnn. it is noted that the increment of the network growth is linear. however, for the case of bfgs-pnn, the expansion of the polynomial is non-linear and heuristic. the optimal state is achieved by unconstrainted hill-climbing method guided by quasi-network and secant methods. let an error function be e(p) where p is a vector of real numbers be a vector of network structure information and parameters, i.e. neurons and layers in an ordered set. at the start, when t= , pt= is initialized by randomly chosen states. let search direction be si at iteration i where time t=i. let hi be hessian which is a square matrix of nd -order partial derivatives of function e. where i is the current iteration, h improves becomes a better estimate as the process iterates. Ñe(pi) is the gradient of the error function which needs to be minimized at t=i by following the quasi-newton search pattern using a gradient function similar to eqn. . it seeks to search for the next state of parameters values pi+ by optimizing e(pi+s*si) where the scalar s must be greater than . eqn. then would have to obey the quasi-newton condition upon solving the approximation of the hessian hi, in a way of eqn. . by the secant equation, we let the hessian matrix take the form as in eqn. . the updating function for hessian matrix is defined as eqn. . following the secant method. the equation tries to impose the condition and symmetry such that ! = !"# ! . let !"# * ! = ! , = ! = ! ! , we can obtain two sub-equations in eqn. . as coefficients to eqn. . substituting eqn. . into eqn. , we obtain the updating function for hessian matrix hi+ . by applying sherman-morrison formula [ ] to eqn. ., we get eqn. . which is the inverse of hessian h matrix. expanding eqn. to eqn. we obtain an equation that can be calculated quickly without needing any buffer space for fast optimization which aims at minimizing e(*). !"# by our grooms+cmcm methodology, raw data from multiple sources are filtered, condensed, converted into insights of future behaviours in several forms. traditionally in mc simulation, probability density functions as simulated outcomes are generated, so is sensitivity chart which ranks how each factor in relevance to the predicted outcome. fuzzy rule induction (fri) plays a role in the methodology by inferring a rule-based model which supplies a series of conditional tests that lead to some consequences based on the same data that were loaded into the mc engine. fri serves the threefold purpose of easy to use, neural and scalable. firstly, the decision rules are interpretable by users. they can complement the probability density functions which show a macro view of the situation. fri helps give another perspective in causality assisting decision makers to investigate the logics of cause-and-effect. furthermore, different from other decision rule models, fri allows some fuzzy relaxation in bracketing the upper and lower bounds, thereby a decision can be made based on the min-max values pertaining to each conditional test (attribute in the data). the fri rules are formatted as branching-logic, which is also known as predicate-logic that preserves the crudest form of knowledge representation. predicate logic has an if-test[min-max]-then-verdict basic structure and a propensity of how often it exists in the dataset. the number of different groups of fri rules depend on how many different labels in the predicted class. the second advantage is that the fri rules are objective and free from human bias as they are derived homogenously from the data. therefore, they are suitable ingredient for scientifically devising policy and strategy for epidemic control. thirdly fri rules can scale up or down not only in quantity, but also in cardinality. a rule can consist of as many tests as the attributes of the data are available. in other words, as a composite mc system, new source of data could be chipped in as per when it becomes necessary or recently available; the attributes of the new data can add on to the conditional tests of the fri rules. one drawback about fri is the lack of indicators for each specific conditional test (or attribute). by the current formulation of fri, the likelihood of the occurrence of the rule is assigned to the rule as a whole. little is known about how each conditional test on the attribute is relatively contributing to the outcome that is specified in the rule. in the light of this shortcoming, our proposed methodology suggests that the scores from the sensitivity charts with respect to the relations between the attributes and the outcome, could be used at the rule by simple majority voting. rules are generated as a by-product of classification in data mining. the process is through fuzzification of the data ranges and the confidence factors in their effects in classification are taken as indicators. let a rule be a series of components constraining the attributes !"#..% (with outcome ! = y) in the classification model building, so that they can remain valid even though the values are fuzzified. so a rule can be expressed in the predicate rule format such that each ! ∈ , where ⊆y is an membership whose labels are where Θ *,↓ and Θ *,↑ are the lower and upper bounds of the argument which will map to a fuzzy membership of value . similarly, the supports of the lower and upper bounds are denoted by Θ *,↑ and Θ ',↑ . the fuzzy rules are built on the decision rules which are generated from standard decision tree algorithm, such as direct rule-based classifier equipped with incremental reduced error pruning via greedy search [ ] . given the rule sets generated, the task here is to find the most suitable fuzzy extension for each rule. the task can be seen as replacing the current memberships of the rules by their corresponding fuzzy memberships, which is not too computationally difficult as long as the rule structures and the elements the same. in order to fuzzify a membership, the following formula is applied over the antecedent (Ωi∈ i) of rule set while considering the relevant data / ! ; at the same time the instances from the other antecedent (Ωj by this approach, the instances / ! are divided into two subsets: one subset contains all the positive instances / ! and the other subset contains all the negative instances /-! . after that, a purity measure is used to further separate the two groups into two extremes, positive and negative subgroups, by eqn. . when it comes to actual operation, a certainty factor which serves as an indicator about how much the new data instances indeed belong to a subgroup, is needed to quantify the division. followed by segregating the data into fuzzy rules # ( ) … < ( ) by machine learning the relations from their attributes and instance values to some label class , further indicator is needed to quantify the strength of each rule. assume we have a new test instance x, eqn computes the support of the rules of x as follow: !"#…? where ℂ( ! ( ) ) is the certainty factor pertaining to the rule ! ( ) . the certainty factor ℂ is expressed in eqn. : where / ( ) denotes the subsets of training instances that are labelled as . the result that is predicted by the default classifier to be one of the class labels, is the one that has the greatest value computed from the support function eqn. . at times, some instances x could not be classified into rule or subgroup, that happens when sj(x)= for all classes λj, x could be randomly assigned or temporarily placed into a special group. otherwise, the fuzzy rules are formed, certainty and support indicators are assigned to each one of them. the indicators mean how strong the rules are with respect to the predictive power to the class label possessed by the rules. for the purpose of validating the proposed grooms+cmcm methodology, empirical data proceeding from the chinese center for disease control and prevention ‡ (cdcp), an official chinese government agency in beijing, china. since the beginning of the covid- outbreak, cdcp has been releasing the data to the public and updating them daily via mainstream media tencent and its subsidiary § . the data come from mainly two sources: one source is known to be deterministic in nature which is harvested from cdcp in the form of time-series starting from jan to feb . a snapshot of the published data is shown in figure which are deterministic in nature as historical facts. the data collected for this experiment are only parts of the total statistics available on the website. the data required for this experiment are the numbers of people in china who have been contracted with the covid- disease in the following ways: suspected of infection by displaying some symptoms, confirmed of infection by medical tests, cumulative confirmed cases, current number of confirmed cases, current number of suspected cases, current number of critically ill, cumulative number of cured cases, cumulative number of deceased cases, recovery (cured) rate % and fatality rate %. this group of time-series are subject to grooms for finding the most accurate machine learning technique for obtaining the forecasts as future trends under development. in this case, bfgs-pnn was found to be the winning candidate model, hence applied here for generating future trends for each of the above-mentioned records. the forecasts based on these selected data by bfgs-pnn are shown in fig . the forecasts are in turn used as deterministic input variables to the cmc model. they have relatively lowest errors in rmse in comparison to other time-series forecasting algorithms as tested in [ ] . the rationale is to use the most accurate possible forecasted inputs for achieving the most reliable simulated outcomes from mc simulation at the best effort. ‡ http://www.chinacdc.cn/en/ § https://news.qq.com/zt /page/feiyan.htm the goal of this monte carlo simulation experiment, which is a part of grooms+cmcm is to hypothetically estimate the direct cost that is needed as an urgent part of national budget planning to control the covid- epidemic. direct cost means the cost of medical resources, that includes but not limit to medicine, personnel, facilities, and other medical supplies, directly involved in providing treatments to those patients due to the covid- outbreak. of course, the grand total cost is much wider and greater than the samples experimented here. the experiment however aims at demonstrating the possibilities and flexibility of embracing both types of deterministic and non-deterministic data inputs by the composite mc methodology. the other group of data that would feed into the cmc are non-deterministic or probabilistic because they would have to bear a high level of uncertainty. they are subject to situation that changes dynamically and there is little control over the outcome. in the case of covid- epidemic control, finding the cure to the virus is a good example. there is best effort put into treatment, but no certainty at all about a cure, let alone knowing when exactly a cure could be developed, tested and proven to be effective for use against the novel virus. there are other probabilistic factors which are used in this experiment as well. selected main attributes are tabulated in table . we assume a simple equation for estimating the direct cost in fighting covid- using only data of quarantining and isolated medical treatment as follow. note that the variables shown are abbreviated from the term names. e.g. d-i-r = days_till_recovery. the assumptions and hypothesis are derived from past experiences about direct costs involved in quarantine and isolation during the epidemic of sars in as published in [ ] , with reasonable adjustment. for the non-deterministic variables ppi/day, d-f-r and d-t-d, the following assumptions are derived from [ ] . these variables are probabilistic in nature as shown in table . e.g. nobody can actually tell how long an infested patient could be recovered and go home, nor how long the isolation needs to be when the patient is in critical condition. all these are bounded by some probabilities that can be expressed in statistical properties, such as min-max, mean, standard deviation and so on. so some probabilism functions are needed to describe them, and random samples from these probabilities distributions are drawn to run the simulation. it is assumed that the growth of daily medical cost ppi/day follows a normal distribution with daily increase rate. the daily increase rate is estimated from [ ] to be rising as days go by, because the chinese government has been increasingly putting in resources to stop the epidemic using national efforts. the increase is due to the daily increase number of medical staff who are flown to wuhan from other cities, and the rise of the volume of consumable medical items as well as their inflating costs. the daily cost is anticipated to become increasingly higher as long as the battle against covid- continues at full force. there are other supporting material costs and infrastructure relocation costs such as imposing curfews and economy damages. however, these other costs are not considered for the purpose of demonstrating with a simple and easy-to-understand cmc model. normal distribution and uniform distribution are assumed accountable for the increase and probability distributions that describe the lengths of hospital stay. when more information become available, one can consider refining them to weibull distribution and rayleigh distribution which can better describe the progress of the epidemic in terms of severity and dual statistical degree of freedom. this is a very simplified approach in guessing the daily cost of the so-called medical expenses, based on only two interventions -quarantine and isolation. nevertheless, this cmc model though simplified, is serving as an example of how monte carlo style of modelling can help generate probabilistic outcomes, and to demonstrate the flexibility and scalability of the modelling system. theoretically, the cmc system can expand from considering two direct inputs (quarantining and isolation) to , or even other direct and indirect inputs to estimate the future behaviour of the epidemic. in practical application, data that are to be considered shall be widely collected, pre-processed, examined for quality check and relevance check (via grooms), and then carefully loading into the cmc system for getting the outcomes. stochastic simulation is well-suited for studying the risk factors of infectious disease outbreaks which always changes in their figures across time and geographical dispersion, thereby posing high level of uncertainty in decision making. each model forecast by mc simulation is an abstraction of a situation under observation -in our experiment, it is the impact of the dynamics of epidemic development on the direct medical costs against covid- . the model forecast depicts the future tendencies in real-life situation rather than statements of future occurrence. the output of mc simulation sheds light in understanding the possibilities of outcomes anticipated. being a composite mc model, the ultimate performance of the simulated outcomes would be sensitive to the choice of the machine learning technique that generated the deterministic forecast as input variable to the cmc model. in light of this, a part of our experiment besides showcasing the mc outcomes by the best available technique, is to compare the levels of accuracy (or error) resulted from the wining candidate of grooms and a standard (default) approach. the forecasting algorithms in comparison are bfgs+pnn and linear regression respectively. the performance criterion is rmse, which is consistent and unitless ! = m +,-). & / * . ! n and rmse=mo ( ! )n, as defined in [ ] . at the same time, the total costs that are produced manually by explicitly use of spreadsheet using human knowledge are compared vis-à-vis with those of the forecast models by cmcm. the comparative performances are tabulated in table ii . the forecasting period is days. the cmcm model is implemented on oracle crystal ball release . . . . ( -bit), running on a i cpu @ ghz, gb ram and ms windows platform. , trials were set to run the simulation for each model. it is apparent that as seen that from table ii , the rmse of the monte carlo forecasting method using linear regression is more than double that of the method using bfgs+pnn (approximately k vs k). that is mainly due to the overly estimate of all the deterministic input variables by linear regression. referring to the first diagram in figure , the variable called new_daily_increase_confirmed is non-stationary and it contains an outlier which rose up unusually high near the end. furthermore, the other correlated variable called new_daily_increase_suspected, which is a precedent of the trends of the confirmed cases, also is non-stationary and having an upward trend near the end, though it dips eventually. by using linear regression, the outlier and the upward trends would encourage the predicted curve to continue with the upward trend, linearly, with perhaps a sharp gradient. consequently, most of the forecast outcomes in the system have been over-forecasted. as such, using linear regression causes unstable stochastic simulation, leading to the more extreme final results, compared to the other methods. this is evident that the total_daily_cost has been largely over-forecasted and under-forecasted by manual and mc approaches, in table ii. on the other hand, when the bfgs+pnn is used, which is able to better recognize non-linear mapping between attributes and prediction class in forecasting, offers more realistic trends which in turn are loaded into the cmcm. as a result, the range between the final total_daily_cost results are narrower compared it to its peer linear regression ([lr: mil - mil] vs [bfgs+pnn: mil - mil]). the estimated direct medical cost for fighting covid- for a fortnight is estimated to be about . million usd given the available data using grooms+cmcm. according to the results in the form of probability distributions in figure , different options are available for the user to choose from when it comes to estimating the fortnightly budget in fighting this covid- given the existing situation. each option comes with different price tag, and at different levels of risks. in general, the higher risk that the user thinks it can be tolerated, the lower the budget it will be, and vice-versa. from the simulated possible outcomes in figure , if budget is of constrained, the user can consider bearing the risk (uncertainty of %) that a mean of $ mil with [min:$ mil, max:$ mil] is forecasted to be sufficient to fulfil the direct medical cost need. likewise, if a high certainty is to be assured, for example at % the chance that the required budget would be met, it needs about a mean of $ mil with [min:$ mil, max:$ mil]. for a high certainty of %, it is forecasted that the budget range will fall within a mean of $ mil and ranging from [min:$ mil, max:$ mil]. as a de-facto practice, some users will take % certainty as pareto principle ( - ) decision [ ] and accept the mean budget at $ mil. $ mil should be a realistic and compromising figure when compared to manual forecast without stochastic simulation, where $ mil and $ mil budgets would have been forecasted by manual approach by linear regression and neural network respectively. sensitivity chart, by its name, displays the extents of how the output of a simulated mc model is affected by changes in some of the input variables. it is useful in risk analysis of a so-called black box model such as the cmcm used in this experiment by opening up the information about how sensitive the simulated outcome is to variations in the input variables. since the mc output is an opaque function of multiple inputs of composite variables that were blended and simulated in a random fashion over many times, the exact relationship between the input variables and the simulated outcome will not be known except through sensitivity chart. an output of sensitivity chart from our experiment is generated and shown in figure . as it can be observed from figure , the top three input variables which are most influential to the predicted output, which is the total medical cost in our experiment are: the average number of days before recovery in day and day , and average cost per day for isolating a patient in day . the first two key variables are about how soon a patient can recover from covid- , near the final days. and the third most important variable is the average daily cost for isolating patients at the beginning of the forecasting period. this insight can be interpreted that an early recovery near the final days and reasonably lower medical cost at the beginning would impact the final budget to the greatest extend. consequently, decision makers could consider that based on the results from the sensitivity analysis, putting in large or maximum efforts in treating isolating patients at the beginning, observe for a period of days or so; if the medical efforts that were invested in the early days take effect, the last several days of recovery will become promising, hence leading to perhaps saving substantially a large portion of medical bill. sensitivity chart can be extended to what-if scenario analysis for epidemic key variable selection and modeling [ ] . for example, one can modify the quantity of each of the variables, and the effects on the output will be updated instantly. however, this is beyond the scope of this paper though it is worth exploring for it is helpful to fine-tune how the variables should be managed in the effort of maximizing or minimizing the budget and impacts. since the effect of a group of independent variables on the predicted output is known and ranked from the chart, it could be used as an alternative to feature ranking or feature engineering in data mining. the sensitivity chart is a byproduct generated by the mc after a long trial of repeating runs using different random samples from the input distributions. figure depicts how the sensitivity chart is related to the processes in the proposed methodology. effectively the top ranked variables could be used to infer the most influential or relevant attributes from the dataset that loads into an fri model (described in section . ) for supervised learning. one suggested approach which is fast and easy is to create a correlogram, from there one can do pairwise matching between the most sensitive variables from the non-deterministic data sources to the corresponding attributes from the deterministic dataset. ranking scores could be mapped over too, by boyer-moore majority vote algorithm [ ] . some selected fuzzy rules generated by the methodology and filtered by the sensitivity chart correlation mapping are show below. the display threshold is . which is arbitrary chosen to display only the top six rules where half of them predicts a reflection point for the struggle of controlling the covid- can be attained, the other half indicate otherwise. an fri model in a nutshell is a classification which predicts an output belonging either one of two classes. in our experiment, we setup a classification model using fri to predict whether an inflection point of the epidemic could be reached. there is no standard definition of inflection point, though it is generally agreed that is a turning point at which the momentum of accumulation changes from one direction to another or vice-versa. that could be interpreted as either an intersection of two curves of which their trajectories begins to switch. in the context of epidemic control, an inflection point is the moment since when the rate of spreading starts to subside, thereafter the trend of the epidemic is leading to elimination or eradication. based on a sliding window of days length, a formula for computing the inflection point based on the three main attributes of the covid- data is given in listed as follow: win: score = w × (d down-trend between the past days of new_daily_increase_confirmed (n.d.i.c)) + w × (d down-trend between the past days of current_confirmed) + w × (d up-trend between the past days of cured_rate) lose: score = w × (d up-trend between the past days of new_daily_increase_confirmed (n.d.i.c)) + w × (d up-trend between the past days of current_confirmed) + w × (d up-trend between the past days of death_rate) where w = . , w = . , and w = . which can be arbitrarily set by the user. the weights reflect the importance which one considers on how the up or downward trends of confirmed cases and cured vs death rates contribute to reaching the inflection point. a dual curve chart that depicts the inflection point is shown in figure . interestingly, when near the end of the timeline ( / - / ) that is from point th onwards, the two curves seem to intervene, as it has been hoping that the winning curve is rise over the losing curve. an inflection point might have reached, but the momentum of the winning is there yet. further observation on the epidemic development is needed to confirm about the certainty of winning. nevertheless, the top six rules that are built from classification of inflection point, and processed by feature selection via sensitivity analysis, are shown below. cf stands for confidence factor which indicates how strong the rule is. on the winning side, the rules reveal that when the variables about new confirmed cases fall below certain numbers, a win is scored, contributing towards a reflection point. (yester days-ndic = '( . .. ∞)') → win= (cf = . ) the strongest rules of the two forces are rules and . rule shows that to win an epidemic control the down trend over consecutive three days must fall below ; on the other hand, the epidemic control may lead to failure, if the cured rate stays less than . % and the new daily increase in confirmed cases remain high between and (round up the decimal points). originated from wuhan, china, the epidemic of novel coronavirus was spreading over many chinese cities, then over other countries worldwide since december . the chinese authorities took strict measures to contain the outbreak resolutely by restricting travels suspending business and schools etc. this gives rise to an emergency situation where critical decisions were demanded for, while the virus was novel and very little information was known about the epidemic at the early stage. with incomplete information, limited data on hand, and ever changing on the epidemic development, it is extremely hard for anybody to make a decision using only deterministic approach which foretells precisely the future behaviour of the epidemic. in this paper a composite monte-carlo model (cmcm) is proposed to be used in conjunction with grooms methodology [ ] which finds the best performing deterministic forecasting algorithm. coupling grooms+cmcm together offers the flexibility of embracing both deterministic and non-deterministic input data into the monte carlo simulation where random samples are drawn from the distributions of the data from the non-deterministic data sources for reliable outputs. during the early period of disease outbreaks, data are scarce and full of uncertainty. the advantage of cmc is that a range of possible outcomes are generated associated with probabilities. subsequently sensitivity analysis, what-if analysis and other scenario planning can be done for decision support. as a part of the grooms+cmcm methodology, fuzzy rule induction is also proposed, which provides another dimension of insights in the form of decision rules for decision support. a case study of the recent novel coronavirus epidemic (which are also known as wuhan coronavirus, covid- or -ncov) is used as an example in demonstrating the efficacy of grooms+cmcm. through the experimentation over the empirical covid- data collected from the chinese government agency, it was found that the outcomes generated from monte carlo simulation are superior to the traditional methods. a collection of soft computing techniques, such as bfgs+pnn, fuzzy rule induction, and other supporting algorithms to grooms+cmcm could be able to produce qualitative results for better decision support, when used together with monte carlo simulation, than any of deterministic forecasters alone. outbreaks chronology: ebola virus disease the impacts on health, society, and economy of sars and h n outbreaks in china: a case comparison study coronavirus: the hit to the global economy will be worse than sars nowcasting and forecasting the potential domestic and international spread of the -ncov outbreak originating in wuhan, china: a modelling study the mathematical theory of epidemics stochastic epidemic models and their statistical analysis how big is an outbreak likely to be? methods for epidemic final-size calculation epidemic process over the commute network in a metropolitan area a queue-based monte carlo analysis to support decision making for implementation of an emergency department fast track monte carlo simulation model to study the inequalities in access to ems services real-time stochastic evacuation models for decision support in actual emergencies on algorithmic decision procedures in emergency response systems in smart and connected communities finding an accurate early forecasting model from small dataset: a case of -ncov novel coronavirus outbreak bayesian prediction of an epidemic curve analytical study of the least squares quasi-newton method for interaction problems numerical analysis for applied science heuristic self-organization in problems of engineering cybernetics estimating the coefficients of polynomials in parametric gmdh algorithms by the improved instrumental variables method adjustment of an inverse matrix corresponding to changes in the elements of a given column or a given row of the original matrix (abstract nonlinear digital filters: analysis and applications medical applications of artificial intelligence a cost-based comparison of quarantine strategies for new emerging diseases how china built two coronavirus hospitals in just over a week fitting mechanistic epidemic models to data: a comparison of simple markov chain monte carlo approaches mathematical and computer modelling of the pareto principle soubeyrand samuel and thébaud gaël using sensitivity analysis to identify key factors for the propagation of a plant epidemic r automated reasoning: essays in honor of woody bledsoe he is a co-founder of the data analytics and collaborative computing research group in the faculty of science and technology. prior to his academic career, simon took up various managerial and technical posts, such as systems engineer, it consultant and e-commerce director in australia and asia. dr. fong has published over international conference and peer-reviewed journal papers, mostly in the areas of data mining, data stream mining, big data analytics, meta-heuristics optimization algorithms, and their applications. he serves on the editorial boards of the journal of network and computer applications of elsevier, ieee it professional magazine, and various special issues of scie-indexed journals. simon is also an active researcher with leading positions such as vice-chair of ieee computational intelligence society (cis) task force on her latest winning work includes the first unmanned supermarket in macau enabled by the latest sensing technologies, face recognition and e-payment systems. she is also the founder of several online offline dot.com companies in trading and retailing both online and offline. ms li is also an active researcher, manager and chiefknowledge-officer in dacc laboratory at the faculty of science and technology rubén gonzález crespo has a phd in computer science engineering. currently he is vice chancellor of academic affairs and faculty from unir and global director of engineering schools from proeduca group. he is advisory board member for the ministry of education at colombia and evaluator from the national agency for quality evaluation and accreditation of spain (aneca) his current research interests include group decision making, consensus models, linguistic modeling, and aggregation of information, information retrieval, bibliometric, digital libraries, web quality evaluation, recommender systems, and social media. in these topics he has published more than papers in isi journals and coordinated more than research projects. dr. herrera-viedma is vice-president of publications of the ieee smc society and an associate editor of international journals such as the key: cord- - xczf authors: zhan, xiu-xiu; liu, chuang; sun, gui-quan; zhang, zi-ke title: epidemic dynamics on information-driven adaptive networks date: - - journal: chaos solitons fractals doi: . /j.chaos. . . sha: doc_id: cord_uid: xczf research on the interplay between the dynamics on the network and the dynamics of the network has attracted much attention in recent years. in this work, we propose an information-driven adaptive model, where disease and disease information can evolve simultaneously. for the information-driven adaptive process, susceptible (infected) individuals who have abilities to recognize the disease would break the links of their infected (susceptible) neighbors to prevent the epidemic from further spreading. simulation results and numerical analyses based on the pairwise approach indicate that the information-driven adaptive process can not only slow down the speed of epidemic spreading, but can also diminish the epidemic prevalence at the final state significantly. in addition, the disease spreading and information diffusion pattern on the lattice as well as on a real-world network give visual representations about how the disease is trapped into an isolated field with the information-driven adaptive process. furthermore, we perform the local bifurcation analysis on four types of dynamical regions, including healthy, a continuous dynamic behavior, bistable and endemic, to understand the evolution of the observed dynamical behaviors. this work may shed some lights on understanding how information affects human activities on responding to epidemic spreading. the spreading dynamic is one of the core issues in network science [ ] [ ] [ ] , where most of the related researches focus on epidemic spreading and information diffusion in recent years. much of the work to date focuses on the analysis of these two processes independently, such as the spread of single contagion [ ] [ ] [ ] or concurrent diseases [ , ] , and the diffusion of various kinds of information (e.g., news [ ] , rumor [ ] , innovation [ ] .). however, the epidemic spreading process is closely coupled with the corresponding disease information diffusion (or saying individuals' awareness of the disease) in the real world. for instance, during the severe acute respiratory syndrome (sars) outbreak in china in , overwhelming number of disease reports have been posted. these kind of information about sars may affect the individuals' behavior in keeping away from sars and thus help to make the disease under control [ , ] . therefore, disease information diffusion may play an important role in the control of the epidemic outbreak, but it is not easy to quantitatively measure the strength of its impact [ ] . nowadays, some models have been proposed to model the interaction between epidemic spreading and information diffusion on complex networks [ ] [ ] [ ] [ ] . the fundamental assumption is that, when a disease starts to spread in the population, people may get the disease information from their friends or media before the advent of the epidemic and take some preventive measures to keep away from being infected [ , , ] . by depicting preventive measures as the reduction of transmitting probability [ , ] or particular states of individuals (immune or vaccination) [ ] , previous models showed that the disease information diffusion indeed inhibits the epidemic spreading significantly (reduce the epidemic prevalence as well as enhance the epidemic threshold) [ , ] . therefore, the emergence of mutual feedback between information diffusion and epidemic spreading [ ] exhibits the intricate interplay between these two types of spreading dynamics. the interplay between these two types of spreading dynamics is similar to the competing epidemics [ , ] to some extent, that is to say, there is a competitive mechanism between epidemic spreading and the in- i.e., the network structure stays fixed when the two processes are spreading on the network. however, individuals would sometimes cut off the connections with the infected ones when they become aware of the disease, leading to the change of network structure. consequently, how to characterize the mutual spreading process on the adaptive networks is a crucial issue we want to address in this work. generally, the network dynamic researches could be classified into two lines: (i) one is the dynamics of the network , which focuses on the time evolution of network structure [ ] [ ] [ ] ; (ii) the other is considered as the dynamics on the network , which concerns the state change of the nodes (or interactions) on networks, such as the epidemic spreading and information diffusion process [ , ] , the evolutionary game [ ] and so forth. currently, researchers became to study how the epidemic would spread on adaptive networks, i.e., considering one epidemic spreading process on dynamical changing networks [ ] . in [ ] , the author proposed a model by considering that the susceptible individuals are allowed to protect themselves by rewiring their links from the infected neighbors to some other susceptible ones [ ] [ ] [ ] . many researches indicate that segregating infected (or susceptible) individuals with the adaptive behavior is an efficient strategy to reduce the fraction of susceptible-infected ( si ) interactions, as well as hinder the outbreak of the whole epidemic spreading [ ] [ ] [ ] . in addition, abundant temporal behaviors are presented to illustrate the spreading dynamics on the adaptive network, such as the coexistence of multiple stable equilibrium and the appearance of an oscillatory region, which are absent in the spreading dynamics on static networks [ , ] . besides the edge rewiring strategy, the link cutting or temporarily deactivating is also a commonly used rule in the adaptive models [ , ] . in this work, we consider a more complicated case that two dynamical processes (i.e., epidemic spreading and disease information diffusion) are spreading on adaptive networks. therefore, three dynamical processes are coupled in this case, we aim to illustrate how the adaptive behavior can affect the interplay between epidemic spreading and information diffusion. the adaptive behavior is aroused by the individuals awareness of the disease. in this model, those who have been informed of the emergence of disease can break their neighbouring connections to prevent further infection. additionally, epidemic spreading and disease information diffusion are described by the si and sis model, respectively. the disease information generation of the infected individuals is considered to form a mutual feedback loop between these two types of spreading dynamics [ ] . therefore, the effect of information diffusion on epidemic spreading could be interpreted by two aspects: (i) reduce the epidemic spreading probability with protective measures; and (ii) cut off si links with the information-driven adaptive process. both numerical analyses based on the pairwise approach and simulation results indicate that the information diffusion and the adaptive behavior of the nodes can inhibit the epidemic outbreak significantly. in addition, we present a full local bifurcation diagram to show the abundant dynamical behaviors in the proposed model. the paper is organized as follows. in section , we give a detailed description of the model as well as mathematical expressions based on the mean-field model and the pairwise model. in section , we first analyze the case of epidemic and disease information spreading on static network, i.e., the case of no adaptive behavior is taken into account. we further give the results of how the epidemic and disease information spreading processes interact with each other on adaptive network. the sensitivity analysis of the parameters and dynamical characterization of the model is given in the end of section . we conclude the paper with some future directions of the work in section . we give a detailed illustration of our model in fig. . the vertical transformation describes the diffusion of disease information by an sis model, where individuals can be at one of the two states: (i) + : indicates that the individuals have known the existence of the disease, denoted as the informed ones; (ii) −: indicates that the individuals have not known the existence of the disease. at each time step, the informed nodes will transmit the information to their unknown ( −) neighbours with probability α, and each informed individual may forget the information of the disease with a probability λ. besides, the one who has been infected by the disease will become to know the information of the disease with a corresponding rate ω [ , ] . in the horizontal transformation of fig. , the epidemic spreading is described by an si model. each node is at one of two states, susceptible (s) or infected (i). the disease can be transmitted through the si links, where the s-state individuals could be infected with the probabilities β, σ i β, σ s β and σ si β respectively through s − i − , s − i + , s + i − and s + i + links, where σ i , σ s and σ si are the impact factors of the information on epidemic spreading. generally, when people know the occurrence of the disease (informed individuals), they would like to take some measures to protect themselves, leading to the reduction in infectivity ( < σ s , σ i < ). in particular, the influence coefficient of the epidemic spreading probability through s + i + links could be calculated as σ si = σ s σ i , with the assumption of the independent effect of the infection probability. additionally, we consider an information-driven adaptive process which the informed individuals would reduce physical contacts to protect themselves or their friends. that is to say, the informed susceptible individuals ( s + ) will keep away from their infected neighbors to protect themselves from being infected, and informed infected individuals ( i + ) will also avoid contacting their susceptible neighbors to prevent the epidemic from further spreading. consequently, the edge-breaking rule of adaptive behavior is adopted [ ] . thus, at each time step, the s + ( i + ) state individuals will break the links connected to their i ( s )-state neighbors with rate r s ( r i ) respectively. specially, the breaking rate of the s + i + pairs could be interpreted as − ( − r s )( − r i ) with the independent assumption. it is worth noting that the deactivation of si links only represents the avoidance of physical contacts between the sand i -state individuals. that is to say, the edge-breaking process will not affect the diffusion of disease information for it can be transmitted through other types of connections such as phone, internet and so forth. the dynamic of the epidemic spreading degen- erates to a classical si model when we set r s = r i = , i.e., there is no edge-breaking in this case. according to the model described above, the spreading process can be summarized as follows. at the beginning, an individual is randomly selected as the i + node, which is considered as the seed of both the epidemic spreading and information diffusion, and all other individuals are set as s − ones. at each time step, (i) the infected individuals would transmit the disease to their susceptible neighbors with the corresponding probabilities; (ii) the informed individuals would transmit the disease information to their uninformed neighbors; (iii) the informed individuals can forget the information; (iv) the informed individuals would also break the links with their relevant neighbors by considering the adaptive mechanism. finally, the spreading process would be terminated when the size of the infected individuals becomes stable. firstly, we develop theoretical analysis to depict the dynamic processes of both information diffusion and epidemic spreading. in particular, mean-field analysis and the pairwise analysis are adopted. let χ be the state variable, thus [ χ] denotes the expected values of individuals of different types on the population (e.g. [ s + ] and [ s + i + ] represent the expected number of informed susceptible nodes and expected number of links connecting an informed susceptible node to an informed infected node respectively). therefore, with the classical mean-field approach, we can obtain: comparatively, with the pairwise approach, we can obtain: where, the first terms of eqs. ( ) and ( ) describe the infection of the s + -state individuals, the second terms describe the information acceptance of the i − -state individuals, the third terms describe the information generation of the i − -state individuals and the last terms represent the information loss of the i + -state individuals. simultaneously, the full set of differential equations based on those two approaches can be illustrated in appendix a . by the way, the adaptive process could be described by the last terms of in the pairwise approach of eq. ( ) . it should be noted that the pairwise analysis is based on a wellknown closure approximation given by with the assumption that the degree of each individual obeys poisson distribution [ , ] . in general, it might be very hard to get exact solutions of such complex differential equations, thus we give numerical solutions of the equations instead of the theoretical analysis in the following analysis. in this work, we perform our model on the er network with a total population of n = , and average degree k = unless otherwise stated. moreover, all the simulation results are given by , realizations. we first consider a simple case of no adaptive behavior when the epidemic and disease information are spreading in the network, i.e., the case of spreading on static network. fig. gives the simulation result of the fraction of infected nodes evolving with time for various information diffusion probabilities α, with the epidemic spreading probability β = . . for the si process, the whole population would be infected when β > for the connected social networks, resulting in that the final infected density equals to for all the values of α in fig. . that is to say, the disease information diffusion cannot avoid the epidemic spreading to the whole population when we perform our model on static network. however, we find that the disease information diffusion can slow down the epidemic spreading when we increase the value of α. furthermore, the time cost for the whole population becomes infected when α = is about three times longer than that of α = . in this sense, the diffusion of the disease information can slow down the epidemic spreading significantly. in addition, the inset of fig. indicates that the epidemic spreading can enhance the disease information diffusion. actually, according to model illustrated in fig. , on the one hand, we realize that the epidemic spreading could be influenced by information diffusion where the epidemic spreading probability of the informed individuals would change; and on the other hand, the information diffusion could be influenced by the epidemic spreading where the social disease information level (namely info in the inset of fig. ) would be higher if more people are infected for the information generation, denoted by the parameter ω. in this way, a mutual feedback between disease spreading and information diffusion emerges: higher prevalence of the infected individuals makes more disease information generated in the population, which in turn gives rise to more informed individuals, thereby weakening the spread of epidemic. fig. shows a comparison of the evolution of infected density from the numerical analysis according to eqs. ( ) and ( ) and the simulation results on er network. infected density curve based on the classical mean-field approach is much quicker than that of the simulation result, which would be caused by the mean-field assumption on the si model. in the mean-field assumption, the iand s -state individuals are well-distributed in the system. however, in the si process, the i -state individuals are all well clustered, resulting in that many i -state individuals have no chance to contact the s -state individuals. in this way, the classical mean-field approach can not exactly describe the si model. however, such problem is not so significant in the pairwise approach, which consider the time evolution of the links as well. fig. shows that the infected density curve of the pairwise approach finds good agreement with the simulation results. in this part, we shall present the spreading dynamics with the information-driven adaptive process, the results are shown in fig. . different from the results of fig. , the saturation value of the infected density at the final state is much smaller than in fig. (a) . that is to say, with the adaptive process based on the information diffusion, many individuals could avoid being infected via reducing some contacts. in addition, we also plot the numerical solution based on the pairwise approach in fig. (a) . it can be seen that the pairwise solution is not well consistent with simulation for the spreading dynamic on the adaptive network. the difference might be caused by the network structure variation in the adap-tive process, where the assumption of the pairwise approach is the poisson degree distribution. this conjecture is proved in fig. (b) , where the degree distribution of the original network is approximate to the poisson-distribution with mean degree around (pink circle markers), while the distribution of the network at the final state (gray diamond markers) deviates from the original distribution. in addition, fig. (a) shows that the difference becomes larger with the increase of time, where the degree distribution deviates more away from the original distribution when the process goes on. the information-driven adaptive process can not only slow down the speed of epidemic spreading, but also can diminish the epidemic prevalence at the final state significantly according to figs. and . for simplicity, we assume r s = r i = r in the following analysis. in order to exhibit the influence of information diffusion in detail, we show the full phase diagram α − β with r = . in fig. , the color gives the infected density in the final state for each combination of α and β. the fig. (a) and (b) are the numerical solution of the pairwise approach and the simulation result, respectively. as stated previously, the numerical solution is not very statistics of haggle network, where n, e, c represent the number of nodes, the number of links, clustering coefficient of each system respectively. in order to intuitively demonstrate the epidemic spreading and the information diffusion process on adaptive network, we show the simulation results of those two types of spreading processes for various α on two different networks, i.e., a × lattice with degree k = as well as a real-world network, e.g., haggle network [ ] . the contacts in haggle network represent connection between people measured by carrying wireless devices. the statistics of the network is given in table . the visualization of how epidemic and disease information interact with each other for these two networks are given in fig. and fig. , respectively. taking lattice as an example, we present four kinds of different levels of information spreading processes (corresponding to different α), and observe how the information diffusion affects the spreading of epidemic. in addition, as the adaptive edge-breaking process is merely executed on the epidemic spreading process, while these edges can still transmit information, thus the density of informed people can still maintain at a high level in the network. for each α in fig. , firstly we give the fraction of the infected individuals at each time step (the red curve in each subfigure). for some particular time steps, we show the states of each individual with the gridding patterns, where the red dots and the gray dots represent the infected and informed individuals respectively (the contact networks and the un-informed susceptible individuals are not shown in the figures). we can intuitively see the distribution of the infected and informed individuals and conclude that when the diffusion of information is slower than the epidemic, we cannot stop the epidemic from spreading ( fig. (a) and (b) ), however, when the information is diffusing faster, the epidemic will be trapped into an isolated area and cannot spread anymore ( fig. (c) and (d)). furthermore, the visualization of these two processes on haggle network displays similar results as the results on lattice. the sensitivity of the edge-breaking probability on epidemic spreading dynamics. the phase diagram in fig. shows the impact of information diffusion rate α on the epidemic spreading dynamics. in general, the adaptive edge-breaking probability r s and r i are also important parameters in affecting the epidemic spreading process. fig. illustrates the epidemic prevalence in the final state versus the adaptive edge-breaking rate ( r ) for various information diffusion rate α. it can be found that the epidemic prevalence diminishes with the increase of r , i.e., the epidemic could be controlled if people are very sensitive with the disease information and subsequently keep away from the infected. it should be noted that there is no disease information diffusion when α = , but with considering the information generation, the infected individuals could stop contacting with the susceptible neighbors to impede the further spreading of epidemic. with the increase of α, the epidemic prevalence reduces sharply versus r and the continuous transition could be observed. by the way, it will change to a total isolation of infected individuals for r = , which seems to be the most effective way in controlling the contagion [ , ] . dynamical characterization of the information-driven rewiring. in order to deeply characterize the complex dynamical features of the proposed process, we concentrate on the distribution of the infected density in the final state ( i * ) rather than the simple average value [ , ] . fig. shows four different types of dynamical behavior by calculating the distribution of the final fraction of infected for various β and r . for the distribution of fig. (a) , we have carried out , realizations of the infected density, and above % of the infected density is . , and the maximal is . , i.e., the infected density i * → , thus we consider this distribution indicates a healthy state (the disease can't spread out) under the parameters setting here. similarly, as to the distribution of fig. (d) , above % of the infected density is higher than . , indicates a case of endemic state (epidemic outbreaks). whereas the case illustrated in fig. (c) is very different, where the infected density i * is around either zero or a nonzero value. this indicates that a bistable state [ ] is located in this model, where healthy state and endemic state are both stable in this case. in addition, a continuous dynamic behavior can also be observed in particular parameter settings ( fig. (b) ). according to the dynamical behavior illustrated in fig. under different parameter sets, bifurcation diagram of the density of the infected as a function of infected probability β for different values of the edge-breaking rate r is given in fig. (a) . without the adaptive edge-breaking mechanism ( r = ), the disease can spread out only if β > for the si process. when r > , the dynamical behaviors become more complicated, where the discontinuous phase transitions, bistable, oscillatory are observed. a fast edge-breaking (large r ) leads to a broad healthy and bistable state range (shows by the range in the arrows) in fig. (a) . in fig. (b) , we give a full r − β bifurcation diagram according to our simulation results, and we can clearly identify the areas of healthy, a continous dynamic behavior, bistability and endemic state in this model. at last, we present the dependence of the average value of infected density over , independent realizations on r and β in fig. (c) , where the changing of the density is consistent with the area classification in fig. (b) . in order to understand the interplay between the dynamics on the network (the spread of epidemic spreading and disease information) and the dynamics of the network (the time varying of network links), we present two types of spreading dynamics with si and sis process respectively on an information-driven adaptive network, where the individuals who have known the disease information would probably cut off their links with others. firstly, we illustrate the mutual feedback between epidemic spreading and information diffusion without considering the edge-breaking process ( r s = r i = ), where the high epidemic prevalence preserves high disease information level, which in turn slows down the epidemic spreading. in this case, the numerical analysis based on the pairwise approach is consistent with the simulation result very well. secondly, the results are very different when the informationdriven edge-breaking process is considered ( r s , r i > ). the epidemic cannot spread out if the spreading probability is smaller than the threshold (shown in fig. ). in addition, the disease spreading and information diffusion pattern on the lattice as well as on a real-world network give visual representations that the disease might be trapped into an isolated field with informationdriven adaptive process. therefore, the information-driven adaptive process can inhibit the epidemic spreading significantly that it can not only slow down the epidemic spreading speed, but also reduce the epidemic prevalence. finally, we give the local bifurcation analysis on four types of dynamical phenomena, including healthy, a continuous dynamic behavior, bistable and endemic, indicating that the state changes from healthy to a continuous dynamic behavior, bistable, endemic state as β increases. in summary, we study the dependence of the epidemic spreading on the disease information diffusion and the informationdriven adaptive process, with considering the simplest spreading model (si) and adaptive process (edge-breaking). recent researches show the different features between the epidemic and the information diffusion [ , ] , and this difference would also impact the interplay between epidemic spreading and disease information diffusion significantly. another area for future extension is to adopt networks prediction [ ] or other adaptation rules rather than the simple edge-breaking strategy, such as the temporarily deactivating, where the broken links would be active again after a fixed time [ ] or, if the corresponding infected node becomes recovered [ ] . how viruses spread among computers and people networks and the epidemiology of infectious disease transmission dynamics of cholera: mathematical modeling and control strategies epidemic processes in complex networks dynamics of information diffusion and its applications on complex networks global stability for a sheep brucellosis model with immigration dynamics of interacting diseases threshold effects for two 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to suppress epidemic spreading effects of behavioral response and vaccination policy on epidemic spreading -an approach based on evolutionary-game dynamics the impact of awareness on epidemic spreading in networks interacting epidemics on overlay networks adaptive networks: coevolution of disease and topology emergence of scaling in random networks collective dynamics in 'small-world' networks temporal networks epidemic spreading in scale-free networks information spreading on dynamic social networks heterogeneous networks do not promote cooperation when humans play a prisoner's dilemma epidemic dynamics on an adaptive network adaptive coevolutionary networks: a review adaptive networks effects of community structure on epidemic spread in an adaptive network epidemic spreading on weighted adaptive networks susceptible-infected-recovered epidemics in dynamic contact networks the structure of coevolving infection networks epidemic threshold and topological structure of susceptible-infectious-susceptible epidemics in adaptive networks epidemics in adaptive social networks with temporary link deactivation intermittent social distancing strategy for epidemic control representing spatial interactions in simple ecological models the effects of local spatial structure on epidemiological invasions impact of human mobility on opportunistic forwarding algorithms probing into the effectiveness of self-isolation policies in epidemic control quarantine-generated phase transition in epidemic spreading how events determine spreading patterns: information transmission via internal and external influences on social networks avalanche outbreaks emerging in cooperative contagions tiirec: a tensor approach for tagdriven item recommendation with sparse user generated content denote [ χ] as the expected values of individuals of different types described in section . , the epidemic spreading is depicted by the parameters β, σ i β, σ s β and σ si β, while the diffusion of disease information is controlled by the parameters: α, λ, ω. all these parameters have been explained in section . . according to the model described above, the differential equations of the meanfield approach ( eq. ( ) ) and pairwise approach ( eq. ( ) ) are given as follows. key: cord- -ab msb m authors: chanchan, li; guoping, jiang title: modeling and analysis of epidemic spreading on community network with node's birth and death date: - - journal: the journal of china universities of posts and telecommunications doi: . /s - ( ) - sha: doc_id: cord_uid: ab msb m abstract in this paper, a modified susceptible infected susceptible (sis) epidemic model is proposed on community structure networks considering birth and death of node. for the existence of node's death would change the topology of global network, the characteristic of network with death rate is discussed. then we study the epidemiology behavior based on the mean-field theory and derive the relationships between epidemic threshold and other parameters, such as modularity coefficient, birth rate and death rates (caused by disease or other reasons). in addition, the stability of endemic equilibrium is analyzed. theoretical analysis and simulations show that the epidemic threshold increases with the increase of two kinds of death rates, while it decreases with the increase of the modularity coefficient and network size. with the development of complex network theory, many social, biological and technological systems, such as the transportation networks, internet and social network, can be properly analyzed from the perspective of complex network. and many common characteristics of most real-life networks have been found out, e.g., small-world effect and scale-free property. for some kind of networks, the degree distributions have small fluctuations, and they are called as homogeneous networks [ ] , e.g., random networks, small world networks and regular networks. in contrary to the homogeneous networks, heterogeneous networks [ ] show power law distribution. based on the mean-field theory, many epidemic models, such as susceptible-infected (si), sis and susceptibleinfected-recovered/ removed (sir), have been proposed to describe the epidemic spreading process and investigate the epidemiology. it has been demonstrated that a threshold value exists in the homogeneous networks, while it is absent in the heterogeneous networks with sufficiently large size [ ] . compared to the lifetime of individuals, the infectious period of the majority of infectious diseases is short. therefore, in most of the epidemic models, researchers generally choose to ignore the impact of individuals' birth and death on epidemic spreading. however, in real life, some infectious diseases have high death rate and may result in people's death in just a few days or even a few hours, such as severe acute respiratory syndrome (sars), hemagglutinin neuraminidase (h n ) and the recent ebola. and some infectious diseases may have longer spreading time, like hbv, tuberculosis. besides, on the internet, nodes' adding and removing every time can also be treated as nodes' birth and death. in ref. [ ] , liu et al. analyzed the spread of diseases with individuals' birth and death on regular and scale-free networks. they find that on a regular network the epidemic threshold increases with the increase of the treatment rate and death rate, while for a power law degree distribution network the epidemic threshold is absent in the thermodynamic limit. sanz et al. have investigated a tuberculosis-like infection epidemiological model with constant birth and death rates [ ] . it is found that the constant change of the network topology which caused by the individuals' birth and death enhances the epidemic incidence and reduces the epidemic threshold. zhang et al. considered the epidemic thresholds for a staged progression model with birth and death on homogeneous and heterogeneous networks respectively [ ] . in ref. [ ] , an sis model with nonlinear infection rate, as well as birth and death of nodes, is investigated on heterogeneous networks. in ref. [ ] , zhu et al. proposed a modified sis model with a birth-death process and nonlinear infection rate on an adaptive and weighted contact network. it is indicated that the fixed weights setting can raise the disease risk, and that the variation of the weight cannot change the epidemic threshold but it can affect the epidemic size. recently, it has been revealed that many real networks have the so-called community structure [ ] , such as social networks, internet and citation networks. a lot of researchers focus on the study of epidemic spreading on community structure networks. liu et al. investigated the epidemic propagation in the sis model on homogeneous network with community structure. they found that community structure suppress the global spread but increase the threshold [ ] . many researchers studied the epidemic spreading in scale-free networks with community structure based on different epidemic model, such as si model [ ] , sis model [ ] , sir model [ ] [ ] and susceptible exposed asymptomatically infected recovered (seair) model [ ] . chu et al. investigated the epidemic spreading in weighted scale-free networks with community structure [ ] . in ref. [ ] , shao et al. proposed an traffic-driven sis epidemic model in which the epidemic pathway is decided by the traffic of nodes in community structure networks. it is found that the community structure can accelerate the epidemic propagation in the traffic-driven model, which is different from the traditional model. the social network has the property of community structure and some infectious diseases have high mortality rates or long infection period, while the previous studies only consider the impact of one of the aforementioned factors. so in this paper, we study the epidemic spreading in a modified sis epidemic model with birth and death of individuals on a community structure network. the rest of this paper is organized as follows. in sect. , we introduce in detail the network model and epidemic spreading process, and discuss the network characteristics either. in sect. , mean-field theory is utilized to analyze the spreading properties of the modified sis epidemic model. sect. gives some numerical and simulations which support the theoretical analysis. at last, sect. concludes the paper. as there exists the phenomena of the individual's birth and death in real networks, the topology of the network changes over time. we consider undirected and unweighted graphs in this paper. the generating algorithm of the network with community structure can be summarized as follows: we assume that each site of this network is empty or occupied by only one individual. ) the probability to have a link between the individuals (non-empty sites) in the same community is p i . ) we create a link between two nodes (non-empty sites) belonging to different communities with probability p e . ) every site has its own state and may change with the evolution of epidemic. in each time step, susceptible individuals and infected individuals may respectively die with probability α and β, meanwhile, the corresponding site becomes empty, and the links of these sites are broken. ) for each empty site, a susceptible individual may be born with probability b, and then it create links with other individuals with probability p i in the same community or p e belonging to different communities. suppose the initial number of edges is k, then we have: the state transition rules of the transmission process are schematically shown in fig. . all the sites of the network are described as parameters: e, s or i, which respectively represent the empty states, susceptible individual occupations and infected individual occupations. the specific process are as follows: an empty site can give birth to a healthy individual at rate b; a healthy individual can be infected by contacting with infected neighbors at rate λ or die at rate α (due to other reasons); an infected individual can be cured at rate γ or die at rate β (on account of the disease). when an individual dies, this site becomes empty. in general, β>α, and all parameters above are non-negative. fig. the schematic diagram of state transition rules an important measurement for community structure networks is the modularity coefficient [ ] . it is defined as follows: where ij e denotes the proportion of edges between community i and j in the total network edges. so ii e and ij j e ∑ can be described as follows: where k represents the total edge number. thus, for our model the modularity coefficient is: therefore, for the given parameters of m, i n and k, combining eqs. ( ) and ( ), we can adjust the values of i p and p e to get community structure networks with various modularity q. for the network has time-varying topology, it is necessary to characterize the network's characteristics. we plot the curves of average degree 〈k〉, average path length l and average clustering coefficient c of networks changing with time. in fig. , the lateral axis denotes time step, a time step is equal to one second. according to the statistics of birth and death rates of our country in recent years, we can approximately assume that the birth rate . b = and the natural death rate = . . α for different infectious diseases have different mortality rate and the mortality rate is affected by many factors (such as the region and personal habit), so we set the disease death rate in addition, the network size is . as shown in fig. , the larger the network's link number k is, the higher the clustering coefficient c is, and the smaller the average path length l is. and the statistical property values remain unchanged with small β. this is because isolated nodes are not easily generated when the disease death rate is sufficiently small. the simulation results are averaged over simulations. let parameters s, i represent the density of healthy individuals and infected individuals of the entire network. s i , i i are respectively the density of the susceptible and infected nodes within community i. based on the classical sis model [ ] , we establish a modified sis epidemic model considering the characteristic of community structure. in addition, the circumstances of node's birth and death are taken into consideration either in this model. therefore, this epidemic model can be established as follows: in eq. therefore, eqs. ( ) and ( ) can be written as: let d d s t = and d d i t = , we get two steady state solutions: for the first solution, the jacobin matrix is: the determinant and the trace of j are: ( ) if > j , then tr < j , and the solution is stable. then we can get the critical value: for the second solution, the jacobin matrix is: ( ) where a is the same as above. clearly, if ( )( ) when c λ λ > , the second solution is stable, and the disease will diffuse in the network, otherwise the disease will die out. from eq. ( ), we find that the threshold value is governed byα, β and b in a given network. in this section, we make a set of monte-carlo simulations on n-node networks to find the relationships between epidemic size and different parameters, such as modularity coefficient, death rate, birth rate and total edge number. the following simulation results are averaged over configurations with different set of random numbers i n (i= , ,…, m). and for each configuration, simulations are taken with one randomly chosen seed node initially. fig. shows the time evolution curves of epidemic size, where β equals to , . and . respectively. some related parameters are n= , m= , k= , q= . , λ= . , b= . , α= . . it is shown that when β≠ , the epidemic size increases to a peak value then decays to tend a stable value, otherwise the epidemic size keeps increase and finally reach a steady state. the existence of disease death rate can prevent the spread of the disease by decreasing the infected fraction directly. the maximum prevalence of epidemic spreading without considering nodes' disease deaths is the largest. in addition, larger β corresponds to smaller stable epidemic size, which agrees well with the reality. fig. shows the critical epidemic value decreases with the increase of birth rate, while the epidemic prevalence increases with the increase of birth rate. the arrows in fig. indicate the theoretic epidemic threshold calculated through eq. ( ) . eq. ( ) clearly shows that the birth rate is inversely proportional to the critical value, which is consistent with the simulation results in fig. . in real life, with the increase of birth rate, the density of whole population and healthy proportion increases, which makes it easier for infectious disease to diffuse. next, we plot the curves to indicate the influence of two kinds of death rates (natural death rate α and disease death rate β) on the epidemic threshold and average disease prevalence. the arrows in fig. and indicate the theoretic epidemic threshold. fig. , β constantly equal to . . for some infectious diseases, such as acquired immune deficiency syndrome (aids), it is necessary to consider the situation of individuals' natural deaths. from fig. , we find that the existence of natural death rate α is conducive to prevent the spread of the disease, and the increase of threshold and decrease of epidemic size are expected with the increase of α. individuals' natural death decreases the density of total population, thus restrains the propagation of epidemic. the arrows in fig. indicate the theoretic epidemic threshold. fig. shows the effect of the existence of individuals' death caused by disease on epidemic threshold. the related parameters are b= . , q= . , k= , and α= . . by comparisons, it is found that the epidemic threshold increases with the growing of β, while the epidemic size decreases with the growing of β. the existing of disease deaths can rapidly reduce the number of infected individual in populations, thus the existence of disease death rate can inhibits the epidemic spreading. in fig. , we study the effects of both modularity coefficient q and the edge number of network k on the epidemic threshold. larger k represents that the individuals in network are linked more closely. it is found that the epidemic threshold decreases with the increase of the modularity coefficient of the network, and the epidemic size of the network with higher modularity coefficient is larger around the epidemic threshold, while the inverse situation occurs when the infection rate is far greater than the threshold. fig. the relationship between i∞ and λ with different modularity coefficient q and edge number k this is because the infectious disease is mainly transmitted within the community, and when the propagation rate is sufficiently, the infectious disease spreads throughout the network through the edges between communities. the edge density of network with higher modularity coefficient is small, this is not conducive to the spread between communities, thereby reducing the spreading size of the entire network. in addition, the epidemic threshold has inverse correlation with the total edge number k. this is consistent with the real network circumstances. considering the circumstances of node's birth and death that may exist in real networks, a modified epidemic model based on the classical sis model is proposed in a community structure network. an approximate formula for the epidemic threshold is obtained by mathematical analysis to find the relative relationships between different parameters. then the stability of endemic equilibrium is analyzed. the simulations in this study illustrate that the epidemic threshold λ increases with the increase of the death rate (natural death or disease death), while it decreases with the increase of the birth rate, modularity coefficient and edge number. through this study, it is helpful to predict the spreading trend of some infectious diseases that may cause the deaths of individuals (such as ebola and h n ) more accurately than ever before. collective dynamics of 'small-world' networks emergence of scaling in random networks epidemic dynamics and endemic states in complex networks the spread of disease with birth and death on networks spreading of persistent infections in heterogeneous populations staged progression model for epidemic spread on homogeneous and heterogeneous networks global attractivity of a network-based epidemic sis model with nonlinear infectivity epidemic spreading on contact networks with adaptive weights proceedings of the rd international conference on image and signal processing (icisp' ) photoocr: reading text in uncontrolled conditions characterize energy impact of concurrent network-intensive applications on mobile platforms iodetector: a generic service for indoor outdoor detection the case for vm-based cloudlets in mobile computing community structure in social and biological networks epidemic spreading in community networks epidemic spreading in scale-free networks with community structure how community structure influences epidemic spread in social networks community structure in social networks: applications for epidemiological modeling a stochastic sir epidemic on scale-free network with community structure epidemic spreading on complex networks with community structure epidemic spreading in weighted scale-free networks with community structure traffic driven epidemic spreading in homogeneous networks with community structure finding and evaluating community structure in networks epidemic outbreaks in two-scale community networks this work was supported by the national natural science key: cord- - pbg ldm authors: hota, ashish r.; gupta, kavish title: a generalized sis epidemic model on temporal networks with asymptomatic carriers and comments on decay ratio date: - - journal: nan doi: nan sha: doc_id: cord_uid: pbg ldm we study the class of sis epidemics on temporal networks and propose a new activity-driven and adaptive epidemic model that captures the impact of asymptomatic and infectious individuals in the network. in the proposed model, referred to as the a-siys epidemic, each node can be in three possible states: susceptible, infected without symptoms or asymptomatic and infected with symptoms or symptomatic. both asymptomatic and symptomatic individuals are infectious. we show that the proposed a-siys epidemic captures several well-established epidemic models as special cases and obtain sufficient conditions under which the disease gets eradicated by resorting to mean-field approximations. in addition, we highlight a potential inaccuracy in the derivation of the upper bound on the decay ratio in the activity-driven adaptive sis (a-sis) model in (ogura et. al., ) and present a more general version of their result. we numerically illustrate the evolution of the fraction of infected nodes in the a-sis epidemic model and show that the bound in (ogura et. al., ) often fails to capture the behavior of the epidemic in contrast with our results. the susceptible-infected-susceptible (sis) epidemic is one of the most well-studied class of spreading processes on networks [ ] , [ ] . early work on sis epidemics focused on analyzing both deterministic [ ] and stochastic [ ] , [ ] dynamic evolution of the epidemic states; often resorting to mean-field approximations for analytical tractability. most of the existing work has analyzed the epidemic dynamics on static networks; both deterministic as well as large-scale complex networks with a structured population [ ] , [ ] . however, the contact pattern in the human population is dynamic and time-varying. furthermore, during the prevalence of an infectious disease, individuals often take precautions and reduce their social activities to protect themselves and others from becoming infected. thus, the characteristics of the network or contact pattern evolves in a time-scale that is comparable to the evolution of the epidemic. consequently, several recent works have analyzed epidemic processes on temporal or dynamical networks [ ] - [ ] . in this work, we consider the class of sis epidemics within the activity-driven network paradigm which is a relatively simple yet expressive paradigm for analyzing the evolution of epidemics and contact pattern in a comparable time-scale [ ] , [ ] . our work is motivated by and builds upon the recent works [ ] , [ ] that study sis epidemics and their close variants on activity-driven networks. specifically, [ ] defines the discrete-time activity-driven adaptive-sis model bound on the decay ratio of the infection probabilities of the nodes and proposes tractable optimization problems for optimal containment of the epidemic by minimizing the bound on the decay ratio. similarly, in [ ] , the authors study a continuous-time sais epidemic with an additional state that captures individuals who are alert and protect themselves from the epidemic. the authors derive conditions for epidemic persistence and investigate optimal policies to mitigate the epidemic by reducing activation probabilities of infected nodes and prompting self-protective behavior. our work is motivated by infectious diseases where a subset of infected individuals do not develop symptoms despite being infectious, i.e., they act as asymptomatic carriers; examples include covid- [ ] , [ ] and ebola [ ] . such individuals are often not aware of being infected and do not reduce their activity and contact patterns. as a result, such diseases are often challenging to contain. however, the above characteristic is not captured by the classical sis epidemic model and its well-established variants that have additional states such as alert, exposed, etc. while recent papers [ ] , [ ] have highlighted the impacts of such asymptomatic carriers on the evolution and control of epidemics, rigorous and quantitative analysis of the above characteristic are few in the existing work on epidemics (on temporal networks). in this paper, we propose a new activity-driven and adaptive generalized sis epidemic model, referred to as the a-siys epidemic, where we treat asymptomatic and symptomatic individuals as distinct infection states (see section ii for a formal definition and discussion). our model captures several well-established epidemic models as special cases. furthermore, in our setting, each node potentially chooses a different number of nodes to connect to; this is in contrast with the homogeneity assumption in [ ] , [ ] . we derive a linearized dynamics that upper bounds the markovian evolution of the epidemic states via a meanfield approximation and present sufficient conditions under which the epidemic gets eradicated. our results and proof techniques are inspired by the analysis in [ ] . as a second contribution, we highlight a potential inaccuracy in the derivation of the upper bound on the decay ratio of the a-sis epidemic model in [ ] and obtain a counterpart of their result for a more general setting where nodes choose different numbers of other nodes to connect to (section iii). we then simulate the epidemic models for various parameter settings and show that the bound obtained in [ ] does not always capture the behavior of the epidemic, in contrast with our results (section iv). we conclude with a discussion on open problems and avenues for future research (section v). in this section, we formally define the activity-driven adaptive siys (a-siys) epidemic model. let v = {v , v , . . . , v n } denote the set of n nodes. each node remains in one of the three possible states: susceptible (s), infected without symptoms or asymptomatic (x) and infected with symptoms or symptomatic (y). both asymptomatic and symptomatic individuals are infectious, which captures the characteristics of certain epidemics such as covid- . the states evolve in discrete-time. if at time t ∈ { , , . . .}, node v i is susceptible (respectively, asymptomatic and symptomatic), we denote this by v i (t) ∈ s (respectively, v i (t) ∈ x and v i (t) ∈ y). given a network or contact pattern, the probabilistic state evolution is defined below. definition : let β x , β y , δ x , δ y , ν ∈ [ , ] be constants pertaining to infection, recovery and transition rates. the state of each node v i evolves as follows. ) if v i (t) ∈ s, then v i (t + ) ∈ x with probability β x for each asymptomatic neighbor and with probability β y for each symptomatic neighbor independently of other neighbors. then v i (t + ) ∈ s with probability δ y . the state remains unchanged otherwise. the possible transitions of the states are illustrated in figure . thus, in our model, both asymptomatic and symptomatic nodes can potentially infect a susceptible node, albeit with different probabilities (β x and β y , respectively). upon being infected, a susceptible node becomes asymptomatic. from there on, it can either get cured and become susceptible with probability δ x , and if not, it transitions to the symptomatic state with probability ν. thus ν − captures the delay in onset of symptoms. the curing rate for symptomatic nodes is δ y . thus, in our model, a node can get infected and cured without ever exhibiting symptoms. with the above definition in place, we now formally define the activity-driven and state-dependent evolution of the network or contact pattern and the epidemic states of individual nodes. as discussed above, our model builds upon the formulation in [ ] for the a-sis epidemic model. definition : for each node v i ∈ v, let a i , χ i , π i ∈ ( , ] be constants referred to as the activity rate, adaptation factor and acceptance rate of v i , respectively. let m i ≥ be the number of nodes v i attempts to connect to upon activation. let β x , β y , δ x , δ y , ν ∈ [ , ] be constants pertaining to infection and recovery rates. the a-siys model is defined by the following procedures: ) at the initial time t = , each node is in one of the three possible states. ) at each time t = , , . . ., each node v i randomly becomes activated independently of other nodes with the following probability: ) node v i , upon activation, randomly and uniformly chooses m i other nodes independently of other activated nodes. if v j is chosen by v i , an edge (v i , v j ) is created with the following probability: these edges are discarded at time t + . ) once the edges are formed following the above procedure, the states of the nodes get updated following definition . ) steps - are repeated for each time t ≥ . thus, for node activation and link formation, susceptible and asymptomatic (who are not aware of being infected) nodes behave in an identical manner. when χ i ∈ ( , ), the probability of node v i getting activated when it is symptomatic is smaller than its activation probability when it is susceptible or asymptomatic. this is potentially due to sickness or reduction of activities by v i so as to not infect others when it learns that it is infected. similarly, a symptomatic node is less likely to accept an edge compared to a susceptible or asymptomatic node. remark : the a-siys epidemic defined above is quite general and captures the following models as special cases. in this case, the nodes never enter the symptomatic state, and the activation and acceptance rates no longer state-dependent; the latter parameters are a i and , respectively. thus, the epidemic behaves as the classical sis epidemic on an activity-driven network (but non-adaptive). ) β x = , δ x = : here, an asymptomatic node is not infectious and eventually becomes symptomatic before becoming susceptible. in this regime, our model is the activity-driven and adaptive analogue of the seis epidemic [ ] with x being the "exposed" state. in order to analyze the evolution of the states in the a-siys epidemic model, we define random variables since a node can only be in one of three possible states, we have exists at time t. we also denote by n x a bernoulli random variable that takes value with probability x ∈ [ , ]. the state transition of v i under the a-siys epidemic model can now be formally stated as: it is easy to see that s i (t + ) the quantities x i (t) and y i (t) are defined in an analogous manner. note that the infection states follow a markov process with a n × n transition probability matrix with the state s i (t) = for all v i ∈ v (i.e., the disease-free state) being the only absorbing state. while analyzing the behavior of this model is computationally intractable, we rely on a meanfield approximation and upper bound the evolution of the infection probability (both asymptomatic and symptomatic) via a linear dynamics. we then derive sufficient conditions under which the epidemic decays to the disease-free state. we start with the following result. theorem : consider the activity-driven adaptive siys (a-siys) epidemic model defined in definition . letm i = m i /(n − ), and for all i, j, define the constants then, for all nodes v i and t ≥ with δ c x = − δ x . proof: we compute expectation on both sides of ( b) and ( c) and obtain and for the product term in the r.h.s. of ( a), the weierstrass product inequality yields consequently, we have we now focus on evaluating the expectation terms in the above equation. recall that a ij (t) is a random variable that indicates the presence of the edge (v i , v j ) at time t and is governed by the states of nodes v i and v j according to definition . in order to bound the expectation terms, we introduce the following notation for events of interest: chooses v j as neighbor at t." ( ) with the above notation in place, we have we now focus on the first equation above and note that since the event sx t ij states that v i is susceptible and v j is infected without symptoms, according to definition , the adaptation and acceptance of node v j is same as the case when it is susceptible. therefore, we have ]. the event sy t ij corresponds to v i being susceptible and v j being infected with symptoms. therefore, the adaptation and acceptance of v j depend on the parameters χ j and π j , respectively. therefore, following definition , we have p(Γ t i→j |sy t ij ) = a imi π j , p(Γ t j→i |sy t ij ) = χ j a jmj . finally, we note that . substituting the above bounds and the expressions for the conditional probabilities obtained in ( ), we obtain the result now follows upon substituting the above expressions in ( ) and the definition of β ij x and β ij y . the above result shows that the evolution of the probability of a node being asymptomatic and symptomatic is upper bounded by a linear dynamics as stated in ( ) . the linearized dynamics can be stated in a compact manner as follows. let z(t) := [x(t) y(t) ] ∈ [ , ] n be the vector of probabilities corresponding to the infected states. from the above theorem, we have where each sub-matrix has dimension n × n. specifically, a xx has diagonal entries ( −δ x )( −ν) and (i, j)-th entry as β ij x for j = i, a xy has diagonal entries and β ij y as the (i, j)th entry with j = i, a yx := diag(( − δ x )ν), and a yy := diag( −δ y ). consequently, we obtain a sufficient condition, stated below, under which the disease is eradicated. the proof follows from the above discussion and standard arguments and is omitted in the interest of space. note further that a is a non-negative irreducible (since each node can potentially choose any other node to connect to) matrix. thus, ρ(a) corresponds to its largest eigenvalue which is real and positive following the perron-forbenius theorem [ ] . we now state the following corollaries of the above results that correspond to certain special cases of our model. furthermore, α ≤ ρ(a xx ). the above setting corresponds to the classical sis epidemic on an activity-driven network discussed in remark . note from the definition of β ij x that the matrix a xx consists of a diagonal matrix and a matrix of rank , and consequently, its spectral radius can be explicitly derived. when symptomatic individuals completely stop interacting with others, we have the following corollary. corollary : suppose χ i = and π i = for all the nodes. then, β ij y = and we have where n×n has all entries equal to . the bound on the decay ratio is given by α ≤ max( − δ y , ρ(a xx )). the above regime corresponds to situations where symptomatic individuals are kept in strict isolation. our analysis shows that even when the decay ratio pertaining to interaction among nodes (corresponding to ρ(a xx )) is small, the epidemic eradication rate (dominated by − δ y ) can be slow if the recovery rate δ y is sufficiently small. as discussed earlier, the proposed model and the above analysis is motivated by and builds upon the activity-driven adaptive sis (a-sis) epidemic proposed in [ ] . in the following section, we highlight a potential inaccuracy in the derivation of the upper bound on the decay ratio in [ ] . the activity-driven a-sis epidemic is not a special case of the a-siys epidemic studied above, but is closely related. in the a-sis epidemic defined in [ ] , a node v i is either susceptible or infected. a susceptible node becomes infected with probability β ∈ [ , ] when it comes in contact with an infected node (independently of other infected nodes) and an infected node recovers with probability δ ∈ [ , ]. thus, the state transition is a special case of definition when ν = , δ x = δ and β x = β and x denoting the infected state. the models differ in the activity-driven adaptive network formation process. while the a-siys epidemic distinguishes between asymptomatic and symptomatic infections, the a-sis epidemic does not. specifically, upon infection, node v i adjusts its activation and acceptance probabilities with the factors χ i and π i , respectively as shown in points and in definition . furthermore, each node upon activation chooses m other nodes to connect to, i.e., m i = m for all v i ∈ v. the rest of the steps are identical to those in definition . we follow the terminology in [ ] and model the state of node v i at time t as a random variable similarly, we define p i (t) := p(v i is infected at time t) and the vector of infection probabilities for all nodes as p(t). the authors in [ ] define decay ratio as follows. we define the decay ratio of the activity-driven a-sis model by α = inf{γ : there exists c > such that ||p(t)|| ≤ cγ t for all t ≥ and x( )}. the quantity α captures the persistence of infection among the nodes. in the a-sis model, the states follow a markov process and the actual decay ratio is the spectral radius of the n × n transition probability matrix. the authors in [ ] upper bound the evolution of p i (t) by a linear dynamics and obtain an explicit upper bound on the decay ratio by noting that it is the spectral radius of a matrix of rank . however, we believe that the derivation of the linearized dynamics in proposition . in [ ] is inaccurate. we start our discussion by first stating proposition . from [ ] . proposition (proposition . [ ] ): letm = m/(n − ), δ c = − δ, and for all i, define the constants then, for all nodes v i and t ≥ . the proof of proposition . in [ ] follows largely analogous steps as the proof of theorem above; the main distinction being the absence of terms related to y j (t) in [ ] . we believe that the evaluation of p(Γ t i→j |Ξ t i,j ) in equation ( . ) in the proof in [ ] is inaccurate. note that Ξ t i,j := "v i is susceptible and v j is infected at time t", in equation ( . ) in [ ] and Γ t i→j is as defined in ( ) above. thus, p(Γ t i→j |Ξ t i,j ) is the probability that the edge (v i , v j ) will be formed when initiated by the activated node v i when v i is susceptible and v j is infected. thus, p(Γ t i→j |Ξ t i,j ) is the product of p(v i is activated while it is susceptible) and p((v i , v j ) are neighbors when v j is infected). following the definition of the a-sis epidemic, we have since v j is infected at time due to the conditioning event Ξ t i,j , the probability of such an edge being formed ismπ j notmπ i as considered in [ ] . in other words, the probability that the edge (v i , v j ) will be formed when initiated by the activated node v i depends on the acceptance rate of the node v j . strengthening equation ( . ) in [ ] when i = j: the authors claim that the inequality trivially holds when i = j. in fact, the event Ξ t i,i = "v i is susceptible and v i is infected at time t" is empty and as a result p(Ξ t i,i ) = . therefore, the bound can be strengthened by treating the above potential inaccuracy has significant implication on the bound derived in theorem . in [ ] . specifically, the authors build upon proposition . and show that the vector of infection probabilities evolves as where i n is the identity matrix and n is the vector of dimension n with all entries being . the authors then argue that the spectral radius of f, denoted ρ(f), is an upper bound on the decay ratio with ρ(f) = − δ + βρ( n n − ( n − ψ)( n − φ) ). since n n − ( n − ψ)( n − φ) is a matrix of rank , the authors could obtain an explicit expression on its spectral radius and consequently on the bound on the decay ratio. however, due to the potential inaccuracy highlighted above, the linear dynamics that bounds the evolution of the vector of infection probabilities is not necessarily a lower-ranked matrix. furthermore, the contributions related to optimal resource allocation for containing the epidemic rely on the bound on the decay ratio and may no longer be applicable. we now state the following theorem that addresses the above inaccuracy and generalizes the result in [ ] . theorem : consider a generalization of the activitydriven a-sis model where node v i , upon activation, chooses uniformly and randomly m i other nodes to connect to. let m i = m i /(n − ), and for all i, j, define the constants then, for all nodes v i and t ≥ . furthermore, the decay ratio is upper bounded as α ≤ ρ * := ρ(f * ) or the spectral radius of the matrix f * with entries in particular, if m i = m for every node v i , then the result holds with φ i = χ i a im and ψ ij = a im π j wherē m = m/(n − ). the proof largely mirrors the proof of theorem and the analysis in [ ] with the above discussed aspects incorporated. we omit it in the interest of space. remark : the upper bound on the decay ratio as shown above is the spectral radius of an n × n matrix. while f * has a larger dimension than the case shown in [ ] , it is still a considerable improvement over the n × n matrix that characterizes the exact decay ratio. from the perron-frobenius theorem, the spectral radius also coincides with the largest eigenvalue of f. we further note that the results in [ ] continues to hold if the acceptance rate is homogeneous across all the nodes, i.e., π i = π, ∀v i ∈ v. in this section, we illustrate the evolution of the epidemic states in both a-siys and a-sis epidemic models. we first show the impact of asymptomatic carriers on the epidemic prevalence in the a-siys epidemic. example : we consider a set of n = nodes and for each node set the rate of infection β x = β y = . , rate of recovery δ x = δ y = . , activity rate = . , adaptation factor = . , acceptance rate = . and degree m = . we initialize with nodes being susceptible, nodes being asymptomatic and nodes being symptomatic and simulate the a-siys epidemic till time steps and independent runs. we show the evolution of the fraction of susceptible, asymptomatic and symptomatic nodes averaged over runs in figure for three different values of the transition rate ν = . , . , . . the upper bound on the decay ratio for these settings are . , . , . , respectively. recall that ν captures the rate at which asymptomatic nodes become symptomatic. given the above parameters, the adaptation and acceptance rates are negligible for symptomatic nodes. therefore, as ν increases, we anticipate that nodes remain asymptomatic for a much shorter period of time and consequently the decay ratio will be small. for small values of ν, nodes tend to remain asymptomatic for a longer period of time during which they continue to activate and connect at the same rate as a susceptible node; consequently, the epidemic sustains in the population. figure shows that our model captures the above phenomenon. we now numerically illustrate that the bound obtained in theorem above better captures the evolution of the epidemic (fraction of infected population) compared to the bound on the decay ratio obtained in [ ] which we denote by ρ p . we consider two settings; one where ρ p is smaller than ρ * and second where ρ p is larger than ρ * as described in the following two examples, respectively. example : we consider a set of n = nodes and set the infection rate β = . , recovery rate δ = . and m = . we assume that out of nodes have activity rate a i = . , adaptation factor χ i = . and acceptance rate π i = . . for the remaining nodes, we choose a i = . and π i = . and vary the adaptation parameter which results in varying values of ρ * and ρ p . we initialize with nodes being infected and nodes being susceptible and simulate the a-sis epidemic. the average fraction of infected nodes across the independent runs for a duration of time steps is reported in figure . the bounds ρ * and ρ p are shown in the titles of the plots. if at a given point of time (before the maximum time-step ), all nodes are susceptible (i.e., the underlying markov chain has reached the disease-free absorbing state) then the simulation ends. the plot on the top left panel of figure corresponds to the case with χ i = . for the second group of nodes and shows that the epidemic sustains in the population. for other cases, the bounds are smaller and it results in the states reaching the disease-free absorbing state of the dynamics. we also plot the histogram of the time the simulation ends for χ i = . and χ i = . (for the second group of nodes) over the runs in the right panel of figure . we note that for these two cases, the epidemic sustains in the population despite the upper bound on the decay ratio obtained in [ ] being smaller than . in contrast, when ρ * < (bottom left panel), the epidemic reaches the absorbing state in less than iterations in all the independent runs. the above example shows that the epidemic sustains in the population even when ρ p < (but ρ * > ). in the following example, we consider parameters with ρ * < ρ p and show that the epidemic reaches the disease-free state much faster when ρ * is close to even when ρ p is relatively large. we consider a similar setting as above with a set of n = nodes and set the rate of infection β = . , the rate of recovery δ = . and m = . we assume that out of nodes have activity rate a i = . , adaptation factor χ i = . and acceptance rate π i = . . for the remaining nodes, we choose a i = . and π i = . and vary the adaptation parameter (three values with χ i = . , . and . ) which results in varying values of ρ * and ρ p . we initialize with all nodes being infected and simulate the a-sis epidemic times. the average fraction of infected nodes across the independent runs for a duration of time steps and the histogram of the time the simulation ends are shown in the top and bottom panel of figure , respectively. as the bounds increase, the epidemic sustains for a longer time period. however, despite a relatively large value of ρ p (but with ρ * closer to ), the epidemic does not sustain for the entire duration in all the simulations. a stark contrast in results can be observed in the top left panel of figure and the top right panel of figure ; in the former, the epidemic sustains for ρ p = . while in the latter it reaches the disease-free state in most runs even when ρ p = . . to summarize, in both the examples considered above, the bound ρ * derived in our work better captures the evolution of the a-sis epidemic. in this paper, we propose a new activity-driven adaptive epidemic model that includes asymptomatic carriers present in several infectious diseases. in the proposed model, symptomatic individuals reduce their activation and acceptance probabilities while asymptomatic individuals do not, potentially because they are not aware of being infected. we show that the proposed model captures several existing epidemic models as special cases. we derive a linearized dynamics that upper bounds the exact markovian evolution by resorting to a mean-field approximation. we also highlight a potential inaccuracy in the upper bound on the decay ratio derived in [ ] for the a-sis epidemic model and generalize their results. the simulation results illustrate that the bound derived in our work better captures the evolution of the a-sis epidemic compared to the bound obtained in [ ] . our work is an early attempt to develop an epidemic model with asymptomatic carriers on temporal networks. there are several promising avenues for future research in this context. the condition based on the decay ratio is only sufficient to guarantee that the disease is quickly eradicated from the population. in contrast, in the classical sis epidemic model, when the decay ratio is larger than , there exists a unique endemic state that serves as an equilibrium of the meanfield dynamics. while we conjecture that the a-sis and a-siys epidemic models would have a similar behavior, an analogous result has not yet been formally established. similarly, developing scalable centralized and decentralized protection schemes for containing the epidemic in large-scale networks in presence of asymptomatic carriers is yet another challenging open problem. optimal containment of epidemics over temporal activity-driven networks the mathematics of infectious diseases epidemic processes in complex networks on the dynamics of deterministic epidemic propagation over networks virus spread in networks stability of spreading processes over time-varying large-scale networks epidemic processes over timevarying networks optimal containment of epidemics in temporal and adaptive networks temporal network epidemiology epidemics on dynamic networks toward epidemic thresholds on temporal networks: a review and open questions activity driven modeling of time varying networks an analytical framework for the study of epidemic models on activity driven networks on assessing control actions for epidemic models on temporal networks clinical characteristics of asymptomatic infections with covid- screened among close contacts in nanjing, china the time scale of asymptomatic transmission affects estimates of epidemic potential in the covid- outbreak ebola control: effect of asymptomatic infection and acquired immunity public health policy: covid- epidemic and seir model with asymptomatic viral carriers implications of asymptomatic carriers for infectious disease transmission and control matrix analysis key: cord- -i v u authors: wang, zhen; andrews, michael a.; wu, zhi-xi; wang, lin; bauch, chris t. title: coupled disease–behavior dynamics on complex networks: a review date: - - journal: phys life rev doi: . /j.plrev. . . sha: doc_id: cord_uid: i v u it is increasingly recognized that a key component of successful infection control efforts is understanding the complex, two-way interaction between disease dynamics and human behavioral and social dynamics. human behavior such as contact precautions and social distancing clearly influence disease prevalence, but disease prevalence can in turn alter human behavior, forming a coupled, nonlinear system. moreover, in many cases, the spatial structure of the population cannot be ignored, such that social and behavioral processes and/or transmission of infection must be represented with complex networks. research on studying coupled disease–behavior dynamics in complex networks in particular is growing rapidly, and frequently makes use of analysis methods and concepts from statistical physics. here, we review some of the growing literature in this area. we contrast network-based approaches to homogeneous-mixing approaches, point out how their predictions differ, and describe the rich and often surprising behavior of disease–behavior dynamics on complex networks, and compare them to processes in statistical physics. we discuss how these models can capture the dynamics that characterize many real-world scenarios, thereby suggesting ways that policy makers can better design effective prevention strategies. we also describe the growing sources of digital data that are facilitating research in this area. finally, we suggest pitfalls which might be faced by researchers in the field, and we suggest several ways in which the field could move forward in the coming years. infectious diseases have long caused enormous morbidity and mortality in human populations. one of the most devastating examples is the black death, which killed to million people in the medieval period [ ] . currently, the rapid spread of infectious diseases still imposes a considerable burden [ ] . to elucidate transmission processes of infectious diseases, mathematical modeling has become a fruitful framework [ ] . in the classical modeling framework, a homogeneously mixed population can be classified into several compartments according to disease status. in particular, the most common compartments are those that contain susceptible individuals (s), infectious (or infected) individuals (i), and recovered (and immune) individuals (r). using these states, systems of ordinary differential equations (odes) can be created to capture the evolution of diseases with different natural histories. for example, a disease with no immunity where susceptible individuals who become infected return to the susceptible class after recovering (sis natural history, see fig. where [s] ([i ]) represents the number of susceptible (infectious) individuals in the population, β is the transmission rate of the disease, and μ is the recovery rate of infected individuals. some diseases, however, may give immunity to individuals who have recovered from infection (sir natural history, see fig. where [r] is the number of recovered (and immune) individuals. in these ode models, a general measure of disease severity is the basic reproductive number r = βn/μ, where n is the population size. in simple terms, r is the mean number of secondary infections caused by a single infectious individual, during its entire infectious period, in an otherwise susceptible population [ ] . if r < , the disease will not survive in the population. however, if r > , the disease may be able to persist. typically, parameters like the transmission rate and recovery rate are treated as fixed. however, new approaches to modeling have been developed in past few decades to address some of the limitations of the classic differential equation framework that stem from its simplifying assumptions. for instance, the impact of behavioral changes in response to an epidemic is usually ignored in these formulations (e.g., the transmission rate is fixed), but in reality, individuals usually change their behavior during an outbreak according to the change of perceived infection risk, and their behavioral decisions can in turn impact the transmission of infection. another limitation of the classical compartmental models is the assumption of well-mixed populations (namely, individuals interact with all others at the same contact rate), which thus neglects heterogeneous spatial contact patterns that can arise in realistic populations. in this review we will describe how models of the past few decades have begun to address these limitations of the classic framework. traditionally, infectious disease models have treated human behavior as a fixed phenomenon that does not respond to disease dynamics or any other natural dynamics. for many research questions, this is a useful and acceptable simplification. however, in other cases, human behavior responds to disease dynamics, and in turn disease dynamics responds to human behavior. for example, the initiation of an epidemic may cause a flood of awareness in the population such that protective measures are adopted. this in turn, reduces the transmission of the disease. in such cases, it becomes possible to speak of a single, coupled "disease-behavior" system where a human subsystem and a disease schematic illustration of disease-behavior interactions as a negative feedback loop. in this example, the loop from disease dynamics to behavioral dynamics is positive (+) since an increase in disease prevalence will cause an increase in perceived risk and thus an increase in protective behaviors. the loop from behavioral dynamics back to disease dynamics is negative (−) since an increase in protective behaviors such as contact precautions and social distancing will generally suppress disease prevalence. transmission subsystem are coupled to one another (see fig. ). moreover, because the human and natural subsystems are themselves typically nonlinear, the coupled system is therefore also typically nonlinear. this means that phenomena can emerge that cannot be predicted by considering each subsystem in isolation. for example, protective behavior on the part of humans may ebb and flow according to disease incidence and according to a characteristic timescale (as opposed to being constant over time, as would occur in the uncoupled subsystems). to explore strategic interactions between individual behaviors, game theory has become a key tool across many disciplines. it provides a unified framework for decision-making, where the participating players in a conflict must make strategy choices that potentially affect the interest of other players. game theory and its corresponding equilibrium concepts, such as the nash equilibrium, emerged in seminal works from the s and s [ , ] . a nash equilibrium is a set of strategies such that no player has an incentive to unilaterally deviate from the present strategy. that is, the nash equilibrium makes strategies form best responses to one other, since every player, who has a consistent goal to maximize his own benefit or utility, is perfectly rational. game theory has been applied to fields such as economics, biology, mathematics, public health, ecology, traffic engineering, and computer science [ ] [ ] [ ] [ ] [ ] [ ] . for example, in voluntary vaccination programs, the formal theory of games can be employed as a framework to analyze the vaccination equilibrium level in populations [ , , ] . in the context of vaccination, the feedback between individual decisions of vaccination (or other prevention behaviors) and disease spreading is captured, hence these systems exemplify coupled disease-behavior systems. in spite of the great progress of game theory, the classical paradigm still shows its limitations in many scenarios. it thus becomes instructive to relax some key assumptions, such as the introduction of bounded rationality. game theory has been extended into evolutionary biology, which has generated great insight into the evolution of strategies [ ] [ ] [ ] [ ] [ ] under both biological and cultural evolution. for instance, the replicator equation, which consists of sets of differential equations describing how the strategies of a population evolve over time under selective pressures, has also been used to study learning in various scenarios [ ] . except for temporal concepts, spatial interaction topology has also proved to be crucial in determining system equilibria (also see refs. [ , ] for a comprehensive overview). evolutionary game theory has been extensively applied to behavioral epidemiology, whose details will be surveyed in the following sections. several methods from statistical physics have become useful in the study of disease-behavior interactions on complex networks. most populations are spatially structured in the sense that individuals preferentially interact with those who share close geographic proximity. perhaps, the most simple population structure is a regular lattice: all the agents are assigned specific locations on it, normally a two-dimensional square lattice, just like atoms in crystal lattice sites, which interact with only nearest neighbors. in a regular lattice population, each individual meets the same people they interact with regularly, rather than being randomly reshuffled into a homogeneous mixture, as in well-mixed population models. in addition, another type of homogeneous network attracting great research interest is the erdös-rényi (er) graph [ ] , which is a graph where nodes are linked up randomly and which is often used in the rigorous analysis of graphs and networks. however, in reality, there is ubiquitous heterogeneity in the number of contacts per individual, and recent studies have shown that the distribution of contact numbers of some social networks is not homogeneous but appears to follow a power-law [ ] . moreover, social contact networks also display small-world properties (i.e., short average path length between any two individuals and strong local clustering tendency), which cannot be well described by regular lattices or random graphs [ ] . with both motivations, two significant milestones were born in the late s: the theoretical models of small-world (sw) networks and scale-free (sf) networks [ , ] . subsequently, more properties of social networks have been extensively investigated, such as community structure (a kind of assortative structure where individuals are divided into groups such that the members within each group are mostly connected with each other) [ ] , clusters [ ] , and the recent proposal of multilayer as well as time-varying frameworks [ ] [ ] [ ] [ ] [ ] . due to the broad applicability of complex networks, network models have been widely employed in epidemiology to study the spread of infectious diseases [ ] . in networks, a vertex represents an individual and an edge between two vertices represents a contact over which disease transmission may occur. an epidemic spreads through the network from infected to susceptible vertices. with the advent of various network algorithms, it becomes instructive incorporating disease dynamics into such infrastructures to explore the impact of spatial contact patterns [ ] [ ] [ ] [ ] [ ] [ ] . replacing the homogeneous mixing hypothesis that any individual can come into contact with any other agents, networked epidemic research assumes that each individual has comparable number of contacts, denoted by its degree k. under this treatment, the most significant physics finding is that network topology will directly determine the threshold of epidemic outbreak and phase transition. for example, compared with the finite epidemic threshold of random network, romualdo et al. found that disease with sis dynamics and even a very small transmission rate can spread and persist in the sf networks (i.e., there is absence of a disease threshold) [ ] . this point helps to explain why it is extremely difficult to eradicate viruses on internet and world wide web, and why those viruses have an unusual long lifetime. but the absence of epidemic threshold is only suitable for sf networks with a power-law degree distribution p (k) ∼ k −γ with γ ∈ ( , ]. if γ is extended to the range ( , ) , an anomalous critical behavior takes place [ , ] . to show the condition of disease spread, it is meaningful to define the relative spreading rate λ ≡ β/μ. the larger is λ, the more likely the disease will spread. generally, for an sf network with arbitrary degree distribution, the epidemic threshold is in particular, for an sf network k diverges in the n → ∞ limit, and so the epidemic threshold is expected to die out. similarly, it is easy to derive the threshold of sir model which is related with average degree k and the second moment k of networks as well. along these findings, more endeavors are devoted to the epidemic threshold of spatial networks with various properties, such as degree correlation [ , ] , sw topology [ ] , community structure [ ] , and k-core [ ] . on the other hand, more analysis and prediction methods (such as mean-field method, generation function) are also proposed to explain the transition of disease on realistic networks [ , ] and immunization strategies of spatial networks are largely identified [ ] . to illustrate the meaning of studying disease-behavior dynamics on complex networks, it is instructive to firstly describe a simple example of such a system. consider a population of individuals who are aware of a spreading epidemic. the information each individual receives regarding the disease status of others is derived from the underlying social network of the population. these networks have been shown to display heterogeneous contact patterns, where the node degree distribution often follows a power-law fashion [ , ] . it is possible to use these complex network patterns to model a realistic population that exhibits adaptive self-protective behavior in the presence of a disease. a common way to incorporate this self-protective behavior is to allow individuals to lower their susceptibility according to the proportion of their contacts that are infectious, as demonstrated by bagnoli et al. [ ] . in this model, the authors reduce the susceptibility of an individual to a disease which has a simple sis natural history by multiplying the transmission rate by a negative exponential function of the proportion of their neighbors who are infectious. specifically, this is given by βi (ψ, k) where β is the per contact transmission probability and models the effect an individual's risk perception has on its susceptibility, where j and τ are constants that govern the level of precaution individuals take, ψ is the number of infectious contacts an individual has, and k is the total number of contacts an individual has. the authors show that the introduction of adaptive behavior has the potential to not only reduce the probabilities of new infections occurring in highly disease-concentrated areas, but can also cause epidemics to go extinct. specifically, when τ = , there is a value of j for which an epidemic can be stopped in regular lattices and sw networks [ ] . however, for certain sf networks, there is no value of j that is able to stop the disease from spreading. in order to achieve disease extinction in these networks, hub nodes must adopt additional self-protective measure, which is accomplished by decreasing τ for these individuals. the conclusions derived from this model highlight the significant impact different types of complex networks can have on health outcomes in a population, and how behavioral changes can dictate the course of an epidemic. the remainder of this review is organized as follows. in section , we will focus on the disease-behavior dynamics of homogeneously mixed populations, and discuss when the homogeneous mixing approximation is or is not valid. this provides a comprehensive prologue to the overview of the coupled systems on networks in section . within the latter, we separately review dynamics in different types of networked populations, which are frequently viewed through the lens of physical phenomena (such as phase transitions and pattern formation) and analyzed with physicsbased methods (like monte carlo simulation, mean-field prediction). based on all these achievements, we can capture how coupled disease-behavior dynamics affects disease transmission and spatial contact patterns. section will be devoted to empirical concerns, such as types of data that can be used for these study systems, and how questionnaires and digital equipment can be used to collect data on relevant social and contact networks. in addition, it is meaningful to examine whether some social behaviors predicted by models really exist in vaccination experiments and surveys. finally, we will conclude with a summary and an outlook in section , describing the implications of statistical physics of spatial disease-behavior dynamics and outlining viable directions for future research. throughout, we will generally focus on preventive measures other than vaccination (such as social distancing and hand washing), although we will also touch upon vaccination in a few places. a large body of literature addresses disease-behavior dynamics in populations that are assumed to be mixing homogeneously, and thus spatial structure can be neglected. incorporating adaptive behavior into a model of disease spread can provide important insight into population health outcomes, as the activation of social distancing and other nonpharmaceutical interventions (npis) have been observed to have the ability to alter the course of an epidemic [ ] [ ] [ ] . table disease-behavior models applied to well-mixed populations, classified by infection type and whether economic-based or rule-based. when making decisions regarding self-protection from an infection, individuals must gather information relevant to the disease status of others in the population. prophylactic behavior can be driven by disease prevalence, imitation of others around them, or personal beliefs of probable health outcomes. in this section, we will survey the features and results of mathematical models that incorporate prophylactic decision making behavior in homogeneously mixed populations. the approaches we consider can be classified into two separate categories: economic-based and rulebased. economic based models (such as game theoretical models) assume individuals seek a maximization of their social utility, whereas rule-based models prescribe prevalence-based rules (not explicitly based on utility) according to which individuals and populations behave. both of these methods can also be used to study the dynamics of similar diseases (see table ), and are discussed in detail below. the discovery of human immunodeficiency virus (hiv)/acquired immune deficiency syndrome (aids) and its large economic impacts stimulated research into behaviorally based mathematical models of sexually transmitted diseases (stds). in disease-behavior models, a population often initiates a behavior change in response to an increasing prevalence of a disease. in the context of stds, this change in behavior may include safer sex practices, or a reduction in the number of partnerships individuals seek out. following this prevalence-based decision making principle, researchers have used the concept of utility maximization to study the behavior dynamics of a population [ ] [ ] [ ] [ ] [ ] . in these models, individuals seek to maximize their utility by solving dynamic optimization problems. utility is derived by members of the population when engaging in increased levels of social contact. however, this increased contact or partner change rate also increases the chance of becoming infected. one consequence of this dynamic is that higher levels of prevalence can result in increased prophylactic behavior, which in turn decreases the prevalence over time. as this occurs, self-protective measures used by the population will also fall, which may cause disease cycles [ , ] . nonetheless, in the case of stds which share similar transmission pathways, a population protecting themselves from one disease by reducing contact rates can also indirectly protect themselves from another disease simultaneously [ ] . in general, the lowering of contact rates in response to an epidemic can reduce its size, and also delay new infections [ ] . however, this observed reduction of contact rates may not be uniform across the whole population. for example, an increase in prevalence may cause the activity rates of those with already low social interaction to fall even further, but this effect may not hold true for those with high activity rates [ ] . in fact, the high-risk members of the population will gain a larger fraction of high-risk partners in this scenario, resulting from the low-risk members reducing their social interaction rates. this dynamic serves to increase the risk of infection of high activity individuals even further. these utility-based economic models show us that when considering health outcomes, one must be acutely aware of the welfare costs associated with self-protective behavior or implementing disease mitigation policies [ ] . a health policy, such as encouraging infectious individuals to self-quarantine, may actually cause a rise in disease prevalence due to susceptible individuals feeling less threatened by infection and subsequently abandoning their own self-protective behavior [ ] . also, a population who is given a pessimistic outlook of an epidemic may in fact cause the disease to spread more rapidly [ ] . recently, approaches using game theory have been applied to self-protective behavior and social distancing [ ] [ ] [ ] . when an individual's risk of becoming infected only depends on their personal investment into social distancing, prophylactic behavior is not initiated until after an epidemic begins, and ceases before an epidemic ends. also, the basic reproductive number of a disease must exceed a certain threshold for individuals to feel self-protective behavior is worth the effort [ ] . in scenarios where the contact rate of the population increases with the number of people out in public, a nash equilibrium exists, but the level of self-protective behavior in it is not socially optimal [ ] . nonetheless, these models also show that the activation of social distancing can weaken an epidemic. some models of disease-behavior dynamics, rather than assuming humans are attempting to optimize a utility function, represent human behavior by specifying rules that humans follow under certain conditions. these could include both phenomenological rules describing phenomenological responses to changes in prevalence, or more complex psychological mechanisms. rule-based compartmental models using systems of differential equations have also used to study heterogeneous behavior and the use of npis by a population during an epidemic. a wide range of diseases are modeled using this approach, such as hiv [ ] [ ] [ ] , severe acute respiratory syndrome (sars) [ , ] , or influenza [ , ] . these models often utilize additional compartments, which are populated according to specific rules. examples of such rules are to construct the compartments to hold a constant amount of individuals associated with certain contact rates [ , , ] , or to add and remove individuals at a constant rate [ , , , ] , a rate depending on prevalence [ ] [ ] [ ] [ ] [ ] [ ] , or according to a framework where behavior that is more successful is imitated by others [ , , ] . extra compartments signify behavioral heterogeneities amongst members of a population, and the disease transmission rates associated with them also vary. reduction in transmission due to adaptive behavior is either modeled as a quarantine of cases [ , , ] , or prophylactic behavior of susceptible individuals due to increased awareness of the disease [ , , [ ] [ ] [ ] [ ] [ ] [ ] ] . these models agree that early activation of isolation measures and selfprotective behavior can weaken an epidemic. however, due to an early decrease in new infections, populations may see a subsequent decrease in npi use causing multiple waves of infection [ , , , ] . contrasting opinions on the impact behavioral changes have on the epidemic threshold also result from these models. for example, perra et al. [ ] show that although infection size is reduced, prophylactic behavior does not alter the epidemic threshold. however, the models studied by poletti et al. [ ] and sahneh et al. [ ] show that the epidemic threshold can be altered by behavioral changes in a population. the classes of models presented in this section use homogeneous mixing patterns (i.e., well-mixed populations) to study the effects of adaptive behavior in response to epidemics and disease spread (see table for a summary). often, populations will be modeled to alter their behavior based on reactions to changes in disease prevalence, or by optimizing their choices with respect to personal health outcomes. if possible, early activation of prophylactic behavior and npis by a population will be the most effective course of action to curb an epidemic. homogeneous mixing can be an appropriate approximation for the spread of an epidemic when the disease to be modeled is easily transmitted, such as measles and other infection that can be spread by fine aerosol particles that remain suspended for a long period. however, this mixing assumption does not always reflect real disease dynamics. for example, human sexual contact patterns are believed to be heterogeneous [ ] and can be represented as networks (or graphs), while other infections, such as sars, can only be spread by large droplets, making the homogeneous mixing assumption less valid. the literature surrounding epidemic models that address this limitation by incorporating heterogeneous contact patterns through networks is very rich, and is discussed in the following section. in section , we reviewed disease-behavior dynamics in well-mixed populations. however, in real populations, various types of complex networks are ubiquitous and their dynamics have been well studied. the transmission of many infectious diseases requires direct or close contact between individuals, suggesting that complex networks play a vital role in diffusion of disease. it thus becomes of particular significance to review the development of behavioral epidemiology in networked populations. many of the dynamics exhibited by such systems have direct analogues to processes in statistical physics, such as how disease or behavior percolate through the network, or how a population can undergo a phase transition from one social state to another social state. perhaps the easiest way to begin studying disease-behavior dynamics in spatially distributed populations is by using lattices and static networks, which are relatively easy to analyze and which have attracted much attention in theoretical and empirical research. we organize research by several themes under which they have been conducted, such as the role of spreading awareness, social distancing as protection, and the role of imitation, although we emphasize that the distinctions are not always "hard and fast". the role of individual awareness. the awareness of disease outbreaks may stimulate humans to change their behavior, such as washing hands and wearing masks. such behavioral responses can reduce susceptibility to infection, which itself in turn can influence the epidemic course. in the seminal work, funk and coworkers [ ] formulated and analyzed a mathematical model for the spread of awareness in well-mixed and spatially structured populations to understand how the awareness of disease and also its propagation impact the spatial spread of a disease. in their model, both disease and the information about the disease spread spontaneously by, respectively, contact and word of mouth in the population. the classical epidemiological sir model is used for epidemic spreading, and the information dynamics is governed by both information transmission and information fading. the immediate outcome of the awareness of the disease information is the decrease in the possibility of acquiring the infectious disease when a susceptible individual (who was aware of the epidemic) contacts with an infected one. in a well-mixed population, the authors found that, the coupling spreading dynamics of both the epidemic and the awareness of it can result in a lower size of the outbreak, yet it does not affect the epidemic threshold. however, in a population located on the triangular lattice, the behavioral response can completely stop a disease from spreading, provided the infection rate is below a threshold. specifically, the authors showed that the impact of locally spreading awareness is amplified if the social network of potential infection events and the communication network over which individuals communicate overlap, especially so if the networks have a high level of clustering. the finding that spatial structure can prevent an epidemic is echoed in an earlier model where the effects of awareness are limited to the immediate neighbors of infected nodes on a network [ ] . in the model, individuals choose whether to accept ring vaccination depending on perceived disease risk due to infected neighbors. by exploring a range of network structures from the limit of homogeneous mixing to the limit of a static, random network with small neighborhood size, the authors show that it is easier to eradicate infections in spatially structured populations than in homogeneously mixing populations [ ] . hence, free-riding on vaccine-generated herd immunity may be less of a problem for infectious diseases spreading spatially structured populations, such as would more closely describe the situation for close contact infections. along similar lines of research, wu et al. explored the impact of three forms of awareness on the epidemic spreading in a finite sf networked population [ ] : contact awareness that increases with individual contact number; local awareness that increases with the fraction of infected contacts; and global awareness that increases with the overall disease prevalence. they found that the global awareness cannot decrease the likelihood of an epidemic outbreak while both the local awareness and the contact awareness do it. generally, individual awareness of an epidemic contributes toward the inhibition of its transmission. the universality of such conclusions (i.e., individual behavioral responses suppress epidemic spreading) is also supported by a recent model [ ] , in which the authors focused on an epidemic response model where the individuals respond to the epidemic according to, rather than the density of infected nodes, the number of infected neighbors in the local neighborhood. mathematically, the local behavioral response is cast into the reduction factor ( − θ) ψ in the contact rate of a susceptible node, where ψ is the number of infected neighbors and θ < is a parameter characterizing the response strength of the individuals to the epidemic. by studying both sis and sir epidemiological models with the behavioral response rule in sf networks, they found that individual behavioral response can in general suppress epidemic spreading, due to crucial role played by the hub nodes who are more likely to adopt protective response to block the disease spreading path. in a somewhat different framework, how the diffusion of individual's crisis awareness affects the epidemic spreading is investigated in ref. [ ] . in this work, the epidemiological sir model is linked with an information transmission process, whose diffusion dynamics is characterized by two parameters, say, the information creation rate ζ and the information sensitivity η. in particular, at each time step, ζ n packets will be generated and transferred in the network according to the shortest-path routing algorithm (n hither denotes the size of networks). when a packet is routed by an infected individual, its state is marked by infection. each individual determines whether or not to accept vaccine based on how many infected packets are received from immediate neighbors, and on how sensitive the individual response is to the information as well, weighed by the parameter η. the authors considered their "sir with information-driven vaccination" model on homogeneous er networks and heterogeneous sf networks, and found that the epidemic spreading can be significantly suppressed in both the homogeneous and heterogeneous networks provided that both ζ and η are relatively large. social distancing as a protection mechanism. infectious disease outbreaks may trigger various behavioral responses of individuals to take preventive measures, one of which is social distancing. valdez and coworkers have investigated the efficiency of social distancing in altering the epidemic dynamics and affecting the disease transmission process on er network, sf networks, as well as realistic social networks [ ] . in their model, rather than the normally used link-rewiring process, an intermittent social distancing strategy is adopted to disturb the epidemic spreading process. particularly, based on local information, a susceptible individual is allowed to interrupt the contact with an infected individual with a probability σ and restore it after a fixed time t b , such that the underlying interaction network of the individuals remains unchanged. using the framework of percolation theory, the authors found that there exists a cutoff threshold σ c , whose value depends on the network topology (i.e., the extent of heterogeneity of the degree distribution), beyond which the epidemic phase disappears. the efficiency of the intermittent social distancing strategy in stopping the spread of diseases is owing to the emergent "susceptible herd behavior" among the population that protects a large fraction of susceptible individuals. impact of behavior imitation on vaccination coverage. vaccination is widely employed as an infection control measure. to explore the role of individual imitation behavior and population structure in vaccination, recent seminal work integrated an epidemiological process into a simple agent-based model of adaptive learning, where individuals use anecdotal evidence to estimate costs and benefits of vaccination [ ] . under such a model, the disease-behavior dynamics is modeled as a two-stage process. the first stage is a public vaccination campaign, which occurs before any epidemic spreading. at this stage, each individual decides whether or not to vaccinate, and taking vaccine incurs a cost c v to the vaccinated individuals. the vaccine is risk-free and offers perfect protection against infection. the second stage is the disease transmission process, where the classic sir compartmental model is adopted. during the whole epidemic spreading process, those susceptible individuals who caught the disease incur an infection cost c i , which is usually assumed to be larger than the cost c v for vaccination. those unvaccinated individuals who remain healthy are free-riding off the vaccination efforts of others (i.e., no any cost), and they are indirectly protected by herd immunity. for simplicity, the authors rescale these costs by defining the relative cost of vaccination c = c v /c i ( < c < ) and c i = . as such, after each epidemic season, all the individuals will get some payoffs (equal to the negative value of corresponding costs) dependent on their vaccination strategies and also on whether they are infected or not, then they are allowed to change or keep their old strategies for the next season, depending on their current payoffs. the rule of thumb is that the strategy of a role model with higher payoff is more likely to be imitated. by doing so, each individual i randomly chooses another individual j from the neighborhood as role model, and imitates the behavior of j with the probability where p i and p j are, respectively, the payoffs of two involved individuals, and β ( < β < ∞) denotes the strength of selection. this form of decision alternative is also known as the fermi law [ , ] in physics. a finite value of β accounts for the fact that better performing individuals are readily imitated, although it is not impossible to imitate one agent performing worse, for example due to imperfect information or errors in decision making. the authors studied their coupled "disease-behavior" model in well-mixed populations, in square lattice populations, in random network populations, and in sf network populations, and found that population structure acts as a "double-edged sword" for public health: it can promote high levels of voluntary vaccination and herd immunity given that the cost for vaccination is not too large, but small increases in the cost beyond a certain threshold would cause vaccination to plummet, and infections to rise, more dramatically than in well-mixed populations. this research provides an example of how spatial structure does not always improve the chances of infection control, in disease-behavior systems. the symbols and lines correspond, respectively, to the simulation results and mean-field predictions (whose analytical framework is shown in appendix a). the parameter α determines just how seriously the peer pressure is considered in the decision making process of the individuals to taking vaccine. the figure is reproduced from [ ] . in the similar vein, peer pressure among the populations is considered to clarify its impact on the decision-making process of vaccination, and then on the disease spreading [ ] . in reality, whether or not to change behavior depends not only on the personal success of each individual, but also on the success and/or behavior of others. using this as motivation, the authors incorporated the impact of peer pressure into a susceptible-vaccinated-infected-recovered (svir) epidemiological model, where the propensity to adopt a particular vaccination strategy depends both on individual success as well as on the strategy-configuration of their neighbors. to be specific, the behavior imitation probability of individual i towards its immediate neighbor j (namely, eq. ( )) becomes where n i is the number of neighbors that have a different vaccination strategy than the individual i, and k i is the interaction degree of i, and the parameter α determines just how seriously the peer pressure is considered. under such a scenario, fig. displays how vaccination and infection vary as a function of vaccine cost in er random graph. it is clear that plugging into the peer pressure also works as a "double-edged sword", which, on the one hand, strongly promotes vaccine uptake in the population when its cost is below a critical value, but, on the other hand, it may also strongly impede it if the critical value is exceeded. the reason is due to the fact that the presence of peer-pressure can facilitate cluster formation among the individuals, whose behaviors are inclined to conform to the majority of their neighbors, similar to the early report of cooperation behavior [ ] . such behavioral conformity is found to expedite the spread of disease when the relative cost for vaccination is high enough, while promote the vaccine coverage in the opposite case. self-motivated strategies related with vaccination. generally, it is not so much the actual risk of being infected, as the perceived risk of infection, that will prompt humans to change their vaccination behavior. previous game-theoretic studies of vaccination behavior typically have often assumed that individuals react to the disease incidence with same responsive dynamics, i.e., the same formulas of calculating the perceived probability of infection. but that may not actually be the case. liu et al. proposed that a few will be "committed" to vaccination, perhaps because they have a low threshold for feeling at risk (or strongly held convictions), and they will want to be immunized as soon as they hear that someone is infected [ ] . they studied how the presence of committed vaccinators, a small fraction of individuals who consistently hold the vaccinating strategy and are immune to influence, impacts the vaccination dynamics in well-mixed and spatially structured populations. the researchers showed that even a relatively small proportion of these agents (such as %) can significantly reduce the scale of an epidemic, as shown in fig. . the effect is much stronger when all the individuals are uniformly distributed on a square lattice, as compared to the case of well-mixed population. their results suggested that those committed individuals can have a remarkable effect, acting as "steadfast role models" in the population to seed vaccine uptake in others while also disrupting the appearance of clusters of free-riders, which might otherwise seed the emergence of a global epidemic. one important message taken away from ref. [ ] is that we might never guess what would happen by just looking at the decision-making rules alone, in particular when our choices will influence, and be influenced by, the choice of other people. another good example can be found in a recent work [ ] , in which zhang et al. proposed an evolutionary epidemic game where individuals can choose their strategies as vaccination, self-protection or laissez faire, towards infectious diseases and adjust their strategies according to their neighbors' strategies and payoffs. the "disease-behavior" coupling dynamical process is similar to the one implemented by ref. [ ] , where the sir epidemic spreading process and the strategy updating process succeed alternatively. by both stochastic simulations and theoretical analysis, the authors found a counter-intuitive phenomenon that a better condition (i.e., larger successful rate of self-protection) may unfortunately result in less system payoff. the trick is that, when the successful rate of self-protection increases, people become more speculative and less interested in vaccination. since a vaccinated individual brings the "externality" effect to the system: the individual's decision to vaccinate diminishes not only its own risk of infection, but also the risk for those people with whom the individual interacts, the reduction of vaccination can remarkably enhance the risk of infection. the observed counter-intuitive phenomenon is reminiscent of the well-known braess's paradox in traffic, where more roads may lead to more severe traffic congestion [ ] . this work provides another interesting example analogous to braess's paradox, namely, a higher successful rate of self-protection may eventually enlarge the epidemic size and thus diminish positive health outcomes. this work raises a challenge to public health agencies regarding how to protect the population during an epidemic. the government should carefully consider how to distribute their resources and money between messages supporting vaccination, hospitalization, self-protection, and so on, since the outcome of policy largely depends on the complex interplay among the type of incentive, individual behavioral responses, and the intrinsic epidemic dynamics. in their further work [ ] , the authors investigated the effects of two types of incentives strategies, partial-subsidy policy in which certain fraction of the cost of vaccination is offset, and free-subsidy policy in which donees are randomly selected and vaccinated at no cost on the epidemic control. through mean-field analysis and computations, they found that, under the partial-subsidy policy, the vaccination coverage depends monotonically on the sensitivity of individuals to payoff difference, but the dependence is non-monotonous for the free-subsidy policy. due to the role models of the donees for relatively irrational individuals and the unchanged strategies of the donees for rational individuals, the free-subsidy policy can in general lead to higher vaccination coverage. these findings substantiate, once again, that any disease-control policy should be exercised with extreme care: its success depends on the complex interplay among the intrinsic mathematical rules of epidemic spreading, governmental policies, and behavioral responses of individuals. as the above subsection shows, research on disease-behavior dynamics on networks has become one of the most fruitful realms of statistical physics and non-linear science, as well as shedding novel light on how to predict the impact of individual behavior on disease spread and prevention [ ] [ ] [ ] , [ ] [ ] [ ] [ ] [ ] ] . however, in some scenarios, the simple hypothesis that individuals are connected to each other in the same infrastructure (namely, the so-called single-layer network in section . ) may generate overestimation or underestimation for the diffusion and prevention of disease, since agents can simultaneously be the elements of more than one network in most, yet not all, empirical systems [ , , ] . in this sense, it seems constructive to go beyond the traditional single-layer network theory and propose a new architecture, which can incorporate the multiple roles or connections of individuals into an integrated framework. the multilayer networks, defined as the combination class of networks interrelated in a nontrivial way (usually by sharing nodes), have recently become a fundamental tool to quantitatively describe the interaction among network layers as well as between these constituents. an example of multilayer networks is visualized in fig. [ ] . a social network layer supports the social dynamics related to individual behavior and main prevention strategies (like vaccination); while the biological layer provides a platform for the spreading of biological disease. each individual is a node in both network layers. the coupled structure can generate more diverse outcomes than either isolated network, and could produce multiple (positive or negative) effects on the eradication of infection. because of the connection between layers, the dynamics of control measures in turn affects the trajectory of disease on biological network, and vice versa. under such a framework, which is composed of at least different topology networks, nodes not only exchange information with their counterparts in other network(s) via inter-layer connections, but also diffuse infection with their neighbors through the intra-layer connections. subsequently, more theoretical algorithms and models, such as interdependent networks, multiplex networks and interconnected networks, have been proposed [ ] [ ] [ ] . the broad applicability of multilayer networks and their success in providing insight into the structure and dynamics of realistic systems have thus generated considerable excitement [ ] [ ] [ ] [ ] [ ] . of course, the study of disease-behavior dynamics in this framework is a young and rapidly evolving research area, which will be systematically surveyed in what follows. interplay between awareness and disease. as fig. illustrates, different dynamical processes for the same set of nodes with different connection topologies for each process can be encapsulated in a multilayer structure (technically, these are referred to as multiplex networks [ , ] ). aiming to explore the interrelation between social awareness and disease spreading, granell et al. recently incorporated information awareness into a disease model embedded in a multiplex network [ ] , where the physical contact layer supports epidemic process and the virtual contact layer supports awareness diffusion. similar to sis model (where the s node can be infected with a transmission probability β, and the i node recovers with a certain rate μ), the awareness dynamics, composed of aware (a) and unaware (u) states, assumes that a node of state a may lose its awareness with probability δ, and re-obtains awareness in the probability ν. then, both processes can be coupled via the combinations of individual states: unaware-susceptible fig. . transition probability trees of the combined states for coupled awareness-disease dynamics each time step in the multilayer networks. here aware (a) state can become unaware (u) with transition probability δ and of course re-obtains awareness with other probability. for disease, μ represents the transition probability from infected (i) to susceptible (s). there are thus four state combinations: aware-infected, (ai) aware-susceptible, (as) unaware-infected, (ui) and unaware-susceptible (us), and the transition of these combinations is controlled by probability r i , q a i and q u i . they respectively denote the transition probability from unaware to aware given by neighbors; transition probability from susceptible to infected, if node is aware, given by neighbors; and transition probability from susceptible to infected, if node is unaware, given by neighbors. we refer to [ ] , from where this figure has been adapted, for further details. (us), aware-susceptible (as), and aware-infected (ai), which are also revealed by the transition probability trees in fig. . using monte carlo simulations, the authors showed that the coupled dynamical processes change the onset of the epidemics and allow them to further capture the evolution of the epidemic threshold (depending on the structure and the interrelation with the awareness process), which can be accurately validated by the markov-chain approximation approach. more interestingly, they unveiled that the increase in transmission rate can lower the long-term disease incidence while raising the outbreak threshold of epidemic. in spite of great progress, the above-mentioned findings are based on two hypotheses: infected nodes become immediately aware, and aware individuals are completely immune to the infection. to capture more realistic scenarios, the authors relaxed both assumptions and introduced mass media that disseminates information to the entire system [ ] . they found that the vaccine coverage of aware individuals and the mass media affect the critical relation between two competing processes. more importantly, the existence of mass media makes the metacritical point (where the critical onset of the epidemics starts) of ref. [ ] disappear. furthermore, the social dynamics are further extended to an awareness cascade model [ ] , during which agents exhibit herd-like behavior because they make decisions referring to the actions of other individuals. interestingly, it is found that a local awareness ratio (of unaware individuals becoming aware ones) approximating . has a two-stage effect on the epidemic threshold (i.e., an abrupt transition of epidemic threshold) and can cause different epidemic sizes, irrespective of the network structure. that is to say, when the local awareness ratio is in the range of [ , . ), the epidemic threshold is a fixed and larger value; however, in the range of [ . , ], threshold value becomes a fixed yet smaller value. as for the final epidemic size, its increasing speed for the interval [ , . ) is much slower than the speed when local awareness ratio lies in [ . , ]. these findings suggest a new way of understanding realistic contagions and their prevention. except for obtaining awareness from aware neighbors, self-awareness induced by infected neighbors is another scenario that currently attracts research attention [ ] , where it is found that coupling such a dynamical process with disease spreading can lower the density of infection, but does not increase the epidemic threshold regardless of the information source. coupling between disease and preventive behaviors. thus far, many achievements have shown that considering simultaneous diffusion of disease and prevention measures on the same single-layer network is an effective method to evaluate the incidence and onset of disease [ , , [ ] [ ] [ ] [ ] , ] . however, if both processes are coupled on the multilayer infrastructure, how does it affect the spreading and prevention of disease? inspired by this interesting question, ref. [ ] suggested a conceptual framework, where two fully or partially coupled networks are employed, to transmit disease (an infection layer) and to channel individual decision of prevention behaviors (a communication layer). protection strategies considered include wearing facemasks, washing hands frequently, taking pharmaceutical drugs, and avoiding contact with sick people, which are the only means of control in situations where vaccines are not yet available. it is found that the structure of the infection network, rather than the communication network, has a dramatic influence on the transmission of disease and uptake of protective measures. in particular, during an influenza epidemic, the coupled model can lead to a lower infection rates, which indicates that single-layer models may overestimate disease transmission. in line with this finding, the author further extended the above setup into a triple coupled diffusion model (adding the information flow of disease on a new layer) through metropolitan social networks [ ] . during an epidemic, these three diffusion dynamics interact with each other and form negative and positive feedback loop. compared with the empirical data, it is exhibited that this proposed model reasonably replicates the realistic trends of influenza spread and information propagation. the author pointed out that this model possesses the potential of developing into a virtual platform for health decision makers to test the efficiency of disease control measures in real populations. much previous work shows that behavior and spatial structure can suppress epidemic spreading. in contrast, other recent research using a multiplex network consisting of a disease transmission (dt) network and information propagation (ip) network through which vaccination strategy and individual health condition information can be communicated, finds that compared with the case of traditional single-layer network (namely, symmetric interaction), the multiplex architecture suppresses vaccination coverage and leads to more infection [ ] . this phenomenon is caused by the sharp decline of small-degree vaccination nodes, whose number is usually more numerous in heterogeneous networks. similarly, wang et al. considered asymmetrical interplay between disease spreading and information diffusion in multilayer networks [ ] . it is assumed that there exists different disease dynamics on communication layer and physical-contact layer, only where vaccination takes place. more specifically, the vaccination decision of the node in contact networks is not only related to the states of its intra-layer neighbors, but also depends on the counterpart node from communication layer. by means of numerous simulations and mean-field analysis, they found that, for uncorrelated coupling architecture, a disease outbreak in the contact layer induces an outbreak of disease in the communication layer, and information diffusion can effectively raise the epidemic threshold. however, the consideration of inter-layer correlation dramatically changes the onset of disease, but not the information threshold. dynamical networks play an important role in the incidence and onset of epidemics as well. along this line of research, the most commonly used approach is adaptive networks [ ] [ ] [ ] [ ] , where nodes frequently adjust their connections according to the environment or states of neighboring nodes. time-varying networks (also named temporal networks) provide another framework for the activity-driven changing of connection topology [ , , ] . here, we briefly review the progress of disease-behavior dynamics on adaptive and time-varying networks. contact switching as potential protection strategy. in the adaptive viewpoint, the most straightforward method of avoiding contact with infective acquaintances amounts to breaking the links between susceptible and infective agents and constructing novel connections. along such lines, thilo et al. first proposed an adaptive scenario: a susceptible node is able to prune the infected link and rewire with a healthy agent with a certain probability [ ] . the probability of switching can be regarded as a measurement of strength of the protection strategy. it is shown that different values of this probability give rise to various degree mixing patterns and degree distributions. based on the low-dimensional approximations, the authors also showed that their adaptive framework is able to predict novel dynamical features, such as bistability, hysteresis, and first order transitions, which are sufficiently robust against disease dynamics [ , ] . in spite of great advances, the existing analytical methods cannot generally allow for accurate predictions about the simultaneous time evolution of disease and network topology. to overcome this limitation, vincent et al. further introduced an improved compartmental formalism, which proves that the initial conditions play a crucial role in disease spreading [ ] . in the above examples, switching contact as a strategy has proven its effectiveness in controlling epidemic outbreak. however, in some realistic cases, the population information may be asymmetric, especially during the process of rewiring links. to relax this constraint, a new adaptive algorithm was recently suggested: an infection link can be pruned by either individual, who reconnects to a randomly selected member rather than susceptible agent (namely, the individual has no previous information on state of every other agent) [ , ] . for example, ref. [ ] showed that such a reconnection behavior can completely suppress the spreading of disease via continuous and discontinuous transitions, which is universally effective in more complex situations. besides the phenomena of oscillation and bistability, another dynamical feature, epidemic reemergence, also attracts great interest in a current study [ ] , where susceptible individuals adaptively break connections with infected neighbors yet avoid being isolated in a growing network. under such operations, the authors observed that the number fig. . panel (a) denotes the time course for the number of infected nodes when the network growth, the link-removal process, and isolation avoidance are simultaneously involved into the adaptive framework. it is clear that this mechanism creates the reemergence of epidemic, which dies out after several such repetitions. while for this interesting phenomenon, it is closely related with the formation of giant component of susceptible nodes. panel (b) shows the snapshot of the network topology of th time step (before the next abrupt outbreak), when there is a giant component of susceptible nodes (yellow). however, the invasion of the infection individuals (red) makes the whole network split into many fragments, as shown by the snapshot of th time step (after the explosion) in panel (c). we refer to [ ] , from where this figure has been adapted, for further details. (for interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) of infected agents stays at a low level for a long time, and then suddenly erupts to high level before declining to a low level again. this process repeats several times until the final eradication of infection, as illustrated in fig. (a) . with regard to potential mechanism, it is actually related with the invasion of infected individuals to susceptible giant components. link-removal process can suppress disease spreading, which makes susceptible (infected) agents form giant components (small yet non-isolated clusters), as shown in fig. (b) . but, the entrance of new nodes may bring new infection risk to such giant components, which accelerates next outbreak of infection and network crashing again (see fig. (c) ). interestingly, this finding may help to explain the phenomenon of repeated epidemic explosions in real populations. now, if we carefully look back upon the above-cited bibliography, we will find a common feature: except for disease processes, the adaptive adjustment of individual connections finally changes the degree distribution of networks. an interesting question naturally poses itself: is there an adaptive scenario that preserves the degree distribution of networks? that is, each individual has a characteristic behavior: keeping total number of its neighbors constant. to fill up this gap, neighbor exchange model becomes a very useful tool [ ] , where individual number of current neighbors remains fixed while the compositions or entities of those contacts change in time. similar to famous algorithm of watts-strogatz sw network [ ] , such a model allows an exchange mechanism in which the destination nodes of two edges are swapped with a given rate. incorporating the diffusion of epidemic, this model constructs a bridge between static network model and mass-action model. based on the empirical data, the authors further displayed that the application of this model is very effective to forecast and control sexually transmitted disease outbreak. along this way, the potential influence of other topology properties (such as growing networks [ ] and rewiring sf networks [ ] ) has recently been identified in the adaptive viewpoint, which dramatically changes the outbreak threshold of disease. vaccination, immunization and quarantine as avoidance behaviors. as in static networks, vaccination can also be introduced into adaptive architectures, where connection adjustment is an individual response to the presence of infection risk among neighborhoods. motivated by realistic immunization situations, disease prevention is implemented by adding poisson-distributed vaccination to susceptible individuals [ ] . because of the interplay between network rewiring and vaccination application, the authors showed that vaccination is far more effective in an adaptive network than a static one, irrespective of disease dynamics. similarly, some other control measures are further encapsulated into adaptive community networks [ ] . except for various transition of community structure, both immunization and quarantine strategies show a counter-intuitive result that it is not "the earlier, the better" for prevention of disease. moreover, it is unveiled that the prevention efficiency of both measures is greatly different, and the optimal effect is obtained when a strong community structure exists. vaccination on time-varying networks. in contrast to the mutual feedback between dynamics and structure in adaptive frameworks, time-varying networks provide a novel angle for network research, where network connection and fig. . vaccination coverage as a function of the relative cost of vaccination and the fraction of imitators in different networks. it is obvious that for small cost of vaccination, imitation behavior increases vaccination coverage but impedes vaccination at high cost, irrespective of potential interaction topology. the figure is reproduced from [ ] . dynamics process evolve according to their respective rules [ ] [ ] [ ] . for example, summin et al. recently explored how to lower the number of vaccinated people to protect the whole system on time-varying networks [ ] . based on the past information, they could accurately administer vaccination and estimate disease outbreaks in future, which proves that time-varying structure can make protection protocols more efficient. in [ ] , the authors displayed that limited information on the contact patterns is sufficient to design efficient immunization strategies once again. but in these two works, the vaccination strategy is somewhat independent of human behavior and decision-making process, which leaves an open issue: if realistic disease-behavior dynamics is introduced into time-varying topology (especially combining with the diffusion process of opinion cluster [ ] ), how does it affect the eradication of disease? we continue to discuss some of these and similar issues in section on empirically-derived networks. some research uses networks derived from empirical data in order to examine disease-behavior dynamics. we discuss these models in this subsection. dynamics on different topologies. heterogeneous contact topology is ubiquitous in reality. to test its potential impact on disease spreading, martial et al. recently integrated a behavior epidemiology model with decision-making process into three archetypical realistic networks: poisson network, urban network and power law network [ ] . under these contact networks, an agent can make decision either based purely on payoff maximization or via imitating the vaccination behavior of its neighbor (as suggest by eq. ( )), which is controlled by the fraction of imitators . by means of numerous simulations, they displayed the diploid effect of imitation behavior: it enhances vaccination coverage for low vaccination cost, but impedes vaccination campaign at relatively high cost, which is depicted by fig. . surprisingly, in spite of high vaccination coverage, imitation can generate the clusters of non-vaccinating, susceptible agents, which in turn accelerate the large-scale outbreak of infectious disease (namely, imitation behavior, to some extent, impedes the eradication of infectious diseases). this point helps to explain why outbreaks of measles have recently occurred in many countries with high overall vaccination coverage [ , , ] . with the same social networks, ref. [ ] explored the impact of heterogeneous contact patterns on disease outbreak in the compartmental model of sars. it is interesting that, compared with the prediction of well-mixed population, the same set of basic reproductive number may lead to completely epidemiological outcomes in any two processes, which sheds light to the heterogeneity of sars around the world. impact of network mixing patterns. as ref. [ ] discovered, high vaccination coverage can guarantee herd immunity, which, however, is dramatically affected and even destroyed by clusters of unvaccinated individuals. to evaluate how much influence such clusters possess, a recent work explored the distribution of vaccinated agents during seasonal influenza vaccination through a united states high school contact network [ ] . the authors found that contact table classification of disease-behavior research outcomes according to dynamic characteristics in networked populations reviewed by section . it is clear that the same type of networks can be frequently used to different problems. table observed physical phenomena and frequently used methods in the study of diseasebehavior dynamics on networks. epidemic threshold mean-field prediction phase transition generation function self-organization percolation theory pattern formation stochastic processes bifurcation and stability analysis monte carlo simulation vaccination/immunization threshold markov-chain approximation networks are positively assortative with vaccination behavior. that is to say, large-degree unvaccinated (vaccinated) agents are more likely to contact with other large-degree unvaccinated (vaccinated) ones, which certainly results in a larger outbreak than common networks since these (positively assortative) unvaccinated agents breed larger susceptible clusters. this finding highlights the importance of heterogeneity during vaccine uptake for the prevention of infectious disease once again. in fact, the currently growing available human generated data and computing power have driven the fast emergence of various social, technological and biological networks [ ] [ ] [ ] [ ] . upon these empirically networks, mass diseasebehavior models can be considered to analyze the efficiency of existing or novel proposed prevention measures and provide constructive viewpoint for policy makers of public health [ ] [ ] [ ] [ ] [ ] [ ] . based on the above achievements, it is now clear that incorporating behavior epidemiology into networked populations has opened a new window for the study of epidemic transmission and prevention. to capture an overall image, table provides a summary for the reviewed characteristics of disease-behavior dynamics in networked populations. here it is worth mentioning that some works (e.g., [ , ] ) may appear in two categories because they simultaneously consider the influence of individual behavior and special network structure. fig. . age-specific contact matrices for each of eight examined european countries. high contact rates are represented by white color, intermediate contact rates are green and low contact rates are blue. we refer to [ ] , from where this figure has been adapted, for further details. (for interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) many of these achievements are closely related with physics phenomena (see table ), via which we can estimate the effect of the proposed strategies and measures. on the other hand, these achievements are also inseparable from classical physics methods (table ). in particular, monte carlo simulation and mean-field prediction have attracted the greatest attention due to simplicity and high efficiency. for a comprehensive understanding, we provide a general example of mean-field theory about behavioral epidemiology in appendix a. the first mathematical models studied the adaptive dynamics of disease-behavior responses in the homogeneously mixed population, assuming that individuals interact with each other at the same contact rate, without restrictions on selecting potential partners. networked dynamics models shift the focus on the effects of interpersonal connectivity patterns, since everyone has their own set of contacts through which the interpersonal transmission can occur. the contacts between members of a population constitute a network, which is usually described by some well-known proxy model of synthetic networks, as shown in section . this physics treatment of using evidence-based parsimonious models is valuable in illustrating fascinating ideas and revealing unexpected phenomena. however, it is not always a magic bullet for understanding, explaining, or predicting realistic cases. in recent years, the studies of social experiments become more and more popular. they contribute new insight in parameterizing and designing more appropriate dynamics models. this section briefly introduces the progress in this field. a large-scale population-based survey of human contact patterns in eight european countries was conducted in ref. [ ] , which collects the empirical data of self-reported face-to-face conversations and skin-to-skin physical contacts. the data analysis splits the population into subgroups on the basis of properties such as ages and locations, and scrutinizes the contact rate between subgroups (see fig. ). it reveals that across these countries, people are more probable to contact others of the same age group. combining self-reporting contact data with serological testing data, . we refer to [ ] , from where this figure has been adapted, for further details. recent case studies are able to reveal location-or age-specific patterns of exposure to pandemic pathogens [ , ] , which provide rich information for complex network modeling. sf networks have been widely used to model the connectivity heterogeneity in human contact networks. in sf networks, each hub member can have numerous connections, including all its potential contacts relevant to the transmission. however, such common consideration might not fully agree with human physiological limitations regarding the capacity in preserving a large number of interactions. generally, the size of individual social network is restricted to around people [ , ] . to better characterize the features of human contact behavior, social experiments studying the active contacts in realistic circumstances will be valuable. thanks to the development of information and communication technologies, the usage of digital equipments becomes increasingly popular in collecting empirical data relevant to human contacts in realistic social circumstances. it is instructive to first review a few brief examples. refs. [ , ] referred to the bluetooth technique embedded in mobile phones, which collects the proxy data of person-to-person interactions of mit media laboratory in the reality mining program; with the help of wireless sensors, the social experiment was conducted to trace the close proximity contacts among the members of an american high school [ ] ; refs. [ ] [ ] [ ] [ ] considered the active radio frequency identification devices (rfid) to establish a flexible platform recording the face-to-face proximity contacts among volunteers, which had been deployed in various social contexts such as conference, museum, hospital, and primary school; and the wifi accessing data among all students and staffs were also analyzed as the indirect proxy records of their concurrent communications in one chinese university [ , ] . compared with the abovementioned data of questionnaires, the electronic data generated by digital experiments is more accurate and objective. moreover, some new interesting findings are also listed as follows. the data analysis reveals an unexpected feature that the distribution of the number of distinct persons each individual encounters every day only has a small squared coefficient of variance [ , , [ ] [ ] [ ] [ ] , irrespective of the specific social contexts (see fig. ). this homogeneity in the so-called node-degree distribution indicates the absence of connectivity hubs, which is, to some extent, subject to our physiological limitations. the dynamics of human interactions is not evolving at an equilibrium state, but is highly fluctuating and timevarying in realistic situations. this can be characterized by measuring the statistical distribution of the duration per contact and the time intervals between successive contacts [ ] . as shown in fig. , these two statistics both have a broad distribution spanning several orders of magnitude. most contact durations and inter-contact intervals are very short, but long durations and intervals also emerge, which corresponds to a burst process without characteristic time scales [ ] . the coexistence of homogeneity in degree of nodes and heterogeneity in contact durations lead to unexpected phenomena. for example, the low-degree nodes which are insignificant in conventional network models can act as hubs in time-varying networks [ ] . the usage of electronic devices provides an easy and nonintrusive approach for contact tracing, which can help understand health-related behaviors in realistic settings. to measure close proximity interactions between health-care fig. (a) . similar to fig. , each symbol denotes one venue (sfhh denotes sfhh, nice, fr; eswc (eswc ) is eswc ( ), crete, gr; and ps corresponds to primary school, lyon, fr). we refer to [ ] , from where this figure has been adapted, for further details. workers (hcws) and their hand hygiene adherence, polgreen et al. performed experiments by deploying wireless sensor networks in a medical intensive care unit of the university of iowa hospital. they confirmed the effects of peer pressure on improving the hand hygiene participation [ ] , i.e., the proximity of other hcws, can promote the hand hygiene adherence. they also analyzed the role of "superspreader", who has a high frequency in encountering others [ ] . the disease severity increases with hand hygiene noncompliance of such people. except for empirical data of contact networks, social behavior experiments (or surveys) also play an important role in the vaccination campaign and disease spreading, especially combined with the decision-making process. here we will review the recent progress within this realm. role of altruistic behavior. game theory has been extensively used in the study of behavior epidemiology, where individuals are usually assumed to decide vaccination or not based on the principle of maximizing self-interest [ , ] . however, in reality, when people make vaccination decision, do they only consider their own benefit? to test this fundamental assumption, ref. [ ] recently conducted a survey about individual vaccination decisions during the influenza season. the questionnaires, from direct campus survey and internet-based survey, are mainly composed of two items: self-interest ones (the concern about becoming infected) and altruistic ones (the concern about infecting others), as schematically illustrated in fig. . if agents are driven by self-interest, they attempt to minimize their cost associated with vaccination and infection, which gives rise to selfish equilibrium (or the so-called nash equilibrium). by contrary, if individual decision is guided by altruistic motivation, the vaccination probability reaches community optimum (or the so-called utilitarian equilibrium), at which overall cost of the community is minimal. the authors unveiled that altruism plays an important role in vaccination decision, which can be quantitatively measured by "degree of altruism". to further evaluate its impact, they incorporated the empirical data and altruistic motivation into svir compartmental model. interestingly, they found that altruism can shift vaccination decisions from individual self-interest to a community optimum via greatly enhancing total vaccination coverage and reducing the total cost, morbidity and mortality of the whole community, irrespective of parameter setup. along this line, the role of altruistic behavior in age-structure populations was further explored [ ] . according to general experience, elderly people, who are most likely to be infected in the case of influenza, should be most protected by young vaccinators, who are responsible for most disease transmission. to examine under which condition young agents vaccinate to better protect old ones, the authors organized the corresponding social behavior experiment: participants are randomly assigned to "young" and "elderly" roles (with young players contributing more to herd immunity yet elderly players facing higher costs of infection). if players were paid based on individual point totals, more elderly than young players would get vaccinated, which is consistent with the theoretical prediction of fig. . schematic illustration of questionnaire used in the voluntary vaccination survey. the survey items can be divided into self-interest ones (i.e., outcomes-for-self) and altruism ones (i.e., outcomes-for-others), which have corresponding scores. based on both, it becomes possible to indirectly estimate the degree of altruism, which plays a significant role in vaccination uptake and epidemic elimination. we refer to [ ] , from where this figure has been adapted, for further details. self-interested behavior (namely, nash equilibrium). on the contrary, players paid according to the group point totals make decisions in a manner consistent with the utilitarian equilibrium, which predicts community-optimal behavior: more young than elderly players get vaccinated yet less cost. in this sense, payoff structure plays a vital role in the emergence of altruistic behavior, which in turn affects the disease spreading. from both empirically studies, we can observe that altruism significantly impacts vaccination coverage as well as consequent disease burden. it can drive system to reach community optimum, where smallest overall cost guarantees herd immunity. it is thus suggested that in realistic policies altruism should be regarded as one potential strategy to improve public health outcomes. existence of free-riding behavior. accompanying altruistic behavior, another type of behavior addressed within decision-making frameworks is free-riding behavior, which means that people can benefit from the action of others while avoiding any cost [ , , ] . in a voluntary vaccination campaign, free riders are unvaccinated individuals who avoid infection because of herd immunity, as illustrated by the gray nodes in fig. . to explore the impact of free-riding behavior, john et al. even organized a questionnaire containing six different hypothetical scenarios twenty years ago [ ] . under such a survey, altruism and free-riding were simultaneously considered as the potential decision motivations for vaccination. they found that, for vaccine conferring herd immunity, the free-riding frame causes less sensitivity to increase vaccination coverage than does the altruism frame, which means that free-riding lowers preference of vaccination when the proportion of others vaccinating increases. in addition to homogeneous groups of individuals, yoko et al. recently conducted a computerized influenza experiment, where the groups of agents may face completely different conditions, such as infection risk, vaccine cost, severity of influenza and age structure [ ] . they found that high vaccination rate of previous rounds certainly decreases the likelihood of individuals' vaccination acceptance in the following round, indicating the existence of free-riding behavior. both empirical surveys thus showed that individuals' decision-making may be driven by the free-riding motive, which depresses vaccination coverage. besides the above examples, there exist more factors, such as individual cognition [ ] and confidence [ ] , affecting the decision of vaccination in reality. if possible, these factors should be taken into consideration by public policy makers in order to reach the necessary level of vaccination coverage. the growth in online social networks such as twitter in recent years provides a new opportunity to obtain the data on health behaviors in near real-time. using the short text messages (tweets) data collected from twitter between august and january , during which pandemic influenza a (h n ) spread globally, salathé et al. analyzed the spatiotemporal individuals' sentiments towards the novel influenza a (h n ) vaccine [ ] . they found that projected vaccination rates on the basis of sentiments of twitter users can be in good accord with those estimated by the centers for disease control and prevention of united states. they also revealed a critical problem that both negative and positive opinions can be clustered to form network communities. if this can generate clusters of unvaccinated individuals, the risk of disease outbreaks will be largely increased. we have reviewed some of the recent, rapidly expanding research literature concerning nonlinear coupling between disease dynamics and human behavioral dynamics in spatially distributed settings, especially complex networks. generally speaking, these models show that emergent self-protective behavior can dampen an epidemic. this is also what most mean-field models predict. however, in many cases, that is where the commonality in model predictions ends. for populations distributed on a network, the structure of the disease contact network and/or social influence network can fundamentally alter the outcomes, such that different models make very different predictions depending on the assumptions about human population and diseases being studied, including findings that disease-behavior interactions can actually worsen health outcomes by increasing long-term prevalence. also, because network models are individual-based, they can represent processes that are difficult to represent with mean-field (homogeneous mixing) models. for example, the concept of the neighbor of an individual has a natural meaning in a network model, but the meaning is less clear in mean-field models (or partial differential equation models) where populations are described in terms of densities at a point in space. we speculate that the surge of research interest in this area has been fuelled by a combination of ( ) the individual-based description that characterizes network models, ( ) the explosion of available data at the individual level from digital sources, and ( ) the realization from recent experiences with phenomena such as vaccine scares and quarantine failures that human behavior is becoming an increasingly important determinant of disease control efforts. we also discussed how many of the salient dynamics exhibited by disease-behavior systems are directly analogous to processes in statistical physics, such as phase transitions and self-organization. the growth in research has created both opportunities as well as pitfalls. a first potential pitfall is that coupled disease-behavior models are significantly more complicated than simple disease dynamic or behavior dynamic models on their own. for a coupled disease-behavior model, it is necessary not only to have a set of parameters describing the human behavioral dynamics and the disease dynamics separately, it is also possible to have a set of parameters to describe the impact of human behavior on disease dynamics, and another set to describe the effect of disease dynamics on human behavior. thus, approximately speaking, these models have four times as many parameters as a disease dynamic model on its own, or a human behavioral model on its own: they are subject to the "curse of dimensionality". a second pitfall is that relevant research from other fields may not be understood or incorporated in the best possible way. for example, the concept of 'social contagion' appears repeatedly in the literature on coupled disease-behavior models. this is a seductive concept, and it appears to be a natural concept for discussing systems where a disease contagion is also present. however, the metaphor may be too facile. for example, how can the social contagion metaphor capture the subtle but important distinction between descriptive social norms (where individuals follow a morally neutral perception of what others are doing) and injunctive social norms (where individuals follow a morally-laden perception of what others are doing) [ ] ? social contagion may be a useful concept, but we should remember that it ultimately is only a metaphor. a third pitfall is lack of integration between theoretical models and empirical data: this pitfall is common to all mathematical modeling exercises. the second and third pitfalls are an unsurprising consequence of combining natural and human system dynamics in the same framework. there are other potential pitfalls as well. these pitfalls also suggest ways in which we can move the field forward. for example, the complexity of models calls for new methods of analysis. in some cases, methods of rigorous analysis (including physics-based methods such as percolation theory and pair approximations (appendix b))-for sufficiently simple systems that permit such analysis-may provide clearer and more rigorous insights than the output of simulation models, which are often harder to fully understand. for systems that are too complicated for pen-and-paper methods, then methods for visualization of large and multidimensional datasets may prove useful. the second and third pitfalls, where physicists and other modelers, behavioral scientists and epidemiologists do not properly understand one another's fields can be mitigated through more opportunities for interaction between the fields through workshops, seminars and colloquia. interactions between scholars in these fields if often stymied by institutional barriers that emphasize a 'silo' approach to academic, thus, a change in institutional modes of operation could be instrumental in improving collaborations between modelers, behavioral scientists and epidemiologists. scientists have already shown that these pitfalls can be overcome in the growing research in this area, and this is evidence in much of the research we have described in this review. the field of coupled disease-behavior modeling has the elements to suggest that it will continue expanding for the foreseeable future: growing availability of data needed to test empirical models, a rich set of potential dynamics created opportunities to apply various analysis methods from physics, and relevance to pressing problems facing humanity. physicists can play an important role in developing this field due to their long experience in applying modeling methods to physical systems. where [ss] is the number of susceptible-susceptible pairs in the population, q(i | ss) is the expected number of infected neighbors of a susceptible in a susceptible-susceptible pair, and similarly q(i | si ) is the expected number of infected neighbors of the susceptible person in a susceptible-infected pair. the first term corresponding to creation of new si pairs from ss pairs, through infection, while the second term corresponds to destruction of existing si pairs through infection, thereby creating ii pairs. an assumption must be made in order to close the equations at the pair level, thereby preventing writing down equations of motion for triples. for instance, on a random graph, the approximation might be applied, where q(i | s) is the expected number of infected persons neighboring a susceptible person in the population. equations and pair approximations for the other pair 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gratefully yao yao, yang liu, ke-ke huang, yan zhang, eriko fukuda, dr. wen-bo du, dr. ming tang, dr. hai-feng zhang and prof. zhen jin for their constructive helps and discussions, also appreciate all the other friends with whom we maintained (and are currently maintaining) interactions and discussions on the topic covered in our report. this work was partly supported by the national natural science foundation of china (grant no. , , ) and the natural sciences and engineering council of canada (nserc; ma and ctb). whenever the classical epidemic spreading processes (sis, sir) are taking place in homogeneous populations, e.g., individuals are located on the vertices of regular random graph, er random graph, completed connected graph, the qualitative properties of the dynamics can be well catched by the mean-field analysis, assuming unbiased random matching among the individuals. for simplicity yet without loss of generality, we here derive the mean-field solution for the peer-pressure effect in vaccination dynamics on the er random graph as an example [ ] . let x be the fraction of vaccinated individuals and w(x) be the probability that a susceptible individual finally gets infected in a population with vaccine coverage x. after each sir epidemic season, individuals get payoffs: vaccinated (i, p i = −c), unvaccinated and healthy (j , p j = ), and unvaccinated and infected (ς ,p ς = − ). individuals are allowed to modify their vaccination strategies in terms of eq. ( ). whenever an individual from compartment i goes to compartment j or ς , the variable x drops, which can be formulated aswhere above we have approximated, in the spirit of mean-field treatment, the fraction of neighbors holding opposite strategy of the vaccinated individuals as − x. the quantity i→j is the probability that individuals from the compartment i change to the compartment j , whose value is determined by eq. ( ) . accordingly, the gain of x can be written astake the two cases into consideration, the derivative of x with respect to time is written as dx/dt = x + + x − . solving for x, we get the equilibrium vaccination level f v . note that the equilibrium epidemic size is expected to be f i = w(x), satisfying the self-consistent equationwhere r is the basic reproductive number of the epidemic. pair approximation is a method by which space can be implicitly captured in an ordinary differential equation framework [ , ] . to illustrate the method, consider the variable [s], defined as the number of susceptible individuals in a population distributed across a network or a lattice. for an sir natural history, the equation of motion for s is: key: cord- -vov o jx authors: burdet, c.; guégan, j.-f.; duval, x.; le tyrant, m.; bergeron, h.; manuguerra, j.-c.; raude, j.; leport, c.; zylberman, p. title: need for integrative thinking to fight against emerging infectious diseases. proceedings of the th seminar on emerging infectious diseases, march , – current trends and proposals date: - - journal: revue d'Épidémiologie et de santé publique doi: . /j.respe. . . sha: doc_id: cord_uid: vov o jx abstract we present here the proceedings of the th seminar on emerging infectious diseases, held in paris on march nd, , with seven priority proposals that can be outlined as follows: encourage research on the prediction, screening and early detection of new risks of infection; develop research and surveillance concerning transmission of pathogens between animals and humans, with their reinforcement in particular in intertropical areas (“hot-spots”) via public support; pursue aid development and support in these areas of prevention and training for local health personnel, and foster risk awareness in the population; ensure adapted patient care in order to promote adherence to treatment and to epidemic propagation reduction measures; develop greater awareness and better education among politicians and healthcare providers, in order to ensure more adapted response to new types of crises; modify the logic of governance, drawing from all available modes of communication and incorporating new information-sharing tools; develop economic research on the fight against emerging infectious diseases, taking into account specific driving factors in order to create a balance between preventive and curative approaches. the objectives of the th edition of the val de grace school's seminar were to take a global, integrative approach to the emergence of new infectious disease agents, putting these in perspective relative to other types of risk, as well as studying crisis situations and the breaches brought on by the occurrence of emerging infectious diseases (eids). two key conferences respectively opened and closed this annual seminar; the first was given by dr. peter daszak (president of the ecohealth alliance and program director of usaid-ept-predict), the second by dr. patrick lagadec (former research professor at the É cole polytechnique, palaiseau). planned for an anticipated up to participants, this seminar is designed for decision-makers, experts, medical doctors and scientists interested in human and animal health, social sciences, environmental sciences, prospective analysis, biosecurity and defense. this day of presentations and debates is presented under the auspices of the french social affairs and health ministries, as well as that of the environment, energy and marine affairs. peter daszak remarks today can be summed up in two primary messages, both personal and that of scientists from the ecohealth alliance. first, we must increase our research capabilities in order to understand the direct and less-direct causes of emerging infections if we hope to fight them once they become responsible for epidemics or pandemics. secondly, this presentation was illustrated with a few projects concerning the economics of eids which reveal the extraordinary costs they incur for national economies. there is at least one obvious reason to speak of this, which is that politicians and public decisionmakers are in fact quite sensitized when the economic damage engendered by the latest epidemics and pandemics are explained to them. if one takes, for example, the sars-cov pandemic, it led to a to % decrease in gross domestic product in several southeast asian countries, for an estimated overall cost of to billion us dollars, relative to the total number of approximately people worldwide who were affected. the appearance of new eids appears both more frequent and also vaster in terms of number of people affected these last years, many of these diseases appearing in developing or low-income countries. taking the case of the ebola virus (ebov) epidemic which broke out in west africa in , it was much more widespread than any other epidemic to ever occur in central africa ( people affected during an epidemic). it is very difficult in the united states -where peter daszak is working -to get public decision-makers interested, as is true with the population which feels very distant from such problems. ecohealth alliance has tried to draw the media and the public's attention to it, in vain! they only received one single email from the management of the boston airport, informing us that our work on the risk of ebola virus propagation via transcontinental air transport was unfounded and that the boston airport could not experience this type of threat. about a month later, when an american citizen was repatriated for treatment, the public began to panic; the media, particularly the tv channel cnn, exaggerated in broadcasting the issue, and the government took several decisions, notably regarding assistance and monitoring of international airports. these measures were decided upon no scientific basis in a moment of panic, and it seems that with every new worrisome eid, it is the same story! the measures taken are often disproportionate to the seriousness of the phenomenon. human demography has exploded in recent years, and populations today are concentrated in megalopolises. this tendency is even more marked in tropical areas in the south where there is also an important biodiversity of animal species. therefore, there exist today more opportunities for a virus or bacteria to pass from an animal to a human, then to propagate among the human population. international air transport makes possible the spread of these new infectious risks on a vast scale. what are governments doing faced with this type of threat when the demands on the part of the population are ever-increasing? vaccines are also considered by the former as a weapon of total destruction, and by the public as a widely-available miracle tool. neither is truly aware that it takes an average of years to produce a vaccine. also, is it the right strategy in that it banks more on cure than on anticipation? in the u.s., president obama opted for a development aid policy through usaid favoring training and improvement of human and technical capacities to prevent future eids in the most needy countries. the american congress, however, did not follow this path, instead directing funds allocated to usaid towards research on a vaccine for and on epidemic management of the ebola virus crisis. recently, in collaboration with economists, ecohealth alliance modeled the risk of a new emergence in a situation identical to that of ebola in - in west africa, estimating the economic damage caused, and attempted to deduce the economic cost of a health policy based on epidemic management as opposed to one favoring prevention and training. according to their estimates, a budget of billion us dollars seems to suffice to prevent a new epidemic in west africa in opting for the second solution. their simulations obviously include many underlying hypotheses. all the same, this analysis indicates that if we were to quickly make available billion of the billion dollars for the purchase of equipment, the setting up of working laboratories on site, field hospitals, sending doctors and nurses to the area, training of our partners in affected countries -as military medical services know how to do -such a strategy would represent a real capital investment in managing epidemic propagation. unfortunately, this was not the option chosen by u.s. current governments, which we can only regret. now let us discuss the ecology of ebola virus transmission. the bat species pteropus are possibly the host reservoirs of ebola virus. as for the marburg fever virus, we are now certain that these bats are in fact the reservoir. the ebola virus is clearly present in a few giant bat species in africa. it can also circulate among primate species or indirectly through other infected mammals. we also know which species of bats are affected or not. even if the reservoir question is still under debate, we know a great deal about the rainforest circulation of this virus and the circumstances of its spreading in the human population with high-risk groups such as hunters. based on this, is it possible to prevent the virus' transmission to humans? although it poses a complex question, it is nonetheless possible to offer some avenues of reflection. william karesh, vicepresident of ecohealth alliance and instigator of the onehealth concept, carried out a research project in the democratic republic of congo, which consisted in educating villagers, and particularly hunters, regarding the danger of recovering primate corpses from the forest. this program was a real success, as the villagers changed their behavior and the eating of monkey meat. this represents a low-cost prevention approach, which in the end functions well if properly implemented. the only real solution when faced with this type of health threat is to work in conjunction with populations, and to treat questions of poverty, equality, and use and transformation of land together. these are arduous and complex tasks which must be carried out over the long-term. this type of message is extremely difficult to make heard among politicians and the public, and obviously more complex that announcing or clamoring for a vaccine. we are faced with primordial questions which are more or less difficult to answer. are we witnessing an increased frequency of eids appearance? are there more cases today? can we predict patterns, or rules, of emergence? are there geographic areas in which these emerging infections are more frequently or widely observed today? do we possess the scientific ability to predict exactly where the next infectious epidemic will start? evidently, if we were so able we might allocate the financial resources and technical and scientific support to suspected areas. at the moment, we do just the opposite, or we do nothing, and we are disconcerted at each new emergence. in order to convince governing bodies and public decision-makers, we must demonstrate to them that predictive approaches are less costly than curative ones. using approaches inherited from ecology and biogeography ecohealth alliance has adapted the same principles to understanding the ecology and spatial distribution of eid principles observed over the last decades. their work shows that of the nearly new eids which have appeared, the so-called zoonotic ones originating in wild animals have been in net increase in the last years; out of new infections which appear each year originate in wild fauna. what's more, the risk of infectious transmission is highly and doubly correlated with human density, as are these diseases of animal origin to the areas' biodiversity. they called these areas ''hot-spots'' for disease risks, mostly situated in intertropical regions. they are advocating for these specific zones to be those on which they concentrate our research efforts as well as international public aid for development. in fact, it is not only biological diversity in animals which must be taken into account, but also the evolution of natural ecosystems and their disappearance over recent years. deforestation and land use changes by populations are driving forces in the appearance in new eids. therefore, international politicians must better link economic strategies to those of habitat and biodiversity coordination if we wish to avoid new pandemics. in further use of the formalism of economic models, they have shown that a stable political strategy appears once joint simulations were conducted on economic damage due to a pandemic health crisis and preventive decision-making. even though the financial cost of preventive strategies may initially appear great, an optimal solution based on prevention shows itself over the mid-and long-term to be finally less costly than cure and control-focused strategies. we have need on an international level for the equivalent of the intergovernmental panel on climate change (ipcc) which, in the same way as does the ipcc on climate change scenarios and their impact, would concentrate on eids and their sociopolitical, economic and environmental consequences. the american development aid agency usaid did not originally give priority to eids, but the different public health crises brought on by the h n bird flu virus in recent years have led usaid to modify their strategic orientation, notably with regard to the economic weight they bring to bear on regional economies. the fact that these epidemics appear first in countries situated in strongly species-rich intertropical areas which are developing or low-income, requires a reconsideration of our western policies on development aid in order to better include these notions. for ten years, usaid funded a program on new emerging infection threats, for a total of . billion u.s. dollars. at ecohealth alliance we have collaborated with this initiative through participation in the predict research project with funding of to million dollars. the goal of the predict program was to identify microorganisms potentially pathogenic for human populations, and which are hosted in animal reservoirs. we took particular interest in three animal groups, not only because it was impossible to work on all the animal groups present, but also because the three groups we choseprimates, rodents and bats -were recognized as being major reservoirs of agents which are pathogenic for humans. these three groups alone make up % of the world's mammal species. within the predict program we applied our knowledge of the high-risk emergence zones to draw samples from a large cohort of these three animal groups. over the first five years of the program we sampled , animals, trained scientists and medical and administrative personnel, and discovered more than new viruses belonging to families of viruses known not to be infectious to humans. this in itself represents a major finding! obviously, the discovery of a microorganism does not in and of itself indicates that a new eid might appear. their work in mexico on bat species demonstrated the existence of a dozen viruses which are very like the mers-cov responsible for the respiratory syndrome in the middle east. they therefore believe that the mers-cov is not hosted by dromedaries but rather by bats, as they found it in our work in mexico. some of these new coronaviruses may potentially be pathological for humans. it is clearly impossible to identify all viruses present on the planet. it would also be necessary to do the same for bacteria, parasitic fungi, and protozoa. as they are innumerable, it is preferable to make strategic choices regarding microorganism research and that on the highest-risk animal groups. based on our knowledge of currently known viruses in bangladesh bats, they extrapolated this data using species curve rarefaction, and capture-recapture techniques well known to ecologists, to estimate the total number of viruses to be expected in the totality of known mammal species in the world. they reached a value of , new viruses which remain to be discovered. were we to carry out biodiscovery research on these viruses, one could catalogue them, classify them in relation to already-known viruses, in particular those known to be pathogenic to humans, and through comparative genome studies assess their pathogenic potential. we are currently in the second phase of the us predict program, with an important accent on our manner of working. in fact we are currently concentrating more on factors involved in emergence and seek particularly to understand three such factors: habitat change and use, intensive agriculture, and the commerce of biodiversity. us development aid policy also focuses on three strategic areas: north africa, west africa, and continued research activity in saudi arabia. these geographic choices are shaped by recent events around the mers-cov and ebola viruses. especially in the case of mers-cov, dromedaries are certainly involved in the transmission cycle of the virus, but we believe that its true reservoir is the bat. thus using the many data at our disposal, we were able to show that the infectious risk of mers-cov for humans is not great in saudi arabia, but it is in other areas of contact between bat, dromedary and human populations, particularly in the horn of africa, especially in somalia. somalia is currently a politically disjointed country, where public health surveillance and care are greatly lacking or simply non-existent. for example, it is currently impossible to state how many mers-cov cases there are in somalia, or how many might exist. our scientific objectives are therefore to better understand the behaviors at the junction of wild or domestic fauna and human populations. for example, understanding human behaviors and practices at the interface of tropical forests and villages could help us to interpret how zoonotic transmission happens. through acting upon these behaviors and habits, we could lower this type of emerging risk. currently ecohealth alliance has research sites in uganda, malaysia and brazil; they are investigating the role played by habitat changes such as deforestation, human interaction with biodiversity through behavior and use. in manaus in brazil for example, the maximum risk of new infection is not in the heart of the city where the major markets are located, but in the peri-urban areas where agriculture and ranching are developing. these zones which ecologists call ''ecotones'', or transition zones, are located near strongly species-rich regions, with high concentrations of livestock which can come into contact with wild fauna, and which are furthermore inhabited by ranchers and farmers. these regions which are now located everywhere in the intertropical world for the purpose of feeding urban populations, are generally those where new infections appear, and where future pandemics will also most likely appear. at the heart of this research is the priority of understanding behaviors, habits and practices of populations with the goal of changing these factors. this is a long-term endeavor which requires developing approaches in the field for communicating with local populations, and for developing community participation in our own research, which we also consider an excellent means of education. o. borraz recalled the fact that we live in a society of risk. it is not that the dangers surrounding us are more numerous or more fearsome than before, but simply that the notion of risk plays a central role in public policies, in public and private organizational management, and in the controversies around new technologies. genetically modified organisms, mobile phones, nuclear waste, urban sanitation sludge; the activities now considered health or environmental risks are countless. this categorization puts public authorities in a position of having to ensure the safety of populations, even as the state itself sometimes represents a risk factor. it is therefore essential to understand how an activity becomes a risk, and how it is then managed by public authorities as well as by companies, associations and local conglomerates. risk from its identification to its management, from its highlighting to its instrumentalization becomes a tool linked to the emergence and expansion of a welfare state. it is used by politicians to justify on the one hand its lack of involvement in risk management, on the other the seizing of power over sectors from which they had previously disengaged. this political power seizure plays on politicians' selective dissemination within society of risk identification and the knowledge required for its management. two different processes exist by which risk represents an organizing principle for political power, a means to assist and contribute to the definition of the state's limits: ''putting at risk'' and ''regulation through risk''. ''putting at risk'' refers to all processes by which an event is described as or constitutes a real or predicted danger, and which thus is categorized as a risk [ ] . there are many events, objects, and situations which have historically been categorized as ''putting at risk'' and which can be studied by sociologists (illness, divorce, food crises, unemployment, nuclear risk, chemical substances, technological risks. . .). this putting at risk can be a product of the state or of interest groups, under the influence of lobbying. this has been part of the organization of modern societies since the th century, and in particular following world war ii with the expansion of the welfare state which took advantage of different factors putting the population at risk in order to enlarge its sphere of activity and thus its power in the name of a protective mission. this welfare state built itself around risk management in creating and organizing agencies, action plans, drills, and monitoring mechanisms for their application through nationwide inspection bodies. the promotion of ''risk instruments'' and a ''risk-based regulation'' approach makes it possible to deal with risk-creating events. for the last two decades, in a context of decreasing means and in reaction to public-health crises which have led, according to some, to an overprotective state, a new tendency has emerged of governments using ''risk instruments'' to better allocate means and to decrease the state's hold. despite their differences, these two approaches are to the same end, which is to define -or perpetually re-define -the limits of the state. ''risk instruments'' contribute in each ''putting at risk'' situation to determining the state's involvement, the reason for its having competencies and resources, and therefore also the state's limits as opposed to that which concerns the private sector and individuals. the outcome of this defining as ''putting at risk'' and of the application of these risk instruments may be used by the state either to invest, or to disinvest; in the latter case for example entrusting risk management which formerly would have been the realm of institutions to local or private agents or to individuals. in the same way, risk instruments (or risk-based regulation or using risks to rationalize public intervention) may lead to state disinvestment or, on the contrary, be used by the state to seize back the reins in certain areas. paradoxically risk instruments serve in this instance to re-centralize or to ''remote-control'' areas to which the state had granted greater autonomy (universities or hospitals, for example). thus the way in which western societies manage risk, and the way in which these risks -their identification, how politicians and individuals perceive them, and their management -transform the links between the state (the political powers-that-be) and civil society are important to understand for those faced with risk management, especially in public-health risk management. what consequences these risk technologies have from one country to another thus greatly depends on institutions, state structure, professional organizations and their interrelationships, the balance of power and the forces involved, and the legal structurewhich may be more or less open to interpretation according to how it is drafted (more or less restrictive laws). risk management is, after all, at the core of the state and has always been central to its transformations. presenter: alfredo pena-vega (ehess, cnrs) climate change can be interpreted, according to a. pena-vega, as a complex system such as edgar morin defined it in his ''introduction to complex thought'' [ ] . the stakes involved in it are multidimensional, and suppose at once the ideas of transformation, uncertainty and unexpectedness, unpredictability and crisis. . . it henceforth seems necessary to arm ourselves with instruments enabling us to understand this reality. the common denominator of such instruments is rationality. because climate change involves stakes which are climatological, economic, social and health-related, as well as questions of governance, ethics, biodiversity etc., cross-disciplinarity appears to be one form of rationality which allows us to avoid the dangers of ''fear-mongering''. a study was conducted among , high school students from different countries, of which the objective was to understand how younger generations see climate change. the results are quite varied. if a minority of responders question the existence of climate change -with an argument largely based on a social construct communicated by the media - % of responders claimed to be concerned and aware of the negative consequences of climate change. the vast majority consider it to be a threat to the survival of humanity, in particular due to the multiplication of natural disasters, dwindling biodiversity, the spread of new infectious diseases, notably those with vector-borne transmission, and the inequalities it fosters between humans. we are currently in the ''age of the unthinkable''. today's world constantly exposes us to new crisis situations which we must learn to confront. these situations are all the more difficult to manage in that they most often occur ''out of framework'', or within a framework in which it is difficult to define the outlines delimiting an increasingly ''volatile'' environment. whereas our benchmarks in terms of crisis management are structured according to typologies (natural/biological/social disaster), the boundaries of current crises are unclear, and their typologies intertwined. unexpected and unpredictable, they emerge within a context where uncertainty reigns and where the response is organized according to the logic of competitive leadership. information no longer follows a downward flow from the state to the public, but circulates in a collaborative manner via widespread connectivity, social networks, which compete with institutional media which are sometimes outdated. it is therefore difficult for decision-makers to circumscribe the areas of operation, to isolate causes, and to distinguish the components which permit specific, technical and successive interventions. good judgment thus becomes key. public health crises, and especially those concerning eids, have pointed up the difficulties in predicting their appearance and development. comparisons and connections between these and other types of crises (natural, technological, industrial. . .) and how they are interpreted can thus prove useful in public health crisis management. the unattainable goal of predicting such crises makes it necessary to prepare to meet with unexpected events during the ongoing management of the crisis; it is no longer a question of predicting the unpredictable, but preparing to deal with it. in the context of our intricate, complex society, coordination and communication are of course necessary, but it has also become imperative to have a thorough knowledge of the steering process. in ''out of framework'' situations, strategic thinking capability takes precedence over the quality of available technical expertise. this can take the form of an ''express thinktank'', a group made up of diverse members capable of and trained to work together in situations of uncertainty. whereas in a ''classic'' situation the command functions is a pyramid, in these ''out of framework'' situations, collaborative and flowing cooperation is required, without leadership's impeding the efficaciousness of the response. in the case of hurricane sandy in the u.s., in , several work teams were set up in order to handle the unprecedented nature of the situation: ''real-time innovation'', ''immediate flaw detection'', ''emergency support functions''. these parallel work teams made it possible to optimize management of the disaster by limiting disastrous consequences. it seems essential to develop such networkbased crisis management in france. p. zylberman recalled to mind the definition of an eid as an unexpected infectious -or presumably infectious -phenome-non, affecting humans, animals or both. according to the definition used in the high council of public health's report [ ] , this can entail an infectious clinical entity which has just appeared (''true'' emergence), one previously identified (known emergence) or a known infectious disease whose incidence has increased or whose characteristics have changed (re-emergence). the hiv epidemic in the th century or the sars-cov epidemic in the early st century are examples of true emergence. the emergence of hepatitis c corresponds to a known clinical entity whose etiological agent was identified at the end of the s. the measles and west nile virus outbreaks on the american continent, in the th and end of the th centuries respectively, are examples of reemergence. nathan d. wolfe has defined five stages of transformation of an animal pathogen into a specifically human pathogen, resulting in a ''true'' emergence, with the possibility of an evolutionary interruption at each stage. stage corresponds to a situation in which a known virus in animals has never yet been detected in humans in natural conditions. in stage , the virus known in animals is capable of infecting humans in natural conditions, but without the capability of person-to-person transmission. in stage , some cycles of secondary person-toperson transmission are possible. in stage , the virus circulates among humans through several secondary person-to-person transmission of varying duration. stage is reached when the virus becomes exclusively human, and also contagious. on a population-wide scale an epidemic goes through four phases: introduction, propagation, amplification, and regression of the infectious phenomenon. the propagation phase is that during which there are the most widespread and frequent sites of infection. it corresponds (particularly for viruses) to the adaptation of the pathogen to its new host with person-toperson transmission taking effect little by little. it is often at this stage that the epidemic phenomenon is detected, sometimes with a considerable delay relative to the introduction of the pathogen. propagation can take place not only by contiguity but also across vast distances. humans thus play a role through their activities, and are what s. morse refers to as ''microbial traffic engineers'' [ ] . what are the major factors in the emergence of new infectious pathogens in humans? a great deal of progress has been made in improving the rapidity in identifying new viruses, as j.-c. manuguerra points out. the time delay between the individualization of a new infectious nosological entity and the identification of the causal agent thus continues to shorten, from years for hepatitis c in the s to years for hiv in , and to weeks for sars in ; even less for mers-cov. even so, the discovery or the knowledge of the pathogen's existence does not provide all the answers about the risks posed for or by a host species. various behaviors of pathogens can nonetheless be observed, in particular the pathogen's adaptation may require passing through several intermediary host species before adapting to its final host. moreover, the epidemic potential of a discovered virus is difficult to determine. among the very numerous known arboviruses, most are of anecdotal importance for human pathology, and little has been undertaken upon their discovery in preparation in case the pathogen were to become epidemic. this is true in the case of the zika virus, first isolated over years ago, and currently responsible for a major epidemic in latin america and in the caribbean. the question of the time lapse between the beginning of an epidemic and identification of the pathogen is progressively slipping toward that between the beginning of the phenomenon and its detection by the health system. this period appears to be critical for eradicating the development of an epidemic. is it possible to narrow the time gap between the beginning of an epidemic and its detection by the healthcare services? early identification of an epidemic-level incident mobilizes all health services professionals, both in regards to human and to animal health, according to m. van kerkhove. human and animal health and the state of ecosystems are inextricably linked, and it is believed that nearly % of eids, including those re-emergent, are of zoonotic origin. it is through this exploration of the connections between animals and humans that the means of transmission and propagation of mers-cov within the human species could be revealed. this virus is an example of a potentially epidemic emergence. schematically, during the mers-cov epidemic, a limited number of person-to-person transmissions, and sporadic cases between dromedaries and humans, were observed, with a certain degree of increase seen in healthcare facilities, sometimes considerable, as was the case recently in korea. during the epidemic % of the mers-cov cases were reported in saudi arabia, and of cases reported to the who task force, % were considered to be primary cases, that is, contracted from an animal host source, and % to be secondary cases, or acquired through another human case. every primary case represents an opportunity to understand how the infection was contracted. it gradually seemed necessary to launch a veterinary investigation as soon as a case was diagnosed. this led to the development of animal surveillance, which made it possible to reveal the seropositivity of certain dromedaries, as well as active excretion of the virus in their environment, which made possible its transmission to humans. this improvement in detection of emerging pathogens and early epidemic detection calls for the improvement as well of the veterinary surveillance network, the so-called onehealth approach. in an area with limited resources, where all animals cannot be tested, it is imperative to concentrate on those areas with high concentrations of animals, such as slaughterhouses, and on areas in which humans come into close contact with animals and thus represent a high risk of transmission (see conference by p. daszak). the data collected in these areas of frequent contact between humans and animals can be utilized to issue recommendations for at-risk populations in order to reduce transmission. once the virus has acquired person-toperson transmission capability, its control is far more complex due to the rapidity of propagation following its introduction into the population. it therefore becomes difficult for the healthcare system to improve detection of the epidemic. establishing health policies to optimize the case reporting system is thus critical. how to provide care to patients in the case of new eids? in an epidemic situation, the treatment of affected patients usually is secondary to the need to control the disease, as a. mcgeer stated. nevertheless, an adapted patient care procedure can change the evolution of an epidemic, to varying degrees according to the pre-existing healthcare infrastructure in the given country. in north america, where the services for the monitoring and managing of infectious diseases and public health are separated from the healthcare system, the organization of care for infected patients is usually left to the physicians. the healthcare system is in fact organized around individual patient care, and not oriented toward an approach of global individual and collective care providing. in the case of eids, care of affected patients becomes a political issue in a country graced with a public health system. health is seen as a human right, and governments are judged not only by their ability to prevent and manage epidemics, but also according to their management of care provided to ill patients. the role of the public healthcare system is therefore to advise physicians and to develop recommendations for the detection of cases and their homogeneous treatment. these guiding principles make the physicians the kingpins between healthcare structures and the treatment of patients, and the public healthcare system. better patient care provision thus improves epidemic response. in fact, treating ill subjects also allows the risk of person-to-person transmission and propagation to be reduced. this treatment role attributed to physicians can be variously interpreted in countries in which the healthcare and public health system are underdeveloped or lacking. in fact, the arrival of healthcare personnel and the setting up of precautionary measures required to contain the epidemic may be experienced as an intrusion. the lack of comprehension and communication between medical staff and the affected community, as well as the potential lack of comprehension of the measures set in place can prompt affected individuals to hide, due to the uncertainty of their fate. this was the case for example in west africa during the ebola virus epidemic, during which affected patients were sometimes hospitalized far from their villages without care being taken to inform their families of their clinical progress and outcome. this led to sometimes-violent rejection of the healthcare personnel, which interfered with the measures meant to control the epidemic. another element to take into consideration in the care of affected patients is protection of the healthcare personnel, which has become a recurring problem. most of the microbial forms with epidemic potential propagate within the community. for a long time hospitals were not troubled over the risk of nosocomial transmission of eid agents. care providers were not aware at the time of the risk of contagion that they themselves ran when providing care to patients. this awareness happened during the recent sars, mers-cov and ebola epidemics, which shared certain physio-pathological characteristics different from those involved in previous epidemics. in fact the peak of virus excretion for measles, chicken pox and influenza generally occur before or upon the appearance of symptoms, and the risk of transmission is virtually nil when the patient arrives at hospital. sars, mers-cov and ebola virus have a different viral excretion rhythm: symptoms appear with a weak viral load, and their intensity increases with the level of viral excretion, which reaches its maximum just when the patient requires the most care. the hospital thus becomes a center for the propagation of the pathogen. the hospital system is therefore in danger of breakdown, as it is both the pole for patient care and the new center of the infection's transmission. these new pathogens therefore require a re-thinking of hospital design, in order to optimize both control of epidemics and patient care. what has been, or is, the extent of nosocomial infection's role in the transmission of sars-cov and mers-cov? the new pathogens require us to re-evaluate modes of prevention for nosocomial transmission, confirmed b. guéry. the sars-cov epidemic serves as a good example of what was learned about the intra-hospital transmission of these new pathogens. person-to-person transmission of sars occurs through droplets, physical contacts and airborne pathways. the sars-cov transmission rate to healthcare providers exclusive of invasive procedures has been estimated at %. the main risk factor identified was the lack of protection of the provider's airway through wearing a mask, with an odds ratio estimated at . wearing scrubs and handwashing were also associated with lower transmission risk. sars is a disease which appeared in in guangdong province in china, then in hong kong, where numerous primary and secondary cases occurred. in total, according to the case index, secondary and tertiary cases occurred, of which . % among healthcare providers. beyond standard hygiene measures, studies conducted on affected healthcare providers revealed that certain categories of personnel, such as technicians and nurse's aids, show an infection rate twice that of the nursing staff, and times greater than the medical personnel. these studies made it possible to identify infection risk factors generally not taken into account in the fight against nosocomial transmission of pathogens: a significantly, greatly increased risk (odds ratio . ) was noted in care providers having used precautionary measures against sars transmission for less than hours, as was the case with those not having understood the protective measures (odds ratio . ). the factors identified as influencing transmission are patient viral load and patient index distance. the ideal conditions for transmission to occur are those of an infected patient excreting large quantities of virus, presenting with a certain number of comorbidities capable of masking the initial profile, and the existence of multiple close contacts with high-risk procedures such as oro-tracheal intubation, performing a fibroscopy, or the administration of treatments through nebulizers. the idea of a ''super-excreter'' patient was also identified during recent respiratory virus epidemics. this concept could play a crucial role. usually it concerns cases of very serious infection occurring in patients with several co-morbidities. in beijing in , the sars case index was also associated with a large number of secondary cases ( cases, of which among healthcare personnel). as with mers-cov, despite a relatively low basal reproduction rate (r ), a large number of care providers were infected during the epidemic. this is what happened, for example, in abu dhabi, where cases of mers-cov were diagnosed, of which % among healthcare providers. each case of provider infection was followed up through an epidemiological study, and each time an obstacle to the isolation of the patient and to the application of hygiene practices was noted. over % of the mers-cov cases identified in korea were thus traceable to ''super-excreter'' patients. this notion remains questionable, as it is reductionist and could lead to the identification only of patients in this category, to the neglect of transmission risks associated with other patients. it is probably more fair to speak of ''hyperexcretion events'' which implies that each patient is at maximum risk, and should be treated using precautionary measures. in conclusion, the intra-hospital control and transmission of eids can only occur in connection with the development of precautionary standards, which should be ongoing over time, and should be applied by all healthcare providers. it is imperative to ensure that caregivers are adequately and regularly trained, and that they constantly keep in mind the importance of isolation of all infected patients. to achieve this, it is probably necessary to resort to specialized units, in reference hospitals, in conjunction with clear decisions at the national level. an integrated approach to health in face of the globalization of risk has been developing over the last few years. the ''onehealth/ecohealth'' concept, or global health, takes into account the fact that human health, animal health and environmental health are inextricably linked, especially in regards to eids, exposure to which is fostered by the multiplication of transcontinental travel, many instances of human-animal contact, and intensive farming and ranching. many recent examples have made it possible to establish the key role played by animal biodiversity in the introduction and transmission of pathogens within human populations. whether it be the role of bats in the ebola virus epidemic, or dromedaries in the mers-cov epidemic, the crucial role of animals and of human-animal contact -being wild or domestical animals -in triggering an epidemic has recently been emphasized. primates, rodents and bats are the three mammal groups most likely to be at the origin of future pandemics due to the high proportion of viruses which they share with humans. the inclusion of fields which appear quite unrelated (infectious diseases, animal health and ecological and environmental sciences) should thus be pursued and improved. it has been possible to establish models which allow the prediction of emergence tendencies in infectious diseases, and certain geographical areas at high risk for emergence have been identified: central africa and west africa, southeast asia, central america. these areas correspond to those at high risk of propagation due to underdeveloped or deficient public health systems, and to the absence of epidemiological surveillance. tools necessary for effective prevention of future epidemics are now available. these are all the more critical in that recent increasing tendencies raise fears of a multiplication of the number of emergent epidemics in future. beyond the fight against pathogen propagation, its introduction into the human population is in fact a key step against which ''battle plans'' can be drawn up. in order to perfect pandemic response, it is necessary to improve the coordination and interconnection between individual and institutional participants, such as healthcare providers and public health systems. a global response approach (oneresponse) should be reflected upon and developed. on an institutional level, a first step in bringing together the fields of environment and animal health occurred in in france with the creation of a national french agency for food, environmental and occupational health & safety (anses), originating in the french agency for food safety (afssa, which also includes the national agency for veterinary drugs) and the french agency for environmental and occupational health & safety (afsset). another case of bringing together the areas of surveillance, prevention and human health intervention occurred in with the creation of the french public health agency, with the merger of the health surveillance institute (invs), the national institute for prevention and health education (inpes), and the organization for preparedness and response to health emergencies (eprus). the relations between these two new institutions should be developed in order to provide a better-coordinated response to future health crises. the response to an eid should take into account not only factors linked to eids, but also to a constellation of political, economic and socio-cultural constraints. the decision to put in place such a battle is in fact a political decision which involves, beyond the scientific aspects, the intervention's impact upon the popularity of the acting political powers-that-be. if governments are judged according to their ability to prevent epidemic crises, they are equally judged on their ability to avoid expenditures deemed excessive given the existing risk. these political considerations can run counter to the scientific rationale behind the response. this is how, in the case of the ebola virus epidemic, the united states became involved: through the declaration by the liberian president on august , , on the threat to national security posed by ebola, and the danger of the spread of the epidemic to the u.s. soil. in parallel with vaccine research and development, the actions of the u.s., the who and the united nations have focused on treatment of infected patients and the epidemiological securing of burials. in addition, despite a sometimes limited human impact, the economic impact of epidemics involving indirect costs (consequence for certain sectors of activity) has shown a marked increase. however, what characterizes modern epidemics is the duration of the economic ''shock'', in that it is temporary, as opposed to previous epidemics during which the shock tended to be drawn out in particular due to the persistence of infectious sources. there are many examples of this: among others, the ''spanish influenza'' of , the effects of which (company closures, loss of revenue) faded out in , or, more recently, the sars-cov epidemic, when the recession, that had been triggered by alerts against travel to southeast asian destinations communicated in march, ceased once these alerts were lifted two or three months later. it is of note that during the sars-cov epidemic only certain sectors (especially tourism) were affected in asia and in ontario, canada, and not the entire global economy. carrying out preventive measures such as staff training makes it possible to limit the number of crises at a lower cost. the costeffectiveness of such an approach has already been shown. it is henceforth necessary to raise awareness in decision-makers of the importance of prevention relative to risk. beyond these constraints, the decision to intervene is complicated by the heterogeneous nature of potential epidemics of the different pathogens. for this reason, and given the absence of technology permitting the prediction of the epidemic potential of a pathogen, prevention which targets the agent is impossible. prevention must therefore adopt other means, such as training locals in order to improve hygiene conditions. the improvement of transversal knowledge on infectious agents' transmission carries particular importance for the goal of preventing emergence. once an emerging agent is introduced into the human population, the pathogen propagation phase within the human population is the key phase in the development of the epidemic, and the one during which it is still possible to act in order to prevent the amplification of the pathogen in the population. the beginning of the propagation phase can be difficult to identify, and improvement in diagnostic techniques as well as the development of rapid diagnostic tests, and even on the field, makes it possible to accelerate detection of an epidemic signal. moreover, given the key role of certain animal species in the development of new epidemics, the development of animal health surveillance would allow us to further shorten the time lapse between the introduction of the pathogen and its propagation; however, this poses significant problems of wild animal monitoring particularly in southern hemisphere countries. better knowledge of states' operational modes in dealing with risk makes it possible to better understand their interventions and to better adapt the scientific response. the notion of risk has, little by little, become political, and the state uses risk to govern. risk management is therefore at the very heart of the state. recent public health crises have led to risk's taking on a new form, that of the unknown, by the fact of the unpredictability of its appearance and evolution. an interaction between scientific and political approaches to risk is absolutely necessary, in order to better evaluate at-risk situations according to modern methods such as structured decisionmaking, and to better handle risk-management tools. the changing nature of risks calls for the emergence of a new form of governance, which puts the individual back into the center of the state's action, as well as the confronting of arguments with expert committees. civil society's participation in risk management should be developed, and observation should once again play its part in crisis response. younger generations might also take greater part in responding to current crises. seven priority proposals can be outlined as follows: encourage research on the prediction, screening and early detection of new risks of infection; develop research and surveillance concerning transmission of pathogens between animals and humans, with their reinforcement in particular in intertropical areas (''hot-spots'') thanks to public support; pursue aid development and support in these areas of prevention and training for local health personnel, and to foster risk awareness in the population; ensure adapted patient care in order to promote adherence to treatment and to epidemic propagation reduction measures; develop greater sensitization and training among politicians and healthcare providers, in order to better prepare them to respond to new types of crises; modify the logic of governance, drawing from all available modes of communication and incorporating new information-sharing tools; develop economic research on the fight against eids, taking into account specific determining factors in order to create a balance between preventive and treatment approaches. the authors declare that they have no competing interest. introduction à la pensée complexe les maladies infectieuses émergentes : état de la situation et perspectives. available online: www global microbial traffic and the interchange of disease we are grateful to the speakers who generously brought their contributions to this seminar: peter daszak, olivier borraz, we thank corinne jadand for helpful organization and management support. key: cord- - mckelv authors: batista, m. title: estimation of a state of corona epidemic in august by multistage logistic model: a case of eu, usa, and world date: - - journal: nan doi: . / . . . sha: doc_id: cord_uid: mckelv the article provides an estimate of the size and duration of the covid- epidemic in august for the european union (eu), the united states (us), and the world using a multistage logistical epidemiological model. this article discusses the corona epidemic that outbreaks in wuhan (china) in december . at the outbreak, the epidemic final size and its duration are common questions. (brauer, a (brauer, , b fisman d, ; hethcote, ; house, ross, & sirl, ) . different models are used to answer such a question. these include models based on logistic function or richards function (batista, a; pongkitivanichkul et al., ; roberts, ; zou y et al., ) , deterministic classical and enhanced sir and seir models (anastassopoulou, russo, tsakris, & siettos, ; giordano et al., ; s. b. he, peng, & sun, ; loli piccolomini & zama, ; lopez & rodo, ; maier & brockmann, ; ming, huang, & zhang, ; nesteruk, ; tang et al., ; wu, leung, & leung, ; c. y. yang & wang, ) , statistical-based models (s. he, tang, & rong, ; mbuvha r & t, ; roda, varughese, han, & li, ; verity, okell, & dorigatti, ; zahiri, rafieenasab, & roohi, ; zhan, tse, lai, hao, & su, ) , time-series models (agosto & giudici, ; ceylan, ) , a new models (nesterov, ; singhal, singh, lall, & joshi, ) . there are at least two problems with the modeling of the epidemic. first, the question is whether a chosen model is an appropriate description of the epidemic, especially if the epidemic has several separate outbreaks or is dragging into a new wave. the second is that at the beginning of the outbreak or at a new wave, the parameters of the models are not known (keeling & rohani, ) , or better they depend on the course of the epidemic. therefore, prediction using such models are unlikely to be successful or should be used with caution, especially if used for long-term forecasting. however, when a model is a reasonable description of the epidemic, then the long term trend of an epidemic may be assessed by monitoring changes in the model parameters. it is clear that when the parameters of the model retain their values, a long-term prediction is possible because the epidemic curve is determined. we will call such an epidemic state stable; otherwise, the state is unstable. here we stress that any new local outbreak or import of infected into the population can destabilize the situation; almost no model can predict this. the best that models can offer are solutions for selected scenarios that may or may not realize (bettencourt & ribeiro, ; klepac, kissler, & gog, ) . (bettencourt & ribeiro, ; klepac, kissler, & gog, ) . in sequel will use a multistage logistic model to assess the state of the epidemic in eu, us and world. the model is not new. two stages logistic model was used for modeling sars outbreak in toronto (canada) (hsieh & cheng, ; wang, wu, & yang, ) , and the multistage logistic model was introduced by chowell et (chowell, tariq, & hyman, ) was used for modeling spanish flu of in genova, switzerland (chowell, ammon, hengartner, & hyman, ) . we note that a multistage model based on seir model was introduced by abdulrahman (abdulrahman, ) . the data used in this article are total confirmed cases up to august , as are daily reported by worldmeter f . we do not enter into the question of how good and reliable these data are. the base of the multistage (or multi-wave) logistic model is the logistic model, which is also called a simple epidemic model (bailey, ) or the si (susceptible-infective) model (frauenthal, ) . the basic equation of the logistic model is (daley & gani, ; frauenthal, ) > is the initial number of cases, then the solution of ( ) is now, assuming that epidemic is composed of w n mutually separated waves, then the model ( ) can be generalized as follows is the author/funder, who has granted medrxiv a license to display the preprint in (which was not certified by peer review) preprint the copyright holder for this this version posted september , . . https://doi.org/ . / . . . doi: medrxiv preprint we follow daley and gani and define the end of the epidemic when the number of infectives is within of its final size (daley & gani, ) . thus, to determine the end of the epidemic must be solved numerically ( ) for t where we set the above model was implemented in the matlab program fitvirusxx (batista, b) . in the program, the parameters of the model are estimated by the ordinary least-squares method by minimizing the following expression where , , , n c c c  are the reported cases in times , , , n t t t  . the above function has many possible local minimum values. therefore, a heuristic approach was used with the brute force search method to determine a quasi-minimum of ( ). european union. figure shows that the course of the epidemic in the eu so far can be described in three waves. eu countries introduced strict quarantine in march so that the first wave peaked in early april and then weakened by mid-june. already in april, a second smaller wave appeared, but it did not have a pronounced peak; its effect was only that the first wave dragged on into june. after the release of the measures, a new summer wave began to rise in early july. is the author/funder, who has granted medrxiv a license to display the preprint in (which was not certified by peer review) preprint the copyright holder for this this version posted september , . . https://doi.org/ . / . . . doi: medrxiv preprint from the graph in figure , we can see that the epidemic in the eu has so far shown no signs of calming down. the estimate of the final number of infections, as well as the duration of the epidemic, has been steadily increasing since april. in august, the course of the epidemic passed into a markedly unstable phase, where, as can be seen from figure , no clear trend can be observed. the current estimate shows a final . to . million infections and a duration of to days, i.e., until the winter of . the united states. in figure , we can see that the epidemic in the u.s. has two waves, the first smaller reaching its peak in early may and the second larger at the end of august. in the graph in figure , we can see that the trend in predicting the size of the epidemic and its duration was linear, then began to rise sharply at the end of june and reached its peak in mid-june with an estimate of million final infections. this was followed by an unstable period of declining size estimates, and in the last two weeks of august, this estimate stabilized at about . million total infections. the estimate of the duration of the epidemic stabilized at days, i.e., the epidemic is expected to last until may . . cc-by-nc-nd . international license it is made available under a perpetuity. is the author/funder, who has granted medrxiv a license to display the preprint in (which was not certified by peer review) preprint the copyright holder for this this version posted september , . . https://doi.org/ . / . . . doi: medrxiv preprint world. similar to the eu, we see in figure that the current course of the epidemic around the world can be divided into three waves. the first peaked in april, the second wave extended the epidemic in june, followed by a stronger third wave, which peaked in mid-august. from the graph in figure , we can see that the course of the epidemic until the beginning of june was a steady increase in the estimation of its final size and duration. this was followed by a period of an indistinct but growing trend, which is not yet showing signs of calming down. the current estimate of the final size is to million infections and a duration of d days, i.e., the epidemic could drag on into winter . . cc-by-nc-nd . international license it is made available under a perpetuity. is the author/funder, who has granted medrxiv a license to display the preprint in (which was not certified by peer review) preprint the copyright holder for this this version posted september , . . https://doi.org/ . / . . . doi: medrxiv preprint we first note that each case under consideration has a different course of estimates of the final size and duration of the epidemic. the absence of a unique pattern makes the prediction of the final size and duration of the epidemic difficult. namely, even if a convergence of parameters is achieved, we cannot be sure that this is the last phase of the epidemic; a new outbreak is possible at any time. is the author/funder, who has granted medrxiv a license to display the preprint in (which was not certified by peer review) preprint the copyright holder for this this version posted september , . . https://doi.org/ . for now, only parameters for the us achieve convergence. it can be estimated that about . million peoples will be infected, and the epidemic will last about days, i.e., until may , if, of course, no third wave will emerge. a new wave of epidemics is rising in the eu, which is expected to peak in october. however, the daily estimates of the model parameters for the eu are extremely unstable, so that every forecast so far is questionable and will certainly change. similarly, we can conclude about the course of the epidemic around the world. the epidemic has so far crossed the top of the third wave, but the situation is not yet stable. in the end, we stress that these predictions are not final but only reflect the current data. . cc-by-nc-nd . international license it is made available under a perpetuity. is the author/funder, who has granted medrxiv a license to display the preprint in (which was not certified by peer review) preprint the copyright holder for this this version posted september , . . https://doi.org/ . / . . . doi: medrxiv preprint simcovid: open-source simulation programs for the covid- outbreak. medrxiv a poisson autoregressive model to understand covid- contagion dynamics. risks data-based analysis, modelling and forecasting of the covid- outbreak. medrxiv the mathematical theory of infectious diseases and its applications estimation of the final size of the covid- epidemic. medrxiv real time bayesian estimation of the epidemic potential of emerging infectious diseases early estimates of epidemic final sizes the final size of a serious epidemic estimation of covid- prevalence in italy transmission dynamics of the great influenza pandemic of a novel sub-epidemic modeling framework for shortterm forecasting epidemic waves epidemic modelling an introduction early epidemic dynamics of the west african ebola outbreak: estimates derived with a simple two-parameter model mathematical modeling in epidemiology modelling the covid- epidemic and implementation of population-wide interventions in italy a discrete stochastic model of the covid- outbreak: forecast and control seir modeling of the covid- and its dynamics the mathematics of infectious diseases how big is an outbreak likely to be? methods for epidemic finalsize calculation real-time forecast of multiphase outbreak modeling infectious diseases in humans and animals contagion! the bbc four pandemic -the model behind the documentary monitoring italian covid- spread by a forced seird model a modified seir model to predict the covid- outbreak in spain and italy: simulating control scenarios and multi-scale epidemics. medrxiv effective containment explains subexponential growth in recent confirmed covid- cases in china bayesian inference of covid- spreading rates in south africa breaking down of healthcare system: mathematical modelling for controlling the novel coronavirus ( -ncov) outbreak in wuhan, china. biorxiv online prediction of covid dynamics. belgian case study statistics based predictions of coronavirus -ncov spreading in mainland china. medrxiv epidemic analysis of covid- in china by dynamical modeling. medrxiv estimating the size of covid- epidemic outbreak a new adaptive logistic model for epidemics and the resurgence of covid- in the united states. medrxiv why is it difficult to accurately predict the covid- epidemic? infectious disease modelling modeling and prediction of covid- pandemic using gaussian mixture model estimation of the transmission risk of the -ncov and its implication for public health interventions estimates of the severity of coronavirus disease : a model-based analysis richards model revisited: validation by and application to infection dynamics nowcasting and forecasting the potential domestic and international spread of the -ncov outbreak originating in wuhan, china: a modelling study. the lancet a mathematical model for the novel coronavirus epidemic in wuhan rational evaluation of various epidemic models based on the covid- data of china. medrxiv prediction of peak and termination of novel coronavirus covid- epidemic in iran. medrxiv prediction of covid- spreading profiles in south korea, italy and iran by data-driven coding outbreak analysis with a logistic growth model shows covid- suppression dynamics in china key: cord- -cj pn f authors: moirano, giovenale; richiardi, lorenzo; novara, carlo; maule, milena title: approaches to daily monitoring of the sars-cov- outbreak in northern italy date: - - journal: front public health doi: . /fpubh. . sha: doc_id: cord_uid: cj pn f italy was the first european country affected by the sars-cov- pandemic, with the first autochthonous case identified on feb st. specific control measures restricting social contacts were introduced by the italian government starting from the beginning of march. in the current study we analyzed public data from the four most affected italian regions. we (i) estimated the time-varying reproduction number (r(t)), the average number of secondary cases that each infected individual would infect at time t, to monitor the positive impact of restriction measures; (ii) applied the generalized logistic and the modified richards models to describe the epidemic pattern and obtain short-term forecasts. we observed a monotonic decrease of r(t) over time in all regions, and the peak of incident cases ~ weeks after the implementation of the first strict containment measures. our results show that phenomenological approaches may be useful to monitor the epidemic growth in its initial phases and suggest that costly and disruptive public health controls might have had a positive impact in limiting the sars-cov- spread in northern italy. with an increasing number of cases throughout the world, on the th of march who declared covid- a pandemic and called for governments to take urgent and aggressive actions ( ) . italy was the first european country affected by local transmission of sars-cov- . the first confirmed autochthonous covid- case in italy was identified on feb. st ( ) , followed by the detection of clusters of cases in relatively small municipalities ( in lombardy and in veneto). on february nd, the italian government introduced quarantine on more than , people from the municipalities. despite this prompt reaction, week later, the number of cases had reached ( ) . on march th, italy became the second most affected country in the world, after china ( ) . in order to contain the sars-cov- burden on the national health system, specific measures restricting social contact were first introduced in the northern regions, where most cases had occurred, then extended to the whole country on march th. these measures were further tightened on march st: all italian businesses were closed, with the exception of those essential to the country's supply chains. in the early phases of an outbreak, epidemiological data is limited and the parameters necessary to inform and calibrate mechanistic transmission models may be difficult to estimate. it is, however, crucial to monitor the pattern of epidemic growth, whilst incorporating uncertainty, in order to understand the current evolution of the outbreak and provide an early assessment of the potential impact restrictive measures. with the current study, we have analyzed public data from the four most affected italian regions (lombardy, veneto, emilia romagna, piedmont) using approaches suitable to the initial phases of an epidemic, which could help the day-by-day monitoring and the decision-making process. we estimated the time-varying reproduction number and used the generalized logistic growth model and the generalized modified richards model to characterize the early behavior of the epidemic. these approaches have been used and validated in previous epidemics and applied to the recent sars-cov- epidemic in china and national data from other countries ( ) ( ) ( ) ) . daily counts of new infections and deaths, to april th, were computed from data available from the website of the italian ministry of health/civil protection ( ). the time-varying reproductive number, r t , is the average number of secondary cases that each infected individual would infect if the conditions remained as they were at time t ( ) . typically, r t decreases over time starting from r , the basic reproductive number, as a consequence of both the depletion of susceptible individuals and effective control efforts ( ) . a monotonic decrease of r t over time may indicate the positive impact of measures introduced to control the epidemic; whereas an unstable behavior or a sudden growth of r t may suggest that corrective or additional measures are necessary. we estimated r t using the epi-estim package in the r software environment ( ), according to the following equation: where i t is the number of new infections at time t, and interval (namely the time between successive cases in a chain of transmission). we sampled the serial interval from a family of gamma distributions with mean . days ( % credible intervals (cri): . , . ) and standard deviation . days ( % cri: . , . ), as recently observed in china ( ) . r t estimates were then smoothed using a -day time window. we analyzed the daily count of new infections using two phenomenological models: (i) the generalized logistic growth model (glm), which extends the simple logistic growth model to accommodate subexponential growth dynamics with a scaling of the growth parameter, p ( ): where c ′ (t) is incidence growth phase over time t, c (t) is the cumulative number of cases at time t, r is the intrinsic growth rate in the absence of any control, p is a scaling of growth parameter, ranging from (constant incidence) to (exponential growth), and k is the final size of the epidemic; (ii) the generalized modified richards model (grm), which allows departures from the s-shaped dynamics of the classical logistic growth model, and incorporates the possibility of growth deceleration ( , ) : where a is the deviation from the s-shaped dynamics of the logistic growth model. both models were fitted to data in order to characterize the pattern of the epidemic in its early phases, produce days forecast of the number of new infections, and estimate the peak time and the final size of the epidemic curve. both models allow for estimation of uncertainly, based on bootstrap resampling. to april th), and piedmont (observed data: feb. th to april th). empty circles represent new observed cases, the vertical dashed line indicates where the real observations stop, the red continuous line the best prediction of the epidemic in the following days, the red dashed lines the % confidence bands, and the blue lines the bundle of models estimated by the prediction algorithm. bootstrap size was set to . r t has decreased over time in all regions, reaching estimates below . (figure ) , the threshold under which the epidemic dies out, at the beginning april in lombardy, emilia-romagna, and veneto and at the end of april in piedmont. in all regions, r t started from values ranging between . and . , consistent with estimates obtained in other contexts ( ) . in veneto, the steep increase on march th likely reflects changes (increases) in the testing practices (between march th and march th the daily number of tests increased by %; previously, the daily average increase was %). the level of uncertainty decreases over time, with the increasing number of events. the four regions experienced an increasing number of observed new cases until march - in lombardy, until a couple of days later in emilia romagna and veneto, and until - days later in piedmont, well-captured by the models. forecasts from the glm (figure ) and grm models ( figure s in supplementary material) are very similar, supporting their reliability. results are also consistent with the decrease of r t . the estimates of the final epidemic size predicted on april th range from , (grm) to , cases (glm) in lombardy, , (glm) to , (grm) in piedmont, , (both glm and grm) in emilia romagna, , (both glm and grm) in veneto. all parameter estimates with their % confidence intervals are shown in table s . the daily variation may be large, especially in the earlier phases of the epidemic, and strongly affected by variations over time in testing practices and, possibly, reporting. the uncertainty is larger, as expected, when using the more flexible grm model. large daily variations in forecasts are observable in figure s , showing consecutive -days forecasts of new cases in lombardy, from march nd to march th, in the week when the epidemic curves reached the peak. figure shows the evolution of the epidemic forecasts in lombardy with an increasing number of observed data, starting from the day of the lockdown (march st, day of the epidemic). the first graph shows that on march st, the glm predicts a sub-exponential growth but days later it identifies the peak and predicts an over-optimistic decline. glm predictions start appearing reasonable after mid-april, when the model captures a decline that appears much slower than the initial rise. epidemic evolution in emilia romagna, veneto and piedmont are shown in figures s -s , respectively. estimated time trends and -day forecasts for daily covid- deaths should theoretically follow, by ∼ - days, the trends of new cases, and are thus less informative for decision making, but are possibly less affected by testing and reporting variations (figure , results from the glm model only). due to the smaller numbers, the uncertainty in the models for both the observed shape of the epidemic and the -day forecast is larger for the number of deaths than for the number of new cases. in this study, we applied empirical models to daily covid- incident cases, in the four italian regions most affected by the outbreak, as april th. we observed an almost monotonic decrease of the estimates of r t in all four regions and a decrease of incident cases starting approximately from march th in lombardy, a few days later in emilia romagna and veneto, and a dozen of days later in piedmont. these findings may reflect the effects of the lockdown, that start being appreciable after ∼ weeks. these results are consistent with what observed in wuhan province, china (who, ). the monitoring of r t provides a useful tool to describe the real-time epidemic strength and to capture potential impact of the implemented control measures. our results suggest that costly and disruptive public health controls have been effective in limiting the sars-cov- spread in northern italy, as suggested by other studies ( , , ) and may support to the implementation of similar policies in other countries. we suggest that reporting of daily updated r t estimates and applying glm and/or grm to observed data may complement more common approaches used to monitor sars-cov- epidemics in its early phases. the same approach may be used also in areas less affected by the epidemic but potentially at risk, such as several regions in the centre and south of italy ( ) . these phenomenological models are relatively easy to implement and offer opportunities to monitor the positive impact of measures introduced to control the epidemic, characterize the pattern of the epidemic both in its early and late phases, produce short-term forecasts and estimate the peak time and the final size of the epidemic curve. whereas, short-term (e.g., days) predictions can be interpreted and used to make timely decisions as the outbreak proceeds, long-term predictions of the epidemic are interpretable only after the peak of the epidemic has been reached, as observed when phenomenological models were fitted at different time-steps (figure ) . being empirical, these approaches are affected by testing and reporting changes over time. however, this limitation is potentially common to the majority of models, both mechanistic and empirical, given that they rely on reported data for the estimation or calibration phase. this limitation should be considered when interpreting the results and forecasts. for instance, r t estimates are influenced by the variation over time of testing policies and thus the probability of identifying new cases. this, for example, can be appreciated in the temporary overestimation of r t observed in veneto around the th of march (figure ) , when the number of tests abruptly increased short-term forecasts provided by glm and/or grm may change every day, as the number of reported cases fluctuate, influencing prediction, especially in the early phases of an outbreak. the more flexible (and quick to capture variations) the model is, the stronger the variation. it is therefore essential to consider the full range of uncertainty, as well as to revise the predictions on a daily basis. taking this into account, forecast models yield a good visual fit to the epidemic curves, and the estimated parameters (supplementary material) can be interpreted in terms of describing the epidemic dynamics. like r t , also glm and grm forecasts rely on reported data and are affected by under-reporting. however, taking this limitation into account, their application can help describing and interpreting the epidemic evolution. for instance, lombardy experienced a slower decrease of daily infection than those predicted by glm (figure ) . this could be explained as an intrinsic pattern of the epidemic curve or as results of a higher testing capacity in the late phase of the epidemic. in conclusion, our study suggests that timely indications for public health authorities and governments are essential to slow down the epidemic and release the pressure on overburdened health systems. models applied in this study may help in underlining early signs of the success of costly and disruptive public health controls and reinforce the idea that collective efforts are working, are vital to "hold the line" and should not be abandoned prematurely. publicly available datasets were analyzed in this study. this data can be found here: https://github.com/pcm-dpc/covid- /tree/master/dati-regioni. the study was based on publicly available aggregate data. no ethics committee approval was necessary. covid- : towards controlling of a pandemic covid- : preparedness, decentralisation, and the hunt for patient zero lessons from the italian outbreak desktop available online at an interactive web-based dashboard to track covid- in real time using phenomenological models to characterize transmissibility and forecast patterns and final burden of zika epidemics real-time forecasts of the covid- epidemic in china from transmission potential and severity of covid- in south korea improved inference of time-varying reproduction numbers during infectious disease outbreaks the effective reproduction number as a prelude to statistical estimation of time-dependent epidemic trends epiestim" title estimate time varying reproduction numbers from epidemic curves serial interval of novel coronavirus ( -ncov) infections a generalized-growth model to characterize the early ascending phase of infectious disease outbreaks fitting dynamic models to epidemic outbreaks with quantified uncertainty: a primer for parameter uncertainty, identifiability, and forecasts the reproductive number of covid- is higher compared to sars coronavirus spread and dynamics of the covid- epidemic in italy: effects of emergency containment measures short-term effects of mitigation measures for the containment of the covid- outbreak: an experience from northern italy approaches to daily monitoring of the sars-cov- outbreak in northern italy: an update ( / / ) for all italian regions time-varying transmission dynamics of novel coronavirus pneumonia in china. biorxive the effects of containment measures in the italian outbreak of covid- all authors conceived the study, carried out the statistical analysis and drafted the final version of the manuscript. the supplementary material for this article can be found online at: https://www.frontiersin.org/articles/ . /fpubh. . /full#supplementary-material conflict of interest: the authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.copyright © moirano, richiardi, novara and maule. this is an open-access article distributed under the terms of the creative commons attribution license (cc by). the use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. no use, distribution or reproduction is permitted which does not comply with these terms. key: cord- -gbi g n authors: fioriti, v.; roselli, i.; chinnici, m.; arbore, a.; sigismondi, n. title: estimating the epidemic growth dynamics within the first week date: - - journal: nan doi: . / . . . sha: doc_id: cord_uid: gbi g n information about the early growth of infectious outbreaks are indispensable to estimate the epidemic spreading. a large number of mathematical tools have been developed to this end, facing as much large number of different dynamic evolutions, ranging from sub-linear to super-exponential growth. of course, the crucial point is that we do not have enough data during the initial outbreak phase to make reliable inferences. here we propose a methodology to estimate the epidemic growth dynamics from the infected cumulative data of just a week, provided a surveillance system is available over the whole territory. the methodology, based on the newcomb-benford law, is applied to italian covid case-study. results show that it is possible to discriminate the epidemic dynamics using the first seven data points collected over fifty italian cities. moreover, the form of the most probable approximating function of the growth, within a six weeks epidemic scenario, is identified. during an outbreak, a major issue to stop or mitigate the virus diffusion is gathering information as soon as possible about the nature of the epidemic from a mathematical point of view. pandemic outbreaks allow a reasonable amount of data to be available only ex-post the event, therefore the analysis is severely limited. on the other hand, well-timed information about the epidemic growth is extremely precious, and justify any effort in this direction. a panoply of tools are available, but their accuracies are subject to limitations, due to the small number of data points available, which also restricts the choice of models for the epidemic curve that is a time-series of the cumulative number of cases per day [ , ] . these curves are produced by different dynamics, ranging from sub-linear to super-exponential, giving rise to a diversity of the early growth profiles that has deep implications for the estimation of the disease transmission and for the countermeasures implementation [ ] . therefore, a fast detection and estimation at least of the basic outbreak characteristics, would be extremely useful, but the mathematical tools able to deal with those very few data are rare. moreover, epidemic data gathered on the field are always polluted by human errors, different collection methods, limited territorial coverage, irregular or random sampling. even the most recent sophisticated signal processing techniques such as the graph spectral analysis, the compressive sensing, the signal on graphs method are affected by these problems [ - ] . however, the newcomb-benford law (nbl) seems able to reveal the epidemic dynamics using only a week of infection data. nbl is the statistic of the first (actually also of the second, third and so on) digit for a set of numbers, discovered and rediscovered independently by s. newcomb and f. benford, today known as the benford law [ , , ] . its wide popularity is due to the apparent ubiquity of the benford distribution and to the extreme simplicity of the calculation procedure involved. in recent years, the nbl has been used to discover fiscal frauds and to confirm scientific data reliability, including epidemic data [ ] . in our work, we are interested to study the capabilities of the nbl to predict the outbreak growth dynamics using very few initial data. it is only necessary to collect the cumulative data of the daily infected over a week in some of the most important cities involved in the outbreak, to form a unique sequence of these numbers and then to calculate the first digit distribution. given the limited amount of data points, the calculated and the actual benford distribution will not coincide exactly, thus to characterize the accuracy an appropriate goodness-of-fit (gof) parameter is used. at this point, by trial-and-error or by any numerical technique, an approximating function is chosen: if its first digit distribution is congruent with that of the italian cities, we can consider the approximating function as an accurate approximation to the real cumulative curve. in the following sections we will show how this is possible invoking the theorems of berger & hill and the ergodicity of the epidemic sis process during the initial expansion phase [ ] . before presenting the essential points of our proposal, we have to introduce the main statistical tool, namely the newcomb-benford law. since an extensive treatment can be found in the fundamental work of hill and berger [ , , ] , we will give just a brief introduction to the nbl from a practical point of view. s. newcomb and f. benford independently observed that the leading digits in many real-life numerical data sets such as macroeconomic, census, financial, fiscal data, were not distributed uniformly, as the common sense would suggest, instead they follow the logarithmic distribution of figure a : more formally, the benford distribution is a logarithmic curve: pr (d = d ) = log ( + /d ), for all d = , , . . . , ( ) where d is the first significant decimal digit. first significant digit means in . , in . , . in . * , . in . * - . when a set of numbers follows exactly the nbl, the digit " " will appear about the % of the times, the digit " " the %, " " the % etc.. the generalized nb law considers also the second, third etc. digit, but here we are interested only to the first one. the compliance to the benford distribution may be found also in some natural data-sets, such as molecular weight tables, sport statistics, drainage areas of rivers, that taken individually do not follow the nbl: what satisfies completely the nbl is the union of all those data-sets. the powers of follow the benford distribution (we say "is benford", for short), but to verify it numerically, we would need of a large set of numbers. this constitutes one first difficulty, because it is not easy to determine the minimum cardinality of the set that guarantees a priori to reveal exactly the benford distribution. moreover, most of the time we do not have enough data to satisfy correctly the nbl, and, as a consequence, an error is introduced. in figure b , c the effect of a limited data set is clearly illustrated: using only data points we obtain a poor fit to the actual benford distribution, although simply doubling the datapoints reduces greatly the error. hence, it is convenient to use a goodness-of-fit parameter to estimate the error committed; here, to this end, we consider the standard measure: but other statistical tests may be used as well. of course, generally the first digit distribution of a data-set may or may not be a benford (first digit) distribution; if this is the case, it will be clearly specified. in any case, the gof indicates the distance between the calculated firs digit distribution and the benford distribution. the main idea is to estimate an approximating function for the epidemic growth curve within a time horizon of tf days, using only the first seven epidemic data points of fifty italian cities, accounting for about the % of the population, considered as a unique sequence formed of x data-points, called _cities sequence. we show that the first digit distribution of the _cities sequence converges to the first digit distribution of the cumulative daily infected italian national sequence, formed summing the infected over all the national territory each day during the first tf days of the epidemic ascending phase. therefore, if the convergence exists, it is possible to know the compliance to benford for the cumulative italian curve in advance of tf - days. in turn, the level of compliance is used as a criterion to predict the accuracy of an approximating function to the real epidemic national curve during the initial phase of tf days (starting from the th february ). now we will sketch the theoretical justification of the above method. first of all, we have to make sure that the italian national cumulative data first digit distribution is benford during the initial spreading period. based on the berger & hill theorems [ , ] , if the sequence is a power law, exponential or super-exponential, its first digit distribution is almost always benford. thus, we have only a sufficient condition. below some of the main results of berger & hill to support our method (formal demonstrations can be found in [ , , ] the next theorem states that the solutions of an ordinary or differential equation system such as many of the classical epidemic models, under general conditions are benford. thus, the nbl is not restricted to discrete dynamics; on the other hand, general results for partial differential, delay or integro-differential equations are not known. theorem (berger & hill ) . consider the dynamic system: all rights reserved. no reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medrxiv a license to display the preprint in the copyright holder for this this version posted august , . . https://doi.org/ . / . . . doi: medrxiv preprint where f: ℝ → ℝ is continuously differentiable with f( ) = , and x ∈ ℝ. let f: ℝ → ℝ be c with f( ) = and assume f'( ) < . then, for every x ≠ sufficiently close to , the solution of the system is benford. related to theorem we have the so-called shadowing lemma. the lemma describes the behavior of the pseudo-trajectories (sequences) near a locally structurally stable hyperbolic invariant set [ ] . shadowing lemma. let t: ℝ → ℝ be a map, and β a real number with |β| > . if supx∈ ℝ |t (x) − βx| < +∞ then there exists, for every x ∈ ℝ , one and only one point x° such that the sequence (t n (x)−β n x°) is bounded. this means that every hyperbolic set has the shadowing property, thus every pseudo-trajectory or sequence stays uniformly close to some true trajectory, i.e. a pseudo-trajectory is "shadowed" by a true one. considering the epidemic curve as the solution of a dynamic system, the shadowing lemma allows to believe that very close to it a pseudo-sequence exists, is related to the dynamic system and is structurally stable. in other words, finding an approximating function to the cumulative epidemic italian curve would not be a mere accident, at least locally. moreover, small perturbations of the system initial conditions do not change the approximation: therefore, errors during the initial data collections do not alter the result. theorem (berger & hill ) . let x be exponential with mean , that is fx(t) = max( , − e −t ) , t ∈ ℝ. even though x is not exactly benford, it is close to being benford for all t ∈ [ , ). theorem (berger & hill ) . the sequences : n , n are benford; n, n + , n!, √ n , n , * n are not. in general, a*x b , with a > and b > is benford almost always, but not always, therefore x is almost always benford. moreover, every mixture of n with a random unbiased sequence, is benford. berger and hill also state that apart from some particular cases, processes with linear growth are not benford. this allows to identify the slow epidemic growths, that are a phenomenon more common than previously though [ ] . by slow we mean a linear, sub-linear or a polynomial growth. theorem (berger & hill ) . if x and y are benford sequences, also their sum x + y is benford. if the sequence z is not benford, x + y + z is benford. hence, if the cumulative infected sequence of the italian cities are benford, also the national cumulative sequence is benford as well, during the weeks of the increasing phase. note that an epidemic cumulative sequence cannot be random, being non-decreasing, therefore by theorems berger & hill , , , the fast cumulative epidemic curves are all benford, but could exist also fast non-benford curves in particular circumstances. thus, we cannot rule out the possibility of non-benford growth curves to have a fast dynamics, thought this would be seldom the case, see table . now we can discuss the convergence of the _cities distribution to the distribution of the cumulative daily infected of the italian national sequence after tf days. the _cities sequence is the union of the first days data for each city, but to fix ideas, let us consider only three cities, a, b, c, whose sequences of seven elements are: indicating b(…) as the operator of the first digit distribution calculation, results: all rights reserved. no reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medrxiv a license to display the preprint in the copyright holder for this this version posted august , . . https://doi.org/ . / . . . doi: medrxiv preprint b( ui,j{ x j (i) }) → b( ∑k,h ( x j (h)) ) ( where i = , , … m. j = , , … n. k = , , … nit . h = , , … tf . in the trivial case, when the sequences x j are (almost all) benford with m = tf and n = nit, berger & hill guarantees that the summation sequence is benford. on the other hand, the union of the sequences is benford too, thus the ( ) is true. when m = , since it is not known an analytical method to determine a priori the values of m that guarantees a small gof, one can only calculate the first digit distribution b(ui,j{ x j (i) }) and compare it to the benford distribution of figure a . if the gof stays high, the simplest heuristics would be to increase m, yet reducing the forecasting time-span of tfm. of course, the number of city-sequences n may well be expanded to all the cities nit : here we have restricted it to fifty cities only for demonstration purposes. therefore, we do know that ( ) is true, but cannot determine the minimum m necessary. actually, we have chosen m = because it is well below the prediction thresholds often suggested in the literature [ , ] . instead, to determine tf , we consider that during the initial phase of the outbreak if: (where is the birth rate, is the cure rate, and is the contact rate), the overall epidemic process is ergodic [ ] . hence, all the local realizations have similar statistics, are non random non decreasing sequences, and by the shadowing lemma there exists an approximant function f to ∑k,h ( x j (h): as a consequence, the first digit distribution of f(x) approximates that of ∑k,h ( x j (h) , but by the ( ) also that of b( ui,j{ x j (i) }). therefore tf can be determined heuristically or numerically as the value that get b(f(x)) closer to b(ui,j{ x j (i) }) in terms of benford goodness-of-fit. from table it is readily seen that both the cubic and the logistic curve approximate the it_real gof very well for tf = . in addition, tf = is very close to the inflection point of the real italian cumulative curve, which indicates the end of the initial phase for the outbreak. basically, we have three dynamics, very fast, fast, and slow (see figure ); we want to determine which one of them is prevailing by means of the benford' gof, and possibly to find an approximating function. as said in the above section, each city provides a sequence of positive integers, and putting them together the fifty sequences make up an unique sequence of x integers called _cities. note that sequences such as in the section above we have indicated that: where i = , , … . j = , , … k = , , … . nit h = , , … , and tf = are now specified to the actual case-study scenario. to classify various possible approximant curves we have calculated their benford gof, showed in the table , together with the gof of the real italian epidemic data, the logistic curve, of the cubic curve and of the _cities. all rights reserved. no reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medrxiv a license to display the preprint in the copyright holder for this this version posted august , . . table ; dotted magenta and red: very fast dynamics; black: the italian cumulative curve and in blue the cubic and logistic approximations; green: slow dynamics. b) days scenario. the cubic function (blue-yellow) approximate well the actual cumulative curve (black) also in this scenario, confirming the same result suggested in [ ] , while the logistic in this scenario performs poorly, and is not in the figure. note the red dotted curve ( * . n ), that seems slow, actually is a fast one; instead, the green black dotted curve ( n ) seems fast, but is very slow. keeping in mind that the union of the sequences of seven data points from some of the most important italian cities, converges to the benford distribution of the sum of all the week sequences for all the cities ( ), theorem berger&hill [ ] guarantee that almost always the exponential growth provides numbers according to the nb distribution. therefore, as explained in other sections, a good benford gof obtained from the epidemic cumulative data of the _cities should be able to identify the type of outbreak dynamic. in table the cities gof is . , very close to the gof for the real italian data of the first six weeks, gof_it = . , while the cubic curve gof_i(ti)*n = . has the minimal distance from the _cities gof. therefore n is the most probable approximating function, whereas in figure a the italy' real epidemic curve is almost coincident with the cubic growth, confirming the results of [ ] . actually, the logistic curve gof is in good agreement with the _cities gof too, and fits very satisfactorily the italy' real data after the fourth week (figure b ), but the cubic curve has an advantage in terms of benford gof and till the fourth week is also the best approximant. therefore, table reveals that the cubic curve determines the initial stage of the growth. again a note of caution: a small gof, say in the interval [ , ] as in table , is only a sufficient condition that guarantees a fast dynamic, but not a necessary one, meaning that a large gof > could represent a rapid growth too, as for the case of the function b * n . thus, most of the times, but not always, a large gof indicates a linear or sub-linear dynamics; instead, a small gof guarantees a rapid growth. a b figure . dotted blue: the italian cumulative curve, red: cubic approximant, black: logistic approximant. a) first four weeks, the cubic curve is very close to the real growth. b) first six weeks: the logistic curve now is a better approximant. the best approximating function function is the cubic i(ti)n . samples is the number of data-points used to calculate the first digit distribution and therefore also the gof; they are , except for the _cities gof, whose distribution is calculated using not more than data-points, the first data from each city. in orange * are indicated the non-congruent dynamics: for example, * n has a very large gof, nonetheless belongs to the class of fast dynamics, instead to that of the slow one. summarizing, the first digit distribution of the _cities sequence converges to the first digit distribution of the cumulative infected curve, that is benford during the ascending epidemic phase. if the _cities gof is small, on the basis of the berger-hill's theorem we have a fast epidemic growth; instead, if the gof is poor, the growth will be probably slow, although this cannot be assured formally. moreover, in order to determine the form of the approximating function that shadows the real epidemic growth, one might extrapolate some of them analytically or heuristically. at this point, it suffices to choose the approximating curve whose gof is close to that of the _cities. if the difference between the two gof is small (in our case study less than %), we assume that the approximating function shadows correctly the real epidemic growth. in this paper, we show how to estimate an approximating function of the epidemic curve within a time horizon of five or six weeks, using only the first seven epidemic data points of fifty italian cities, considered as an unique sequence. the level of compliance of the sequence to the benford test is used as a criterion to predict the approximating function accuracy with respect to the real epidemic national curve. this procedure is made possible by the convergence of the unique sequence first digit distribution to the benford distribution, since the national italian cumulative data first digit distribution is benford (almost always) when its sequence is a power, exponential or faster curve. therefore, when a fast epidemic spread is taking place on the territory, its fingerprint will be the benford distribution, otherwise the spreading will be, with high probability, slow (quasilinear) or made of sporadic outbursts. unfortunately, the benford compliance of the fast growth is only a sufficient condition, not a necessary one. our results make this point clear. on the other hand, early indications about the dynamic nature of the outbreak are made available through a simple statistical test applied to a handful of data. this method has been applied to the italian covid case study, where the most probable approximating function of the first five weeks has been identified clearly as a cubic curve. a generalized-growth model to characterize the early ascending phase of infectious disease outbreaks building test data from real outbreaks for evaluating detection algorithms bayesian prediction of an epidemic curve discrete signal processing on graphs: sampling theory the emerging field of signal processing on graphs: extending high-dimensional data analysis to networks and other irregular domains discrete signal processing on graphs adaptive least mean squares estimation of graph signals distributed recursive least squares strategies for adaptive reconstruction of graph signals online temperature estimation using graph signals predicting the sources of an outbreak with a spectral technique locating the source of diffusion in large scale network the role of the airline transportation network in the prediction and predictability of global epidemics locating multiple sources of contagion in complex networks under the sir model the network topology of connecting things: defense of iot graph in the smart city modelling dynamical processes in complex socio-technical systems epidemic spreading in scale-free networks epidemic thresholds in real networks epidemic spreading in real networks: an eigenvalue viewpoint utility and potential of rapid epidemic intelligence from internet-based sources a statistical derivation of the significant digit law a basic theory of benford's law the first digit phenomenon using benford's law to investigate natural hazard dataset homogeneity extinction and ergodic property of stochastic sis epidemic model with nonlinear incidence rate key: cord- -yx oyv authors: amar, patrick title: pandæsim: an epidemic spreading stochastic simulator date: - - journal: biology (basel) doi: . /biology sha: doc_id: cord_uid: yx oyv simple summary: in order to study the efficiency of countermeasures used against the covid- pandemic at the scale of a country, we designed a model and developed an efficient simulation program based on a well known discrete stochastic simulation framework along with a standard, coarse grain, spatial localisation extension. our particular approach allows us also to implement deterministic continuous resolutions of the same model. we applied it to the covid- epidemic in france where lockdown countermeasures were used. with the stochastic discrete method, we found good correlations between the simulation results and the statistics gathered from hospitals. in contrast, the deterministic continuous approach lead to very different results. we proposed an explanation based on the fact that the effects of discretisation are high for small values, but low for large values. when we add stochasticity, it can explain the differences in behaviour of those two approaches. this system is one more tool to study different countermeasures to epidemics, from lockdowns to social distancing, and also the effects of mass vaccination. it could be improved by including the possibility of individual reinfection. abstract: many methods have been used to model epidemic spreading. they include ordinary differential equation systems for globally homogeneous environments and partial differential equation systems to take into account spatial localisation and inhomogeneity. stochastic differential equations systems have been used to model the inherent stochasticity of epidemic spreading processes. in our case study, we wanted to model the numbers of individuals in different states of the disease, and their locations in the country. among the many existing methods we used our own variant of the well known gillespie stochastic algorithm, along with the sub-volumes method to take into account the spatial localisation. our algorithm allows us to easily switch from stochastic discrete simulation to continuous deterministic resolution using mean values. we applied our approaches on the study of the covid- epidemic in france. the stochastic discrete version of pandæsim showed very good correlations between the simulation results and the statistics gathered from hospitals, both on day by day and on global numbers, including the effects of the lockdown. moreover, we have highlighted interesting differences in behaviour between the continuous and discrete methods that may arise in some particular conditions. france was hit by the sars-cov- epidemic probably at the beginning of january , the first case being reported on january [ ], and went into lockdown on march [ ] . in response to the expected reduction of the number of cases, the french government eased the lockdown restrictions on may and eased them again on may (except in the ile-de-france region, where the density of population is very high). these measures have been taken to stop the exponential growth of the number of cases, as observed earlier in china [ , ] . the basic reproduction number r tells us the average number of new infections caused by an infective individual and it describes the exponential growth of the epidemic [ ] . if r is greater than the epidemic will spread; otherwise, when r is less than , the disease will gradually fade out [ ] . compared to the r of h n ( . ) [ ] the reproduction number of covid- indicates awful potential transmission. the r was estimated as . [ ] , . [ ] and . [ , ] by many different research sources around the world. the world health organization (who) published an estimated r of . to . [ ] . many approaches have already been used to model the covid- epidemic using compartment models and deterministic ordinary differential equations (ode) [ , ] and also to estimate the effects of control measures on the dynamics of the epidemic [ ] . these particular approaches give good results, but they do not take into account the stochastic nature or the spatial aspects of the propagation mechanism. however, stochastic differential equations (sde) have been successfully used to tackle the stochastic aspects of epidemic propagation [ ] [ ] [ ] [ ] . more recently, multi-region epidemic models using discrete and continuous models, taking into account the effectiveness of movement control have been published [ , ] , as well as sde multi-region models [ ] . stochastic models based on economic epidemiology have been applied to the covid- epidemic, for example, in south korea, to determine the optimal vaccine stockpile and the effectiveness of social distancing [ ] . approaches using agent-based systems have also been used to model both the stochastic and spatial characteristics of epidemic propagation [ , ] . in agent-based methods the number of machine instructions needed for each timestep, relative to the size of the data (algorithmic complexity), is at best proportional to the number of agents. those using one agent per individual may need a high computing power when used on large populations. these approaches are often applied to smaller areas (towns mainly) than the entire country, and/or use one agent to model a set of individuals ( in [ ] ). population-centred methods have an algorithmic complexity that does not depend on the size of the population, but on the number of rules considered at each iteration (for example, the number of reactions for biochemistry systems). when used on large populations these methods are much more efficient than entity-centred methods, but they do not take into account the spatial localisation. we adopted here a hybrid model derived from the sub-volumes method that adds coarse-grained spatial localisation capabilities to the standard stochastic simulation algorithm (ssa) used, for example, in the domain of biochemistry. to increase the computing efficiency we also used an original variant [ ] of the gillespie algorithm with tau-leaping [ , ] that automatically adapts the proportion of randomness vs. average-calculation, at each timestep. our implementation allows us to easily switch from this stochastic variant of ssa to a deterministic continuous solver (dcs), and therefore compare the two methods. to test our approach we applied it to the sars-cov- epidemic in france where relevant data [ , ] have been made available throughout the duration of the epidemic. most of the simulation parameters we used have been obtained from statistics gathered in the literature, such as the proportion of cases that needed hospitalisation and the proportion of severe forms among them [ , ] that needed beds in icu (intensive care unit). the number of infectious individuals and their localisations at the beginning of the epidemic have been inferred from statistical data made available by the french government and from the literature [ ] [ ] [ ] . we used our simulation tool to ascertain the effects of control measures on the dynamics of the epidemic and compared the results to the real statistical data. we focused our study of the impacts of the epidemic only on the part of the population that moves on a daily basis: workers, pupils, students, retired people, etc. people in nursing homes were not taken into account since their environment and way of life are very different. starting from a known initial state, we wanted to compute a stochastic sample of the evolution in time of the number of people at each state of the disease. a transition between such states is often described by a set of probabilistic rules, or by a stochastic automaton. the epidemic spreading can be modeled as a markovian process in the sense that the number of people in each state at time t + ∆t depends only on the numbers at time t (and on other variables that do not depend on t). in most of the cases, it is not possible to find an analytic solution that gives those numbers as a function of time. hopefully, iterative numerical methods exist. one of them is the gillespie algorithm, frequently used to find the evolutions of the quantities of chemical species s(t) = {s (t), ..., s n (t)} that can react according to chemical rules r = {r , ..., r m } and their kinetics k = {k , ..., k m }. starting from the initial value s( ) of the n species, the algorithm computes the values at time t > by iterating the following process: . based on the quantities s(t), the rules and their kinetics, compute stochastically at what time each reaction is triggered {t , ..., t m }. . let r i being the next reaction: t i = in f {t , ..., t m }. . apply r i ; i.e., update the vector s(t i ) by decreasing the quantities of the substrates of r i and increasing the quantities of its products. . update the time: t ← t i . this algorithm gives an exact stochastic trajectory of the system, but can be slow when some reactions are quick. these quick reactions will often be triggered, so the time increment at each iteration will be small and the number of iterations per second high. to decrease the computing time, the tau-leaping method uses a fixed timestep, τ. at each iteration, the number of times each reaction is triggered during the time interval τ is stochastically estimated based on the quantities at time t. this method gives an approximation of the stochastic trajectory of the system, which is accurate as τ is small. the value of τ must be chosen to be large enough to minimise the number of iterations per second, but not too large to get good precision. the algorithm used in pandaesim, a variant of the tau-leaping gillespie method, is detailed at the end of this section. the population-centred methods such as those presented here share the same constraint: the entities evolving in the environment are considered homogeneously distributed in the environment. in other words, the spatial localisation is not taken into account. the entity-centred approaches, which compute the behaviour of each individual at each timestep, take into account the spatial localisation of each individual, but need much more computing power. to add coarse grained spatial localisation to our model, we partitioned the territory in sub-regions where one instance of a population-centred ssa is run. these instances use the same timestep and are synchronised. the interactions between sub-regions are modelled by taking stochastic samples of individuals that travel between sub-regions. this is done at a higher time scale since such travelling is less frequent than the travelling inside the original sub-region. most of the individuals that travel go back in their home sub-regions after a variable period of time. thus, the population of each sub-region remains approximately the same, although people enter and leave the sub-region. if this is not taken into account in the model, the population of each sub-region may tend to become the same as time goes on. we describe in the next section how this constraint is implemented in our model. the territory studied is partitioned in two levels of geographical organisation: region and sub-region. a region contains at least two sub-regions, a sub-region belongs to only one region and all the territory is covered (partition). in our case study, france, the first level is the administrative région, each one containing from two to a dozen départements. there are régions and départements in france. of course this can be applied to any partition of a territory. for example in england we could use the nine regions for the first level, and the ceremonial counties and greater london for the second level. the population is divided into four age slices: to years old, to years old, to years old and over years old [ ] [ ] [ ] . each of these four sub-populations has its own values for the population parameters (infection immunity, travelling rate, etc.). we used one instance of a population-centred simulation process for each sub-region, with a one hour timestep. the simulation of the upper level (region) uses a bigger timestep, one day, and mainly processes the people which are travelling to another sub-region. thus, the population distribution is supposed homogeneous inside each sub-region, but can be heterogeneous at the region level and therefore at the level of the entire territory. depending on the age, and except for ill or hospitalised people, each day, people have a probability to travel from their homeplace to some place else either belonging to the same sub-region (local travel) or to another region (remote travel). these probabilities are part of the population parameters mentioned earlier. of course, quarantine type control measures forbid any kind of local or remote travel; people must stay in their respective homes sub-regions. the number of people of each age slice leaving their home sub-regions is a stochastic sample (or averaged value for the deterministic continuous solver) of a percentage of the population of this sub-region. for local travel, they are scattered according to the relative population of each sub-region belonging to their region. the more populated sub-regions attract more of the travellers. for remote travel, people go from their home-regions to the most populated sub-regions of the other regions, where airports and train stations are. the same method is used to dispatch the travellers according to the relative populations of their destination sub-regions. this way of computing how many individuals travel and where they go is a simple way to maintain constant the density of population of each sub-region. the sub-region population-centred model is a variant of the widely used susceptible, exposed, infectious and removed model. we added two states: hospitalised and deceased. the exposed and infectious states have slightly different meanings in our model; they have been renamed to asymptomatic and ill ( figure ). unlike ill people, who show symptoms of the disease, recently infected people are asymptomatic hosts, but both of them are infective. hospitalised patients are also contagious, but to a lesser extent because they are confined inside the hospital. the three red dotted arrows in the figure indicate the potential sources and targets of the infection. we have assumed that people in recovered state are immune to the virus and therefore cannot be reinfected [ ] . an incubation period of approximately five to six days before the apparition of the first symptoms has been observed [ , ] . in consequence, in our model, asymptomatic people are subdivided into six subcategories according to the number of days since contamination. a large majority of cases, around %, present a mild form of the disease which is probably even not reported. the other cases need hospitalisation, and among them, from % [ ] to more than % [ ] present severe forms wherein patients need to be admitted in icu. the duration of the disease, after the incubation period, depends on the age of the patient an on the severity of the form of the disease. in our model it has been set to a maximum of days, and therefore we have subdivided the ill (resp. hospitalised) people into at most subcategories according to the number of days since the apparition of the first symptoms (resp. the date of the hospitalisation). people with mild infections will recover after a stochastically variable period of time ( to days) that depends on their age. the severe form of the disease is (stochastically) lethal according to a rate also varying with the age of the patient. the deterministic solver uses fixed average values. all these rates, probabilities and average durations are parameters of the model. their values came or were inferred from observed statistics of real cases. as mentioned before, the simulation algorithm uses a one hour timestep. it mainly computes in a stochastic way the state vector: i.e., the number of people that is in each state and subcategory, at each timestep. there are four state vectors, one for each age slice. of course these four vectors are not independent since whatever their age is, contagious people can infect susceptible people regardless of their own age. basically, from the value of the state vector at time t, the process computes the new value of the state vector at time t + τ (here τ = h). thus, starting from a known initial value of the state vector at time t = , we can obtain its value at any time (t = t end ) > by iterating this process until t end is reached, or until a specific value of the state vector is reached. pandaesim automatically stops the simulation when there are no more infective people. our model assumes that people have uniform daily routines. without specific measures, the daily schedule begins at o'clock in the morning for work (or school, university, etc.) with the use of public transportation for one hour. next comes staying at work three hours, followed by a two-hour midday break, four hours in the afternoon at work, another hour in public transportation to go back home and the remaining hours at home. we defined four possible environments, each one having its probability of contagion: home, public transportation, workplace and restaurant. these parameters have default values that reflect the local concentrations of people: very low at home, higher at work and restaurant and much higher in public transportation. to reduce the number of parameters we used the same value for the workplace and the restaurant. many kinds of measures can be used to slow down the propagation of the epidemic; we implemented two examples of such measures: . soft quarantine: people do not use public transportation at all and do not go to restaurants during the midday break. . full quarantine: this corresponds to what actually happened in france; people were confined at home except for a one hour stroll per day in low populated areas (public parks, forests, etc., were forbidden). again, to reduce the number of parameters, we assumed that the probability of contagion during the stroll was the same as at work. this also allowed us to take into account errands made to get food in more populated places such as groceries or supermarkets. starting from an initial state (number of contagious people in each sub-region), the simulation algorithm iterates the following process at each timestep until either the epidemic ends or the maximum duration of the simulation is reached (defaults to days). . first, the infection rate at time t, i rt (t), is computed as the product of the global daily rate of infection, g dri (t), by the infection factor of the current location (home, workplace, public transportation) l in f (t). this infection rate i rt (t) is used the same way the propensity is in the standard ssa. then, for each of the four age slices the deterministic continuous solver computes the average number of individuals of that age that will go from susceptible to asymptomatic state, avnew asympt , as the product of the population in that state and the infection rate at time t: the stochastic discrete solver (sds) computes stochastic integer numbers such that, on the long run, they will average to the same values as the continuous solver. even when the population is an integer number of individuals, this product, avnew asympt , is generally a floating point number because the infection rate is itself a floating point number. this number has an integral part (≥ ) and a fractional part (between and ). the (discrete) number of new asymptomatic hosts is then computed as the integer part of the average number, plus if a uniform random number taken into the interval [ . . . ] is below the fractional part: as the difference is . on the average, the higher the value is, the lower the relative impact of this stochastic discretisation becomes and the result is equivalent to a discrete averaged approach. conversely, the lower the value is, the more important the stochastic discretisation becomes. this mechanism allows the simulator to automatically choose the best strategy to adapt to the value range of the population [ ] . . finally, when the current time indicates the beginning of a new day, t ≡ (mod ), individuals in each state either remain in the same state but shifted by one day, or change to another state. all the states transitions are computed stochastically by the sds (or deterministically by the dcs) using the method described earlier. • the population in the asymptomatic state that has on average reached the / day limit is moved to the first day of the ill state. • according to the illness duration by age slice parameter, a proportion of the population in the ill state is moved to the hospitalised or to the recovered state. the others remaining in the ill state one more day. • according to the disease severity by age slice parameter, a proportion of the population in the hospitalised state is moved to the deceased or recovered state. the others remain in the hospitalised state one more day. the global daily rate of infection is then simply computed by multiplying the constant of propagation of the virus, k prop , by the proportion of the total contagious population: by fitting the simulation results after the beginning of the lockdown to the data gathered from hospital statistics, we empirically found a good estimation of k prop for the sars-cov- to . . we think that using pandaesim to model another type of epidemic, only this constant, along with the severity parameters, needs to be changed. we applied our simulation tool to the sars-cov- epidemic in france. we used the partitions of région and département in the country for the regions and sub-regions of our model. most of the parameters we used were gathered from the literature and statistical data made available by the french government. a few others were obtained empirically, mainly the number of contagious people in each région at the beginning of the simulations, and the constant of propagation of the sars-cov- . the per-age values of the percentage of lethality [ ] , illness duration and percentage of local and remote travellers are shown on table a , the various rates of contamination on table a , and the initial number of contagious people in each département on table a in appendix a. in order to test our population-centred algorithm, we first ran simulations without countermeasures and without any travel possibility, either local or remote. these simulations were run using successively the stochastic discrete solver and the deterministic continuous solver. when the initial number of contagious people was relatively high, for example, in the val-de-marne sub-region ( ), the results for both solvers were nearly identical: deaths for the average of stochastic runs and deaths for a deterministic run (figures and ) . the standard deviation for these runs went from ≈ at the beginning of the simulations (with a few tens of deaths) to ≈ at the peak of the infection (a few thousands of deaths), and then ≈ at the end. the same kinds of results appeared for the ill people with the maximum value of the standard deviation of ≈ reached on the th day, with , ill people. on the other hand, when the initial number of contagious people was low, as in loiret ( ), the dcs did not find any deaths, whereas runs of the sds showed two distinct behaviours; of these runs showed the same results as the dcs, no deaths at the end of the epidemic. the other runs took another direction leading to deaths on average with a standard deviation of ≈ ( figure ). the reasons for this apparent inconsistency will be explained in the discussion section. using the countermeasure applied in france (lockdown) the simulations showed us retrospectively that the probable date whereat there was a total of contagious people in france (beginning of the simulations) was approximately the end of january . this correlates with the period of time when the first deceased person was reported ( january). the view of the main window of pandaaesim shown on figure displays the real numbers of deceased people in each département. the map shown on figure displays the mean values of runs of a stochastic simulation. the overall results are very close, , for the real statistics and , for the mean value of the simulations. the département by département results are also fairly close, except for a few départements, but the orders of magnitude are more or less identical. to determine whether there is a form of convergence of stochastic trajectories to average values, we ran hundreds simulations and computed the mean value of the number of deaths (and of the other states) at each time step, in each département. the results showed no unique limit values, but the averages obtained with many runs stayed inside a range of values near the real statistics. we also ran pandaaesim using the deterministic continuous solver with the same parameters. the results were completely different: the epidemic ran only for days ( to weeks less) and reported deaths (figure ) , far from the , obtained with the stochastic simulations. the results département by département are also very different, with more than half the départements showing no deaths at all. again, probable reasons for this inconsistent behaviour are proposed in the next section. we developed a hybrid model and simulation programme derived from standard models and simulation techniques widely used in the fields of epidemic propagation and biochemistry. our approach used an original variant of the gillespie ssa with tau-leaping, where the inner algorithm can be easily switched from stochastic discrete to deterministic continuous. this allowed us to compare these two methods of simulation. to test our approach we applied it to the sars-cov- epidemic in france, for which relevant data were available. we also tested the consequences and the efficiency of the lockdown countermeasure applied in france for days. in order to gain spatial localisation but with an efficient population-centred algorithm where the population was supposedly being homogeneous, we partitioned the territory into relatively small units for which an instance of the population-centred simulation was run. the movements of populations between these units were taken into account at a higher scale, with a larger timestep. we first tested one instance of our population-centred algorithm, where no countermeasure was used. using each method (sds and dcs) with the same parameters values, we compared the results in two different situations: (i) with a moderately high number, and (ii) with a very low number of initially contagious people. when the numbers were relatively high, the results of both methods were very similar. this was not surprising because at each timestep the absolute value of the increment computed by each method must be significantly higher than , and the stochastic rounding to the inferior or superior integer cannot be relatively very far from the floating point value computed by the continuous method. however, when the numbers are low, the absolute value added at the next timestep is only a bit higher than , and therefore the stochastic rounding to or to drastically changes the future trajectory. this is particularly important in this very case where the populations experience an exponential growth. this may look like chaotic behaviour since a small difference in initial conditions can lead to very different futures, but when the numbers grow, the importance of this switch effect is dampened. we used many simulations batches with initially only two contagious individuals in the sub-region. the results of , , and simulations showed approximately the same proportions of cases, ≈ %, ending with no death at all, while the rest of the batch converged to approximately deaths. the same model using the dcs show no death at all. we think this behaviour is a consequence of a bifurcation due to the high non-linearity of the system. when the number of contagious individuals is below a certain threshold, the contagion tends to fade, but if this number goes over the threshold, there is a kind of positive feedback that increases it until a large enough part of the total population is removed. if we assume that the initial number of contagious individuals in our example ( ) is below the threshold, the result shown by the dcs is therefore correct. due to both its discrete increments and its stochastic behaviour, the sds can sometimes compute a trajectory that goes above the threshold and switches the other way. in order to deepen the study of this bifurcation phenomenon, we have tried to find the approximate value of the threshold. first we used the dcs with the initial number of contagious individuals varying from to . no deaths were found up to ; then deaths from to ; and deaths for and above. then we did the same tests with sds runs, counting the number of runs leading to zero deaths, and in the other case, the average number of deaths. with initially to contagious individuals, the number of runs leading to no deaths decreased from to ; with six and above initially contagious individuals no more simulations lead to zero deaths. for all the runs not leading to zero deaths, the average number of deaths was ≈ . the threshold for the sds is somewhere below . as expected, this value is very low. then we tested the whole simulator with all the population-centred processes, running independently for timesteps in each sub-region and then synchronised by exchanging a portion of each population either stochastically or deterministically. again, depending on the type of solver chosen and for the reasons mentioned earlier, the results were different but not by too much. with the number of people travelling from a given sub-region being a (small) fraction of the total population of this sub-region, the consequences in terms of infection spreading are very dependent on the value itself: less than , it is amplified by the stochastic processing, or else smoothed with the continuous calculation. both global results and sub-regions' local results were found to be very similar using the two methods. this can be explained by noticing that sub-regions with low initial contagious populations "benefit" from the migration of contagious people from more populated sub-regions, and as no countermeasure is applied, the number of contagious people grows rapidly over the threshold. the main difference appears in the shape of the nglobal curves: the deterministic solver showed a bigger dependency on the propagation effect ( figure ). since the dates sub-regions had their peaks of contamination were very different, the propagation effect was slower. although the global number of deaths is approximately the same ( , for the dcs, , for the sds) the slope of the curve obtained with the sds is steeper than the one obtained with the dcs (figure ). this can be explained by the relative sequentiality of the infection peaks showed by the continuous solver, whereas with the stochastic solver all the peaks are almost simultaneous and therefore the resultant is higher. for our last test, we set the simulator with the equivalent of the lockdown countermeasure used in france. the effect of this countermeasure was to decrease the number of contagious people, and while the sds gave results that correlate with the real statistics ( figure ), the dcs did not work well mainly because the initial number of contagious people was too low to be taken into account (figure ). more than half the départements did not show any death and therefore the total number of deaths was largely underestimated. we speculate that if we start from an initial state where there are enough contagious people in most sub-regions, it is very likely that the dcs will yield reliable results. this study gave us the opportunity to compare two different methods to get the trajectory of a complex system. at the beginning we were confident that they would yield very similar results, but facts proved us wrong. the reasons that caused the inconsistency of the behaviour of the stochastic discrete algorithm on the one hand and of the deterministic continuous algorithm on the other hand, lead us to be more confident in the stochastic approach for the simulation of this particular epidemic spreading model. more generally, with this type of model, an exponential growth phase is very sensitive to any variation, even small, in the initial values, and to artefacts, or calculation errors, and can therefore sometimes exhibit chaotic behaviours. nevertheless, this hybrid approach, a mix of an efficient population-centred process that plays the role of an agent in a multi-agent system, seems very promising. the stochastic simulations' results were very similar to the real statistics gathered from hospital data. future works could include improvements to the simulator such as the implementation of other types of countermeasures, the use more accurate methods to model the behaviour of individuals and the use different types of sub-regions to reflect their diversity. in this study we supposed no possible reinfection, so the epidemic effectively stopped after certain amount of time. although simplifying the model, this assumption forbids the possibility of modelling other waves of infection. recent publications discussed the consequences of different transmission scenarios, with and without permanent immunity, that can lead to multiple waves of infection [ ] . an interesting perspective would be to include in our model a probability of reinfection in order to test the effectiveness of countermeasures. funding: this research received no external funding. acknowledgments: many thanks to martin davy at sys diag, for the early version of the parameter dialog box, and the gathering of information about the sars-cov- . the authors declare no conflict of interest. the following abbreviations are used in this manuscript: in order to fit the simulation results to the real statistics, we estimated the number of asymptomatic hosts in each sub-region (départements) at the beginning of the simulations (table a ) . per-age values of the percentage of lethality (extrapolated from [ ] ), illness duration, and percentage of local and remote travellers (table a ). rates of contamination according to the location, percentage of hospitalised patients who can infect healing people, and proportion of severe form of the illness (table a ) . first cases of coronavirus disease (covid- ) in france: surveillance, investigations and control measures portant réglementation des déplacements dans 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-bwa wz authors: jung, kwonil; saif, linda j. title: porcine epidemic diarrhea virus infection: etiology, epidemiology, pathogenesis and immunoprophylaxis date: - - journal: vet j doi: . /j.tvjl. . . sha: doc_id: cord_uid: bwa wz porcine epidemic diarrhea virus (pedv), a member of the genera alphacoronavirus in the family coronaviridae, causes acute diarrhea/vomiting, dehydration and high mortality in seronegative neonatal piglets. for the last three decades, pedv infection has resulted in significant economic losses in the european and asian pig industries, but in – the disease was also reported in the us, canada and mexico. the ped epidemic in the us, from april to the present, has led to the loss of more than % of the us pig population. the disappearance and re-emergence of epidemic ped indicates that the virus is able to escape from current vaccination protocols, biosecurity and control systems. endemic ped is a significant problem, which is exacerbated by the emergence (or potential importation) of multiple pedv variants. epidemic pedv strains spread rapidly and cause a high number of pig deaths. these strains are highly enteropathogenic and acutely infect villous epithelial cells of the entire small and large intestines although the jejunum and ileum are the primary sites. pedv infections cause acute, severe atrophic enteritis accompanied by viremia that leads to profound diarrhea and vomiting, followed by extensive dehydration, which is the major cause of death in nursing piglets. a comprehensive understanding of the pathogenic characteristics of epidemic or endemic pedv strains is needed to prevent and control the disease in affected regions and to develop an effective vaccine. this review focuses on the etiology, epidemiology, disease mechanisms and pathogenesis as well as immunoprophylaxis against pedv infection. porcine epidemic diarrhea virus (pedv), a member of the genera alphacoronavirus in the family coronaviridae of the order nidovirales, causes acute diarrhea, vomiting, dehydration and high mortality in neonatal piglets, resulting in significant economic losses. the disease was initially reported in european and asian pig industries over the last years, with the virus first appearing in england (wood, ) and belgium (pensaert and de bouck, ) in the early s. recently, pedv has also been reported in the us (stevenson et al., ) . since then, the virus has rapidly spread nationwide throughout the usa (cima, ) and to other countries in north america, including canada and mexico. as a result of the significant impact of pedv, the us pig industry has lost almost % of its domestic pig population after only a year-epidemic period, amounting to approximately million piglets. similar epidemiological and clinical features between pedv and another alphacoronavirus, transmissible gastroenteritis virus (tgev), have led to complications in diagnosis, requiring differential laboratory tests (saif et al., ) . since the emergence of a natural spike gene deletion mutant of tgev, porcine respiratory coronavirus (prcv) in , the spread of tgev has been reduced in prcv-seropositive herds due to cross-protective immunity with tgev (saif et al., ) . in contrast, pedv continues to spread and cause economic problems worldwide. based on genetic analysis, the family coronaviridae can be divided into the four genera: alphacoronavirus, betacoronavirus, gammacoronavirus, and deltacoronavirus. bats are the projected host for the gene source of alphacoronaviruses and betacoronaviruses, while birds are the suspect host for gammacoronaviruses and deltacoronaviruses (woo et al., ) . in different us regions where pedv is epidemic, a new coronavirus genetically distinct from pedv, porcine deltacoronavirus (pdcov), has been simultaneously (and frequently) detected in diarrheic fecal samples from pigs (wang et al., a) . the clinical impact and disease severity of pdcov in the field is reportedly less than that of pedv. a recent study confirmed that pdcov is enteropathogenic in pigs and acutely infects the small intestine, causing severe diarrhea and/or vomiting and atrophic enteritis, similar to the clinical signs of pedv and tgev infections (jung et al., ) . at present, differential diagnosis of pedv, pdcov, and tgev is critical to control viral epidemic diarrheas in us pig farms. this review focuses on current understanding of the etiology, epidemiology, disease mechanisms and pathogenesis of pedv and the control measures that may be used to prevent pedv infection. pedv is enveloped and pleomorphic with a range in diameter of - nm, including the projections, which are approximately nm in length (pensaert and de bouck, ) . details of the pedv structure and genome can be found elsewhere (song and park, ) . pedv has a single-stranded positive-sense rna genome of approximately kb in size (excluding the poly a-tail) that encodes four structural proteins, namely, spike (s), envelope (e), membrane (m), and nucleocapsid (n) protein, and four nonstructural proteins: a, b, a, and b (kocherhans et al., ) . among the viral proteins, the s protein is critical for regulating interactions with specific host cell receptor glycoproteins to mediate viral entry and for inducing neutralizing antibodies (bosch et al., ) . the s protein is also associated with growth adaptation in vitro and attenuation of pedv virulence in vivo (sato et al., ) . the m protein is the most abundant component among viral proteins in the envelope and plays an important role in virus assembly by interacting with the s and n proteins (klumperman et al., ; vennema et al., ) . the n protein of coronavirus binds rna and packages viral genomic rna into the nucleocapsid of virus particles (spaan et al., ) . a previous study using the cell-adapted german isolate v / documented the biological and physicochemical properties of pedv (hofmann and wyler, ) . pedv showed a buoyant density of . . pedv was easily inactivated by ether or chloroform, and it was relatively stable at - °c compared to higher temperatures. after incubation in cell culture media at °c with a ph range ( - ) for h, pedv exhibited low to moderate residual infectivity, whereas at °c for h, it retained its infectivity only between the ph range and . , but the virus was completely inactivated at ph < and > ph . these data indicate that pedv will be inactivated by acidic or alkaline disinfectants if they are applied for a certain period at a higher temperature (> °c). the pedv strain v / was not neutralized by an antiserum to tgev (hofmann and wyler, ) . this finding was supported by another report , which showed no crossreactivity of pedv cv strain with either a belgian strain of tgev or feline infectious peritonitis virus (fipv), as determined by immune-electron microscopy and immunofluorescence (if). however, a subsequent study found a detectable, two-way crossreactivity between pedv and fipv by more sensitive assays, such as enzyme linked immune-sorbent assay, immunoblotting and immune-precipitation (zhou et al., ) . these discrepancies indicate that cross-reactivity between pedv and other coronaviruses probably varies depending on the sensitivity of the techniques and the viral strains tested. a recent study reported evidence of antigenic cross-activity between the prototype cv and recent us pedv strains and tgev (miller strain) by sharing at least one conserved epitope on the n-terminal region of their n proteins (lin et al., ) . pospischil et al. ( ) demonstrated that pedv is inactivated by disinfectants, namely, oxidizing agents (virkon s), bleach, phenolic compounds (one-stroke environ; tek-trol), % sodium hydroxide, formaldehyde and glutaraldehyde, sodium carbonate ( % anhydrous or % crystalline, with . % detergent), ionic and nonionic detergents, % strong iodophors in phosphoric acid, and lipid solvents such as chloroform. vero (african green monkey kidney) cells support the isolation and serial propagation of pedv in cell cultures supplemented with the exogenous protease trypsin. another african green monkey kidney cell line, marc- , also supported a subsequent cell passage of pedv (lawrence et al., ) . trypsin plays an important role in cell entry and release of pedv virions in vero cells, contributing to efficient replication and spread of the virus to neighboring cells in vitro (shirato et al., ; wicht et al., ) . trypsin resulted in the cleavage of the s protein into s and s subunits, which most likely accounts for cell-to-cell fusion and the release of virions from infected vero cells (shirato et al., ) . cytopathic effects consist of vacuolation and formation of syncytia as a result of apoptotic cell death (hofmann and wyler, ; kim and lee, ) . the hemagglutinating activity of pedv was demonstrated with rabbit erythrocytes only after trypsin treatment (park et al., ) . only one serotype of pedv has been reported from different countries (saif et al., ) . pedv first appeared in the united kingdom (wood, ) and belgium (pensaert and de bouck, ) in the early s. the virus was first isolated in in belgium and was classified in the family coronaviridae (pensaert and de bouck, ) . subsequently, in the s and s, pedv was identified as a cause of severe epidemics in japan and south korea (takahashi et al., ; kweon et al., ) . despite extensive application of pedv vaccines, ped has remained endemic in south korea (park et al., ) . during the s and s in europe, outbreaks of ped appeared infrequently, but the virus continued to spread and persisted in an endemic form in the pig population. subsequent serological surveys showed a low to moderate prevalence of pedv in european pigs (van reeth and pensaert, ; carvajal et al., ) . the prevalence of pedv in european pigs then declined greatly although the reasons are unclear. outbreaks of ped were observed only sporadically in europe: in the netherlands in - (pijpers et al., ) ; in hungary in (nagy et al., ) , and in england in (pritchard et al., ) . however, a typical epidemic outbreak of ped was identified in italy in - (martelli et al., . in thailand in - , several outbreaks of severe ped were reported with thai pedv isolates in the same clade phylogenetically as the chinese strain js- - (puranaveja et al., ) . this new genotype of pedv continues to cause sporadic outbreaks in thailand. in china in - , severe ped outbreaks in seropositive pigs were reported in different regions (li et al., ; sun et al., ; wang et al., ) . for almost two decades since pedv first emerged in china, many pig herds have been vaccinated with the prototype strain cv -inactivated or related vaccines. however, the moderate to high mortality of suckling piglets in vaccinated herds indicates a low effectiveness of the cv vaccines (li et al., ) . the ped outbreaks in china, in - , were caused by both classical and new pedv variant strains that differ genetically from the prototype cv (wang et al., ) . the us pedv strains identified during the initial outbreak in were closely related genetically to the chinese strains (china/ / ah ) reported in - chen et al., ) , indicating emergence of ah -like chinese pedv strains in the us. the us-like pedv strains were also found in diarrheic piglets in south korea and taiwan during late and early (cho et al., ; lin et al., ) , although whether chinese or us pedv strains could have been transmitted to pigs in south korea and taiwan is unknown. further investigations are needed to clarify if chinese or us pedv strains were already present in south korea and taiwan before the related outbreaks were first identified. for < year since the first outbreak, other novel us pedv strains (oh/oh ) with multiple deletions and insertions in their s gene, which clustered closely with chinese strain hbqx- or ch/ zmzdy/ , rather than ah , were found to possess low nucleotide identity in their ′-end s region (first nucleotides) and high nucleotide identity in the remaining s gene, compared to the major us pedv strains wang et al., b) . possible recombination events involving strain(s) from china may have contributed to a rapid evolution of us pedv and the emergence of multiple variants, complicating the molecular epidemiology of us pedv strains (tian et al., ) . remarkably, another pedv variant, which has a large amino acid (aa) deletion in the n-terminal portion of the s protein of major cell-cultured us pedv strains, such as pedv strain tc-pc a (genbank accession number km ), has emerged only year after the first outbreak (oka et al., ) . another pedv variant with a large ( aa) deletion at positions - of the s protein was identified among korean pedv strains . the fecal-oral route is the main means of pedv transmission, although aerosolized pedv remains infectious (alonso et al., ) . diarrheal feces and/or vomitus and other contaminated fomites, such as transport trailers (lowe et al., ) and feed (dee et al., ) , can be major transmission sources of the virus. another possible reservoir for pedv includes carriers, such as older pigs with a-symptomatic infection, in which the virus spreads subclinically. previous studies showed a low to moderate detection rate ( - %) of pedv rna in milk samples of affected, lactating sows (li et al., ; sun et al., ) , suggesting that sow milk might be a potential route for the vertical transmission of pedv. our study demonstrated a significant detection rate of pedv rna in acute serum samples ( - %) of experimentally infected piglets or naturally infected grower pigs . whether pork plasma used as a feed additive could be a transmission source of pedv remains questionable, since discrepant results were reported in two different infection studies that investigated whether spray-dried porcine plasma that had tested positive for pedv rna was infectious in seronegative pigs (opriessnig et al., ; pasick et al., ) . porcine small intestinal villous enterocytes express large amounts of aminopeptidase n (apn), a -kda glycosylated transmembrane protein, identified as the cellular receptor for pedv (li et al., ) . high density of the receptor on enterocytes allows pedv to enter and replicate through virus-receptor interactions (li et al., ) . pedv is cytolytic, and infected enterocytes rapidly undergo acute necrosis, leading to marked villous atrophy in the small but not in the large intestine ( fig. a ) . pedv antigens are observed mainly in villous enterocytes of the small (duodenum to ileum) ( fig. b ) and large intestines (except the rectum) stevenson et al., ; jung et al., ; madson et al., ) . like tgev (kim et al., ) , pedv may not induce apoptotic death of enterocytes in the small intestine of infected pigs (figs. c, d). occasionally, a few pedv-positive cells were detected in the intestinal crypt cells or peyer's patches during the late-stages of infection sueyoshi et al., ; stevenson et al., ; jung et al., ) . in our preliminary study, mean numbers of goblet cells per intestinal villi of infected gnotobiotic pigs (< /villus) at postinoculation hours (pih) - were fewer than those ( - / villus) of the negative counterparts (fig. ) . as with tgev (schwegmann-wessels et al., ) , pedv might infect goblet cells, leading to a dramatic decrease in this cell type during the early phase of diarrhea. goblet cells secrete mucins and provide the first line of defense against microbes in the intestine (kim and ho, ) . lung tissues of oronasally infected pigs were negative for pedv antigen, indicating no evidence of pedv replication in the lower respiratory tract sueyoshi et al., ; stevenson et al., ; jung et al., ) . pedv antigens were not detected in other major organs, such as pylorus, tonsils, spleen, liver and kidneys. however, a recent study reported the replication of pedv in porcine pulmonary macrophages in vitro and in vivo (park and shin, ) . whether extra-intestinal replication of pedv occurs still remains uncertain. pedv binds and infects enterocytes expressing apn. assembly of the virus in infected enterocytes occurs rapidly by budding through intracytoplasmic membranes, such as the endoplasmic reticulum and golgi apparatus (ducatelle et al., ) . during the incubation period, pedv antigen-positive cells were seen throughout the small intestine and as many as - % of the absorptive epithelial cells were positive , consistent with fecal shedding of asymptomatic pigs during the acute stage of infection. from the acute stage to mid-stage ( - h after onset of clinical signs) of infection, moderate to large numbers of pedv antigenpositive cells were observed throughout the small and large intestine, frequently affecting the entire villous epithelium . during the later-stage of infection (> h after onset of clinical signs), large numbers of pedv-infected epithelial cells were still observed, suggesting pedv re-infection of regenerating enterocytes . diarrhea induced by pedv is a consequence of malabsorption due to massive loss of absorptive enterocytes. functional disorders of infected enterocytes also contribute to the malabsorptive diarrhea. in the infected enterocytes examined by electron microscopy, loss of electron density of the cellular cytoplasm and rapid degeneration of mitochondria result in a lack of transport energy needed for absorption . ultrastructural changes and mild vacuolation observed in the infected colonic epithelial cells may interfere with the vital reabsorption of water and electrolytes . dehydration is exacerbated by vomiting but the mechanisms by which vomiting is induced in pedv infection are poorly understood. similar to hyperkalemia and acidosis in acute tgev infections (saif et al., ) , our preliminary study showed that pedvinoculated piglets at day after onset of severe watery diarrhea showed hypernatremia, hyperkalemia, and hyperchloremia, but with low calcium and bicarbonate levels. brush border membranebound digestive enzymes such as disaccharidases (lactase, sucrase, and maltase), leucine apn, and alkaline phosphatase are significantly decreased in the small intestine of diarrheic piglets jung et al., a) . reduced enzymatic activity in the small intestine results in maldigestive diarrhea. in our preliminary study, disorganized, irregular distribution and decreased expression of the tight junction protein, zonula occludin (zo)- , and adherens junction protein, e-cadherin, was observed in the small intestine of infected gnotobiotic pigs at pih - (fig. ) . the impaired gut integrity might lead to loss of water into the intestinal lumen with high osmotic pressure caused by pedv infection as well as uptake of luminal bacteria causing co-infections. the mechanisms by which pedv infection induces greater disease severity and deaths in nursing versus weaned pigs have not been clearly defined (shibata et al., ; madson et al., ) . several anatomical and physiological factors that may influence the higher susceptibility of suckling piglets to pedv infection and a longer recovery from disease include the slower turnover of enterocytes ( - days) in neonatal piglets compared to - days in -week-old weaned pigs (moon et al., ) . the high turnover rate of the intestinal epithelium depends on the stem cells found in the intestinal crypt. intestinal stem cells consist mainly of three cell types, namely, lgr (leucine-rich repeatcontaining g protein-coupled receptor )-positive crypt base columnar cells (lgr + cells), + cells, and paneth cells (sato and clevers, ) . however, the presence of paneth cells in the intestine of pigs is debatable (burkey et al., ) . our preliminary study revealed localization of large numbers of lgr + cells in the crypt cell layers of pedv-infected pigs (fig. ) , indicating the presence of stem cells that are critical to the epithelial cell renewal during the acute-stage of pedv infection (k. jung et al., unpublished data) . that study also revealed a lack of lgr + cells and low proliferation of crypt cells (small expression of ki protein in crypt cells) in the small intestine of nursing piglets ( -day-old) without pedv infection, possibly causing the slow turnover of enterocytes. at - days after pedv infection, however, the number of lgr + cells and proliferation of crypt cells were remarkably increased, leading to the replacement of necrotic enterocytes shed from infected villi. on the other hand, weaned pigs ( -week-old) without pedv infection exhibited high proliferation of intestinal crypt cells and large numbers of lgr + cells in the crypts, relating to the rapid turnover rate of enterocytes. large numbers of lgr + cells and high proliferation of crypt cells were maintained at - days after pedv infection, possibly resulting in a rapid recovery from ped in weaned pigs. viremia where viral rna in serum ranged from . to . log genomic equivalents (ge)/ml was detected in gnotobiotic piglets inoculated with a us pedv strain (pc a) at acute-to later-stages of infection . similar findings were observed in field samples, showing that / acute serum samples ( %) collected from diarrheic - -week-old pigs had viral rna titers ( . - . log ge/ml) . the early, severe diarrhea/ vomiting and high pedv fecal shedding titers might be accompanied by viremia, but no one has yet confirmed the presence of infectious virus in the serum. there is a dearth of information on the innate and adaptive immune responses to pedv. after pedv infection, infiltration of lymphocytes (cd + and cd + t cells at pih - ) (fig. ) , mononuclear cells, eosinophils and neutrophil was observed in the lamina propria of the small intestine coussement et al., ; sueyoshi et al., ) . isotype-specific antibody-secreting cells in systemic and mucosal associated lymphoid tissues and serum antibody responses were studied in conventional pigs inoculated with the cv strain (de arriba et al., ) . cultured intestinal epithelial cells expressing the e protein of pedv up-regulated interleukin (il)- expression in vitro (xu et al., ) . the pathogenicity of epidemic pedv strains is commonly severe, as evidenced by the high mortality of infected nursing piglets. however, attenuation of the virulence of pedv strains has been induced through high cell-culture passages ( rd- th) (kweon et al., ; song et al., ; sato et al., ) . the attenuated pedv strains have multiple nucleotide changes in their s and open reading frame (orf ) genes compared to those of their parent wild-type strains (song et al., ; sato et al., ) . among the nucleotides of orf , two deletions and seven changes were identified between the parent wild-type dr pedv and the cell-adapted pedv ( th) that was confirmed to be attenuated (song et al., ; sato et al., ) . notably, the s genes of the two attenuated pedv strains, korean dr ( th) and japanese p- ( th), had a remarkable similarity with comparable nucleotide mutations and aa substitutions relative to their parental viruses. the attenuated p- had nucleotide mutations and predicted aa substitutions in the s gene. similarly, the sequence analysis of a us pedv strain and in vitro passaged virus ( th in marc- cells) showed that the cell culture adaptation specifically modifies pedv s protein (six aa substitutions) whereas the open reading frame a/b (orf a/b)-encoded polyprotein, orf , e, m, and n proteins remained unchanged (lawrence et al., ) . multiple nucleotide mutations and aa substitutions in the s gene of pedv might contribute to attenuation of its in vivo pathogenicity, but the entire pedv genomes should be sequenced to verify other changes after attenuation. detailed clinical disease and complications as a result of typical epidemic ped were documented on seronegative pig breeding farms in the uk in - (wood, , belgium in (pensaert and de bouck, ), japan in (sueyoshi et al., ), italy in - (martelli et al., ), thailand in (puranaveja et al., , and the us in (stevenson et al., ) . the clinical outbreaks on seronegative farms were characterized by a sudden epidemic of severe diarrhea and/or vomiting, accompanied by anorexia and significantly reduced appetite, in pigs of all ages. the severity of clinical signs and mortality appeared to be inversely related to the age of the pigs (shibata et al., ) . in weaner to finisher pigs, including pregnant sows, clinical signs are selflimiting within - days after onset of disease and are not as severe as those of nursing piglets under weeks of age (martelli et al., ; puranaveja et al., ) . when pregnant sows become immune after virus exposure, they protect their offspring by lactogenic immunity. the interval between onset and cessation of the disease is generally - weeks (puranaveja et al., ) , however clinical signs mainly develop in the seronegative lactating sows and their suckling piglets. in farrowing herds, morbidity can approach % in piglets, but varies in sows. mortality of piglets < weeks of age can exceed % ( % on average) at - days after onset of severe watery diarrhea and/or vomiting. field observations on epidemic ped in the uk in - (wood, and in the us in (stevenson et al., ) as well as experimental findings (pensaert and de bouck, ) suggest that the incubation period of pedv before clinical signs are detected varied, ranging from to days (us pedv) or - days (uk pedv). experimental studies using the prototype cv showed that - day-old, caesarean-derived, colostrum-deprived (cdcd) pigs developed diarrhea within pih - (pensaert and de bouck, ; debouck et al., ) . another us pedv infection study using - -day-old gnotobiotic pigs with . - . log ge showed that severe diarrhea and/or vomiting were detected commonly within pih - original magnification, × . nuclei were stained with blue-fluorescent ′, -diamidino- -phenylindole dihydrochloride. immunofluorescence staining using monoclonal antibodies against human recombinant zo- and e-cadherin (invitrogen). . unlike cdcd or gnotobiotic pigs, conventional nursing piglets inoculated with . - . log % tissue culture infectious dose (tcid ) of a chinese pedv strain had a longer incubation period ( - days after inoculation) before clinical signs were detected (wang et al., ) . detailed clinical disease and problems caused by endemic ped were documented in a farrow-to-finish farm in the netherlands in - (pijpers et al., . during the outbreak in , diarrhea was most severe in fattening pigs and pregnant sows, and was mild or absent in nursing and weaning pigs with no mortality. for at least months after the onset of the first outbreak, pedv became endemic on this farm and the infection persisted in seronegative gilts or - -week-old pigs newly introduced to the farm. another typical endemic ped has been manifested in korean pig farms. korean farms have employed live or inactivated pedv vaccines using three korean strains dr , kpedv- and sm - or a japanese strain p- v. studies reported that recent prevalent korean pedv field isolates are closely related to chinese strains and differ genetically from the four vaccine strains used in korea and the prototype cv (park et al., ) . this divergence of historic vaccine and recent field pedv strains may contribute to the reduced efficacy of the vaccines, causing difficulty with eradication of pedv from pig farms with endemic ped in the korean pig population. like endemic tge, pedv-related mortality and morbidity of nursing piglets passively immunized is lower than is seen in seronegative pigs (bohl et al., ) . endemic ped is manifested mainly in weaned pigs (pijpers et al., ) , and the severity of clinical disease in nursing piglets may be exacerbated by co-infections of other enteropathogens (escherichia coli, % for chinese piglets or % for canadian piglets) (turgeon et al., ; wang et al., ) , or viruses including porcine circovirus type (pcv ) ( - % for korean piglets), tgev ( % for chinese piglets), and rotavirus ( % for chinese piglets) (hirai et al., ; jung et al., b; wang et al., ) . gross lesions are limited to the gastrointestinal tract and are characterized by thin and transparent intestinal walls (duodenum to colon) with accumulation of large amounts of yellow fluid in the intestinal lumen sueyoshi et al., ; stevenson et al., ) . the stomach is filled with curdled milk, possibly due to reduced intestinal peristalsis. congestion of the mesenteric vessels is frequently detected, and mesenteric lymph nodes (mln) are edematous. lack of intestinal lacteals, as an indicator of malabsorption, is frequently seen (puranaveja et al., ) . despite persistent severe diarrhea, infected pigs had low to moderate appetite at - days after onset of diarrhea after which they became moribund . histological lesions consist of acute diffuse, severe atrophic enteritis and mild vacuolation of superficial epithelial cells and subepithelial edema in the cecum and colon coussement et al., ; sueyoshi et al., ; jung et al., ) . based on electron microscopy, one of four piglets infected with cv had ultrastructural changes in the colonic epithelial cells, but with a lack of histological lesions . during acute infection, vacuolated enterocytes or massive cell exfoliation were seen on the tips or the entire villi in the jejunum. atrophied villi are frequently fused and covered with a degenerate or regenerated flattened epithelium. infiltration of inflammatory cells is evident in the lamina propria. the crypts of lieberkuhn in the duodenum appeared normal . no lesions were seen in the spleen, liver, lung, kidney, and mln of orally and/or intranasally infected piglets . during the incubation period, i.e. prior to onset of clinical signs, infected pigs exhibited normal villous lengths but with vacuolated enterocytes undergoing necrosis . for - days after the onset of diarrhea, infected pigs exhibited severe villous shortening . piglets euthanased at a later stage of infection ( - h after onset of clinical signs) had moderate to severe villous atrophy jung et al., ) , indicative of continued cellular necrosis. after pedv infection, intestinal crypt layers included lgr + cells (fig. ) and crypt cells positive for ki protein that is a marker for proliferating cells (jung et al., ) . the time of onset and severity of malabsorptive diarrhea induced by pedv may depend on the extent of villous atrophy in the jejunum and the rapidity of replacement by the crypt stem cells. when ped occurs in a seronegative breeding farm, immunization or vaccination of pregnant sows is important in the control of epidemic ped and to reduce the number of deaths of suckling piglets. if the sows are due to farrow within weeks or more, immunization can be undertaken by exposure to virulent autogenous virus, such as fecal slurry or minced intestines from infected neonatal piglets. however, there is a potential risk of incidental widespread infection of other pathogenic viruses, such as pcv , contained in the pedv-infected piglets' feces or intestines among sows or their suckling piglets via vertical transmission routes (jung et al., c; park et al., ; ha et al., ) . the importance and mechanisms of passive lactogenic immunity to provide newborn piglets with immediate protection against tgev infection have been reviewed by saif et al. ( ) . all strains of epidemic pedv in europe, asia and the us are highly enteropathogenic, as evidenced by the high mortality of infected nursing piglets. however, attenuation of the virulence of korean (kpedv- and dr ) or japanese ( p- ) pedv strains could be induced through high cell-culture passages ( rd- th) (kweon et al., ; song et al., ; sato et al., ) . in addition, the attenuated cell-adapted pedv strains have been used as oral (korean strain dr only) or intramuscular (im) live virus vaccines. the im administration of live attenuated kpedv- pedv vaccine ( ml of tcid /ml; twice at or weeks before farrowing) reduced the % mortality rate of piglets challenged with five % lethal dose (ld ) of the parent wild-type strain and the % mortality rate of piglets challenged with ld to % and %, respectively (kweon et al., ) . the efficacy might be associated with high pedv specific igg levels in the serum and colostrum of vaccinated sows (song et al., ) . a study using im live attenuated dr pedv vaccine ( ml of tcid /ml; twice at or weeks before farrowing) reduced the % mortality of piglets challenged with a high-dose of the parent dr to % (song et al., ) . based on these observations, pregnant sows can be vaccinated using live attenuated pedv strains via an im route, but induction of complete protection was not observed in the nursing piglets. active immunization of nursing or feeder pigs is important for the control of endemic pedv infections (saif et al., ) . a field study (song et al., ) showed that compared to vaccination via im route, oral administration with live attenuated pedv (dr strain) vaccine twice or weeks before farrowing was more effective in boosting or initiating immunity in pregnant sows and their suckling piglets ( -day-old). the vaccinated sows and their piglets exhibited higher iga (mucosal immunity) and virus neutralization antibody (humoral immunity) levels in the colostrum or sera compared to those of the counterparts administered the im vaccine with the same dose. however, the presence of maternal antibodies in vaccinated pigs can interfere with active antibody production after pedv infection, as observed in tgev infection (sestak et al., ; saif et al., ) . whether the oral live vaccine strain is genetically stable and remains non-infectious in the fields needs to be further studied. disappearance and re-emergence of epidemic ped indicates that pedv is effectively able to escape from the current vaccination protocols, biosecurity and control systems. endemic ped is a significant problem, which is exacerbated by the emergence or potential importation of multiple pedv variants into countries. epidemic pedv strains spread rapidly and cause a high number of pig deaths and substantial economic losses. these strains are highly enteropathogenic and acutely infect villous epithelial cells of the entire small and large intestines although the jejunum and ileum are the primary sites of infection. pedv infections cause acute, severe atrophic enteritis accompanied by viremia (viral rna) that leads to severe diarrhea and vomiting, followed by extensive dehydration and imbalanced blood electrolytes as the major cause of death in nursing piglets. a better understanding of the pathogenic characteristics of epidemic or endemic pedv strains is needed to prevent and control the disease in affected regions and in the development of effective vaccine. high mortality of pedv-infected, seronegative nursing piglets is most likely associated with extensive dehydration as a result of severe villous atrophy. in infected nursing piglets, there is an increased proliferation of crypt cells as well as numbers of lgr + crypt stem cells in the intestine, reorganization of the damaged intestinal epithelium, and migration of mature enterocytes to the tips of villi which may be not sufficient to prevent severe dehydration in nursing piglets. the time taken until dehydration of pedv-infected nursing piglets in the field appears to be too short to enable the animals to recover from the disease through naturally occurring epithelial cell renewal by crypt stem cells. further studies are needed to define the extent to which intestinal stem cells in nursing versus weaned pigs organize and migrate to replace pedv-infected villous epithelial cells. pharmacological or biological mediators such as epidermal growth factor that promote stem cell regeneration or maturation would be interesting targets to try to shorten the time for epithelial cell renewal and to reduce pedv death losses from dehydration. neither of the authors of this paper has a financial or personal relationship with other people or organizations that could inappropriately influence or bias the content of the paper. whose contributions to pedv research may have been inadvertently and unintentionally missed. salaries and research support were provided by state and federal funds appropriated to the ohio agricultural research and development center, the ohio state 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porcine epidemic diarrhea virus proteolytic activation of the porcine epidemic diarrhea coronavirus spike fusion protein by trypsin in cell culture discovery of seven novel mammalian and avian coronaviruses in the genus deltacoronavirus supports bat coronaviruses as the gene source of alphacoronavirus and betacoronavirus and avian coronaviruses as the gene source of gammacoronavirus and deltacoronavirus an apparently new syndrome of porcine epidemic diarrhoea porcine epidemic diarrhea virus e protein causes endoplasmic reticulum stress and up-regulates interleukin- expression porcine epidemic diarrhea virus (cv ) and feline infectious peritonitis virus (fipv) are antigenically related we thank bryan eyerly and xiaohong wang for technical assistance in immunofluorescence staining. we apologize to authors key: cord- - gvx swf authors: xie, zhixiang; qin, yaochen; li, yang; shen, wei; zheng, zhicheng; liu, shirui title: spatial and temporal differentiation of covid- epidemic spread in mainland china and its influencing factors date: - - journal: sci total environ doi: . /j.scitotenv. . sha: doc_id: cord_uid: gvx swf abstract this paper uses the exploratory spatial data analysis and the geodetector method to analyze the spatial and temporal differentiation characteristics and the influencing factors of the covid- (corona virus disease ) epidemic spread in mainland china based on the cumulative confirmed cases, average temperature, and socio-economic data. the results show that: ( ) the epidemic spread rapidly from january to february , , and the distribution of the epidemic areas tended to be stable over time. the epidemic spread rate in hubei province, in its surrounding, and in some economically developed cities was higher, while that in western part of china and in remote areas of central and eastern china was lower. ( ) the global and local spatial correlation characteristics of the epidemic distribution present a positive correlation. specifically, the global spatial correlation characteristics experienced a change process from agglomeration to decentralization. the local spatial correlation characteristics were mainly composed of the‘high-high’ and ‘low-low’ clustering types, and the situation of the contiguous layout was very significant. ( ) the population inflow from wuhan and the strength of economic connection were the main factors affecting the epidemic spread, together with the population distribution, transport accessibility, average temperature, and medical facilities, which affected the epidemic spread to varying degrees. ( ) the detection factors interacted mainly through the mutual enhancement and nonlinear enhancement, and their influence on the epidemic spread rate exceeded that of single factors. besides, each detection factor has an interval range that is conducive to the epidemic spread. j o u r n a l p r e -p r o o f total of countries or regions in the world appeared to be hit by the covid- epidemic, and more than , people have been diagnosed. with the continuous spread of the covid- epidemic, several countries or regions of the world have been forced to take emergency measures such as closing cities, stopping production, suspending school classes, and restricting population movement, causing great harm to economic development and residents' health (an and jia, ) . therefore, it has become an urgent scientific problem to grasp the spatial and temporal changes of the covid- epidemic spread, and clarify the driving mechanism. since the outbreak of covid- epidemic, scholars have carried out abundant studies on the epidemic spread and achieved fruitful research results, which are of great guiding significance for the prevention and control of the epidemic. joseph et al. ( ) estimated the size of the epidemic by using a mathematical model based on the data of confirmed cases of covid- and residents' travel (including via trains, planes, and roads), and concluded that about , people were infected in the wuhan city during the early outbreak stage of the epidemic. david et al. ( ) compared covid- with other viruses, claiming that a sustained epidemic would pose a serious threat to global health, and proposing that the goal of sustainable development could be achieved by building a human-environment-animal health alliance. liu et al. ( a) used the exponential growth and maximum likelihood estimation method to determine the transmission dynamics of covid- in wuhan, and found that the average incubation period of the virus was . days, and the basic regeneration index reached . ( % confidence interval (ci): . - . ) and . ( % ci: . - . ). ai et al. ( ) used the statistical analysis method to investigate the impact of lockdown measures in wuhan (january , ) on the covid- epidemic spread in other parts of china. they claim that if the closure j o u r n a l p r e -p r o o f measures were implemented days in advance, it could have been possible to effectively prevent from being infected of , people, if the city was closed days later, there would have been , more infections. bai et al. ( ) used the transmission dynamics model to describe the evolution rule of the epidemic based on the data of confirmed covid- cases in the shaanxi province, revealed that the high incidence areas were mainly located in xi 'an, ankang, and hanzhong, and that the outbreak peak period was in early february , with the basic regeneration index of the epidemic spread reaching . . wang et al. ( a) used the spearman correlation analysis method to find the relationship between the incidence of covid- and the baidu migration index in guangdong province, and found that there was a positive correlation between the daily incidence and the -day migration index. wang et al. ( b) used the complex network model to explore the impact of resuming work in surrounding cities on the epidemic situation in hubei province on february , february , and march , and came to a conclusion that resuming work on march would not cause a second outbreak of the epidemic. yan et al. ( ) predicted the trend of the covid- epidemic by building a time-delay dynamics model, and claimed that the epidemic could be controlled in the short period if the prevention and control efforts were kept unchanged. chen and cao ( ) made an epidemiological analysis of the daily confirmed cases in china, affirming that the situation of epidemic prevention and control in china was severe, and that targeted control measures should be formulated for the returning of enterprises and personnel in the future. liu et al. ( b) analyzed the spatial and temporal characteristics of the epidemic spread in guangdong province, and found that the prevention and control measures adopted were effective, and high-risk areas were located in economically developed areas. liu et al. ( c) used the statistical analysis method to analyze the temporal and spatial j o u r n a l p r e -p r o o f characteristics and the transmission path of the covid- epidemic in zhuhai, revealing that the input from the epidemic area and family gatherings were the causes of epidemic spread. the research report published by the yellow river civilization (ai et al., ; wang et al., b) . although some scholars try to reveal the epidemic spread rules from a geographical perspective, they mainly focus on the spatial and temporal evolution characteristics of the epidemic, and seldom discuss the driving causes of the epidemic spread (liu et al., c) . ( ) in terms of research methods, current studies employ mainly the correlation analyses and regression analyses method, while the application of modern information technology and spatial analysis method are relatively limited (wang et al., a) . ( ) in terms of research scale, scholars generally investigate the epidemic spread characteristics at the city or regional scale, and there are few studies at the national level (liu et al., b; liu et al., b) . ( ) in relation to data sources, the data of covid- cases can be obtained very easily; however, there are great difficulties in obtaining environmental and socio-economic data related to the epidemic spread, which is why current researches lag behind in the driving j o u r n a l p r e -p r o o f mechanism of epidemic spread. in this paper, the number of confirmed covid- cases in mainland china was taken as the measurement index, and the spatial and temporal differentiation of the epidemic spread were described by the exploratory spatial data analysis method. then, the key factors affecting the covid- epidemic spread were identified by using the geodetector method, so as to provide references for clarifying the epidemic spread rule, formulating some protection policies, and promoting the resumption of work and production. the basic research objects of this paper are the administrative units at prefecture- baidu migration data in the paper is from january to , , specifically referring to the top cities toward which people move out of wuhan every day. the winter average temperature data for each unit are from the weather network (https://www.tianqi.com). in addition, since it is impossible to obtain data on the population, gross domestic product, and number of beds in medical institutions for each region during the covid- epidemic period, this paper employs the corresponding data in , which is derived from the provincial statistical yearbooks or the statistical bulletins. using the cumulative number of covid- cases as an indicator to measure the epidemic spread rate is biased due to the large differences in base population for different regions of mainland china. therefore, the cumulative number of covid- cases was divided by the number of days to calculate the epidemic spread rate, using the following formula: where v i represents the epidemic spread rate in region i; s i represents the cumulative number of covid- cases in region i by february ; m represents february ; and n i represents the date of the first confirmed case in region i. j o u r n a l p r e -p r o o f the exploratory spatial data analysis method was used to verify whether the observed value of a unit has spatial correlation with the observed values of its neighboring units (li et al., ) . the global moran's i index is used to measure the global spatial correlation, while the local moran's i index in lisa (local indicators of spatial association) was used to measure the local spatial correlation (rong et al., ) . their formulas (anselin, ; gallo and ertur, ) are as follows: where i is the global moran's i index; x i and x j are the observed values of unit i and j; w ij is the spatial weight matrix (with as adjacent, and as non-adjacent), s represents the variance; k represents the number of observation units; i* is the local moran's i index; w pq is the normalized form of the spatial weight matrix; and z p , z q are the normalized forms of the observed values in unit p and q. spatial differentiation is a basic characteristic of geographical phenomena, the geodetector method can measure the degree of spatial stratified heterogeneity and test its significance, through the within-strata variance less than the between strata variance . the geodetector method comprises four modules: factor detection, interaction detection, risk detection and ecological detection. the factor detection is expressed by q value (wang and xu, ) , its formulas are as follows: where q represents the explanatory power of detect factor x on the spatial distribution of detected factor y, the value of q ranges from to ; h= ,…, l, which represents the stratification of the detect factor x and detected factor y; n h and n are the number of samples for the layer h and the whole study area; ℎ and are the variance of y value for the layer h and the whole study area; ssw and sst are the sum of intra-layer variances and the total variance of the whole study area. the interaction detection can identify the explanatory power of the detect factors x and x to the detected factor y, whose operation steps are as follows: first, we calculate the q values of x and x , respectively. second, a new layer x ∩x can be obtained by stacking the layer x and x , on this basis, the q (x ∩x ) value can be calculated. third, the interaction type between x and x can be determined by comparing q (x ), q (x ), and q (x ∩x ) values. the risk detection is used to determine whether there exists a significant difference in the mean value of an attribute between the two sub-regions, which is tested by the t-statistic. its formula is as follows : where y h represents the average value of epidemic spread rate in the layer h, n h is the number of samples in the layer h, var represents the variance. we can compare whether there are significant differences in the influence of any detect factors x and x on the spatial distribution of the detected factor y by using the ecological detection, which is measured by the f-statistic. where and represent the sample sizes of the detect factors x and x ; and are the sum of the variances in the layers formed by x and x ; and l and l are the number of layers of x and x . the null hypothesis h is: if h is rejected at the significance level of , which indicates that x and x have significantly different effects on the spatial distribution of y. the arcgis software was used to classify the cumulative number of covid- cases in the following categories: ; - ; - ; - ; and > persons. the epidemic spread rate was classified into the following categories: < ; - ; - ; - ; and > persons/day ( figure ). j o u r n a l p r e -p r o o f ( ) global spatial correlation characteristics in this paper, the cumulative number of confirmed covid- cases and the epidemic spread rate were taken as variables, the spatial weight matrix based on geographical adjacency was selected, and the global moran's i index, the p test value and the z statistic score of the cumulative number of confirmed covid- cases and the epidemic spread rate were calculated by using the geoda software, so as to clarify the global spatial correlation characteristics (table ) . respectively, passing the significance test at the % level, implying that the spatial pattern of the epidemic spread rate was also characterized by a clustering distribution. ( ) local spatial correlation characteristics the global moran's i index has the defect of ignoring the instability of local spatial processes. therefore, it is necessary to draw a lisa cluster map to analyze the local spatial correlation characteristics of covid- epidemic (figure ). cluster areas were located in anqing, lu'an, jiujiang, nanyang, qianjiang, shennongjia forest region, and changde; and the range of 'low-low' cluster was basically consistent with that of february . in terms of quantity change, the number of units classified in the 'high-high' cluster first increased and then decreased; the number of units included in the 'high-low' cluster continued to decrease until they disappeared; that in the 'low-high' cluster experienced a process of initial decline and then rose again; and the number of units belonged to the 'low-low' cluster showed an increasing trend. therefore, it is not difficult to see that the layout trend of the j o u r n a l p r e -p r o o f cumulative number of confirmed covid- cases at the time nodes has not changed fundamentally, and was dominated by the 'high-high' and 'low-low' type. this indicates that the local spatial correlation characteristics of the confirmed covid- cases were also dominated by a positive correlation, although the clustering trend was weakened. overall, the 'high-high' cluster areas showed a layout trend from centralization to decentralization, which tended to be stable over time, especially for wuhan and its surrounding areas. there was a contiguous layout trend of the 'lowlow' cluster areas, which were mainly located in inner mongolia, gansu, ningxia, qinghai, tibet, and xinjiang. as for the epidemic spread rate, there were administrative units in the 'high-high' cluster, in the 'high-low' cluster, in the 'low-high' cluster, and in the 'low-low' cluster. the high-high cluster areas were located in wuhan, huangshi, yichang, xiangyang, ezhou, jingmen, xiaogan, jingzhou, huanggang, xianning, suizhou, xiantao, qianjiang, tianmen, nanyang, and xinyang; the 'low-high' cluster areas were located in anqing, lu'an, jiujiang, shennongjia forest region, and changde; and the 'low-low' cluster areas were located in western china. the covid- epidemic first occurred in wuhan, and then spread to other parts of china. therefore, people have been the carrier, the transportation network has been the channel, and the social and economic connections have been the internal driving force in the process of the epidemic spread. thus, we selected the indicators reflecting the population distribution, population inflow from wuhan, traffic accessibility, economic connection intensity, average temperature, and medical facilities conditions j o u r n a l p r e -p r o o f as the detection factors (table ) , and the epidemic spread rate as the detected factor to assess the formation mechanism for the spatial pattern of covid- epidemic. note: the gravity model was used to calculate the intensity of economic contact between each region and wuhan, and the distance was the time reachable distance (meng and lu, ). firstly, the classification method of natural discontinuities in arcgis . software was used to divide detection factors into categories, the classified maps of the detection factors were drawn (figure ). according to formulas ( )-( ), the determination ability of detection factors was calculated by using the geodetector software to analyze the influencing factors of epidemic spread. j o u r n a l p r e -p r o o f ( ) factor detection analysis the q values of all the detection factors passed the significance test at the % level, indicating that these factors have a significant determination ability of the spatial distribution of the covid- epidemic spread. specifically, the q (p) values of x , x , x , x , x and x were equal to . ( . ), . ( . ), . ( . ), . ( . ), . ( . ) and . ( . ), respectively. according to the size of q value, the inflow of population from wuhan was the primary factor affecting the epidemic spread, and its explanatory power reached . %. the economic connection intensity was the secondary determinant factor, and its explanatory power was . %. the availability of medical facilities was the third determinant factor, which accounted for a . % of explanation power. the determination ability of population distribution was %, while the traffic accessibility and average temperature were both relatively weak, below %. it is worth noting that the differentiation and factor detection analysis discussed only the determination ability of single factor on the epidemic spread rate, and did not consider the interaction effect of factors. ( ) interaction detection analysis the interaction detector analysis is used to identify the interactions between any j o u r n a l p r e -p r o o f two factors. table shows the interactions detection results between factors. it can be seen from table ( ) ecological detection analysis according to table , it could be found that the differences among the detection factors were statistically significant. specifically, the influence of the population distribution (x ) on the spatial distribution of the epidemic spread rate was significantly different from the population inflow from wuhan (x ), economic connection intensity (x ), and average temperature (x ), but not different from the traffic accessibility (x ) and medical facility conditions (x ). the influence of the population inflow from wuhan (x ) was significantly different from that of the traffic accessibility (x ), economic connection intensity (x ), average temperature (x ), and medical facilities conditions (x ). there was a significant difference between the influence of traffic accessibility (x ) and that of economic connection intensity (x ), but there were no significant difference with the average temperature (x ) and medical facilities conditions (x ). the influence of economic connection intensity (x ) was different from that of the average temperature (x ) and medical facility condition (x ). there was no significant difference between the average temperature (x ) and the medical facilities conditions (x ). generally speaking, the detection factors selected in this paper are reasonable, and the differences among them are statistically significant. note: y means the difference of the influence of the two factors is significant with the confidence of %, while n means no significant difference. ( ) risk detection analysis table showed that the epidemic had the fastest spread rate when the population density was , - , persons/km . when the proportion of population inflow from wuhan was maintained at . - . %, the epidemic spread rate was fastest. when the economic contact intensity with wuhan was kept in the range of , . - , , . , the epidemic spread rate was fastest. when the geographical distance from wuhan was . - . km, the spread rate was fastest. when the average temperature in winter was maintained at - °c, the epidemic spread rate was higher. the epidemic spread rate was higher when there were between . and . beds for , persons. it can also be found that the population distribution, population inflow from wuhan, economic connection intensity, medical facilities, and the epidemic spread rate were significantly positively correlated, while the traffic accessibility was negatively correlated with the epidemic spread rate. this paper studied the spatial and temporal variation and the influencing factors of the covid- epidemic spread in mainland china, which can provide references for formulating the public health policies and promoting the resumption of production. however, there exist the following problems. in terms of data sources, although many countries or regions have published the epidemic announcements of covid- in real time, and the epidemic data was very convenient, virtually most of countries or regions had more people infected than registered, which could affect the accuracy of the evaluation results. then, the population density data in was used as a replacement due to a fact that the population density for the each administrative unit in mainland china during the epidemic period was unavailable. the treatment method hid the drastic changes in the data because the covid- epidemic happened during the chinese spring festival period, which had a characteristic that the scale and frequency of population movements were intensified. it's worth noting that the population density is an important indicator to explain the epidemic spread rate, so the alternative data inevitably weakened the explanatory power of current research from this perspective. in addition, the factors affecting the epidemic spread were complex, and involved both the quantitative and the non-quantitative indicators. this paper constructed an indicator system of the multiple factors influencing the epidemic spread based on the principle of data availability; the other non-quantitative indicators might be ignored, which increased the uncertainty of evaluation results. for the research method, the formula of epidemic spread rate was applicable to compare the epidemic spread rate of different administrative units at three time nodes, which actually did not conform to the exponential growth rule of infectious diseases (such as the covid- , sars, and mers (middle east respiratory syndrome)) in the exposed population. how to accurately measure the actual spread rate of the epidemic in each region was the direction of future research. second, the exploratory spatial data analysis method investigated the spatial clustering characteristics of covid- epidemic in administrative units at prefectural level and above, and did j o u r n a l p r e -p r o o f not consider the agglomeration development situation at a finer spatial scale, which inevitably weakened the application value of the research results. third, the geodetector method was adopted to obtain the most favorable range of the covid- epidemic spread in this paper, which was developed from the perspective of statistics. the sample data directly affected the final evaluation result, and no epidemiological investigation on the residents' health status was implemented, so the conclusions drawn from current research were uncertain to some extent. finally, there might have multicollinearity between the strength of economic connection economic and other factors in this paper, and the geodetector method was not used to deal with it, which would weaken the persuasiveness of the research results. ( ) the temporal changes of the covid- epidemic in mainland china are clear, and the epidemic spread rate has an evident spatial variation. in terms of temporal change, the epidemic quickly spread to most regions from january to february . the epidemic spread rate slowed down from february to february , although the epidemic situation in some cities worsened sharply. the areas where the epidemic spread quickly were mainly located in the hubei province, its surrounding areas, and some economically developed cities. the western part of china, as well as the remote areas of central and eastern china experienced a slow epidemic spread. ( ) the global and local spatial correlation characteristics of the covid- epidemic were dominated by clustering situations. specifically, the global spatial correlation characteristics initially increased and then decreased, while the local spatial correlation characteristics tended to be stable with the passage of time, and were mainly composed of the 'high-high' and 'low-low' cluster types. the 'high-j o u r n a l p r e -p r o o f high' cluster areas were located in wuhan, huangshi, yichang, xiangyang, ezhou, jingmen, xiaogan, jingzhou, huanggang, xianning, suizhou, xiantao, qianjiang, tianmen, nanyang and xinyang. the 'low-low' cluster areas were located in parts of inner mongolia, gansu, ningxia, qinghai, tibet, and xinjiang. ( ) the population distribution, population inflow from wuhan, traffic accessibility, economic connection intensity, average temperature and medical facilities conditions had significant effects on the epidemic spread rate. the population inflow from wuhan was the primary factor affecting the epidemic spread, followed by the economic connection intensity, and the medical facilities conditions. the population distribution, traffic accessibility, and average temperature also had different degrees of influence on the epidemic spread. from the perspective of action direction, the population distribution, population inflow from wuhan, economic connection intensity and medical facilities conditions played a positive role in the process of epidemic spread, while the traffic accessibility played a negative role. ( ) detection factors interacted through mutual enhancement and nonlinear enhancement, and their influence on the epidemic spread rate exceeded that of single detection factors. the interaction between the population inflow from wuhan and medical facilities conditions, as well as that between the population distribution and population inflow from wuhan, that between the population distribution and economic connection intensity, and that between the economic connection intensity and medical facilities conditions had a great influence on the epidemic spread. the interaction between the population distribution and traffic accessibility, as well as that between the population distribution and average temperature, that between the traffic accessibility and average temperature, and that between the average temperature and medical facilities conditions had little impact on the epidemic spread. influencing factors are analyzed. ) the global and local spatial correlation characteristics of the epidemic distribution present a positive correlation. ) the population inflow from wuhan and strength of economic connection are the main factors affecting the epidemic spread. ) the interaction influence of detection factors on the epidemic spread exceeds that of the single factor. ) when the average temperature in winter is maintained at - °c, the epidemic spread rate is higher. population movement, city closure and spatial transmission of the -ncov infection in china analysis of the economic impact of the ncp and countermeasure study local indicators of spatial association-lisa early transmission dynamics of novel coronavirus pneumonia epidemic in shaanxi province incidence trend of novel coronavirus (sars-cov- )-infected pneumonia in china the continuing -ncov epidemic threat of novel coronaviruses to global health-the latest novel coronavirus outbreak in wuhan exploratory spatial data analysis of the distribution of regional per capita gdp in europe nowcasting and forecasting the potential domestic and international spread of the -ncov outbreak originating in wuhan, china: a modeling study evolution of patterns in the ratio of gender at birth in henan province transmission dynamics of novel coronavirus the diffusion characteristics of an outbreak of novel coronavirus diseases (covid- ) in guangdong province analysis of the spatio-temporal characteristics and transmission path of covid- cluster cases in zhuhai impact of high-speed railway on accessibility and economic linkage of cities along the railway in henan province spatial differentiation patterns of carbon emissions from residential energy consumption in small and medium-sized cities: a case study of kaifeng geodetector: principle and prospective preliminary analysis on the early epidemic and spatiotemporal distribution of new coronavirus pneumonia in guangdong province when will be the resumption of work in wuhan and its surrounding areas during covid- epidemic? a data-driven network modeling analysis determinants and identification of the northern boundary of china's tropical zone modeling and prediction for the trend of outbreak of ncp based on a time-delay dynamic system quantifying the influence of nature and socioeconomic factors and their interactive impact on pm . pollution in china backtracking transmission of covid- in china based on big data source key: cord- - unrcb f authors: gaeta, giuseppe title: social distancing versus early detection and contacts tracing in epidemic management date: - - journal: chaos solitons fractals doi: . /j.chaos. . sha: doc_id: cord_uid: unrcb f different countries – and sometimes different regions within the same countries – have adopted different strategies in trying to contain the ongoing covid- epidemic; these mix in variable parts social confinement, early detection and contact tracing. in this paper we discuss the different effects of these ingredients on the epidemic dynamics; the discussion is conducted with the help of two simple models, i.e. the classical sir model and the recently introduced variant a-sir (arxiv: . ) which takes into account the presence of a large set of asymptomatic infectives. different countries are tackling the ongoing covid- epidemics with different strategies. awaiting for a vaccine to be available, the three tools at our disposal are contact tracing, early detection and social distancing . these are not mutually exclusive, and in fact they are used together, but the accent may be more on one or the other. within the framework of classical sir [ ] [ ] [ ] [ ] [ ] and sir-type models, one could say (see below for details) that these strategies aim at changing one or the other of the basic parameters in the model. in this note we want to study -within this class of modelswhat are the consequences of acting in these different ways. we are interested not only in the peak of the epidemics, but also in its duration. in fact, it is everybody's experience in these days that social distancing -with its consequence of stopping all kind of economic activities -has a deep impact on our life, and in the long run is producing impoverishment and thus a decline in living conditions of a large part of population. in the present study we will not specially focus on covid, but discuss the matter in general terms and by means of generalpurpose models. our examples and numerical computations will however use data and parameters applying to (the early phase of) the current covid epidemic in northern italy, in order to have realistic examples and figures; we will thus use data and parameters arising e-mail address: giuseppe.gaeta@unimi.it from our analysis of epidemiological data in the early phase of this epidemic [ , ] . unavoidably, we will also here and there refer to the covid case. some observations deviating from the main line of discussionor which we want to pinpoint for easier reference to them -will be presented in the form of remarks. the symbol marks the end of remarks. in the sir model [ ] [ ] [ ] [ ] [ ] , a population of constant size (this means the analysis is valid over a relatively short time-span, or we should consider new births and also deaths not due to the epidemic) is subdivided in three classes: susceptibles, infected (and by this also infectives), and removed. the infected are supposed to be immediately infective (if this is not the case, one considers so called seir model to take into account the delay), and removed may be recovered, or dead, or isolated from contact with susceptibles. we stress that while in usual textbook discussions of the sir model [ ] [ ] [ ] [ ] the removed are either recovered or dead, in the framework of covid modeling the infectives are removed from the infective dynamics -i.e. do not contribute any more to the quadratic term in the eqs. ( ) below -through isolation. this means in practice hospitalization in cases where the symptoms are heavy and a serious health problem develops, and isolation at home (or in other places, e.g. in some countries or region specific hotels were used to this aim) in cases where it is estimated that there is no relevant risk for the health of the infective. in this sense, the reader should pay attention to the meaning of r in the present context. the nonlinear equations governing the sir dynamics are written as d s/d t = − α s i d i/d t = α s i − βi ( ) d r/d t = βi. these should be considered, in physicists' language, as mean field equations; they hold under the (surely not realistic) assumption that all individuals are equivalent, and that the numbers are sufficiently large to disregard fluctuations around mean quantities. note also that the last equation amounts to a simple integration, r (t) = r + β t t i(y ) dy ; thus we will mostly look at the first two equations in ( ) . we also stress, however, that epidemiological data can only collect time series for r ( t ): so this is the quantity to be compared to experimental data [ ] . in fact, as stressed in remark , in the case of a potentially dangerous illness (as covid), once the individuals are identified as infective, they are effectively removed from the epidemic dynamic through hospitalization or isolation. according to our eqs. ( ) , s ( t ) is always decreasing until there are infectives. the second equation in ( ) immediately shows that the number of infectives grows if s is above the epidemic threshold γ = β/α. ( ) thus to stop an epidemic once the numbers are too large to isolate all the infectives, we have three (non mutually exclusive) choices within the sir framework: (a) do nothing, i.e. wait until s ( t ) falls below the epidemic threshold; (b) raise the epidemic threshold above the present value of s ( t ) by decreasing α; (c) raise the epidemic threshold above the present value of s ( t ) by increasing β. in practice, any state will try to both raise β and lower α, and if this is not sufficient await that s falls below the attained value of γ . in order to understand how this is implemented, it is necessary to understand what α and β represent in concrete situations. the parameter β represents the removal rate of infectives; its inverse β − is the average time the infectives spend being able to spread the contagion. raising β means lowering the time from infection to isolation, hence from infection to detection of the infected state. the parameter α represents the infection rate , and as such it includes many thing. it depends both on the infection vector characteristics (how easily it spreads around, and how easily it infects a healthy individual who gets in contact with it), but is also depends on the occasions of contacts between individuals. so, roughly speaking, it is proportional to the number of close enough contacts an individual has with other ones per unit of time. it follows that -if properly implemented -social distancing results in reducing α. each of these two actions presents some problem. there is usually some time for the appearance of symptoms once an individual is infected, and the first symptoms can be quite weak. so early detection is possible only by fast tracing and laboratory checking of all the contacts of those who are known to be infected. this has a moderate cost (especially if compared to the cost of an intensive care hospital stay) but requires an extensive organization. on the other hand, social distancing is cheap in immediate terms, but produces a notable strain of the societal life, and in practice -as many of the contacts are actually work related -requires to stop as many production and economic activities as possible, i.e. has a formidable cost in the medium and long run. moreover, it cannot be pushed too far, as a number of activities and services (e.g. those carrying food to people, urgent medical care, etc.) can not be stopped. let us come back to ( ) ; using the first two equations, we can study i in terms of s , and find out that as we know that the maximum i * of i will be reached when s = γ , this allows immediately to determine the epidemic peak . in practice, i is negligible and for a new virus s corresponds to the whole population, s = n; thus note that only γ appears in this expression; that is, raising β or lowering α produces the same effect as long as we reach the same γ . on the other hand, this simple formula does not tell us when the epidemic peak is reached, but only that it is reached when s has the value γ . but if measures are taken, these should be effective for the whole duration of the epidemic, and it is not irrelevant -in particular if the social and economic life of a nation is stopped -to be able to evaluate how long this will be for. acting on α or on β to get the same γ will produce different timescales for the dynamics; see fig. , in which we have used values of the parameters resulting from our fit of early data for the northern italy covid- epidemic [ ] . this observation can be made more precise considering the scaling properties of ( ) . in fact, consider the scaling numerically integrated and i ( t ) plotted in arbitrary units for given initial conditions and α, β parameters (solid), the maximum i * being reached at t = t * . then they are integrated for the same initial condition but raising β by a factor ϑ = / (dashed) with maximum i β = r i * reached at time t β = σ β t * ; and lowering α by the same factor ϑ = / (dotted) with maximum i α = i β reached at time t α = σαt * . time unit is one day, α = ( / ) * − , β = / ; these parameters arise from our fitting of data from the early phase of covid epidemics in northern italy [ ] ; the population of the most affected area in the initial phase is about million, that of the whole italy is about million. the numerical simulation is ran with n = * ; it results it is clear that under this scaling γ remains unchanged, and also the equations are not affected; thus the dynamics is the same but with a different time-scale . the same property can be looked at in a slightly different way. first of all, we note that one can write α = β/γ ; moreover, α appears in ( ) only in connection with s , and it is more convenient to introduce the variable now, let us consider two sir systems with the same initial data but different sets of parameters, and let us for ease of notation just consider the first two equations of each. thus we have the two systems we can consider the change of variables ( λ > ) with this, ( ) becomes we can thus eliminate the factor λ in both equations. however, if we had chosen λ = β/β, we get ˆ β = β; if moreover γ = γ , the resulting equation is just but we had supposed the initial data for { s, i } and for { s , i } (and hence also for ϑ and ϑ ) to be the same. we can thus directly compare ( ) with ( ) . we observe that { ϑ , i } have thus exactly the same dynamics in terms of the rescaled time τ as { ϑ, i } in terms of the original time t . in particular, if the maximum of i is reached at time t * , the maximum of i is reached at τ * = t * , and hence at t * = λ τ * = λ t * . ( ) analytical results on the timescale change induced by a rescaling of the α and β parameters have recently been obtained by m. cadoni [ ] ; see also [ ] . we have supposed infected individuals to be immediately infective. if this is not the case an "exposed" class should be introduced. this is not qualitatively changing the outcome of our discussion, so we prefer to keep to the simplest setting. (moreover, for covid it is known that individuals become infective well before developing symptoms, so that our approximation is quite reasonable.) one of the striking aspects of the ongoing covid- epidemic is the presence of a large fraction of asymptomatic infectives [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] ; note that here we will always use "asymptomatic" as a shorthand for "asymptomatic or paucisymptomatic", as also people with very light symptoms will most likely escape to clinical detection of covid -and actually most frequently will not even think of consulting a physician. in order to take this aspect into account, we have recently formulated a variant of the sir model [ ] in which together with known infectives i ( t ), and hence known removed r ( t ), there are unregistered infectives j ( t ) and unregistered removed u ( t ). note that in this case removal amounts to healing; so while the removal time β − for known infected corresponds to the time from infection to isolation, thus in general slightly over the incubation time t i (this is t i . days for covid), the removal time η − for unrecognized infects will correspond to incubation time plus healing time. in the model, it is supposed that symptomatic and asymptomatic infectives are infective in the same way. this is not fully realistic, as one may expect that somebody having the first symptoms will however be more retired, or at east other people will be more careful in contacts; but this assumption simplifies the analysis,and is not completely unreasonable considering that for most of the infection-to-isolation time β − the symptoms do not show up. the equations for the a-sir model [ ] are note that here too we have a "master" system of three equations (the first three) while the last two equations amount to di- the parameter ξ ∈ [ , ] represents the probability that an infected individual is detected as such, i.e. falls in the class i . in the absence of epidemiological investigations to trace the contacts of known infectives, this corresponds to the probability of developing significant symptoms. in the first (arxiv) circulated version [ ] of our previous work [ ] , some confusion about the identification of the class j was present, as this was sometimes considered to be the class of asymptomatic infectives, and sometimes that of not registered ones . while this is not too much of a problem considering the "natural" situation, it becomes so when we think of action on this situation. actually, and unfortunately, this confusion has a consequence exactly on one of the points we want to discuss here, i.e. the effect of a campaign of chasing the infectives, e.g. among patients with light symptoms or within social contacts of known infectives; let us thus discuss briefly this point. if j is considered to be the set of asymptomatic virus carriers, then a rise in the fraction of these who are known to be infective, and thus isolated, means that the average time for which asymptomatic infectives are not isolated is decreasing. in other words, we are lowering η − and thus raising η. on the other hand, in this description ξ is the probability that a new infective is asymptomatic, and this depends only on the nature of the virus and its interactions with the immune system of the infected people; thus in this interpretation ξ should be considered as a constant of nature, and it cannot be changed. (this is the point of view taken in [ ] ; however some of the assumptions made in its first version [ ] were very reasonable only within the concurrent interpretation, described in a moment.) on the other hand, if j is the class of unknown infectives, things are slightly different. in fact, to be in this class it is needed ( a ) that the individual has no or very light symptoms; but also ( b ) that he/she is not traced and analyzed by some epidemiological campaign, e.g. due to contacts with known infected or because belonging to some special risk category (e.g. hospital workers). in this description, η is a constant of nature, depending on the nature of the virus and on the response of the "average" immune system of (asymptomatic) infected people, while effort s to trace asymptomatic infectives will act on raising the probability ξ . we want to discuss the effect of early detection of infectives, or tracing their contacts, within the second mentioned framework. note that a campaign of tracing contacts of infectives is useful not only to uncover infectives with no symptoms, but if accompanied by effective isolation of contacts with known infectives, and thus of those who are most likely to be infective, it will also reduce the removal time of "standard" (i.e. symptomatic) infectives, possibly to a time smaller than the incubation time itself. in this sense, we will look at an increase in ξ as early detection of infectives , and at an increase in both β and η (thus a reduction in the removal times β − and η − ) as tracing contacts of infectives . this should be kept in mind in our final discussion about the effect of different strategies. as mentioned above, one should also avoid any confusion between asymptomatic and pre-symptomatic infection. in our description, pre-symptomatic infectives -i.e. individuals which are infective and which do not yet display symptoms, but which will at a later stage display them -are counted in the class of "standard" infectives, i.e. those who will eventually display symptoms and hence be intercepted by the health system with no need for specific test or contact racing campaigns, exactly due to the appearance of symptoms. actually one expects that except for the early phase of the epidemics in the countries which were first hit in a given area (such as china for asia, or italy for europe), when symptoms could be attributed to a different illness, most infections by symptomatic people are actually pre-symptomatic , as with the appearance of symptoms people are either hospitalized or isolated at home; and even before any contact with the health system they will avoid contacts with other -and other people will surely do their best to avoid contacts with anybody displaying even light covid symptoms. in the case of asymptomatic infectives, instead, unless they are detected by means of a test or contact tracing campaign -see the forthcoming discussion -they remain infective until they recover, so that in this case removal is indeed equivalent to (spontaneous) recovery. this approach, indeed, was taken in one of the areas of early explosion of the contagion in northern italy, i.e. in vò euganeo; this had the advantage of being a small community (about residents), and all of them have been tested twice while embargo was in operation. in fact, this was the first systematic study showing that the number of asymptomatic carriers was very high, quite above the expectations [ ] . apart from its scientific interest, the approach proved very effective in practical terms, as new infectives were quickly traced and in that specific area the contagion was stopped in a short time. while testing everybody is not feasible in larger communities, the "follow the contacts" approach could be used on a larger scale, especially with the appearance of new very quick kits for ascertaining positivity to covid. the model will thus react to a raising of ξ by raising the fraction of i within the class of infectives, i.e. in k = i + j; but at the same time, as critical patients are always the same, i.e. represents always the same fraction of k , we should pay attention to the fact they will now represent a lower fraction of i . the chinese experience shows that critical patients are about % of hospitalized patients (i.e. of those with symptoms serious enough to require hospitalization); and hospitalized patients represented about half of known infected, the other being cured and isolated at home. similar percentages were observed in the early phase of the covid epidemic in italy; the fraction of infectives isolated at home has afterwards diminished, but it is believed that this was due to a different policy for lab exams, i.e. checking prioritarily patients with multiple symptoms suggesting the presence of covid rather than following the contacts. actually this policy was followed in most of italy, but in one region (veneto) the tracking of contacts and lab exams for them was pursued, and in there the percentages were much more similar to those known to hold for china. in our previous work [ ] we have considered data for the early phase of covid epidemics in italy, and found that β − best fits them while the estimate η − was considered as a working hypothesis. this same work found as value of the contact rate in the initial phase α . * − , and we will use this in our numerical simulations. it should be stressed that the extraction of the parameter α from epidemiological data is based on the number s n of susceptibles at the beginning of the epidemic, thus α and hence γ depend on the total population. the value given above was obtained considering n = * , i.e. the overall population of the three regions (lombardia, veneto and emilia-romagna) which were mostly affected in the initial phase. our forthcoming discussion, however, does not want to provide a forecast on the development of the covid epidemic in northern italy; we want instead to discuss -with realistic parameters and framework -what would be the differences if acting with different strategies in an epidemic with the general characteristics of the covid one. thus we will adopt the aforementioned parameters as "bare" ones (different strategies consisting indeed on acting on one or the other of these) but will apply these on a case study initial condition; this will be given by one important parameter is missing from this list, i.e. the detection probability ξ . following li et al. [ ] we assumed in previous work that ξ is between / and / . later works (and a general public interview by the head of the government agency handling the epidemic [ ] ) suggested that the lower bound is nearer to the truth; moreover a lower ξ will give us greater opportunity to improve things by acting on it (we will see this is not the best strategy, so it makes sense to consider the setting more favorable to it). we will thus run our simulation starting from a "bare" value as for the total population, we set n = * . with these choices we get a projection of what could have happened if no action was undertaken. a note by an oxford group [ ] , much discussed (also in general press [ ] ) upon its appearance, hinted that in italy and uk this fraction could be as low as ξ = / . we have ascertained that with this value of ξ , and assuming α was not changed by the restrictive measures adopted in the meanwhile, the a-sir model fits quite well the epidemiological data available to the end of april. however, despite this, we do not trust this hypothesisat least for italy -for various reasons, such as (in order of increasing relevance): ( i ) a viral infection showing effects only in % of affected individuals would be rather exceptional; ( ii ) albeit in our opinion the effect of social distancing measures adopted in italy is sometimes overestimated, we trust that there has been some effect; ( iii ) if only % of infected people was detected, in some parts of italy the infected population would be over %. on the other hand, the main point made by this report [ ] , i.e. that only a large scale serological study, checking if people have covid antibodies, will be able to tell how diffuse the infection is -and should be performed as soon as possible -is by all means true and correct. see also [ ] . a look at eqs. ( ) shows that i will grow provided where again γ = β/α, and we have introduced the ratio x ( t ) of known infectives over total infectives. in other words, now the epidemic threshold depends on the distribution of infectives in the classes i and j . note that if x = ξ (as one would expect to happen in early stages of the epidemic), then γ i = γ . needless to say, we have a similar result for j , i.e. j will grow as far as thus the epidemic threshold for unregistered infectives is it is important to note that x is evolving in time. more precisely, by the equations for i and j we get dx dt the behavior observed in fig. , which displays x ( t ) and related quantities on a numerical solution of eq. ( ) , can be easily understood intuitively. in the first phase of the epidemic, there is an exponential growth of both i and j ; due to the structure of the equations, they grow with the same rate, so their ratio remains constant; on the other hand, once the dynamics get near to the epidemic peak, the difference in the permanence time of the two (that is, the time individuals remain in the infect class) becomes relevant, and we see (plots (a ) and (b ) of fig. ) that not only the peak for j is higher than the one for i , but it occurs at a slightly later time. moreover, descending off the peak is also faster for i , as β − < η − , and thus x further decreases, until it reaches a new equilibrium while both classes i and j go exponentially to zero. if we look at ( ) we see that for fixed s the variable x would have two equilibria (one stable with < x < and one unstable with x > , stability following from β − η > ), easily determined solving d x/d t = . numerical simulations show that -apart from an initial transient -actually x ( t ) stays near, but in general does not really sticks to, the stable fixed point determined in this way. a relevant point should be noted here. if we consider the sum ( ) of all infectives, the a-sir model can be cast as a sir model in terms of s, k , and q = r + u as as x varies in time, this average removal rate is also changing. on the other hand, the basic reproduction number (brn) ρ (this is usually denoted as r , but we prefer to change this notation in order to avoid any confusion with initial data for the known removed r ( t )) for this model will be in other words, not taking the asymptomatic infectives into account leads to an underestimation of the brn. if the standard sir model predicts a brn of ρ , the a-sir model yields a brn ˆ ρ given this means that the epidemic will develop faster, and possibly much faster, than what one would expect on the basis of an estimate of ρ based only on registered cases, which in the initial phase are a subset of symptomatic cases as the symptoms may easily be leading to a wrong diagnosis (in the case of covid they lead to a diagnosis of standard flu). with our covid-related values β = / , η = / , and assuming that in the early phase there is thus a good reason for being surprised by the fast development of the epidemic: the actual brn is substantially higher than the one estimated by symptomatic infections [ ] . more generally, one would wonder what is the effect of the "hidden" infectives j ( t ) on the dynamics of the known infectives i ( t ) -which, we recall, include the relevant class of seriously affected infectives -and it appears that there are at least two, contrasting, effects: . on the one hand, the hidden infectives speed up the contagion spread and hence the rise of i ( t ); . on the other hand, they contribute to group immunity, so the larger this class the faster (and the lower the i level at which) the group immunity will be reached. the discussion above shows that the balance of these two factors leads to a much lower epidemic peak, and a shorter epidemic time, than those expected on the basis of the standard sir model (albeit in the case of covid with no intervention these are still awful numbers). on the other hand, we would like to understand if uncovering a larger number of cases (thus having prompt isolation of a larger fraction of the infectives) by early detection , i.e. raising ξ , would alter the time-span of the epidemic. it appears that this effect can be only marginal, as it appears only past the epidemic peak. we stress that this statement refers to "after incubation" analysis; if we were able to isolate cases before they test positive -i.e. to substantially reduce β − -the effect could be different. we will discuss this point, related to contact tracing , later on. an ongoing epidemic is not a laboratory experiment, and apart from not having controlled external conditions, i.e. constant parameters, the very collection of data is of course not the top priority of doctors fighting to save human lives. there has been considerable debate on what would be the most reliable indicator to overcome at least the second of these problems. one suggestion is to focus on the number of deaths; but this is itself not reliable, as in many cases covid is lethal on individuals which already had some medical problem, and registering these deaths as due to covid or to some other cause depends on the protocol adopted, and in some case also on political choices, e.g in order to reassure citizens (or on the other extreme, to stress great care must be taken to avoid contagion). another proposed indicator, possibly the most reliable in order to monitor the development of the epidemic, is that of patients in intensive care units. this appears to be sufficiently stable over different countries, and e.g. the italian data tend to reproduce in this respect -at least in regions where the sanitary system is not overstretched -the chinese ones. in this case, ic patients are about % of the total number of hospitalized cases; in china and for a long time also in italy (when protocols for choosing would-be cases to be subject to laboratory analysis have been stable), hospitalized cases have been about half of the known infection cases, the other having shown only minor symptoms and been cured (and isolated) in their home. the other, more widely used, indicator is simply the total number of known cases of infection. in view of the presence of a large class of asymptomatic infectives, this itself is strongly depending on the protocols for chasing infectives. on the other hand, this is the most available indicator: e.g., the w.h.o. situation reports [ ] provide these data. each of these indicators, thus, has advantages and disadvantages. we will just use the who data on known infected. in particular, in the case of covid we expect that with ξ the "bare" constant describing the probability that an infection is detected, out of the class i ( t ) we will have a % of infected with little or no symptoms ( i l ), a % of standard care hospitalized infected ( i h ), and a % of ic hospitalized infected ( i ic ). needless to say, this class is the most critical one, also in terms of strain on the health system. more generally, we say that with ξ the "bare" constant describing the probability that the infection under study is detected, there is a fraction χ (of the detected infections) belonging to the i ic class; that is, i ic (t) = χ i(t ) . we stress this depends on the protocol used to trigger laboratory tests; in our general theoretical discussion, this is any such protocol and we want to discuss the consequences of changing this in the sense of more extensive tests. we are now ready to discuss how modification of one or the other of the different parameters ( α, β, ξ ) on which we can act by various means will affect the a-sir dynamics. as it should be expected, this will give results similar to those holding for the sir model, but now we have one more parameter to be considered and thus a more rich set of possible actions. fig. . the effect of a change in ξ on the i ic class. we have used β = / , η = / , and α = . * − as in fig. , with a total population of n = * , and ran simulations with ξ = / (solid curve) and with ξ = / (dashed curve). the substantial increase in ξ produces a reduction in the epidemic peak and a general slowing down of the dynamics, but both these effects are rather small. a more extensive test campaign will raise ξ , say from ξ to ξ ; but of course this will not change the number of the most serious cases, as these are anyway getting to hospital and detected as being due to the infection in question. thus the new fraction χ of detected infections which need special care will be such that in order to describe the result of raising ξ , we should thus compare plots of this is what we do, indeed, in fig. . raising ξ corresponds to having more infective detected, and has some advantages from the point of view of the epidemic dynamics. in practical terms, this means extending tests to a larger class of subjects, and be able to isolate a larger fraction of asymptomatic infectives with the same speed and effectiveness as symptomatic ones. a different strategy for rapid action is also possible, and it consists of rapid isolations of subjects who had contacts with people known to have been infected, or who have themselves been in contact with known infectives (and so on). in other words, the strategy would be to isolate would-be infection carriers before any symptom could show up. this means that β − could be even smaller than the usual infection-to-isolation time (about seven days for covid) for symptomatic infectives, and even shorter than the incubation time (about five days for covid). it should be stressed that as each of these "possible infected" might have a small probability of being actually infected (depending on the kind of contacts chain leading to him/her from known infectives), here "isolation" does not necessarily mean top grade isolation, but might amount to a very conservative lifestyle, also -and actually, especially -within home, where a large part of registered chinese contagions took place. (the same large role of in-home contagion was observed in italy in the course of lockdown.) we have thus ran a simulation in which ξ is not changed, but β is raised from β = / to β = / ; the result of this is shown in fig. . in this case we have a marked diminution of the epidemic peak, and a very slight acceleration of the dynamics. . the effect of a change in β on the i ic class. we have used ξ = / , η = / , and α = . * − as in fig. , with a total population of n = * , and ran simulations with β = / (solid curve) and with β = / (dashed curve). the substantial increase in β produces a marked reduction in the epidemic peak and a very slightly faster pace in the dynamics. we have so far not discussed the most basic tool in epidemic containment, i.e. social distancing. this means acting on the parameter α by reducing it. direct measurement on the epidemiological data for northern italy show that this parameter can be reduced to about % of its initial value with relatively mild measures. in fact, albeit the media speak of a generalized lockdown in italy, the measures have closed schools and a number of commercial activities, but for the rest were actually more pointing at limiting leisure walk and sports and somewhat avoiding contacts in shops or in work environment than to a real lockdown as it was adopted in wuhan. this is a basic action to be undertaken, and in fact it is being taken by all nations. it is also the simplest one to be organized (albeit with high economic and social costs in the long run) and an action which can be taken together with other ones. no doubt this should be immediately taken when an epidemic is starting, and accompanied by other measures -such as those discussed above. but here we want to continue our study of what it means by itself in terms of modification of the epidemic dynamics. it is not clear what can be achieved in terms of reduction of social contacts. in fact, once the epidemic starts most of the dangerous contacts are the unavoidable ones, such as those arising from essential services and production activity (e.g. production and distribution of food or pharmaceutical goods), contacts at home, and above all contacts in hospitals. thus, after a first big leap downward corresponding to closing of schools and universities on the one side, and a number of unessential commercial activities on the other, and restrictions on travels, it is difficult to further reduce social contacts, not to say that this would have huge economic and social costs, and also a large impact on the general health in terms of sedentariness-related illness (and possibly mental health). a number of countries tried to further reduce social contacts by forbidding citizens to get out of their home; this makes good sense in densely populated areas, but is useless in many other areas. the fortunate slogan "stay home" risks to hide to the general public that the problem is not to seclude oneself in selfpunishment, but to avoid contacts . we point out that there is a further obstacle to reducing social contacts: as seen in the context of the simple sir model, reducing α will lower the epidemic peak, but it will also slow down the whole dynamic . while this allows to gain precious time to prepare fig. . the effect of a change in α on the i ic class. we have used β = / , ξ = / , η = / , with a total population of n = * , and ran simulations with α = . * − (solid curve) and with α = . * − (dashed curve). the reduction in α produces a marked reduction in the epidemic peak and also a marked slowing down in the dynamics. hospitals to stand the big wave, there is some temporal limit to an extended lockdown, and thus this tool cannot be used to too large an extent. we have thus ran a simulation in which β and ξ are not changed, while α is reduced by a factor . (smaller factors, i.e. smaller α, produce an untenable length of the critical phase); the result of this is shown in fig. . in this case we have a relevant diminution of the epidemic peak, and also a marked slowing down in the dynamics. an important remark is needed here. it may seem, looking at this plot, that social distancing is less effective than other way of coping with the epidemic. but these simulation concern a sir-type model; this means in particular that there is no spatial structure in our model [ ] . the travel ban is the most effective way of avoiding the spreading of contagion from one region to the others; while the "local" measures of social distancing can (and should) be triggered to find a balance with other needs, travel ban is the simplest and most effective way of protecting the communities which have not yet been touched by the epidemic. we can thus compare the different strategies we have been considering. this is done in fig. where we plot together i ic ( t ) for all our different simulations; and in table where we compare the height of the epidemic peak -again for i ic ( t ) -and the time at which it is reached. fig. . the effect of different strategies. we plot i ic ( t ) for n = * in the "bare" case, i.e. for α = . * − , β = / , ξ = / , η = / , and in cases where (only) one of the parameters is changed. in particular we have the bare case (solid line), the case where ξ is changed into ξ = / (dotted), the case where β is changed to β = / (dashed), and that where α is changed to α = . * − (solid, blue). we also plot a horizontal line representing a hypothetical maximal capacity of ic units. (for interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) table epidemic peak (for i ic ) and time for reaching it (in days) as observed in our numerical simulations. all simulation were ran with n = * and η = in fig. we have also drawn a line representing the hypothetical maximal capacity of ic units. this stresses that not only the different actions lower the epidemic peak, but they also -and to an even larger extent -reduce the number of patients which can not be conveniently treated. in looking at this plot, one should remember that the model does not really discuss permanence in ic units, and that i ic are the infected which when detected will require ic treatment; this may go on for a long time -which is the reason why ic units are saturated in treating covid patients. so the plots are purely indicative, and a more detailed analysis (also with real parameters) would be needed to estimate the ic needs in the different scenarios. it should be stressed that the strategies of contacts tracing and early detection are usually played together; but as confusion could arise on this point, let us briefly discuss it. we have tried to stress that these two actions are not equivalent: one could conduct random testing, so uncovering a number of asymptomatic infectives, and just promptly isolate them without tracing their contacts;or on the other extreme one could just isolate everybody who had a (direct or indirect) contact with a known infective, without bothering to ascertain if they are themselves infective or not. this strategy would be as effective in containing the contagion (and less costly in terms of laboratory tests) than that of tracking contacts, test them (after a suitable time for the infection to develop and test give positive if this happens), and isolate only those who really turn infective. the difference is that if we isolate everybody this would involve a huge number of people (e.g. all those who have been in the same supermarket the same day as an infective; and their families and contacts etc etc); so in this context early detection actually should be intended as early detection of non-infectives , so that cautionary quarantine can be kept reasonably short in all the cases where it is not really needed. finally we recall that it is a triviality, and it was already mentioned in the introduction, that in real situations one has not to choose between acting on one or the other of the parameters, and all kind of actions should be pursued simultaneously. the numerical computations of the previous subsections suggest that increasing ξ -that is, detection of a larger fraction of asymptomatic -is not a very efficient strategy to counter the diffusion of an infection with a large number of asymptomatic infectives, while a prompt isolation of infectives is a more effective action. it should be recalled, however, that in our computations -and in particular on fig. , where their outcomes are compared -we are focusing on the number of patients needing ic support, i.e. the most critical parameter from the point of view of the health system. in order to substantiate our conclusions, it is worth considering also different ways to evaluate the effect of different strategies. we have thus considered also a different indicator, i.e. the total number of infectives we have run several simulations, with total population n = * and with parameters α = μ α α β = μ β β η = μ η η ξ = μ ξ ξ . the outcome of these simulations is displayed in fig. ; see its caption for the parameter (that is, the modulation factor) values in different runs. we see from fig. that action on α slows down substantially the epidemic dynamics and reduce the epidemic peak, while action on ξ or on β alone produce only a moderate effect. on the other hand, actions affecting the value of η (alone or together with the value of β) reduce substantially the epidemic peak and slightly slow down the dynamics. it may be noted that the shapes of the i ic ( t ) (see fig. ) and of the k ( t ) (see fig. ) are different; in particular, the decay of i ic ( t ) after attaining its peak is faster than the decay of k ( t ). this corresponds to what is observed in the epidemiological data for italy. we have considered epidemic dynamics as described by "mean field" models of the sir type; more specifically, we have first considered the classical kermack-mckendrick sir model [ ] [ ] [ ] [ ] [ ] and then a recently introduced modified version of it [ ] taking into account the presence of a large set of asymptomatic -and thus most frequently not detected -infectives. these models depend on several parameters, and different types of measures can to some extent change these parameters and thus the epidemic dynamics. in particular, this action can effect two basic characteristics of it, i.e. the height of the epidemic peak and the time-span of the epidemic. while it is clear that in facing a real lethal epidemics (such as the ongoing covid epidemic) all actions which can contrast it should be developed at the same time, in this paper we have considered the result -within these models -of different tools at our disposal, i.e. (generalized) social distancing, early detection (of asymptomatic infectives) and contacts tracing (of symptomatic and asymptomatic infectives). it turns out that -both in the classical sir model and in the modified a-sir one -social distancing is effective in reducing the epidemic peak, and moreover it slows down the epidemic dynamics. on the other hand, early detection of asymptomatic infectives seems to have only a moderate effect in the reduction of the epidemic peak for what concerns critical cases, and also a very little effect on the temporal development of the epidemic. in contrast, contact tracing has a strong impact on the epidemic peak -also in terms of critical cases -and does not substantially alter the temporal development of the epidemic, at least for what concerns the curve describing the most serious cases. remark . the conclusion that early detection of asymptomatic has only a moderate effect may appear to be paradoxical, and requires some further discussion. first of all we should remind that we are here actually talking about an increase of the parameter ξ (see remark ) , while in a real situation early detection of asymptomatic will most likely go together with early detection of symptomatic, and hence a reduction in β as well. the increase of ξ per se means that some fraction of asymptomatic will be recognized as infective and be isolated on the same timescale β − as the symptomatic infectives, while the other asymptomatic will escape recognition and still be infective on a timescale η − . on the other hand, a realistic contact tracing campaign will lead to prompt isolation of symptomatic and asymptomatic alike, and thus correspond to a reduction in β − and in η − , and we have seen that this action is indeed the most effective one in terms of contrasting the spread of the epidemic. in other words, our result suggests that the key to fight covid is not so much in detection , but in prompt isolation of infectives, and most notably of asymptomatic ones. this can be achieved only by contact tracing -as already suggested by experienced epidemiologists. slowing down the epidemic dynamic can be a positive or negative feature depending on the concrete situation and on the desired effects. it is surely positive in what concerns getting ready to face the epidemic peak, in particular in the presence of a faltering health system. on the other hand, it may be negative in that maintaining a generalized lockdown for a long time can have extremely serious economic and social consequences. balancing these two aspects is not a matter for the mathematician or the scientist, but for the decision maker; so we will not comment any further about this. it should also be recalled that our analysis was conducted in terms of very simple sir-type models, with all their limitations. in particular, we have considered no age or geographical or social structure, and only considered a population of "equivalent" indi-viduals. in particular, as we have noted above, in the early stage of an epidemic, which presumably develops in very populated areas, a generalized travel ban can simply stop the contagion to propagate to other (possibly less well equipped in medical terms) areas; moreover, social distancing measures can be implemented very simply -basically, by a government order (albeit if we look at the goal of these measures, i.e. reducing the occasion of exchanging the virus, a substantial role would be played by individual protection devices, such as facial masks; in many european countries, these were simply not available to the general public, and in some cases neither to medical operators, thus substantially reducing the impact of these measures) -and are thus the first action to be taken. in fact, in relation with the ongoing covid epidemics, one of the reproaches made to many governments is usually to have been too slow or too soft in stopping crowd gatherings, surely not the contrary. on the other hand, we hope that this study makes clear what are the consequences of different options. in particular, our study shows that contacts tracing , followed by prompt isolation of wouldbe infected people -is the only way to reduce the impact of the epidemic without having to live with it for an exceedingly long time. the veneto experience [ ] shows that this strategy can be effectively im plemented without hurting privacy or personal freedom. the authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. we are now going to briefly discuss these matters; we point out that this appendix was inserted in the revised version of this paper, so it can make use of knowledge not available at the time of writing the first submitted version, nd mentions papers appeared after the first submittal. compartment models, i.e. sir-type ones in this context, are based on several implicit and explicit assumptions, which are not realistic in many cases and surely when attempting to describe the covid epidemic, in particular in a full country. that is, among other aspects, sir-type models are (in physics' language) mean field (averaged) models and as such describe the dynamics and the underlying system as if: • all individuals are equivalent in medical sense, i.e. they all have equivalent pre-existent health status and equivalent immune system and react in the same way to contact with the pathogen; • in particular, as we know that covid is statistically more dangerous for older people, we are completely disregarding the age structure of the population, as well as the existence of other high risk classes related to pre-existent pathologies: all these contribute to an average over the whole population; • all individuals are equivalent in social sense, i.e. they all have an equivalent social activity and hence the same number and intensity of contacts with other members of the group, thus the same exposure to (possible) infectives; • in particular, this means we are completely disregarding any geographical structure in the population, and consider in the same way people living in large cities or in remote villages, just considering them in the same global average; • similarly, we do not consider that work can cause some people to be specially exposed through contact with a large number of people (e.g. shop cashiers) or even with a large number of infected people (e.g. medical doctors or nurses). thus one cannot hope to retain, through such models, effects like the faster spreading of the infection in more densely populated areas or the specially serious consequences of the covid infection among older people. we stress that these could be obtained by including geographical, age or social structures into the model, i.e. increasing the number of considered classes; in principles this should provide a finer and more realistic description of the epidemic dynamic, and in fact it is done in cases for which there is a large set of data, e.g. for influenza. such structured models would of course loose the main attractive of the sir model, i.e. its simplicity -which also allows to understand in qualitative terms the mechanisms at work. in particular, a relevant intermediate class of models is that of sir-type models on networks: these take into account geographical and social structures and make use of known information about contacts between different groups of individuals and about different health characteristics of different groups. the problem with these networked or however more structured models is that the network should be inferred from data. in this respect, it could be objected that the influenza monitoring over many years could give us the relevant data for reconstruction of such network; but it is everybody's experience, by now, that the social behavior of people are completely different if dealing with a well known and not so serious (except for certain categories) illness like influenza or with an unknown and potentially lethal one like covid; this not to say that the restrictive measures put into effect by many governments have completely changed the interaction patterns among people, so that previously accumulated data cannot be used in the present situation. when thinking of covid; it should be kept in mind that even if the countries which were first hit by the epidemic, we only have data over some months; e.g. for italy we have about days of data. if we were trying to give the model a geographical structure at the level of departments (which are themselves administrative units mostly with a very varied internal geographical structure), as there are departments in italy this would require in the simplest form to evaluate a × interaction matrix, and i cannot see any way to reliably build this out of such a scarce set of data. moreover, the epidemiological data are to some extent not reliable, especially around the epidemic peak, in that they are collected in an emergency situation, when other priorities are present in hospitals (e.g. in italy the data show a weekly modulation, which appears to be due simply to the procedure of data collection); so an even larger amount of data would be needed to filter out statistical noise and random fluctuations. in this sense, the weak point of sir-type models, i.e. their being based on an average over the whole population, turns out to be an advantage: they contain few parameters (two for the sir, four for the a-sir) and are thus statistically more robust in that fluctuations are averaged efficiently with less data than for more refined models with a large number of parameters. similar considerations hold when one compares sirtype models to a purely statistical description or to an "emerging behavior" approach. these approaches are extremely powerful, but are effective when one has a large database to build on and to which compare the outcome of the "experiment" (in this case the epidemic) under consideration. when we deal with a completely new pathogen,like for covid, we simply don't have a database, and we can only rely on the very general features of infective dynamics -which are well coded by sir and sir-like models. in other words, we are not claiming the sir approach to be superior to others, but only that it is appropriate when we have few data -as for covid. within the sir-type class, the a-sir model is specially simple; from the theoretical point of view its appeal lies in that it is the simplest possible model taking into account the presence of a large class of asymptomatic infectives; thus it focuses on the effect of this fact without the complications of a more detailed model. but, of course, it makes sense to rely on this model only if it is able to give a good, or at least a reasonable, agreement with observed data. of course each infective agent has its own characteristics, and using only the general sir model would completely overlook them, apart from the different values of the α and β parameters. thus we have to do something more than just evaluating the sir parameters. in our study we have identified the presence of a large class of asymptomatic infectives as one of the key problems in facing the covid epidemic, and we have considered a simple model which allows to focus precisely on this aspect. one should be aware that the a-sir model is focusing on this and not considering other features of covid, and indeed other more detailed sir-type models for covid have been formulated and studied (see also below). here we are taking an approach which is classical in mathematical physics and mathematical modeling, i.e. try to build and study the simplest model describing the phenomenon of interest. this will give results which are quantitatively worse than a more detailed models, but which are qualitatively good in that the model is simple enough to see more clearly what are the mechanisms at work and to understand the qualitative features if the dynamics and the qualitative outcome of any intervention able to modify the parameters of the model. having said that, it remains true that -as mentioned aboveit makes sense to rely on this model only if it is able to give a reasonable agreement with observed data. this is not the argument of this paper, and it was discussed in a previous paper [ ] ; the success of this model was the justification for this paper,i.e. for dis- however, the first version of this paper was submitted at mid-may, hence with two and half months of data available, while at the time of preparing this revised version we have four months of data; that represents a substantial increase in the available data, and it makes sense to wonder if the model is still describing the covid epidemic in italy. this is indeed the case, as shown in fig. ; they represent epidemiological data as communicated by the italian health ministry and by who (and widely available online through the standard covid databases) against a numerical integration of the a-sir eqs. ( ) . we refer to gaeta [ ] for a discussion of the parameters and their determination. note that the contact rate α is assumed to vary in response to the restrictive measures (and to the availability of individual protection devices); as these measures were taken in different steps, we also have different values of α in different time intervals. more precisely, the equations were integrated for a total population of n = * for the period february , through june , with initial data at day ( we stress that the parameter values are the same as in [ ] , even for the most recent time, not considered in that paper: the model continues to reasonably well describe the development of the epidemic in italy. we focused on a specific sir-type model, but several models of this type have been considered in the context of covid modeling. here we give a very short overview of these, with no attempt to completeness -which cannot even be imagined in such a rapidly evolving field. first of all, we note that other researchers have considered, motivated by the ongoing covid epidemic, the temporal aspects of the standard sir dynamics. we mention in particular cadoni [ ] (a related, but quite involved, approach had been considered by harko, lobo and mak [ ] ) and barlow and weinstein [ ] , who obtained an exact solution for the sir equations in terms of a divergent but asymptotic series [ ] ; see also [ , ] for a different approach to exact solution of sir and sir-type models. we also note that nonlinear modifications of the bilinear infection term of the standard sir model have been proposed -explicitly or implicitly -in the attempt to relate the standard sir model to covid dynamics [ , ] . we find [ ] of special interest, as this work introduces a model for the epidemic dynamics coupled to the immune system, and is thus able to take into account aspects related to the viral charge of infectives. extension of the sir model in the direction of allowing timedependence of the parameters -also to account for shifting public attitude -has also been considered [ ] . as mentioned above, see remark , considering the delay between infection and beginning of infectiveness would lead to consider seir-type models. the problem of temporal aspects of the dynamics for this class of models has been considered by becaer [ ] . the role of asymptomatic transmission in this class of models has also been considered [ , ] . the approach to sir by barlow and weinstein [ ] leading to exact solution has been extended to seir model [ ] . a generalization of the a-sir model, allowing for different infectiveness of symptomatic and asymptomatic infectives, has been considered by neves and guerrero [ ] . more elaborated compartment models with a larger number of compartments have been considered by a number of authors. we would like to mention in particular two papers which we consider specially significant, i.e. the work by the pavia group, in which mathematicians, statisticians and medical doctors collaborated [ ] , and the work by fokas, cuevas-maraver and kevrekidis [ ] , in which such a model -involving five compartments like the present paper, but chosen in a different way -is used to discuss (as in the present paper) exit strategies from the covid lockdown. as mentioned in the main text, one could -and should -consider epidemic dynamics on networks [ ] . attempts to analyze the covid epidemic in this way have of course been pursued, both on a small scale, with a network structure which can be determined by direct sociological study [ ] , and on a nationwide scale [ ] where the network structure has to be determined. this latter study [ ] also attempted to evaluate the effect of the containment measures; such a matter is of course very relevant and has been considered by many authors in many countries; even a cursory mention of these is impossible, and we will just mention one study applying to italy [ ] . we also stress that many of the papers mentioned above, see in particular [ , ] aim at using the models they study to evaluate the effect of interventions and containment measures. finally we would like to end on a positive note, and mention that while on the one hand it was found that the presence of asymptomatic makes that the basic reproduction number of covid is higher than initially estimated [ , , ] , the fact that the social contact rate is not uniform in the population makes that the herd immunity level should be lower than predicted on the basis of the standard sir-type models [ ] ; this is a specially nice result of the analysis on networks,as it only depends on general -and very reasonable -properties of the network and not on its detailed structure, thus overcoming the low statistics problem mentioned in remark above. contributions to the mathematical theory of epidemics mathematical biology. i: an introduction essential mathematical biology the mathematics of infectious diseases mathematical models in biology. siam arxiv: . ; data 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covid- epidemic in italy: effects of emergency containment measures the impact of a nation-wide lockdown on covid- transmissibility in italy the impact of undetected cases on tracking epidemics: the case of the disease-induced herd immunity level for covid- is substantially lower than the classical herd immunity level the work was carried out in lockdown at smri. i am also a member of gnfm-indam. our discussion was based on sir-type models, and in particular on the a-sir model. this raises several kind of questions, which we address in this appendix. key: cord- -fkdep cp authors: thompson, robin n.; hollingsworth, t. déirdre; isham, valerie; arribas-bel, daniel; ashby, ben; britton, tom; challenor, peter; chappell, lauren h. k.; clapham, hannah; cunniffe, nik j.; dawid, a. philip; donnelly, christl a.; eggo, rosalind m.; funk, sebastian; gilbert, nigel; glendinning, paul; gog, julia r.; hart, william s.; heesterbeek, hans; house, thomas; keeling, matt; kiss, istván z.; kretzschmar, mirjam e.; lloyd, alun l.; mcbryde, emma s.; mccaw, james m.; mckinley, trevelyan j.; miller, joel c.; morris, martina; o'neill, philip d.; parag, kris v.; pearson, carl a. b.; pellis, lorenzo; pulliam, juliet r. c.; ross, joshua v.; tomba, gianpaolo scalia; silverman, bernard w.; struchiner, claudio j.; tildesley, michael j.; trapman, pieter; webb, cerian r.; mollison, denis; restif, olivier title: key questions for modelling covid- exit strategies date: - - journal: proc biol sci doi: . /rspb. . sha: doc_id: cord_uid: fkdep cp combinations of intense non-pharmaceutical interventions (lockdowns) were introduced worldwide to reduce sars-cov- transmission. many governments have begun to implement exit strategies that relax restrictions while attempting to control the risk of a surge in cases. mathematical modelling has played a central role in guiding interventions, but the challenge of designing optimal exit strategies in the face of ongoing transmission is unprecedented. here, we report discussions from the isaac newton institute ‘models for an exit strategy’ workshop ( – may ). a diverse community of modellers who are providing evidence to governments worldwide were asked to identify the main questions that, if answered, would allow for more accurate predictions of the effects of different exit strategies. based on these questions, we propose a roadmap to facilitate the development of reliable models to guide exit strategies. this roadmap requires a global collaborative effort from the scientific community and policymakers, and has three parts: (i) improve estimation of key epidemiological parameters; (ii) understand sources of heterogeneity in populations; and (iii) focus on requirements for data collection, particularly in low-to-middle-income countries. this will provide important information for planning exit strategies that balance socio-economic benefits with public health. as of august , the coronavirus disease (covid- ) pandemic has been responsible for more than million reported cases worldwide, including over deaths. mathematical modelling is playing an important role in guiding interventions to reduce the spread of severe acute respiratory syndrome coronavirus (sars-cov- ). although the impact of the virus has varied significantly across the world, and different countries have taken different approaches to counter the pandemic, many national governments introduced packages of intense non-pharmaceutical interventions (npis), informally known as 'lockdowns'. although the socio-economic costs (e.g. job losses and long-term mental health effects) are yet to be assessed fully, public health measures have led to substantial reductions in transmission [ ] [ ] [ ] . data from countries such as sweden and japan, where epidemic waves peaked without strict lockdowns, will be useful for comparing approaches and conducting retrospective cost-benefit analyses. as case numbers have either stabilized or declined in many countries, attention has turned to strategies that allow restrictions to be lifted [ , ] in order to alleviate the economic, social and other health costs of lockdowns. however, in countries with active transmission still occurring, daily disease incidence could increase again quickly, while countries that have suppressed community transmission face the risk of transmission reestablishing due to reintroductions. in the absence of a vaccine or sufficient herd immunity to reduce transmission substantially, covid- exit strategies pose unprecedented challenges to policymakers and the scientific community. given our limited knowledge, and the fact that entire packages of interventions were often introduced in quick succession as case numbers increased, it is challenging to estimate the effects of removing individual measures directly and modelling remains of paramount importance. we report discussions from the 'models for an exit strategy' workshop ( ) ( ) ( ) ( ) ( ) may ) that took place online as part of the isaac newton institute's 'infectious dynamics of pandemics' programme. we outline progress to date and open questions in modelling exit strategies that arose during discussions at the workshop. most participants were working actively on covid- at the time of the workshop, often with the aim of providing evidence to governments, public health authorities and the general public to support the pandemic response. after four months of intense model development and data analysis, the workshop gave participants a chance to take stock and openly share their views of the main challenges they are facing. a range of countries was represented, providing a unique forum to discuss the different epidemic dynamics and policies around the world. although the main focus was on epidemiological models, the interplay with other disciplines formed an integral part of the discussion. the purpose of this article is twofold: to highlight key knowledge gaps hindering current predictions and projections, and to provide a roadmap for modellers and other scientists towards solutions. given that sars-cov- is a newly discovered virus, the evidence base is changing rapidly. to conduct a systematic review, we asked the large group of researchers at the workshop for their expert opinions on the most important open questions, and relevant literature, that will enable exit strategies to be planned with more precision. by inviting contributions from representatives of different countries and areas of expertise (including social scientists, immunologists, epidemic modellers and others), and discussing the expert views raised at the workshop in detail, we sought to reduce geographical and disciplinary biases. all evidence is summarized here in a policy-neutral manner. the questions in this article have been grouped as follows. first, we discuss outstanding questions for modelling exit strategies that are related to key epidemiological quantities, such as royalsocietypublishing.org/journal/rspb proc. r. soc. b : the reproduction number and herd immunity fraction. we then identify different sources of heterogeneity underlying sars-cov- transmission and control, and consider how differences between hosts and populations across the world should be included in models. finally, we discuss current challenges relating to data requirements, focusing on the data that are needed to resolve current knowledge gaps and how uncertainty in modelling outputs can be communicated to policymakers and the wider public. in each case, we outline the most relevant issues, summarize expert knowledge and propose specific steps towards the development of evidencebased exit strategies. this leads to a roadmap for future research (figure ) made up of three key steps: (i) improve estimation of epidemiological parameters using outbreak data from different countries; (ii) understand heterogeneities within and between populations that affect virus transmission and interventions; and (iii) focus on data needs, particularly data collection and methods for planning exit strategies in low-to-middle-income countries (lmics) where data are often lacking. this roadmap is not a linear process: improved understanding of each aspect will help to inform other requirements. for example, a clearer understanding of the model resolution required for accurate forecasting ( § a) will inform the data that need to be collected ( § ), and vice versa. if this roadmap can be followed, it will be possible to predict the likely effects of different potential exit strategies with increased precision. this is of clear benefit to global health, allowing exit strategies to be chosen that permit interventions to be relaxed while limiting the risk of substantial further transmission. (a) how can viral transmissibility be assessed more accurately? the time-dependent reproduction number, r(t) or r t , has emerged as the main quantity used to assess the transmissibility of sars-cov- in real time [ ] [ ] [ ] [ ] [ ] . in a population with active virus transmission, the value of r(t) represents the expected number of secondary cases generated by someone infected at time t. if this quantity is, and remains below, one, then an ongoing outbreak will eventually fade out. although easy to understand intuitively, estimating r(t) from case reports (as opposed to, for example, observing r(t) in known or inferred transmission trees [ ] ) requires the use of mathematical models. as factors such as contact rates between infectious and susceptible individuals change during an outbreak in response to public health advice or movement restrictions, the value of r(t) has been found to respond rapidly. for example, across the uk, country-wide and regional estimates of r(t) dropped from approximately . - in mid-march [ , ] to below one after lockdown was introduced [ , ] . one of the criteria for relaxing the lockdown was for the reproduction number to decrease to 'manageable levels' [ ] . monitoring r(t), as well as case numbers, as individual components of the lockdown are relaxed is critical for understanding whether or not the outbreak remains under control [ ] . several mathematical and statistical methods for estimating temporal changes in the reproduction number have been proposed. two popular approaches are the wallinga-teunis method [ ] and the cori method [ , ] . these methods use case notification data along with an estimate of the serial interval distribution (the times between successive cases in a transmission chain) to infer the value of r(t). other approaches exist (e.g. based on compartmental epidemiological models [ ] ), including those that can be used alongside different data (e.g. time series of deaths [ , , ] or phylogenetic data [ ] [ ] [ ] [ ] ). despite this extensive theoretical framework, practical challenges remain. reproduction number estimates often rely on case notification data that are subject to delays between case onset and being recorded. available data, therefore, do not include up-to-date knowledge of current numbers of infections, an issue that can be addressed using 'nowcasting' models [ , , ] . the serial interval represents the period between symptom onset times in a transmission chain, rather than between times at which cases are recorded. time series of symptom onset dates, or even infection dates (to be used with estimates of the generation interval when inferring r(t)), can be estimated from case notification data using latent variable methods [ , ] or methods such as the richardson-lucy deconvolution technique [ , ] . the richardson-lucy approach has previously been applied to infer incidence curves from time series of deaths [ ] . these methods, as well as others that account for reporting delays [ figure . research roadmap to facilitate the development of reliable models to guide exit strategies. three key steps are required: (i) improve estimates of epidemiological parameters (such as the reproduction number and herd immunity fraction) using data from different countries ( § a-d); (ii) understand heterogeneities within and between populations that affect virus transmission and interventions ( § a-d); and (iii) focus on data requirements for predicting the effects of individual interventions, particularly-but not exclusively-in data-limited settings such as lmics ( § a-c). work in these areas must be conducted concurrently; feedback will arise from the results of the proposed research that will be useful for shaping next steps across the different topics. (online version in colour.) royalsocietypublishing.org/journal/rspb proc. r. soc. b : useful avenues to improve the practical estimation of r(t). further, changes in testing practice (or capacity to conduct tests) lead to temporal changes in case numbers that cannot be distinguished easily from changes in transmission. understanding how accurately and how quickly changes in r(t) can be inferred in real time given these challenges is crucial. another way to assess temporal changes in r(t), without requiring nowcasting, is by observing people's transmissionrelevant behaviour directly, e.g. through contact surveys or mobility data [ ] . these methods come with their own limitations: because these surveys do not usually collect data on infections, care must be taken in using them to understand and predict ongoing changes in transmission. other outstanding challenges in assessing variations in r(t) include the decrease in accuracy when case numbers are low, and the requirement to account for temporal changes in the serial interval or generation time distribution of the disease [ , ] . when there are few cases (such as in the 'tail' of an epidemic- § d), there is little information with which to assess virus transmissibility. methods for estimating r(t) based on the assumption that transmissibility is constant within fixed time periods can be applied with windows of long duration (thereby including more case notification data with which to estimate r(t)) [ , ] . however, this comes at the cost of a loss of sensitivity to temporal variations in transmissibility. consequently, when case numbers are low, the methods described above for tracking transmission-relevant behaviour directly are particularly useful. in those scenarios, the 'transmission potential' might be more important than realized transmission [ ] . the effect of population heterogeneity on reproduction number estimates requires further investigation, as current estimates of r(t) tend to be calculated for whole populations (e.g. countries or regions). understanding the characteristics of constituent groups contributing to this value is important to target interventions effectively [ , ] . for this, data on infections within and between different subpopulations (e.g. infections in care homes and in the wider population) are needed. as well as between subpopulations, it is also necessary to ensure that estimates of r(t) account for heterogeneity in transmission between different infectious hosts. such heterogeneity alters the effectiveness of different control measures, and, therefore, the predicted disease dynamics when interventions are relaxed. for a range of diseases, a rule of thumb that around % of infected individuals are the sources of % of infections has been proposed [ , ] . this is supported by recent evidence for covid- , which suggests significant individual-level variation in sars-cov- transmission [ ] with some transmission events leading to large numbers of new infections. finally, it is well documented that presymptomatic individuals (and, to a lesser extent, asymptomatic infected individuals-i.e. those who never develop symptoms) can transmit sars-cov- [ , ] . for that reason, negative serial intervals may occur when an infected host displays covid- symptoms before the person who infected them [ , ] . although methods for estimating r(t) with negative serial intervals exist [ , ] , their inclusion in publicly available software for estimating r(t) should be a priority. increasing the accuracy of estimates of r(t), and supplementing these estimates with other quantities (e.g. estimated epidemic growth rates [ ] ), is of clear importance. as lockdowns are relaxed, this will permit a fast determination of whether or not removed interventions are leading to a surge in cases. (b) what is the herd immunity threshold and when might we reach it? herd immunity refers to the accumulation of sufficient immunity in a population through infection and/or vaccination to prevent further substantial outbreaks. it is a major factor in determining exit strategies, but data are still very limited. dynamically, the threshold at which herd immunity is achieved is the point at which r(t) ( § a) falls below one for an otherwise uncontrolled epidemic, resulting in a negative epidemic growth rate. however, reaching the herd immunity threshold does not mean that the epidemic is over or that there is no risk of further infections. great care must be taken in communicating this concept to the public, to ensure continued adherence to public health measures. crucially, whether immunity is gained naturally through infection or through random or targeted vaccination affects the herd immunity threshold, which also depends critically on the immunological characteristics of the pathogen. since sars-cov- is a new virus, its immunological characteristics-notably the duration and extent to which prior infection confers protection against future infection, and how these vary across the populationare currently unknown [ ] . lockdown measures have impacted contact structures and hence the accumulation of immunity in the population, and are likely to have led to significant heterogeneity in acquired immunity (e.g. by age, location, workplace). knowing the extent and distribution of immunity in the population will help guide exit strategies. as interventions are lifted, whether or not r(t) remains below one depends on the current level of immunity in the population as well as the specific exit strategy followed. a simple illustration is to treat r(t) as a deflation of the original (basic) reproduction number (r , which is assumed to be greater than one): where i(t) is the immunity level in the community at time t and p(t) is the overall reduction factor from the control measures that are in place. if i(t) . À =r , then r(t) remains below one even when all interventions are lifted: herd immunity is achieved. however, recent results [ , ] show that, for heterogeneous populations, herd immunity occurs at a lower immunity level than À =r . the threshold À =r assumes random vaccination, with immunity distributed uniformly in the community. when immunity is obtained from disease exposure, the more socially active individuals in the population are over-represented in cases from the early stages of the epidemic. as a result, the virus preferentially infects individuals with higher numbers of contacts, thereby acting like a well-targeted vaccine. this reduces the herd immunity threshold. however, the extent to which heterogeneity in behaviour lowers the threshold for covid- is currently unknown. we highlight three key challenges for determining the herd immunity threshold for covid- , and hence for understanding the impact of implementing or lifting control measures in different populations. first, most of the quantities for calculating the threshold are not known precisely and require careful investigation. for example, determining the immunity level royalsocietypublishing.org/journal/rspb proc. r. soc. b : in a community is far from trivial for a number of reasons: antibody tests may have variable sensitivity and specificity; it is currently unclear whether or not individuals with mild or no symptoms acquire immunity or test seropositive; the duration of immunity is unknown. second, estimation of r , despite receiving significant attention at the start of the pandemic, still needs to be refined within and between countries as issues with early case reports come to light. third, as discussed in § , sars-cov- does not spread uniformly through populations [ ] . an improved understanding of the main transmission routes, and which communities are most influential, will help to determine how much lower diseaseinduced herd immunity is compared to the classical threshold to summarize, it is vital to obtain more accurate estimates of the current immunity levels in different countries and regions, and to understand how population heterogeneity affects transmission and the accumulation of immunity. quantitative information about current and past infections are key inputs to formulate exit strategies, monitor the progression of epidemics and identify social and demographic sources of transmission heterogeneities. seroprevalence surveys provide a direct way to estimate the fraction of the population that has been exposed to the virus but has not been detected by regular surveillance mechanisms [ ] . given the possibility of mild or asymptomatic infections, which are not typically included in laboratory-confirmed cases, seroprevalence surveys could be particularly useful for tracking the covid- pandemic [ ] . contacts between pathogens and hosts that elicit an immune response can be revealed by the presence of antibodies. typically, a rising concentration of immunoglobulin m (igm) precedes an increase in the concentration of immunoglobulin g (igg). however, for infections by sars-cov- , there is increasing evidence that igg and igm appear concurrently [ ] . most serological assays used for understanding viral transmission measure igg. interpretation of a positive result depends on detailed knowledge of immune response dynamics and its epidemiological correspondence to the developmental stage of the pathogen, for example, the presence of virus shedding [ , ] . serological surveys are common practice in infectious disease epidemiology and have been used to estimate the prevalence of carriers of antibodies, force of infection and reproduction numbers [ ] , and in certain circumstances (e.g. for measles) to infer population immunity to a pathogen [ ] . unfortunately, a single serological survey only provides information about the number of individuals who are seropositive at the time of the survey (as well as information about the individuals tested, such as their ages [ ] ). although information about temporal changes in infections can be obtained by conducting multiple surveys longitudinally [ , ] , the precise timings of infections remain unknown. available tests vary in sensitivity and specificity, which can impact the accuracy of model predictions if seropositivity is used to assess the proportion of individuals protected from infection or disease. propagation of uncertainty due to the sensitivity and specificity of the testing procedures and epidemiological interpretation of the immune response are areas that require attention. the possible presence of immunologically silent individuals, as implied by studies of covid- showing that - % of symptomatically infected people have few or no detectable antibodies [ ] , adds to the known sources of uncertainty. many compartmental modelling studies have used data on deaths as the main reliable dataset for model fitting. the extent to which seroprevalence data could provide an additional useful input for model calibration, and help in formulating exit strategies, has yet to be ascertained. with the caveats above, one-off or regular assessments of population seroprevalence could be helpful in understanding sars-cov- transmission in different locations. (d) is global eradication of sars-cov- a realistic possibility? when r is greater than one, an emerging outbreak will either grow to infect a substantial proportion of the population or become extinct before it is able to do so [ ] [ ] [ ] [ ] [ ] . if instead r is less than one, the outbreak will almost certainly become extinct before a substantial proportion of the population is infected. if new susceptible individuals are introduced into the population (for example, new susceptible individuals are born), it is possible that the disease will persist after its first wave and become endemic [ ] . these theoretical results can be extended to populations with household and network structure [ , ] and scenarios in which r is very close to one [ ] . epidemiological theory and data from different diseases indicate that extinction can be a slow process, often involving a long 'tail' of cases with significant random fluctuations (electronic supplementary material, figure s ). long epidemic tails can be driven by spatial heterogeneities, such as differences in weather in different countries (potentially allowing an outbreak to persist by surviving in different locations at different times of year) and varying access to treatment in different locations. regions or countries that eradicate sars-cov- successfully might experience reimportations from elsewhere [ , ] , for example, the reimportation of the virus to new zealand from the uk in june . at the global scale, smallpox is the only previously endemic human disease to have been eradicated, and extinction took many decades of vaccination. the prevalence and incidence of polio and measles have been reduced substantially through vaccination but both diseases persist. the foot and mouth disease outbreak in the uk and the sars pandemic were new epidemics that were driven extinct without vaccination before they became endemic, but both exhibited long tails before eradication was achieved. the - ebola epidemic in west africa was eliminated (with vaccination at the end of the epidemic [ ] ), but eradication took some time with flare ups occurring in different countries [ , ] . past experience, therefore, raises the possibility that sars-cov- may not be driven to complete extinction in the near future, even if a vaccine is developed and vaccination campaigns are implemented. as exemplified by the ebola outbreak in the democratic republic of the congo that has only recently been declared over [ ] , there is an additional challenge of assessing whether the virus really is extinct rather than persisting in individuals who do not report disease [ ] . sars-cov- could become endemic, persisting in populations with limited access to healthcare or circulating in seasonal outbreaks. appropriate royalsocietypublishing.org/journal/rspb proc. r. soc. b : communication of these scenarios to the public and policymakers-particularly the possibility that sars-cov- may never be eradicated-is essential. (a) how much resolution is needed when modelling human heterogeneities? a common challenge faced by epidemic modellers is the tension between making models more complex (and possibly, therefore, seeming more realistic to stakeholders) and maintaining simplicity (for scientific parsimony when data are sparse and for expediency when predictions are required at short notice) [ ] . how to strike the correct balance is not a settled question, especially given the increasing amount of available data on human demography and behaviour. indeed, outputs of multiple models with different levels of complexity can provide useful and complementary information. many sources of heterogeneity between individuals (and between populations) exist, including the strong skew of severe covid- outcomes towards the elderly and individuals from specific groups. we focus on two sources of heterogeneity in human populations that must be considered when modelling exit strategies: spatial contact structure and health vulnerabilities. there has been considerable success in modelling local contact structure, both in terms of spatial heterogeneity (distinguishing local and long-distance contacts) and in local mixing structures such as households and workplaces. however, challenges include tracking transmission and assessing changes when contact networks are altered. in spatial models with only a small number of near-neighbour contacts, the number of new infections grows slowly; each generation of infected individuals is only slightly larger than the previous one. as a result, in those models, r(t) cannot significantly exceed its threshold value of one [ ] . by contrast, models accounting for transmission within closely interacting groups explicitly contain a mechanism that has a multiplier effect on the value of r(t) [ ] . another challenge is the spatio-temporal structure of human populations: the spatial distribution of individuals is important, but longdistance contacts make populations more connected than in simple percolation-type spatial models [ ] . clustering and pair approximation models can capture some aspects of spatial heterogeneities [ ] , which can result in exponential rather than linear growth in case numbers [ ] . while models can include almost any kind of spatial stratification, ensuring that model outputs are meaningful for exit strategy planning relies on calibration with data. this brings in challenges of merging multiple data types with different stratification levels. for example, case notification data may be aggregated at a regional level within a country, while mobility data from past surveys might be available at finer scales within regions. another challenge is to determine the appropriate scale at which to introduce or lift interventions. although measures are usually directed at whole populations within relevant administrative units (country-wide or smaller), more effective interventions and exit strategies may target specific parts of the population [ ] . here, modelling can be helpful to account for operational costs and imperfect implementation that will offset expected epidemiological gains. the structure of host vulnerability to disease is generally reported via risk factors, including age, sex and ethnicity [ , ] . from a modelling perspective, a number of open questions exist. to what extent does heterogeneous vulnerability at an individual level affect the impact of exit strategies beyond the reporting of potential outcomes? where host vulnerability is an issue, is it necessary to account for considerations other than reported risk factors, as these may be proxies for underlying causes? once communicated to the public, modelling results could create behavioural feedback that might help or hinder exit strategies; some sensitivity analyses would be useful. as with the questions around spatial heterogeneity, modelling variations in host vulnerability could improve proposed exit strategies, and modelling can be used to explore how these are targeted and communicated [ ] . finally, heterogeneities in space and vulnerabilities may interact; modelling these may reveal surprises that can be explored further. (b) what are the roles of networks and households in sars-cov- transmission? npis reduce the opportunity for transmission by breaking up contact networks (closing workplaces and schools, preventing large gatherings), reducing the chance of transmission where links cannot be broken (wearing masks, sneeze barriers) and identifying infected individuals (temperature checks [ ] , diagnostic testing [ ] ). network models [ , ] aim to split pathogen transmission into opportunity (number of contacts) and transmission probability, using data that can be measured directly (through devices such as mobility tracking and contact diaries) and indirectly (through traffic flow and co-occurrence studies). this brings new issues: for example, are observed networks missing key transmission routes, such as indirect contact via contaminated surfaces, or including contacts that are low risk [ ] ? how we measure and interpret contact networks depends on the geographical and social scales of interest (e.g. wider community spread or closed populations such as prisons and care homes; or subpopulations such as workplaces and schools) and the timescales over which the networks are used to understand or predict transmission. in reality, individuals belong to households, children attend schools and adults mix in workplaces as well as in social contexts. this has led to the development of household models [ , [ ] [ ] [ ] [ ] , multilayer networks [ ] , bipartite networks [ , ] and networks that are geographically and socially embedded to reflect location and travel habits [ ] . these tools can play a key role in understanding and monitoring transmission, and exploring scenarios, at the point of exiting a lockdown: in particular, they can inform whether or not, and how quickly, households or local networks merge to form larger and possibly denser contact networks in which local outbreaks can emerge. regional variations and socio-economic factors can also be explored. contact tracing, followed by isolation or treatment of infected contacts, is a well-established method of disease control. the structure of the contact network is important in determining whether or not contact tracing will be successful. for example, contact tracing in clustered networks is known to be most effective [ , ] , since an infected contact can be royalsocietypublishing.org/journal/rspb proc. r. soc. b : traced from multiple different sources. knowledge of the contact network enhances understanding of the correlation structure that emerges as a result of the epidemic. the first wave of an epidemic will typically infect many of the highly connected nodes and will move slowly to less connected parts of the network, leaving behind islands of susceptible and recovered individuals. this can lead to a correlated structure of susceptible and recovered nodes that may make the networks less vulnerable to later epidemic waves [ ] , and has implications for herd immunity ( § b). in heterogeneous populations, relatively few very wellconnected people can be major hubs for transmission. such individuals are often referred to as super-spreaders [ , ] and some theoretical approaches to controlling epidemics are based on targeting them [ ] . however, particularly for respiratory diseases, whether specific individuals can be classified as potential super-spreaders, or instead whether any infected individual has the potential to generate super-spreading events, is debated [ , , ] . as control policies are gradually lifted, the disrupted contact network will start to form again. understanding how proxies for social networks (which can be measured in near real time using mobility data, electronic sensors or trackers) relate to transmission requires careful consideration. using observed contacts to predict virus spread might be successful if these quantities are heavily correlated, but one aim of npis should be at least a partial decoupling of the two, so that society can reopen but transmission remains controlled. currently, a key empirical and theoretical challenge is to understand how households are connected and how this is affected by school opening ( § c). an important area for further research is to improve our understanding of the role of within-household transmission in the covid- pandemic. in particular, do sustained infection chains within households lead to amplification of infection rates between households despite lockdowns aimed at minimizing between-household transmission? even for well-studied household models, development of methods accommodating time-varying parameters such as variable adherence to household-based policies and/or compensatory behaviour would be valuable. it would be useful to compare interventions and de-escalation procedures in different countries to gain insight into: regional variations in contact and transmission networks; the role of different household structures in transmission and the severity of outcomes (accounting for different household sizes and agestructures); the cost-effectiveness of different policies, such as household-based isolation and quarantine in the uk compared to out-of-household quarantine in australia and hong kong. first few x (ffx) studies [ , ] , now adopted in several countries, provide the opportunity not only to improve our understanding of critical epidemiological characteristics (such as incubation periods, generation intervals and the roles of asymptomatic and presymptomatic transmission) but also to make many of these comparisons. a widely implemented early intervention was school closure, which is frequently used during influenza pandemics [ , ] . further, playgrounds were closed and social distancing has kept children separated. however, the role of children in sars-cov- transmission is unclear. early signs from wuhan (china), echoed elsewhere, showed many fewer cases in under s than expected. there are three aspects of the role of children in transmission: (i) susceptibility; (ii) infectiousness once infected; and (iii) propensity to develop disease if infected [ , ] . evidence for age-dependent susceptibility and infectiousness is mixed, with infectiousness the more difficult to quantify. however, evidence is emerging of lower susceptibility to infection in children compared to adults [ ] , although the mechanism underlying this is unknown and it may not be generalizable to all settings. once infected, children appear to have a milder course of infection, and it has been suggested that children have a higher probability of a fully subclinical course of infection. reopening schools is of clear importance both in ensuring equal access to education and enabling carers to return to work. however, the transmission risk within schools and the potential impact on community transmission needs to be understood so that policymakers can balance the potential benefits and harms. as schools begin to reopen, there are major knowledge gaps that prevent clear answers. the most pressing question is the extent to which school restarting will affect population-level transmission, characterized by r(t) ( § a). clearer quantification of the role of children could have come from analysing the effects of school closures in different countries in february and march, but closures generally coincided with other interventions and so it has proved difficult to unpick the effects of individual measures [ ] . almost all schools in sweden stayed open to under- s (with the exception of one school that closed for two weeks [ ] ), and schools in some other countries are beginning to reopen with social distancing measures in place, providing a potential opportunity to understand within-school transmission more clearly. models can also inform the design of studies to generate the data required to answer key questions. the effect of opening schools on r(t) also depends on other changes in the community. children, teachers and support staff are members of households; lifting restrictions may affect all members. modelling school reopening must account for all changes in contacts of household members [ ] , noting that the impact on r(t) may depend on the other interventions in place at that time. the relative risk of restarting different school years (or universities) does not affect the population r(t) straightforwardly, since older children tend to live with adults who are older (compared to younger children), and households with older individuals are at greater risk of severe outcomes. thus, decisions about which age groups return to school first and how they are grouped at school must balance the risks of transmission between children, transmission to and between their teachers, and transmission to and within the households of the children and teachers. return to school affects the number of physical contacts of teachers and support staff. schools will not be the same environments as prior to lockdown, since physical distancing measures will be in place. these include smaller classes and changes in layout, plus increased hygiene measures. some children and teachers may be less likely to return to school because of underlying health conditions and if there is transmission within schools, there may be absenteeism following infection. models must, therefore, consider the different effects on transmission of pre-and post-lockdown school royalsocietypublishing.org/journal/rspb proc. r. soc. b : environments. post-lockdown, with social distancing in place in the wider community, reopening schools could link subcommunities of the population together, and models can be used to estimate the wider effects on population transmission as well as within schools. these estimates are likely to play a central role in decisions surrounding when and how to reopen schools. (d) the pandemic is social: how can we model that? while the effects of population structure and heterogeneities can be approximated in standard compartmental epidemiological models [ , , ] , such models can become highly complex and cumbersome to specify and solve as more heterogeneities are introduced. an alternative approach is agent-based modelling. agent-based models (abm) allow complex systems such as societies to be represented, using virtual agents programmed to have behavioural and individual characteristics (age, sex, ethnicity, income, employment status, etc.) as well as the capacity to interact with other agents [ ] . in addition, abm can include societal-level factors such as the influence of social media, regulations and laws, and community norms. in more sophisticated abm, agents can anticipate and react to scenarios, and learn by trial and error or by imitation. abm can represent systems in which there are feedbacks, tipping points, the emergence of higher-level properties from the actions of individual agents, adaptation and multiple scales of organization-all features of the covid- pandemic and societal reactions to it. while abm arise from a different tradition, they can incorporate the insights of compartmental models; for example, agents must transition through disease states (or compartments) such that the mean transition rates correspond to those in compartmental models. however, building an abm that represents a population on a national scale is a huge challenge and is unlikely be accomplished in a timescale useful for the current pandemic. abm often include many parameters, leading to challenges of model parametrization and a requirement for careful uncertainty quantification and sensitivity analyses to different inputs. on the other hand, useful abm do not have to be all-encompassing. there are already several models that illustrate the effects of policies such as social distancing on small simulated populations. these models can be very helpful as 'thought experiments' to identify the potential effects of candidate policies such as school re-opening and restrictions on long-distance travel, as well as the consequences of non-compliance with government edicts. there are two areas where long-term action should be taken. first, more data about people's ordinary behaviour are required: what individuals do each day (through timeuse diaries), whom they meet ( possibly through mobile phone data, if consent can be obtained) and how they understand and act on government regulation, social media influences and broadcast information [ ] . second, a large, modular abm should be built that represents heterogeneities in populations and that is properly calibrated as a social 'digital twin' of our own society, with which we can carry out virtual policy experiments. had these developments occurred before, they would have been useful currently. as a result, if these are addressed now, they will aid the planning of future exit strategies. (a) what are the additional challenges of data-limited settings? in most countries, criteria for ending covid- lockdowns rely on tracking trends in numbers of confirmed cases and deaths, and assessments of transmissibility ( § a). this section focuses on the relaxation of interventions in lmics, although many issues apply everywhere. perhaps surprisingly, concerns relating to data availability and reliability (e.g. lack of clarity about sampling frames) remain worldwide. other difficulties have also been experienced in many countries throughout the pandemic (e.g. shortages of vital supplies, perhaps due in developed countries to previous emphasis on healthcare system efficiency rather than pandemic preparedness [ ] ). data about the covid- pandemic and about the general population and context can be unreliable or lacking globally. however, due to limited healthcare access and utilization, there can be fewer opportunities for diagnosis and subsequent confirmation of cases in lmics compared to other settings, unless there are active programmes [ ] . distrust can make monitoring programmes difficult, and complicate control activities like test-trace-isolate campaigns [ , ] . other options for monitoring-such as assessing excess disease from general reporting of acute respiratory infections or influenza-like illness-require historical baselines that may not exist [ , ] . in general, while many lmics will have a well-served fraction of the population, dense peri-urban and informal settlements are typically outside that population and may rapidly become a primary concern for transmission [ ] . since confirmed case numbers in these populations are unlikely to provide an accurate representation of the underlying epidemic, reliance on alternative data such as clinically diagnosed cases may be necessary to understand the epidemic trajectory. some tools for rapid assessment of mortality in countries where the numbers of covid- -related deaths are hard to track are starting to become available [ ] . in settings where additional data collection is not affordable, models may provide a clearer picture by incorporating available metadata, such as testing and reporting rates through time, sample backlogs and suspected covid- cases based on syndromic surveillance. by identifying the most informative data, modelling could encourage countries to share available data more widely. for example, burial reports and death certificates may be available, and these data can provide information on the demographics that influence the infection fatality rate. these can in turn reveal potential covid- deaths classified as other causes and hence missing from covid- attributed death notifications. in addition to the challenges in understanding the pandemic in these settings, metrics on health system capacity (including resources such as beds and ventilators), as needed to set targets for control, are often poorly documented [ ] . furthermore, the economic hardships and competing health priorities in low-resource settings change the objectives of lifting restrictions-for example, hunger due to loss of jobs and changes in access to routine healthcare (e.g. hiv services and childhood vaccinations) as a result of lockdown have the potential to cost many lives in themselves, both in the short and long term [ , ] . this must be accounted for when deciding how to relax covid- interventions. royalsocietypublishing.org/journal/rspb proc. r. soc. b : we have identified three key challenges for epidemic modellers to help guide exit strategies in data-limited settings: (i) explore policy responses that are robust to missing information; (ii) conduct value-of-information analyses to prioritize additional data collection; and (iii) develop methods that use metadata to interpret epidemiological patterns. in general, supporting lmics calls for creativity in the data that are used to parametrize models and in the response activities that are undertaken. some lmics have managed the covid- pandemic successfully so far (e.g. vietnam, as well as trinidad and tobago [ ] ). however, additional support in lmics is required and warrants special attention. if interventions are relaxed too soon, fragile healthcare systems may be overwhelmed. if instead they are relaxed too late, socio-economic consequences can be particularly severe. (b) which data should be collected as countries emerge from lockdown, and why? identifying the effects of the different components of lockdown is important to understand how-and in which order-interventions should be released. the impact of previous measures must be understood both to inform policy in real time and to ensure that lessons can be learnt. all models require information to make their predictions relevant. data from pcr tests for the presence of active virus and serological tests for antibodies, together with data on covid- -related deaths, are freely available via a number of internet sites (e.g. [ ] ). however, metadata associated with testing protocols (e.g. reason for testing, type of test, breakdowns by age and underlying health conditions) and the definition of covid- -related death, which are needed to quantify sources of potential bias and parametrize models correctly, are often unavailable. data from individuals likely to have been exposed to the virus (e.g. within households of known infected individuals), but who may or may not have contracted it themselves, are also useful for model parametrization [ ] . new sources of data range from tracking data from mobile phones [ ] to social media surveys [ ] and details of interactions with public health providers [ ] . although potentially valuable, these data sources bring with them biases that are not always understood. these types of data are also often subject to data protection and/or costly fees, meaning that they are not readily available to all scientists. mixing patterns by age were reasonably well-characterized before the current pandemic [ , ] ( particularly for adults of different ages) and have been used extensively in existing models. however, there are gaps in these data and uncertainty in the impacts that different interventions have had on mixing. predictive models for policy tend to make broad assumptions about the effects of elements of social distancing [ ] , although results of studies that attempt to estimate effects in a more data-driven way are beginning to emerge [ ] . the future success of modelling to understand when controls should be relaxed or tightened depends critically on whether, and how accurately as well as how quickly, the effects of different elements of lockdown can be parametrized. given the many differences in lockdown implementation between countries, cross-country comparisons offer an opportunity to estimate the effects on transmission of each component of lockdown [ ] . however, there are many challenges in comparing sars-cov- dynamics in different countries. alongside variability in the timing, type and impact of interventions, the numbers of importations from elsewhere will vary [ , ] . underlying differences in mixing, behavioural changes in response to the pandemic, household structures, occupations and distributions of ages and comorbidities are likely to be important but uncertain drivers of transmission patterns. a current research target is to understand the role of weather and climate in sars-cov- transmission and severity [ ] . many analyses across and within countries highlight potential correlations between environmental variables and transmission [ ] [ ] [ ] [ ] [ ] [ ] , although sometimes by applying ecological niche modelling frameworks that may be ill-suited for modelling a rapidly spreading pathogen [ ] [ ] [ ] . assessments of the interactions between weather and viral transmissibility are facilitated by the availability of extensive datasets describing weather patterns, such as the european centre for medium-range weather forecasts era dataset [ ] and simulations of the community earth system model that can be used to estimate the past, present and future values of meteorological variables worldwide [ ] . temperature, humidity and precipitation are likely to affect the survival of sars-cov- outside the body, and prevailing weather conditions could, in theory, tip r(t) above or below one. however, the effects of these factors on transmission have not been established conclusively, and the impact of seasonality on short-or long-term sars-cov- dynamics is likely to depend on other factors including the timing and impact of interventions, and the dynamics of immunity [ , ] . it is hard to separate the effect of the weather on virus survival from other factors including behavioural changes in different seasons [ ] . the challenge of disentangling the impact of variations in weather on transmission from other epidemiological drivers in different locations is, therefore, a complex open problem. in seeking to understand and compare covid- data from different countries, there is a need to coordinate the design of epidemiological studies, involving longitudinal data collection and case-control studies. this will help enable models to track the progress of the epidemic and the impacts of control policies internationally. it will also allow more refined conclusions than those that follow from population data alone. countries with substantial epidemiological modelling expertise should support epidemiologists elsewhere with standardized protocols for collecting data and using models to inform policy. there is a need to share models to be used 'in the field'. collectively, these efforts will ensure that models are parametrized as realistically as possible for particular settings. in turn, as interventions are relaxed, this will allow us to detect the earliest possible reliable signatures of a resurgence in cases, leading to an unambiguous characterization of when it is necessary for interventions to be reintroduced. (c) how should model and parameter uncertainty be communicated? sars-cov- transmission models have played a crucial role in shaping policies in different countries, and their predictions have been a regular feature of media coverage of the pandemic [ , ] . understandably, both policymakers and journalists generally prefer single 'best guess' figures from models, rather than a range of plausible values. however, the ranges of outputs that modellers provide include important information about the variety of possible scenarios and guard royalsocietypublishing.org/journal/rspb proc. r. soc. b : against over-interpretation of model results. not displaying information about uncertainty can convey a false confidence in predictions. it is critical that modellers present uncertainty in a way that is understandable and useful for policymakers and the public [ ] . there are numerous and often inextricable ways in which uncertainty enters the modelling process. model assumptions inevitably vary according to judgements regarding which features are included [ , ] and which datasets are used to inform the model [ ] . within any model, ranges of parameter values can be considered to allow for uncertainty about clinical characteristics of covid- (e.g. the infectious period and case fatality rate) [ ] . alternative initial conditions (e.g. numbers and locations of imported cases seeding national outbreaks, or levels of population susceptibility) can be considered. in modelling exit strategies, when surges in cases starting from small numbers may occur and where predictions will depend on characterizing epidemiological parameters as accurately as possible, stochastic models may be of particular importance. not all the uncertainty arising from such stochasticity will be reduced by collecting more data; it is inherent to the process. where models have been developed for similar purposes, formal methods of comparison can be applied, but in epidemiological modelling, models often have been developed to address different questions, possibly involving 'what-if?' scenarios, in which case only qualitative comparisons can be made. the ideal outcome is when different models generate similar conclusions, demonstrating robustness to the detailed assumptions. where there is a narrowly defined requirement, such as short-term predictions of cases and deaths, more tractable tools for comparing the outputs from different models in real time would be valuable. one possible approach is to assess the models' past predictive performance [ , ] . ensemble estimates, most commonly applied for forecasting disease trajectories, allow multiple models' predictions to be combined [ , ] . the assessment of past performance can then be used to weight models in the ensemble. such approaches typically lead to improved point and variance estimates. to deal with parameter uncertainty, a common approach is to perform sensitivity analyses in which model parameters are repeatedly sampled from a range of plausible values, and the resulting model predictions compared; both classical and bayesian statistical approaches can be employed [ ] [ ] [ ] . methods of uncertainty quantification provide a framework in which uncertainties in model structure, epidemiological parameters and data can be considered together. in practice, there is usually only a limited number of policies that can be implemented. an important question is often whether or not the optimal policy can be identified given the uncertainties we have described, and decision analyses can be helpful for this [ , ] . in summary, communication of uncertainty to policymakers and the general public is challenging. different levels of detail may be required for different audiences. there are many subtleties: for instance, almost any epidemic model can provide an acceptable fit to data in the early phase of an outbreak, since most models predict exponential growth. this can induce an artificial belief that the model must be based on sensible underlying assumptions, and the true uncertainty about such assumptions has vanished. clear presentation of data is critical. it is important not simply to present data on the numbers of cases, but also on the numbers of individuals who have been tested. clear statements of the individual values used to calculate quantities such as the case fatality rate are vital, so that studies can be interpreted and compared correctly [ , ] . going forwards, improved communication of uncertainty is essential as models are used to predict the effects of different exit strategies. we have highlighted ongoing challenges in modelling the covid- pandemic, and uncertainties faced devising lockdown exit strategies. it is important, however, to put these issues into context: at the start of , sars-cov- was unknown, and its pandemic potential only became apparent at the end of january. the speed with which the scientific and public health communities came together and the openness in sharing data, methods and analyses are unprecedented. at very short notice, epidemic modellers mobilized a substantial workforce-mostly on a voluntary basis-and state-of-the-art computational models. far from the rough-and-ready tools sometimes depicted in the media, the modelling effort deployed since january is a collective and multi-pronged effort benefitting from years of experience of epidemic modelling, combined with long-term engagement with public health agencies and policymakers. drawing on this collective expertise, the virtual workshop convened in mid-may by the isaac newton institute generated a clear overview of the steps needed to improve and validate the scientific advice to guide lockdown exit strategies. importantly, the roadmap outlined in this paper is meant to be feasible within the lifetime of the pandemic. infectious disease epidemiology does not have the luxury of waiting for all data to become available before models must be developed. as discussed here, the solution lies in using diverse and flexible modelling frameworks that can be revised and improved iteratively as more data become available. equally important is the ability to assess the data critically and bring together evidence from multiple fields: numbers of cases and deaths reported by regional or national authorities only represent a single source of data, and expert knowledge is even required to interpret these data correctly. in this spirit, our first recommendation is to improve estimates of key epidemiological parameters. this requires close collaboration between modellers and the individuals and organizations that collect epidemic data, so that the caveats and assumptions on each side are clearly presented and understood. that is a key message from the first section of this study, in which the relevance of theoretical concepts and model parameters in the real world was demonstrated: far from ignoring the complexity of the pandemic, models draw from different sources of expertise to make sense of imperfect observations. by acknowledging the simplifying assumptions of models, we can assess the models' relative impacts and validate or replace them as new evidence becomes available. our second recommendation is to seek to understand important sources of heterogeneity that appear to be driving the pandemic and its response to interventions. agent-based modelling represents one possible framework for modelling complex dynamics, but standard epidemic models can also be extended to include age groups or any other relevant strata in the population as well as spatial structure. network royalsocietypublishing.org/journal/rspb proc. r. soc. b : models provide computationally efficient approaches to capture different types of epidemiological and social interactions. importantly, many modelling frameworks provide avenues for collaboration with other fields, such as the social sciences. our third and final recommendation regards the need to focus on data requirements, particularly (although not exclusively) in resource-limited settings such as lmics. understanding the data required for accurate predictions in different countries requires close communication between modellers and governments, public health authorities and the general public. while this pandemic casts a light on social inequalities between and within countries, modellers have a crucial role to play in sharing knowledge and expertise with those who need it most. during the pandemic so far, countries that might be considered similar in many respects have often differed in their policies; either in the choice or the timing of restrictions imposed on their respective populations. models are important for drawing reliable inferences from global comparisons of the relative impacts of different interventions. all too often, national death tolls have been used for political purposes in the media, attributing the apparent success or failure of particular countries to specific policies without presenting any convincing evidence. modellers must work closely with policymakers, journalists and social scientists to improve the communication of rapidly changing scientific knowledge while conveying the multiple sources of uncertainty in a meaningful way. we are now moving into a stage of the covid- pandemic in which data collection and novel research to inform the modelling issues discussed here are both possible and essential for global health. these are international challenges that require an international collaborative response from diverse scientific communities, which we hope that this article will stimulate. this is of critical importance, not only to tackle this pandemic but also to improve the response to future epidemics of emerging infectious diseases. data accessibility. data sharing is not applicable to this manuscript as no new data were created or analysed in this study. the effect of control strategies to reduce social mixing on outcomes of the 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harnessing multiple models for outbreak management control fast or control smart: when should invading pathogens be controlled? accurate quantification of uncertainty in epidemic parameter estimates and predictions using stochastic compartmental models fitting dynamic models to epidemic outbreaks with quantified uncertainty: a primer for parameter uncertainty, identifiability, and forecasts infectious disease pandemic planning and response: incorporating decision analysis improving the evidence base for decision making during a pandemic: the example of influenza a/h n potential biases in estimating absolute and relative case-fatality risks during outbreaks estimates of the severity of coronavirus disease : a model-based analysis acknowledgements. thanks to the isaac newton institute for mathematical sciences, cambridge (www.newton.ac.uk), for support during the virtual 'infectious dynamics of pandemics' programme. this work was undertaken in part as a contribution to the 'rapid assistance in modelling the pandemic' initiative coordinated by the royal society. thanks to sam abbott for helpful comments about the manuscript. key: cord- -jzke fop authors: hollingsworth, t. déirdre; klinkenberg, don; heesterbeek, hans; anderson, roy m. title: mitigation strategies for pandemic influenza a: balancing conflicting policy objectives date: - - journal: plos comput biol doi: . /journal.pcbi. sha: doc_id: cord_uid: jzke fop mitigation of a severe influenza pandemic can be achieved using a range of interventions to reduce transmission. interventions can reduce the impact of an outbreak and buy time until vaccines are developed, but they may have high social and economic costs. the non-linear effect on the epidemic dynamics means that suitable strategies crucially depend on the precise aim of the intervention. national pandemic influenza plans rarely contain clear statements of policy objectives or prioritization of potentially conflicting aims, such as minimizing mortality (depending on the severity of a pandemic) or peak prevalence or limiting the socio-economic burden of contact-reducing interventions. we use epidemiological models of influenza a to investigate how contact-reducing interventions and availability of antiviral drugs or pre-pandemic vaccines contribute to achieving particular policy objectives. our analyses show that the ideal strategy depends on the aim of an intervention and that the achievement of one policy objective may preclude success with others, e.g., constraining peak demand for public health resources may lengthen the duration of the epidemic and hence its economic and social impact. constraining total case numbers can be achieved by a range of strategies, whereas strategies which additionally constrain peak demand for services require a more sophisticated intervention. if, for example, there are multiple objectives which must be achieved prior to the availability of a pandemic vaccine (i.e., a time-limited intervention), our analysis shows that interventions should be implemented several weeks into the epidemic, not at the very start. this observation is shown to be robust across a range of constraints and for uncertainty in estimates of both r( ) and the timing of vaccine availability. these analyses highlight the need for more precise statements of policy objectives and their assumed consequences when planning and implementing strategies to mitigate the impact of an influenza pandemic. in the event of the emergence of a new human influenza a strain with a high case fatality rate indicating the possibility of a global pandemic with severe impact, control strategies primarily aim at limiting morbidity and mortality rather than halting transmission completely. this is because transmission of influenza a is difficult to block due to its short generation time and efficient transmission characteristics [ ] . in the early days of the h n influenza pandemic in mexico in [ ] , social distancing measures were implemented with the aim of slowing the epidemic during its early stages. for any future pandemic of a directlytransmitted infectious agent, it is expected that similar strategies will be used in high resource settings while the pathogen is being identified, epidemiological studies to both characterize transmission [ , , , , ] and determine pathogenicity are completed [ , ] and strain-specific control options, such as vaccines, are being developed [ , ] . for influenza, policy options are clearly outlined in national pandemic plans, but there is rarely any clear statement of policy objectives [ ] . the problem is that these different objectives are potentially conflicting in their effects, and clear prioritisation is therefore necessary. is the aim to minimize mortality and morbidity, is it to limit the peak prevalence of serious disease so that public health resources are not overwhelmed or is it to minimise the impact of the intervention on society and economy? in this paper we form a framework for policy makers to consider these potentially conflicting objectives. a number of studies have investigated the role of targeted interventions at different phases of the epidemic based on mathematical models which include various levels of population structure and spatial complexity [ , , , , , , , ] . however, none of these studies have addressed how multiple policy objectives are met by the common interventions, or how a clear statement of the key policy aims guides which set of interventions work best. it is typically assumed by policy makers that the more intervention measures implemented as early as possible in the course of the epidemic the better the outcome in terms of mitigation. reservations about this strategic approach rest on the costs, and societal impact plus economic implications of sustaining control measures over a long period of time. in recognition of this the usa pandemic plan, for instance, mentions a maximum duration of weeks for many transmission-reducing interventions [ ] . however, there has been no quantitative analysis of when such an intervention should be initiated. should it be as soon as the first cases are discovered, or later in the outbreak when more cases have arisen? neither has it been acknowledged that planned levels of coverage with antiviral treatment or pre-pandemic vaccines may implicitly determine the magnitude of social distancing interventions required. studies have shown that during the - influenza pandemic public health control strategies and changes in population contact rates lowered transmission rates and reduced mortality and case numbers [ , ] . similar measures were arguably effective for h n in mexico in [ ] . strategies used then, and to be considered in future, include social distancing measures, such as school closures [ , ] , restaurant and cinema closures [ ] , and transport restrictions [ , , ] . there are a number of other measures, such as hand washing and the use of face masks [ ] , which may reduce contact rates [ , ] . transmission will also be affected by changes in human behaviour in response to a pandemic, as was observed in travel and mixing patterns during the severe acute respiratory syndrome (sars) outbreak in [ ] . within the last years, there have been two international outbreaks of a directly transmitted pathogen with high case fatality rates in which social distancing measures were implemented. the first was the influenza pandemic of , where non-pharmaceutical public health strategies were effective at reducing morbidity and mortality in a number of settings [ ] . however, the impact of these interventions on transmission was highly variable. an analysis of cities in the usa showed reductions in transmission ranged from approximately - % ( figure ). these interventions were held in place from week to months. one might expect that interventions with higher impact were held in place for shorter time, but there was no systematic relationship between the duration and the impact of interventions (figure , black circles) . during the sars outbreak of , the aim of intervention strategies was to eliminate transmission, not only to mitigate the effects of the epidemic. elimination was possible due to the characteristics of the virus -post-symptomatic transmission and a long generation time [ ] . large scale reductions in the transmission rate of sars (. %, figure , [ ] ) were brought about by a number of public health interventions. these interventions were held in place for several weeks. the small amount of data available perhaps suggest a trend towards lower impact interventions being held in place for longer to achieve elimination ( figure , open triangles), but an important driver of the duration of these interventions was the number of cases that were present when the interventions started. these empirical data from two severe outbreaks suggest that moderate reductions in influenza transmission can be achieved and maintained at a population level for a number of weeks. the impact of any particular intervention is difficult to estimate from past epidemics due to variation in the viral strain and its transmission properties, and due to the concurrent effects of many different behavioural responses and government led initiatives. planning therefore depends increasingly on the predictions of mathematical models of viral spread that permit analyses of the potential impact of various interventions, alone or in combination [ , , , , , , ] . in this paper we consider the effectiveness of contact-reducing interventions during the first six months after the initial cases, before a pandemic vaccine is available, and evaluate optimum interventions for a range of policy objectives or constraints, such as a limited stockpile of treatments or non-specific vaccine. analyses are based on a mathematical model of virus transmission and the impact of control measures. we focus on the identification of policies that minimise peak demand for public health services and those which minimise the potential costs or socio-economic impact as evaluated by a simple cost function. this paper is not designed [ ] (open triangles) and during the influenza pandemic in cities in the usa [ ] (closed circles). a transmission reduction of % reflects an intervention which was estimated to have no effect on transmission. doi: . /journal.pcbi. .g in the event of an influenza pandemic which has high mortality and the potential to spread rapidly, such as the - pandemic, there are a number of non-pharmaceutical public health control options available to reduce transmission in the community and mitigate the effects of the pandemic. these include reducing social contacts by closing schools or postponing public events, and encouraging hand washing and the use of masks. these interventions will not only have a non-intuitive impact on the epidemic dynamics, but they will also have direct and indirect social and economic costs, which mean that governments will only want to use them for a limited amount of time. we use simulations to show that limitedtime interventions that achieve one aim, e.g., contain the total number of cases below some maximum number of treatments available, are not the same as those that achieve another, e.g., minimize peak demand for health care services. if multiple aims are defined simultaneously, we often see that the optimal intervention need not commence immediately but can begin a few weeks into the epidemic. our research demonstrates the importance of tailoring pandemic plans to defined policy targets with some flexibility to allow for uncertainty in the characteristics of the pandemic. to give specific policy guidance. box outlines a number of factors which should be considered in designing policy which are not covered here. our aim is to develop an understanding of how different policy objectives determine the optimal mix, timing of introduction and duration of implementation of the available mitigation strategies. all results have been obtained with a model based on the wellknown deterministic sir-model, that has proven its value in many studies of infectious diseases [ , ] . we parameterized the model with a mean infectious period of . days (recovery rate c = / . ), and a basic reproduction number r = . (see ferguson et al [ ] ) with a population of size n = . million. the population was subdivided into proportions of the population in the classes of x susceptibles, y infectives, and z immunes, with dynamics given by the parameter b t ð Þ is the transmission rate, i.e. the number of contacts an infective has per day in which the infection is passed on, and has the baseline value b ~r c~ : = : . simulations were started with infective, n susceptibles, and no immunes. we investigated the impact of a social distancing intervention on transmission through a constant reduction in transmission, w, resulting from an unspecified combination of public health measures, maintained over a time period, d. in model terms, the transmission rate b t ð Þ was assumed to change during intervention from the baseline rate b to a reduced rate {w ð Þb . this happened from t~t , the start of the intervention, until t ~t zd, the end of the intervention of duration d. for the duration we considered three options, first an intervention that is kept in place indefinitely, second an intervention with a fixed duration of twelve weeks, which is the maximum duration mentioned in the usa national pandemic plan [ ] , and third an intervention until the a pandemic specific vaccine is available, after six months. in the 'indefinite' scenario, the duration of the epidemic was formally defined as the time until ynv . transmission-reducing public health interventions for influenza are unlikely to completely halt transmission [ , , , ] . it is most likely that mitigation strategies will be 'sub-critical' interventions which reduce the effective reproduction ratio (the mean number of new infections per infected individual) towards, but not below, . thus, we assumed that wv { =r ~ : . numerical simulations of the model were used to evaluate the impact of the interventions twelve months after the first case. impact is primarily measured by (the reduction in) the total number of cases. we also evaluated two other measures of effectiveness: firstly, the (reduction in) peak prevalence, since high prevalence may overwhelm public health facilities and as such increase both morbidity and mortality; and secondly, the socioeconomic costs of the interventions, determined both by the level of intervention and the duration they are in place, calculated as the simple cost function w|d. many countries have stockpiled antiviral drugs in preparation for an influenza pandemic [ ] . whilst these may be used prophylactically to reduce transmission [ , , ] , most pandemic strategies advocate the use of antivirals to treat cases of infection or to treat those cases where other risk factors suggest that disease severity may be high [ ] . the treatment of cases will reduce morbidity and mortality and has been shown to be cost-effective for high risk patients [ ] . we focus on the treatment of cases in combination with transmission-reducing intervention as above. we make the assumption that treatment of cases does not affect transmission. the assumption is made firstly because drugs are given upon case notification, which is when much infectiousness may have passed [ ] , and secondly because symptomatic patients will be advised to remain at home reducing their contacts. the additional transmission reduction in transmission due to antivirals will thus be minor. the use of antivirals for severely ill patients could have implications for occupancy and therefore availability of isolation units and high dependency beds. whilst this might change the infectious profile of the few severely ill patients who would have access to these facilities, it does not affect the majority of cases and detailed consideration of these logistics is outside the scope of this study. in addition, we do not include the possible effect of mass treatment on resistance [ ] and therefore on the efficacy of the drugs. consideration of these effects may lead to a range of different policy objectives, taking into account combination therapy or sequential deployment of different lines of therapy [ ] . as well as stockpiling antivirals, it may be possible to reduce transmission and severity of disease by stockpiling a partially-box . epidemic-specific characteristics affecting suitability of interventions. n epidemiological characteristics of a future pandemic are not yet known and will be uncertain early in the epidemic. however, transmission estimates used for influenza pandemic planning proved to be close to those observed during the h n pandemic [ ] . key parameters include r , epidemic growth rate, generation time distribution, age-specific attack rate, asymptomatic case ratio, case fatality ratio, hospitalisation rates, treatment requirements, cross-immunity, drug resistance. n setting specific parameters will affect the growth rate and peak prevalence of an outbreak. these include age structure of the population, contact rates within and between age-groups, household structure, school attendance patterns, pre-existing immunity. n spatial structure may be important in certain settings, particularly population density, transport links and accessibility of health care services. therefore interventions may be applied differently in different areas, depending on the spatial scale. influenza growth rates are very rapid, so spread between areas could be rapid. n the early course of an outbreak. when there are small numbers of cases and variable importation rates, there will be stochastic effects which will facilitate or slow the transition from localised outbreaks to exponential growth of the epidemic. this will affect the optimal timing of interventions. protective pre-pandemic vaccine in advance of the pandemic [ ] . even partially effective vaccines can have large beneficial effects because the unvaccinated are indirectly protected from infection by those portions of the vaccinated population who are not infected or are less severely affected and possibly have reduced infectiousness ('herd' immunity -see [ ] ). use of an imperfect vaccine can, however, also lead to increased incidence if reductions in infectiousness are associated with corresponding increases in the infectious period [ , ] . effectiveness estimates for a prepandemic vaccine are not available, but evidence from crossprotection studies led to the assumption that both susceptibility to infection and infectiousness may be reduced by % [ , ] . the duration of infectiousness is assumed to be unchanged, precluding any increased incidence in the presence of the vaccine. we evaluate a partial vaccination strategy, in combination with a transmission reducing intervention, aiming to keep the number of unvaccinated cases (epidemic size) less than % of the population. to consider vaccination with a pre-pandemic vaccine, the transmission model was adjusted to include infection of vaccinated individuals: in this adjusted model, x v , y v , and z v are the proportion of vaccinated individuals, and e i ( = . ) and e s ( = . ) are the relative infectiousness and susceptibility of vaccinated versus unvaccinated individuals. it is assumed that vaccinated cases would not require treatment, and therefore were not included in the epidemic size or peak prevalence. simulations were carried out with a vaccine coverage of %, starting with one unvaccinated infective. to place our results in a more realistic context whilst not giving precise policy guidance, we consider two scenarios for pandemic planning in high resource settings. they are scenarios which are covered in a number of pandemic plans. we will outline the range of interventions which can achieve these aims. scenario : a strain-specific vaccine is expected to be available within months of the start of a pandemic. in order to minimize morbidity and mortality, social-distancing interventions will be used to 'buy time' until the vaccine is available. antiviral drugs are available to treat symptomatic cases with a stockpile for up to % of the population. social-distancing interventions will be used to ensure that symptomatic cases are kept below this level and to minimize socio-economic impact and peak demand for hospital and other public health services by minimizing prevalence in the population. scenario : this scenario is very similar to scenario , except that in addition a pre-pandemic vaccine is available which can be rapidly rolled out to % of the population. the question of interest will be the extent to which the pre-pandemic vaccine will reduce the level of intervention required. since we are considering interventions implemented early in the epidemic, key epidemiological parameters may still be in the process of being estimated. therefore, we investigated which strategies are least sensitive to incorrect estimation of r , i.e. r = . or . . in addition, availability of a pandemic vaccine may be delayed, or the pre-pandemic vaccine may be less effective than anticipated, so we ran our simulations out to an eight-month period and with a vaccine efficacy of e s~ei~ : ( % less reduction in transmission). we first investigate the impact of social distancing interventions alone. the received wisdom of outbreak control strategies is that the maximum level of control measures should be put in place as rapidly as possible. however, there may be delays before control strategies are implemented due to difficulties in identifying the early stages of a novel outbreak, as well as other logistical, political and economic constraints. because the interventions considered here are sub-optimal, cases will continue to occur whilst the intervention is in place, but at a slower rate than in the unconstrained epidemic. this means controls may need to be held in place for a long time, which may be costly. detailed derivations of the analytical results are given in a text s . one possible policy choice is to maintain an intervention irrespective of cost until the last case has recovered from the disease. this will always reduce the total number of cases and peak prevalence. these quantities can be expressed or approximated by analytical expressions, which we derive in text s and illustrate using numerical simulations. the final proportion of the population affected by an unconstrained epidemic, a ni , is given by solving [ , ] the final size increases monotonically with increasing r and does not depend on the generation time of the infection [ ] . for a long term intervention, implemented at t and held in place until there are no cases (figure ), the final epidemic size, a li (proportion of the population who have been infected) is given by where i t ð Þ is cumulative incidence up to time t . in the exponential growth phase, the cumulative incidence can be approximated by where r is the epidemic growth rate, given by r~r { ð Þc. for our parameter values, this approximation works well until about t = days ( weeks), when equation ( ) overestimates i t ð Þ by %. the final epidemic size decreases monotonically as the timing of the intervention, t , becomes earlier, and as the size of the intervention, w, becomes larger ( figure ). however, before week i t ð Þ is very small, so interventions starting earlier do not have much effect (figure ). in the absence of an intervention the maximum prevalence occurs when dy=dt~ , or when x~ =r , and the maximum prevalence is (using the equations above and x ð Þ& approximations to the initial conditions) is [ ] which increases with increasing r , and, as with the unconstrained epidemic size, does not depend on the generation time. in the presence of the intervention, maximum prevalence is dependent on the proportion of the population who are still susceptible at the time of the intervention. if the intervention is initiated before the peak in the unconstrained epidemic, and if cumulative incidence is sufficiently high and the proportion of the population still susceptible at the start of the intervention is less than = r {w ð Þ ð Þ , then peak prevalence will be at the start of the intervention, y t ð Þ. on the other hand, if the cumulative incidence is less than { = r {w ð Þ ð Þthere will be a peak during the intervention (figure ), which is given by if the intervention is initiated after the peak of the unconstrained epidemic, then there will not be another peak in prevalence during the intervention, since there will be too few susceptible individuals. these analytical results can be used to understand the effect of an intervention on the final size and peak prevalence, but we do not have neat expressions for the resulting duration of the whole epidemic (time until final case recovers) when an intervention is in place, and therefore we turn to simulation (figure ). the higher the transmission rate, the shorter the epidemic, which may be a desirable policy outcome. for influenza-like parameters, a few weeks delay may have only moderate deleterious consequences for peak prevalence, peak incidence or epidemic size (figure ) . this delay will result in higher peak prevalence, but it will also result in a considerably shorter epidemic than an early intervention (figure a circular inset and b) . this may be a desirable outcome in economic terms. the level of reduction in transmission has similar effects, where a more effective intervention put in place early in the epidemic will lead to the smallest epidemic size and peak prevalence, but the longest epidemic duration ( figure c and d) . in brief, the earlier a long term intervention is put in place and the more effective it is at reducing transmission, the greater the beneficial effect in terms of total epidemic size and peak prevalence. interventions of this kind are likely to be the most costly, and, counter-intuitively, may have to be held in place the longest. a strong argument to start an intervention early, however, is that the epidemic peak occurs later for early interventions (figure a) , allowing time to prepare public health facilities, to manufacture a strain specific vaccine and because there is great uncertainty about severity in the early stages of an outbreak [ ] . the drawbacks of a long intervention period are recognised in the usa national pandemic plan, where a maximum duration of weeks intervention is anticipated -another policy choice we considered. as above, we first consider some analytical expressions, and illustrate them using numerical simulation. for a single short term intervention from t to t ~t zd, the final epidemic size, a si , is given by note that, although i t ð Þ can still be approximated during the exponential phase of the epidemic (equation ( )), we cannot approximate i t zd ð Þ . in this case, the relationship between the final epidemic size and intervention parameters is more complex because cumulative incidence at the time the intervention is lifted depends both on cumulative incidence at the time the intervention is initiated and the size of the intervention, w. for example, if the duration of the intervention and its starting time are fixed, the epidemic size is optimized for intermediate values of the size of the intervention, w ( figure b, d) . with a short-term intervention, there are three possible maximum prevalence points. firstly, prior to the intervention (equation ( )), during the intervention (equation ( )), or after the intervention (note that i t ð Þvi t zd ð Þ ). the peak value could also occur at the point at which the intervention starts, i.e. when y~y t ð Þ. the conditions for each peak being the maximum are given in table . a large magnitude intervention (large w) may actually be deleterious, leading to a larger resurgence in prevalence after the intervention than an intervention with a smaller reduction in transmission. with a short-term intervention, there is no longer a monotonic relationship between the policy outcomes and the magnitude and length of the intervention. therefore strategies which contain the epidemic size below certain levels are unlikely to be the same interventions which contain peak prevalence below particular targets. for influenza-like parameters a -week intervention will almost certainly lead to a resurgence of the epidemic once the controls are lifted ( figure a, c) . if peak prevalence is very much lower during the intervention than it would be with no intervention, the implemented policy may even result in almost no change in the total epidemic size (figure ). for late, or less effective, interventions, prevalence during the intervention is higher than for early, or more effective, interventions,, resulting in fewer susceptible individuals remaining when the intervention is lifted. in this case the second peak is smaller, and reductions in total epidemic size are larger (figure ). for short term interventions, in contrast to long-term strategies, peak prevalence, peak incidence, and epidemic size cannot all be minimized by the same strategy. for instance, a % reduction in transmission timed to minimise total epidemic size ( figure a , b, initiated week ) may not be the intervention which minimises peak prevalence ( figure a , b, initiated week ). both these strategies have small and late resurgent epidemics ( figure a , circular inset), with cases beyond the end of the year. similarly, an intervention initiated at week may minimise peak prevalence for a % reduction in transmission ( figure c, d) , or minimize epidemic size with a % reduction in transmission ( figure c , d), but neither of these strategies are optimal if the aim is to have the epidemic exhaust itself most rapidly, with the quickest epidemic being the one without any intervention. the intervention always reduces peak prevalence from what it would have been in the absence of an intervention. however, which particular value is the peak value is determined by the timing of the intervention and the magnitude of the intervention ( table ) . each of these vary according to the characteristics of the intervention, and the underlying epidemic. for a fixed starting time and duration, there is a non-linear relationship between peak prevalence and the reduction in transmission, w (figure ). the value of w for which peak prevalence is minimized is almost certainly not that at which the total epidemic size is minimized (figure ). it is not possible to achieve a symptomatic epidemic size of % of the population with a week intervention for these parameter values. we therefore consider a scenario in which an intervention is initiated in the first weeks or months of the outbreak and held in place until months after the start of the outbreak. many different interventions can be used to constrain the epidemic size to % of the population. they range from an early intervention with a mild reduction in transmission, to a late, more impactful intervention ( figure a ). to achieve this aim whilst minimising peak prevalence it is not necessary to initiate the intervention early, in fact a delay may even be beneficial ( figure b ). but, the intervention must start before weeks (for these parameter values), when the number of cases prior to the intervention becomes large. if we evaluate the socio-economic 'cost' of these interventions as a simple product of the duration of the intervention and the reduction in transmission achieved, a delay also reduces the costs of the intervention, and the ideal intervention is more clearly defined ( figure b ). delay is valuable because transmission is being reduced, not eliminated, and therefore some of the effort in constraining the epidemic at the early stages is redundant. choices about intervention policy will be made early in the epidemic when parameters are uncertain. for example, r and the date of availability of the vaccine could be over or under estimated. of course, designing this intervention based on an overestimate of r means that the epidemic is smaller than expected, and so the intervention is too large and there are fewer cases overall ( figure c ). an underestimate in r means that the epidemic is larger than expected and so the intervention is not large enough to contain the epidemic and there are more cases than expected ( figure c ). in either of these cases, the intervention would have to be adjusted during the outbreak. if the 'optimum' intervention, which minimised peak prevalence, is chosen, it is more robust to changes in r than the other options ( figure c ). the interventions range from late interventions at the top of the a delay in the availability of vaccine increases the number of cases, but picking a late intervention minimises this effect. use of an imperfect vaccine for only % of the population results in a slower epidemic with fewer cases ( figure ) . the use of a pre-pandemic vaccine means that interventions which contain the total number of cases and peak prevalence can be rolled out later ( figure a ), compared to the non-vaccination scenario. also, as can be seen from the simple cost function (figure b ), the level of intervention can be reduced if pre-pandemic vaccines are used. the true economic value of this reduction in costs depends on the relative costs of vaccination, cases and interventions. the general picture remains the same as without vaccination. to minimize peak prevalence, the intervention should be initiated earlier than to minimize costs, but both objectives require interventions that commence several weeks into the epidemic growth phase ( figure b ). sensitivity to the value of r or the effectiveness of the pre-pandemic vaccine highlights that once again the most robust strategies are those that are minimize peak prevalence ( figure c ). in the absence of detailed analyses, it is often argued that epidemic outbreak control is best achieved by putting all mitigation options into play as early as is feasible. there may be delays before control strategies are implemented due to difficulties in identifying the early stages of a novel outbreak [ ] , as well as other logistical, political and economic constraints. of course, if interventions are held in place until a pandemic vaccine is available a greater level of reduction and earlier start of intervention will result in fewer cases, and a lower peak prevalence and incidence if intervention starts before the peak. however, not only are the costs of an intervention held for a long time likely to be high, but high demand for health services will be extended over a longer time period. our results indicate that an intervention starting at a few weeks into the epidemic is almost as effective at reducing epidemic size and peak prevalence as one starting at week . as such, given that the social and economic burden will be greater when starting earlier, starting a little bit later may be a better policy option. however, this will crucially depend on the socio-economic costs of both cases and interventions and on the estimated severity of the epidemic, which may be uncertain in the early stages of the epidemic [ ] . as noted in the introduction, the drawbacks of a long intervention period are recognised in the usa national pandemic plan, where a maximum intervention duration of twelve weeks is anticipated [ ] . using a twelve-week intervention, we have illustrated how the introduction of a short term intervention complicates the dynamics and increases the potential for conflict between policy aims. interventions of limited duration are very likely to result in a resurgence of the epidemic once they are lifted, unless it is imposed late in the epidemic or with low effectiveness. however, the height of this resurgence can be managed. a twelveweek interventions minimizing peak logistical pressure (peak prevalence and incidence) need not be very strong but require a timely start. on the other hand, an intervention that minimizes total epidemic size needs to be stronger and can start later, preventing a second peak. a number of american cities experience a second peak in mortality following the lifting of interventions during the pandemic [ , ] . re-analyses of a number of cities showed that multiple interventions were more effective at controlling transmis- figure . comparison of intervention strategies which 'buy time' until a strain-specific vaccine is available months into the epidemic and contain symptomatic cases to utilize a stockpile of treatments for % of the population. a uncontrolled epidemic (black dotted curve) and epidemic curves for five different strategies, starting at different times: t = , , , , or weeks into the epidemic. the required reductions in transmission are w = %, %, %, % and %. b peak prevalence (solid curve) and costs of interventions calculated as wt (dashed curve), in relation to the time of commencement of intervention. c excess number of cases for the five strategies if the parameters of the epidemic are different to those for which these interventions were designed: the availability of a strain specific vaccine is delayed until months (black), transmission has been overestimated and r = . (dark grey), or transmission has been underestimated and r = (light grey). doi: . /journal.pcbi. .g sion than single interventions [ ] . in addition, it was found that the later multiple interventions were implemented, the less effective they were in reducing mortality [ , ] . this was most notable when controls were implemented when excess mortality was higher than , per , [ ] . this conclusion cannot be so easily drawn in epidemics for which interventions were initiated prior to this threshold [ ] . here, we have shown that for short term interventions implemented during this early part of the epidemic earlier commencement is not always better, and that the outcome is highly sensitive to the timing and effectiveness of interventions. our two scenarios for policy design illustrate that applying one objective and then another sequentially (e.g. limiting total cases and then minimising peak prevalence for that epidemic size) can be used to resolve potentially conflicting aims. our results also show that the most extreme and earliest mitigation interventions are not always the best, and not always the least costly. it has not previously been highlighted that the level of stockpiles will quantitatively affect the required magnitude of social-distancing interventions so that all those who require treatment will receive it. any level of stockpiled antiviral drugs will reduce morbidity and mortality and therefore reduces the need for transmission-reducing interventions, as not all cases need to be prevented, but the availability of drugs means that demand for these drugs should not exceed supply. in addition, our results illustrate that even low coverage with imperfect vaccines can lead to reductions in the required interventions level to meet a defined objective for control. there are many complexities involved in quantifying the effect of interventions which are not included here, the complexities of transmission by age and spatial heterogeneities, the likely behavioral changes during an epidemic that affect transmission, seasonal variation in transmission, the logistics of delivery of prepandemic vaccines and drugs, the economic costs of an outbreak and potential development of resistance to antiviral drugs. detailed investigations are required to tailor general policies to particular settings, and therefore we are not attempting to make quantitative policy recommendations (see box ). however, uncertainties with regard to characteristics of the next pandemic strain will make it difficult in general to do very detailed optimization analyses. decisions on stockpiling must be based on knowledge from previous pandemics and seasonal influenza, but when a pandemic is at hand one has to work with the stockpiles available. intervention measures can be additionally imposed if a shortage of drugs is expected, or lifted to reduce the impact of intervention on society and economy, if drug supplies permit. our analyses show that there is indeed some time to choose the appropriate level of control, as very early commencement of intervention is hardly ever optimal for these time-limited interventions. our analyses also illustrates that even a simple inclusion of 'costs' changes what is optimal by comparison with analyses that are just based on impact on epidemiological measures. economic costs typically enter the equations in a non-linear term as indicated in our model formulation. however, including empirically derived cost functions will probably lead to the inclusion of more highly non-linear functions. this highlights the need to include more robust economic constraints into future epidemiological model analyses for public health policy support. in our view, this is a more urgent need than that of increasing the complexity of epidemiological description within models of infectious disease control. concomitantly, there is the associated need for measurement of the appropriate cost functions. data is available for both drug and vaccine purchase but this is regarded as confidential at present as neither the pharmaceutical industry nor government figure . addition of a pre-pandemic vaccine for % of the population. comparison of intervention strategies which 'buy time' until a strain-specific vaccine is available months into the epidemic and contain symptomatic cases to utilize a stockpile of treatments for % of the population when % of the population are vaccinated with a vaccine which reduces susceptibility and infectiousness by %. a uncontrolled epidemic (black dotted curve) and epidemic curves for five different strategies, starting at different times: t = , , , , or weeks into the epidemic. the required reductions in transmission are w = %, %, %, % and %. b peak prevalence (solid curve) and costs of interventions calculated as wt (dashed curve), in relation to the time of commencement of intervention. c excess number of cases for the five strategies if the parameters of the epidemic are different to those for which these interventions were designed: the pre-pandemic vaccine is less effective (black), transmission has been overestimated and r = . (dark grey), or transmission has been underestimated and r = (light grey). doi: . /journal.pcbi. .g health departments are keen to say how much was paid per dose as a function of total volume purchased. future research must address the detail of cost and benefit, both in terms of measurement of direct and indirect socio-economic costs, the costs of stockpiling and the benefits of reducing the impact of the epidemic and in terms of using a template for analysis that reflects the dynamics of virus transmission and the impact of control measures. in our model we have considered contact-reducing interventions, the use of antiviral medication, and vaccination with a prepandemic vaccine. for insight into the effect of other control options, it is useful to understand what characterizes these three particular control measures. antivirals work on the individual level, contact reduction on the population level, and vaccination on both. contact reduction and vaccination are preventive measures, whereas treatment is reactive. treatment and vaccines require stockpiling, and both are flexible with respect to possible timings of introduction during the epidemic. contact reduction is flexible in both planning and timing, but has major implications for the normal functioning of society. this flexibility implies that a broad range of more complex strategies could be envisaged, for example implementing and lifting a hierarchy of controls in response to the dynamics of the epidemic and importation of cases. however, the simple scenarios illustrated here highlight the complexities in selecting the best intervention policy, in terms of magnitude, timing and duration of interventions. the optimum intervention in terms of minimising peak logistical pressures (peak prevalence or incidence), may not be the same as one which minimises total epidemic size, and will almost certainly not be the one minimising direct social or economic impact from the intervention itself. the aims of a public 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predicting pandemics date: - - journal: hemorrhagic fever viruses doi: . / - - - - _ sha: doc_id: cord_uid: hayhbs u as successive epidemics have swept the world, the scientific community has quickly learned from them about the emergence and transmission of communicable diseases. epidemics usually occur when health systems are unprepared. during an unexpected epidemic, health authorities engage in damage control, fear drives action, and the desire to understand the threat is greatest. as humanity recovers, policy-makers seek scientific expertise to improve their “preparedness” to face future events. global spread of disease is exemplified by the spread of yellow fever from africa to the americas, by the spread of dengue fever through transcontinental migration of mosquitos, by the relentless influenza virus pandemics, and, most recently, by the unexpected emergence of ebola virus, spread by motorbike and long haul carriers. other pathogens that are remarkable for their epidemic expansions include the arenavirus hemorrhagic fevers and hantavirus diseases carried by rodents over great geographic distances and the arthropod-borne viruses (west nile, chikungunya and zika) enabled by ecology and vector adaptations. did we learn from the past epidemics? are we prepared for the worst? the ultimate goal is to develop a resilient global health infrastructure. besides acquiring treatments, vaccines, and other preventive medicine, bio-surveillance is critical to preventing disease emergence and to counteracting its spread. so far, only the western hemisphere has a large and established monitoring system; however, diseases continue to emerge sporadically, in particular in southeast asia and south america, illuminating the imperfections of our surveillance. epidemics destabilize fragile governments, ravage the most vulnerable populations, and threaten the global community. pandemic risk calculations employ new technologies like computerized maintenance of geographical and historical datasets, geographic information systems (gis), next generation sequencing, and metagenomics to trace the molecular changes in pathogens during their emergence, and mathematical models to assess risk. predictions help to pinpoint the hot spots of emergence, the populations at risk, and the pathogens under genetic evolution. preparedness anticipates the risks, the needs of the population, the capacities of infrastructure, the sources of emergency funding, and finally, the international partnerships needed to manage a disaster before it occurs. at present, the world is in an intermediate phase of trying to reduce health disparities despite exponential population growth, political conflicts, migration, global trade, urbanization, and major environmental changes due to global warming. for the sake of humanity, we must focus on developing the necessary capacities for health surveillance, epidemic preparedness, and pandemic response. infectious diseases have swept the world, taking the lives of millions of people, causing considerable upheaval, and transforming the future of entire populations. every year pathogens cause nearly million deaths worldwide, mostly in developing countries. more than infectious diseases have emerged between the s and [ ] . also among the known arboviruses, only are known to be human pathogens, while the others only infect wild animals and/or arthropods. to anticipate an epidemic one must identify the risk, prepare an appropriate response, and control the disease spread by first identifying the vulnerabilities of the population and circumscribing the potential space into which a disease will extend. when the epidemic expansion risk is identified, adequate information must be communicated to decision makers. ultimately, an appropriate response will depend on biosurveillance, prevention, sustained data processing, communication, strategic immunization campaigns, resilience, and mitigation strategies. the viral hemorrhagic fevers (vhfs) are a diverse group of human illnesses caused by rna viruses including approximately species of the arenaviridae, filoviridae, bunyavirales, flavi viridae, and rhabdoviridae (table ) . despite the efforts placed on early detection, viruses like dengue, ebola, lassa, crimean-congo hemorrhagic fevers continue to threaten the health of millions of people, mostly in areas where demographic changes, and political and socio-economic instability interrupt vaccination campaigns [ ] . however, the threat of vhf to global health is increased by intercontinental travel and global trade. moreover, because of the high case fatality rate of some of these pathogens, such concerns extend to the potential use of these viruses by bio-terrorists [ ] . global expansion of several diseases is exemplified by the spread of yellow fever from africa to the americas, the spread of dengue fever across continents, and recently, the spread of ebola virus from the democratic republic of the congo to western africa. the concept of an epidemic, as a disease affecting many persons at the same time and spreading from person to person in a locality where the disease was not previously prevalent, was not enunciated until when john snow produced his admirable demonstration of the emergence of an infectious disease in an urban area: the emergence of a cholera epidemic in london. at that time, none could clearly comprehend the mechanisms of emergence and spread since the existence of microbes had just been demonstrated by louis pasteur in the late s and microbe transmission modes were more speculative than based on medical or scientific facts, until when robert koch demonstrated that bacteria can be transmitted and responsible for diseases. nowadays, it is extremely difficult to make a retrospective diagnosis of historical pandemics, there are currently species in the orthohantavirus genus. the pathogeny of most of them is unknown during times when clinical descriptions were rare or lacking accuracy, and the extent of an epidemic was extremely subjective. thus, it is common to note that the first outbreak described in the western world was that of the plague of athens for which thucydides rather precisely reported the symptoms; today this epidemic has often been attributed to typhus through its clinical picture and epidemic profile [ ] . the first historically recorded outbreaks due to viral agents date to antiquity when the roman armies were returning from distant countries bringing with them "exotic" diseases. indeed, the rise of a "new" virus is an extremely rare event. most often, in terms of pathogen emergence, a virus adapts through mutation and selection pressure to a human host causing disease. presumably, smallpox, measles, and influenza were among the plagues that struck the ancient latins in gusts of epidemics more or less severe. the antonin plague that extended from to ad in much of western europe, when the troops of emperor lucius verus returned from war against the parthians, is often attributed to a smallpox pandemic by historians. in the middle ages, it seems that smallpox made a return around ad to france, germany, belgium, and the british islands [ ] . the acute respiratory infections reported during the winter of - ad accompanying the return of the carolingian armies from italy have been attributed by historians to a flu epidemic. many soldiers of charlemagne died then. the disease returned regularly and fiercely in and ad to the western european peninsula [ , ] (table ) . from the plague (sensu lato, including all transmissible diseases) of antiquity, to the severe acute respiratory syndrome that emerged on the eve of the third millennium, pandemics have followed in the history of mankind. as noted by mirko grmek, a historian of medicine, it seems that one pandemic will drive in another. if several diseases circulate concomitantly, one of them will take precedence over the other, an epidemic over the previous, and it is more likely that a pandemic will prevail [ ] . plague temporarily replaced the leprosy that appeared in eurasia for over , years; during the first millennium, plague was manifested by successive pandemics that crossed continents. during the first half of the past millennium, syphilis started its expansions, crossed oceans, and became global. tuberculosis originated in europe more than , years ago, but it was only at the turn of the seventeenth century that it was considered a pandemic; smallpox was also manifest as epidemics and then was pandemic at its peak in the late nineteenth century, then smallpox persisted until the jenner area. although early medical records of smallpox are available (egypt, china, india), large and devastating epidemics were only identified in the late fifteenth century of the millennium. smallpox was introduced into the americas by spanish settlers in the caribbean island of hispaniola in and arrived in mexico in . on hispaniola island, one third of a million of the inhabitants died of smallpox in the following years. smallpox devastated the native amerindian population and was an important factor in the conquest of the aztecs and the incas by the spaniards [ ] . in , children died in goa, india, from a smallpox epidemic. in europe, smallpox was a leading cause of death in the eighteenth century, killing an estimated , europeans each year [ ] . during the twentieth century, it is estimated that smallpox was responsible for - million deaths. the last known natural case of smallpox occurred in somalia in [ ] . it is only at the end of the first millennium that all these pathologies were better understood and their infectious origins elucidated. the first pandemic of the twentieth century was attributed to the h n spanish flu that emerged in kansas in . however, this "flu pandemic" is now thought to have had subepidemic circulation earlier in france or germany or even prior emergence in china in or [ ] , and to be exascerbated by concurrent bacterial infections. although it burned out quickly by , it has been estimated that one third of the world's population was afflicted; million people died, half of them in the first weeks of the outbreak. since the s, the frequency and magnitude of dengue fever epidemics increased dramatically as the viruses and the mosquito vectors have both expanded geographically in pandemic proportions [ ] largely extending the pandemic to all the intertropical zone. in the early s, human immunodeficiency viruses (hiv- and hiv- ) spread as an acquired immunodeficiency syndrome (aids), a pandemic that continues to take its terrible toll at the global level. since the emergence of aids, organization updates, as of june only million people were accessing antiretroviral treatment and among them, seven of ten pregnant women received treatment. in , a severe acute respiratory syndrome, sars, inaugurated the twenty-first century as a first pandemic of the millennium, involving more than countries with secondary epidemic chains in asia, europe, north america, south america, and a total of cases [ ] . ultimately, one of the major characteristics that defines today's pandemics, apart from the introduction of the disease within several continents or the rapid expansion across the administrative borders of countries, is the initiation of locally active transmission of the pathogen. although, the first ebola virus disease outbreak of western africa was considered a pandemic and witnessed several exported cases with secondary epidemic chains in distant countries of the african continent (i.e., nigeria, mali), outside of africa, exported cases rarely sparked local transmission. emergence from a sporadic case to an outbreak, to an epidemic, and ultimately to a pandemic depends upon effective transmission among nonimmune hosts, host availability (density), characteristics of the vector (natural or human made) that would enable it to circumvent distances, and the pathogen infectiousness. all these dynamics are essential for an effective disease transmission and spread. an outbreak is a sudden increase in occurrences of a disease in a particular time and place, more localized than an epidemic. an epidemic occurs as the disease spreads to a large number of people in a given population within a short period of time. to spark an epidemic chain of transmission depends on factors like immune population density, virus infectiousness, promiscuity, vulnerability, etc., while the efficiency of such transmission depends on how many persons will be infected by one person (i.e., the reproductive ratio or r ). an epidemic event will therefore expand in space (beyond the first cluster of cases) and time (rapid spread). a pandemic is essentially spatial, and represents an epidemic of infectious disease that has spread through human populations across a large region, extensively across two or more continents, to worldwide. however, all these typologies harbor the same fundamentals: emergence from one index case, transmission from one host to another, and spatial expansion. altogether, an epidemic and a pandemic are respectively a local and a global network of inter connected infectious disease outbreaks (i.e., epidemic chains). ultimately, understanding how disease (i.e., pathogens) spread in the social system is fundamental in order to prevent and control outbreaks, with broad implications for a functioning health system and its associated costs [ ] . also, after the last case occurs at the end of an epidemic, the goal is to control the risk of transmission for a -day time period. this three-week period represents an incubation when the infected subject does not transmit the virus and remains asymptomatic. the " days" is based on experimental methods use in virology to detect virus replication: influenza virus infected eggs should hatch in days, there is a -day limit for an arbovirus to infect a living model (suckling mice, mice, rats, guinea pigs, cell lines). moreover, most viral infectious diseases have a maximal incubation period of days, with few exceptions (e.g., hiv, and rabies). ultimately, such -day periods multiplied by the potential of a carrier to travel will produce the risk area for the emergence of secondary cases (from a walking distance to the long distances covered by commercial jets). however, it is important to clarify that many vhf including ebola virus can be carried by an asymptomatic host for several months [ , ] . the mode of transmission profiles the epidemic pattern of a transmissible disease. it is extremely helpful when a disease emerges to rapidly surmise the mode of transmission and how to respond (e.g., water-borne disease, arthropod-borne disease, human-tohuman transmission). pathogen transmission can be interspecific or hetero-specific, direct or indirect. direct transmission occurs by close contact with infected biological products (e.g., blood, urine, saliva). indirect transmission occurs with intermediate hosts such as arthropod vectors (e.g., mosquito, tick) or mammalian vector/reservoir (e.g., rodent, chiropteran) or from infected environmental means (e.g., soil, water, etc.). mobility and transportation are the main factors for diseases dispersion, as an emblematic example, one can simply show how the - evd outbreak of western africa expanded due to the transportation of patients during their -day incubation periods, first by foot-paths, then by motorbike, then taxis and public transportation, finally becoming a global concern with patients traveling by boat or commercial airline [ , ] . host population density and promiscuity, crowded places (like schools, markets, mass transportation system) also play an important role in the efficiency of transmission as well as the level of herd immunity (e.g., annual pandemic flu), altogether this gives us the level of population susceptibility (i.e., vulnerability). environmental factors can also be major drivers of pathogen expansion, for example the emergence of nipah encephalitis. the nipah virus, when it emerged for the first time in malaysia in , was transported by its natural host, a frugivorous chiropteran. a year earlier, an immense forest fire affecting several indonesian islands had forced the escape of disease-carrying bats that took refuge in malaysian orchards, planted to nurture newly developed pig farms. both pigs and farmers became infected and nipah virus was discovered for the first time. another classical example, more associated with human environment and behavior, is the old story of the spread of dengue virus via the used tires carrying infected aedes aegypti eggs and transporting dengue across oceans and continents [ ] . understanding the mechanisms of transmission and expansion of disease vectors with respect to the typology (epidemic pattern) of a disease is the ultimate challenge for controlling and preventing disease. typologies from human-to-human transmission, zoonotic diseases, arboviruses, water-borne diseases, and others play different roles in the rate of disease spread and need to be clearly understood. finally, while an epidemic pattern is driven intrinsically by the virus and its vector, the host population, the mode of transmission, and even the human environment (e.g., population density, urbanization, agricultural practices, health system, public health policies) as well as physical environment (season, meteorology, climate changing, latitude, altitude) factor into the rate of disease spread. with respect to pandemic risk (the rapidity and area covered by disease), the main characteristics of a virus are found in its environmental persistence while remaining infectious. environmental persistence depends on: virus structure, enveloped viruses are more sensitive than the naked viruses; its mode of entry into the body of the susceptible subject (transdermal, oral, respiratory); its ability to diffuse out of the body for a sufficient period of time which will, in turn, enable transmission to a greater number of subjects (r ). altogether these intrinsic factors link to the infectivity of the virus, indeed, viruses transmitted by aerosol possess certainly the most efficient way to spark an epidemic that increases with population density and vulnerability as well as with the resistance of the virus to environmental factors outside the host cells. the cycle of transmission shapes the epidemic in time and spatial dispersion. for example, animal to human zoonoses are dictated by chance encounters between host (population density, animal farming, pets, hunting) and, eventually transmission such as that observed between human and nonhuman primates [ ] . vectortransmitted diseases (i.e., arthropod-borne diseases) depend on the vector ecology (ability to transmit, length of the intrinsic cycle of the virus, trophic preferences, vector density, seasonality, reproduction, breeding sites, food abundance for hematophagous arthropods). mobility of hosts/vectors that are part of the natural cycle will also play a role in the potential for disease expansion (e.g., mosquito-flying distance, cattle transhumance, human migration). also, other factors associated with the hosts will render a more efficient transmission: human behaviors like fear/social responses, nosocomial infections, super-spreaders); viruses having multiple natural hosts (vicariates) or vectors; vectors with multiple trophic preferences (e.g., biting cattle, birds, and primates); the incubation period in the vertebrate hosts as well as the intrinsic replication in the arthropod vectors will also intervene; ultimately subclinical infection is also an underestimated factor of virus dispersion and transmission that modifies the epidemiological pattern of disease. one can distinguish also a typology of communicable diseases that reflects the spatial and temporal mode of transmission including arthropod-borne transmission, human-to-human transmission, human-to-animal (and vice versa) transmitted diseases (i.e., zoo- predicting hfv pandemics noses) including vector and nonvector transmitted diseases, and some other types of environmentally transmitted diseases. all of them represent unique types of transmission and risk of spread with a variable path of time, and also dependent on multiple factors (environment, climate, behavior, etc.). we have to consider territories as spaces where disease can potentially expand and that can be characterized by the fundamental factors of emergence and spread: the vulnerability of the population, the level of favorable transmission factors, and the probability for the population to be exposed to the virus. vhf are exemplary for their epidemic patterns of expansion dependent on the above reviewed factors (i.e., fundamentals of emergence) and their epidemiological characteristics (i.e., virus, host, environments). for example, let us consider the control of arenavirus spread by their strong host-species association. on a geological time scale, arenaviruses such as the agent for argentinian hemorrhagic fever (ahf) coevolved with their natural rodent host and then spread according to the expansion of the rodent host. one host-one virus ultimately produces a localized endemic cycle, the distribution of the disease overlaps the distribution of the rodent host while enzootic patterns appear naturally limited to an ecosystem (e.g., local rodent populations, behaviors, and environmental factors). hantaviruses also appear as a global complex, resulting from the coevolution of virus and rodent hosts and a global dispersion of generally localized enzootic diseases [ ] [ ] [ ] . as for the pandemic risk associated with a natural virus reservoir, chiropterans are unique flying and migratory mammals that have been associated with filoviruses and other viruses of major public health importance [ ] , their potential as vectors will eventually favor the spread of these viruses into new territories. also because there is potential for a long coevolution, epidemiological patterns are also dependent on virus-host spillover, host vicariate, and other environmental factors (e.g., climate change and man-made changes in land use). other arboviruses such as yellow fever virus, dengue virus, as well as west nile, chikungunya, or zika viruses show a pandemic risk associated with the existing distribution of their respective arthropod vector, vector density, and ability to transmit virus. investigating the fundamental factors of transmission and favorable territories for disease emergence are necessary to evaluate the risk, respond to the epidemic, and control its expansion from an index case to a pandemic. ultimately, when the fundamentals are understood and epidemic/pandemic risk identified, suitable emergency funding needs to be identified and made available in endemic areas to insure political willingness and community participation. ultimately, a suitable response will improve biosurveillance, data processing, communication, strategic immunization campaigns, and research for future risk prevention. several emblematic vhf and their original "epidemiological engineering" are presented in herein. vhf such as ebola virus disease, lassa fever, rift valley fever, or marburg virus disease are highly contagious and deadly diseases, with potential to become pandemics. remarkably, vhf are essentially caused by viruses of eight families; arenaviridae, filoviridae, hantaviridae, nairoviridae, peribunyaviridae, phenuiviridae, flaviviridae, and more recently rhabdoviridae [ ] (table ) . hemorrhagic fever viruses (hfv) have been classified as "select agents" because they are considered to pose a severe threat to both human and animal health due to high mortality rate, human-to-human transmission, and, in some cases, the potential to be aerosolized and used as bioweapons [ ] . each of these hfv shares some common features that define the nosology of the vhf group, from virus structures to the clinical and epidemiological characteristics of their diseases. -hfv spread person-to-person through direct contact with symptomatic or asymptomatic patients, body fluids, or cadavers. -vhf can have a zoonotic origin, as when humans have contact with infected livestock via slaughter or consumption of raw meat, unpasteurized milk, bushmeat, inhalation or contact with materials contaminated with excreta from rodents or bats. -hfv can be vector-borne, i.e., transmitted via rodents, mosquitos, and ticks. -vhf are zoonotic diseases. accidental transmission from the natural host to humans can eventually lead to human-to-human transmission, human infection, and sporadic outbreaks. -with a few noteworthy exceptions (i.e., ribavirin), there is no cure or established drug treatment for vhf, while limited vaccines could be available, including yf, ahf, and rvf (the latter is for animals only). -vhf have common features: they affect many organs, they damage blood vessels, and they affect the body's ability to regulate itself. clinical case definitions describe vhf with at least two of the following clinical signs: hemorrhagic or purpuric rash; epistaxis, hematemesis, hemoptysis, melena, among other hemorrhagic symptoms without known predisposing host factors for hemorrhagic manifestations. in fact, during an epidemic, all infected patients do not show these signs and a specific case definition needs to be defined in accordance with the suspected or proven viral etiology of the disease [ ]. also, vhf pathogenesis encompasses a variety of mechanisms including: ( ) alteration of hepatic synthesis of coagulation factors, cytokine storm, increased vascular permeability, complement activation, disseminated intravascular coagulation. moreover, severe pathogenic syndrome is often supported by an ineffective immunity, high viral loads, and severe plasma leakage and co-infection with other pathogens [ ] . the present chapter will mainly focus on the factors that can specifically and eventually contribute to a pandemic risk and how did we learn from historical spread of the vhf. the yellow fever disease pandemic is thought to have originated in africa, where the virus emerged in east or central africa and spread to western africa. in the seventeenth century, it spread to south america through the "triangular" slave trade, after which several major outbreaks occurred in the americas, africa, and europe [ , ] . the yellow fever vaccine is a fantastic gift from pioneering vac- cinology; it is efficient, affordable for developing countries, and protects for at least a decade or even life-long. however, yf remains a particular concern at the global level and the number of cases has unexpectedly increased this past decade. nowadays, yfv causes , infections and , deaths every year, with nearly % occurring in africa. nearly a billion people live in an endemic area [ ] . although yfv is common in tropical areas of south america and africa, it has never been isolated in asia [ ] . ultimately, the pandemic risk is there, from the uncontrolled epidemic as for example in the inland remote area of the brazilian mato grosso state, to the recent burst of epidemics in west and central africa including angola, drc, as well as imported cases in kenya and china [ , ] . indeed, the risk of a pandemic exists if any imported case goes to an area where the fundamentals of emergence are present (i.e., aedes aegypti and a nonimmune human population). for years it has been stressed that yf coverage needs to be exhaustive in the endemic area, and the who international health regulations (ihr) need to be strictly respected when peoples are crossing frontiers to or from an endemic area [ ] . even though the virus was known to actively circulate in asia, north america, and africa years ago, a global pandemic of dengue fever began in southeast asia in the s [ , ] . dengue virus (denv) expansion was followed by the emergence of a dhf pandemic that occurred in the late twentieth century (see above, the "tire-mosquito larvae connection"). by the end of the century, dhf emerged in the pacific and the americas, and extended to all asian continents [ ] . lately, in the s, epidemic dengue fever occurs in africa, with a predominant activity in east africa, while sylvatic denv circulation was described in western africa [ ] . the different dengue virus serotypes spread also independently to all continents. while it is remarkable that infection with one serotype does not provide cross-protective immunity against the others, epidemics caused by multiple serotypes became more frequent, and highly pathogenic denv were identified [ ] . dengue fever to date has a global distribution with an estimated . billion people at risk. yearly, hundreds of thousands of dhf cases occur [ ] . altogether, the requirements for a dhf pandemic are globally present [ ] : the highly competent aedes aegypti and aedes albopictus denv vectors, the globally distributed denv serotypes and highly pathogenic strains, and finally, climate change that opens new breeding opportunities for these mosquitoes to expand and eventually transmit imported denv into new populations and territories [ ] . mankind will have to live with this pandemic until the new denv vaccines can be implemented. in , an unknown disease was reported by a group of laboratory workers in west germany and former yugoslavia [ ] . over the course of months, cases and seven deaths occurred. conclusions made by treating physicians at the time (and published shortly thereafter) highlighted the following: high fatality rate, risk of relapse; risk of sexual transmission [ ] . a connection was made to infected african primates, chlorocebus aethiops, when laboratory workers were exposed to their imported tissues. it took years to effectively connect marburg virus, marv, to a bat, rousettus aegyptiacus, as a natural marv reservoir in central africa [ ] . marv is considered to be extremely dangerous for humans, is classified as a risk group pathogen, and also is listed as a select agent; however, the pandemic risk cannot be assessed because only four epidemics have occurred. although marv expansion appears to be limited to a few countries in africa, the recent emergence (estimated at a few decades ago) of a second human pathogenic marburgvirus known as ravn virus, and the widely distributed old world rousette fruit bats (rousettus spp.) serving as reservoir for both viruses [ ] , are two factors that favor pandemic risk. although more than years after its emergence from a remote area on the ebola river in the central african rain forest, ebola virus (ebov) remained hidden in a cryptic natural cycle. then a series of outbreaks occurred in the large congolese rain forest of central africa [ ] . the epidemic risk was always considered to be localized and circumscribed [ ] . then, suddenly without warning, in the late months of , ebov emerged for the first time in a remote area of western africa and sparked an outbreak more massive than ever witnessed before. more than , people were infected, ten countries recorded cases (transmitted or imported), the pandemic risk raised fear, and who declared it as an inter national health emergency that requires a coordinated global approach [ ] . besides the lack of preparedness of national and international public health systems, the other major factor that played an immense role for the dispersion of evd in western africa was the extreme mobility of village populations. they followed the kissidougou forest foot-paths to the towns in guinea using motorbikes, cars, and other public transportation, then later evd traveled by plane to the global level. the evd epidemic went from outbreak to pandemic risk. like marburg virus, another member of the filoviridae, ebola virus, shares bats as a potential virus reservoir, human and nonhuman primates are highly sensitive to the virus, and inter-epidemic periods play an important role since the epidemic silences tend to diminish the attention of health services and increase epidemic risk. in this way, the first western african evd epidemic is exemplary for showing the hidden risks contained in the natural cycle of a virus, and the sudden emergence followed by an unprecedented velocity of spreading. in the absence of biosurveillance, a pandemic risk remains. hemorrhagic fever with renal syndrome, hfrs, appears first as a global concern of one virus family, several human pathogenic viruses of the genus orthohantavirus, multiple clinical presentations, and different epidemiological patterns [ ] . hantaviruses and hfrs were first described in asia [ ] ; nowadays, hantaviruses are the cause of zoonoses that are expanding worldwide. indeed, since when a previously unknown hantavirus was implicated in the first hantavirus pulmonary syndrome (hps) outbreak in the united states, several other hantavirus infections were reported in western europe, and then hantaviruses were described in south america. ultimately, after an early suspicion of the presence of the hanta viruses in africa [ ] , a novel hantavirus, sangassou virus, was isolated in in guinea [ ] . altogether we observed the emergence of the hantaviridae in the western hemisphere, from the old world to the new world, and recently discovered its first tentative steps on the african continent. with respect to the orthohantavirus genus, a real pandemic exists even when multiple viruses are involved. ultimately, as for the arenaviridae, hosts are specific and certainly the major vectors of virus dispersion. the arenaviridae includes different viral species grouped as old or new world arenaviruses [ ] , each is maintained by rodents of individual species as natural reservoir host and as vector for the viruses that are human pathogens. the rodent hosts are chronically infected without obvious illness and they pass virus vertically to their offspring. de facto, the distribution of the virus covers that of its natural hosts but is isolated in an ecosystem generally limited by natural barriers, e.g., mountains, river. a phenomenon in which rodent lineages are naturally infected by a virus and remain in such a limited environment is called "nidality" [ ] . this is what it is observed for argentinian hf, venezuelan hf, bolivian hf, and lassa hf. regarding the pandemic risk of any of these hf, arenaviruses because of their strict association with their natural hosts, like the hantaviruses, have their expansion potential limited by their natural hosts even though the latter are widely spread and could certainly be infected. such risk lies in an unexpected encounter between infected and noninfected populations under the pressures of (as yet unknown) factors that favor their migration from enzootic to non-enzootic areas. in that matter, lymphocytic choriomeningitis virus, another member of the arenaviridae, has a worldwide distribution through its domesticated natural host, the ubiquitous house mouse, mus musculus. although crimean-congo hemorrhagic fever, cchf, is a widespread disease endemic to africa, the balkans, western asia, and asian countries south of the th parallel north, it is generally transmitted by ticks to livestock or humans and therefore geographically limited to regions where tick vectors feed on humans. although the competent ixodid vector is limited, as is the abundance of their natural hosts, climate change modifies the distribution and abundance of tick hosts (i.e., tick abundance) [ ] . additionally the cchfv pandemic risk is limited by low mobility, geographical repartition, and seasonal activity, although its main natural hosts are widely dispersed from africa, to asia and europe [ ] . ultimately, human-to-human transmission occurs from close contact with the blood, secretions, or other biological fluids of infected persons but these remain rare events with a r < . altogether, a cchf pandemic risk remains hypothetical but underlined by the risk of human-to-human transmission [ ] . as for cchf, rift valley fever, rvf, is first a disease of cattle and illustrates a unique subcontinental zoonotic spread along the path of traditional herders. rvf became a transcontinental risk with trade and transportation when the virus spread from north east africa to western africa, and even to madagascar [ ] . if one considers its pandemic risk, with respect to rvf epidemiology as a mosquito-transmitted disease, two factors have to play concomitantly: the presence of infected cattle (i.e., nonimmune) and competent mosquito abundance, both considered hazards, while concretizing the risks from human vulnerability (nonimmune; mosquito bite; direct exposure to infected blood). in order to streamline the prevention and the actions to reduce epidemic risk, the various elements involved in an outbreak are here considered from a systemic point of view, considering the risk as the convergence of a hazard and vulnerability: -the presence of the threat (or "hazard" pathogen, i.e., vector, virus reservoir) is considered to be a necessary-but not sufficient-condition for the development of a disease. it is often known only in terms of probabilities, sometimes very low and therefore often subject to significant random variability in time and space. we often seek to evaluate the spatial and temporal differences of this probability, trying to measure its significance. sometimes, it only uses one character necessary to the presence of the pathogen or vector (e.g., the presence of water, a minimum temperature, a type of vegetation). -the susceptibility of the host (which is essentially linked to individual characters, genetic, biological, such as immune status or age) is individual, and often given by a probability. -direct exposure of the host to the hazard is an element of active vulnerability, depending on the behavior of the host that increases the likelihood of contact between host and hazard by exposing it to an environment conducive to his presence (e.g., travel and contacts, professional activities). it also includes all the known "risk" behaviors that increase the likelihood of direct exposure to the hazard. -passive vulnerability of the host, which is not directly dependent on the pathology, is not even necessary nor sufficient for pathology, but influences the exposure of the host to the hazard or to protection from the pathology. this protection consists of prophylaxis, access to care, availability of care. it is independent of the real presence of the hazard; the host can be vulnerable without being exposed to the threat. the vulnerability is often defined by several levels (individual, context). it is very often "spatial" as linked to phenomena of segregation or spatial concentration. this is an area primarily studied by geography. ultimately, this vision can differentiate what is active, often subject to high variability, random in time and space (the emergence or the presence of hazards is often difficult if not impossible to control) from what is passive, generally situated among more stable population levels (sensitivities, exhibitions, behaviors, and vulnerabilities). this allows for better public health preventive actions, and also to understand rationally crisis situations by preemptively targeting the most important elements of the system in terms of vulnerability, and secondly by optimizing risk reduction (elimination of vectors, vaccinations, quarantine, etc.). in all cases, these actions must be adapted to social contexts to have a real impact on risk behaviors and vulnerabilities that they generate, hence the increasing role of anthropology in the field of health. to prevent or reduce the epidemic risk, it is necessary to act on each component of this system: -reducing the susceptibility of the host (e.g., immunization, vaccination, prophylaxis). -reducing host exposure to the pathogen (e.g., vector control, quarantine, exclusion zone). -eliminating the pathogen directly (e.g., animal slaughter, disinfection, hygiene), or indirectly (e.g., suppress transmission). -reducing host vulnerability (e.g., socio-economic, behavioral, access to health care system). -reducing host exposure to emergency condition (e.g., realtime data collection, warning systems for emergency, crisis management, implementation of treatment). the rapid detection of emergence is the key to controlling the spread of an epidemic. it requires comprehensive monitoring to trigger alerts and all other risk-reducing actions, in particular, reducing the exposure of the host to the pathogen and, if possible, the elimination of the pathogen. in parallel to the monitoring and warning systems, protocols must always take into account local characteristics of political power and decision-making bodies that could otherwise render ineffective year-long action plans or warning systems (for example, the management of the chikungunya epidemic in reunion island was largely impacted by bottlenecks related to local political system) [ ] . biosurveillance and efficiency in data collection and management will be the technical keys for prevention (early detection of epidemic risk) and forecasting epidemic emergence and spread (i.e., analyzing the data in near real time taking into account the vulnerability of a given population). also, this can be achieved only by exhaustive capacity building (human and technical) mostly in the more vulnerable developing countries but also where the most advanced technology needs to be developed. networking biosurveillance systems are a major undertaking from regional to global, involving politics and diplomacy. taking in account the local characteristics of political structures and decision systems is fundamental. despite our current recognition of the risks posed by emerging and re-emerging infectious diseases to global public health and stability, reliable structured data remains a major gap in our ability to measure (and therefore manage) globally infectious diseases. who has long served as an information hub for infectious disease events worldwide; however, extracting quantitative data from who information bulletins (weekly epidemiological record and the more recent disease outbreak news alerts) proves to be a time-consuming effort with limited results in terms of operability, and exists more for the record and future analysis. the current proliferation of geospatial information tools (i.e., geographical information system, gis) and stepwise advances in data extraction capabilities have made it possible to develop robust, systematic databases facilitating anomaly detection (like clusters), infectious disease models (and model evaluation), and apples-to-apples comparisons of historic infectious disease events worldwide. however, biosurveillance capabilities-the key to global prevention and health securityremain inadequate to support true early detection and response. increased access to technology, rapidly developing communications infrastructures, smartphone usage for suspected-case reporting, and global networks of (formal and informal) disease surveillance practitioners provide an explosive opportunity to patch and improve surveillance networks. the challenge is to leverage all these developments, implement technical and capacity building where needed, before the next epidemic with global impact emerges. several organizations have developed systems to collect epidemic information and facilitate rapid response: who has the department of pandemic and epidemic diseases (ped) that develops mechanisms to address epidemic diseases, thereby reducing their impact on affected populations and limiting their international spread. among them some have self-explanatory titles: the battle against respiratory viruses (brave); early warning and response systems for epidemics in emergency (eware); emerging and dangerous pathogens laboratory network (edpln); international coordinating group for access to vaccines for epidemics (icg); global infection prevention and control network; (gipcn ); global influenza surveillance and response system (gisrs); global leptospirosis environmental action network (glean); meningitis environmental risk information technologies (merit); weekly epidemiological record (wer); emerging diseases clinical assessment and response network (edcarn). global commitment to these efforts will insure their readiness in times of need. most certainly and most importantly, any preparedness and response requires emergency funding [ ] . it has been estimated that if the ebola virus disease response started months earlier, it could have reduced the total number of deaths by % in liberia and sierra leone [ ] . we learned from this last evd epidemic that in march , the african union's minister of finance requested the african risk capacity (arc) agency to help member states to better plan, prepare, and respond to devastating outbreaks by developing new applications for financial tools, like insurance, that can significantly improve the speed of funds to affected countries and shorten the time between event and response. the agency is now developing an outbreak and epidemic insurance product primarily based on responsibly and timely budget reallocation; however, viruses do not wait. moreover, the world bank's pandemic emergency facility is designed to finance surge capacity and support international government partners to actively participate to the response. ultimately, epidemics are not one-off events, but rather demonstrate financial patterns similar to other natural catastrophes. as natural catastrophes, large epidemics can be insured by creating financial mechanisms to facilitate the movement of critical resources within affected countries and ultimately manage the spread of disease and minimizing macroeconomic impact [ ] . classical tools and strategies for predicting epidemics encompass human disease surveillance (e.g., public health and hospital statistics) and, sometimes, environmental surveys (e.g., climate, el niño, earthquake, tsunami); also more recently complying with one health concept, human and veterinary health as well environmental risk factors have been reunited in a comprehensive approach of public health risk (i.e., outbreak, epidemic risks). however, this heuristic approach of health remains limited to specific diseases and territories and does not apply as a global predictor of pandemics. first, historical data is the only available objective view of past epidemics and pandemics, needs to be collected, formatted, corrected, and analyzed. this will be the foundation of the different tools and strategies described below. in that matter, with respect to the depth of the past data available, time series of disease observation, modern tools such as internet search data have actually led to the development of several specific sites (e.g., google flu and dengue) [ ], whose search-term reports have correlated strongly with incidence estimates in several public health reports in europe, asia, and the u.s. however, even though such tools can complement classical disease surveillance, most of these sites are geographically limited and cannot be used for live monitoring of epidemic risk and for neglected tropical disease surveillance [ , ] . however, from such historical and live-collected data, health alert systems can be implemented, and prediction models can be developed. moreover, thanks to the spatial analyses, combining multiple data sources will provide the ultimate tools for livemapping an outbreak, which will lead to an efficient response when tools and strategy have been specifically identified (i.e., sufficient and available in-country heath system resources and funding; identifying variations in pathogen sequences that contribute to ro and pathogenicity; monitoring population movement; etc.). the amount of data being digitally collected and stored is exponentially accumulating. it is estimated that, as of september of , the world wide web reached . billion pages containing eight zettabytes of accessible data, and the accumulation of information is growing around % every year [ ] . this situation has generated much discussion about how to use the unprecedented availability of information and computational resources and the sophistication of new analytic and visualization algorithms for decision-making to reduce the impact of infectious diseases. in fact, it is argued that the paradigm of "big data" will change not only the way business and research is done, but significantly improve the understanding of factors leading to the emergence of infectious diseases. big data could lead to the implementation of a decentralized biosurveillance enterprise allowing organizations and individuals to take full advantage of a large collection of disparate, unstructured qualitative, and quantitative datasets. with the proper integration and the right analytics, big data could find unusual data trends leading to better pathogen detection systems, as well as therapeutic and prophylactic countermeasures. however, the impact of these analyses and forecasts depends not only on how the data is collected, ingested, disambiguated and processed, but also on how it is relayed in different operational contexts to users with different backgrounds and understandings of technology. while impressive in data mining capabilities, real-time content analysis of social media data misses much of the factual complexity. quality issues within freeform user-provided hashtags and biased referencing can significantly undermine our confidence in the information obtained to make critical decisions about the natural versus intentional emergence of a pathogen. risk factors associated with a health event in a population are often linked to environmental factors (fig. ) . they are also linked to spatial relationships between individuals, especially for infectious diseases. the geographical distribution of these phenomena reflects spatial relationships. beyond "classic" epidemiology mainly based on statistical analysis, using the location and spatial distribution is essential in the understanding of health events and analysis of their mechanisms. spatial analysis in epidemiology is a method to help determine the location (georeferenced) of risk factors. it allows one to identify the spatial and temporal differentiation in the distribution of events, using their location in time and space. when the location is available, with precision for each studied object (i.e., individuals or geographical units), it is possible to: -characterize the overall spatial distribution, using synthetic indices on the absolute position of an object, on the average spatial arrangement of objects or their values (grouping/ fig. mapping environmental factors that have a major impact on insect vector population (i.e., mosquitoes and ticks). this map of laos constitutes the basis of a risk map showing part of the hazards contributing to virus vector density that could be matched with human density and pathogen prevalence leading to a risk map (spatial risk) and eventually extended through seasonality (temporal risk). mean temperature and mean rainfalls are interpolated as climatic conditions, as environmental factors influencing the presence of mosquitoes dispersion, spatial dependence, variogram measure of autocorrelation space). -look for characteristics of the overall shape of the phenomenon (tendency, shape), and search for a theoretical spatial distribution, or for a process to model the observed spatial distribution. -look for unusual places (geographical centers and source sites; aggregates; exclusions; hot spots, cold spots), and to study the spatial relationships at the individual level. -conduct spatiotemporal analysis: search index cases, reconstruction of paths, diffusion models, models of extinction, etc. -spatial analysis allows the development of applications for modeling epidemics, preparing warning systems, as well as crisis management systems, risk prevention and analysis systems, and vaccination campaigns. many tools for biomonitoring and prevention of epidemic risk have been developed (fig. ) , as well as software tools to: (a) visualize spatial distributions. (b) synthesize and analyze position and spatial relationships between events (continuity, consolidation, attractionrepulsion, shape, centrality, displacement, diffusion processes). (c) to analyze the relationship between spatial distribution of attributed values and environmental characteristics of the phenomenon (environmental correlations). (d) to model the phenomena of emergence, dissemination, extinguishment of an epidemic. cluster detection, space-time analysis, and spatial integration with environmental and demographic data are widely used in such warning systems. multiple and complex factors are associated with the emergence and impact of pathogens in a given geographical area. therefore, public health analysts are confronted with the task to identify the likely, and unlikely, consequences and alternative critical outcomes of a given vhf outbreak. this requires the ability to monitor in near real time the dynamics of the geographical dissemination of these viruses in villages, cities, countries, continents, or the globe using new analytical techniques within the emerging field of genomicbased biosurveillance. this concept integrates microbial genotyping, next generation sequencing, metagenomics, big data and database analytics, and contextualized visualization to identify, characterize, and attribute known and unknown pathogens and generate estimates of how different contingencies will affect their impact [ ] . a genomic-based biosurveillance system includes powerful microbial genomic characterization to rapidly identify a pathogen [ ] . this characteristic makes a genomic-based biosurveillance a useful approach not only for public health but serves as a deterrence tool for intentional biological weapon development and deployment. the initial step consists of integration of signals generated by molecular-based assays and next generation dna sequencing and unbiased microbial characterization for pathogen source tracing, attribution and forensics. while each of these techniques has been discussed in the literature in detail [ ] , the integration of this information can yield a more extended view of the scale of a pathogen outbreak. the development of high-throughput the exemplary case of the highly pathogenic avian influenza virus h n in thailand. from the emergence of one imported case (red-filled circle), the pathway direction (arrowed green lines) of h n infection in farms (yellow points) is reconstituted, using dates of infection and distance between farms. results show local spread with time-to-time medium distance jumps dna sequencing technologies (i.e., dna and cdna forms of rna viral genomes) is allowing the genomic characterization of previously unknown pathogens without relying on prior reference molecular information [ , ] . this information is available within days, and even hours, of sample collection, and well before the development of animal infection models. because of their portability, this technology will become widely used in the next years in routine clinical settings. however, to be clinically and epidemiologically relevant, dna sequences must be rapidly and effectively translated into actionable information defining pathogen characteristics (i.e., virulence or drug resistance), it must point to a source of origin, and discriminate a natural event from a manmade release [ ] . while some government agencies are considering use of genomic information to develop next generation level- and level- detection/surveillance devices [ , ] , there is no reference database where researchers can retrieve standardized genomic signatures and motif fingerprints to develop primer-, probe-, and antibody-based detection technology using reference moieties. the impact of genomic-based biosurveillance in public health and biodefense will not be fully realized until addressing the current impracticality of transferring the terabytes of genomic data generated by dna sequencing devices to a centralized architecture performing analysis operations, as that might take hours or even days. therefore, a new paradigm could emerge from encouraging the development of decentralized algorithms that first determine in situ the presence of pathogen-specific genomic signatures or motif fingerprints, summarize and relay the results into an operational biosurveillance metadata format for contextualized decision support. the localized data management, time, and space required for spatial analysis is performed by geographic information systems (gis). these are computer systems that manage large volumes of data and easily use the location to perform spatial analysis. most gis are not limited to data management functions, but also integrate multiple analysis tools, data transformation, and cartographic representation. these are for the most part complex applications with enormous features. the "gis" designation covers a wide variety of software projects built according to different technical options, functionality, and diverse performances. a gis is essentially a management tool (structure, organization, entry, storage), an analytical tool (statistical and geographical treatment, spatial analysis), and a communication tool (data visualization, descriptive mapping, thematic mapping, atlas). it is also a tool that allows the use of a spatial model for the simulation of a process, such as the development of an epidemic. gis facilitates the interface between modeling and simulation program, and the geographic database, and can ultimately take over the whole of access to spatial information needed by the modeling program. the gis should thus be at the heart of organizing the collection and processing of monitoring data. to ensure the management of this system, it is important to set up a body specifying all the collection, validation, processing and dissemination of information and results (alerts, risk modeling, near real-time dissemination of results). this body must be proposed and validated by political authorities, preemptively, to avoid further blockage and to ensure effectiveness in situations of epidemic crisis. mathematical modeling is a mathematical formulation of a parameter or risk; it depends on identified or hypothesized risk factors whose coefficients are determined by a statistical or heuristic analysis from historical or observed data with the use of r , as a basic reproduction rate, to timely and spatially predict the spread-speed of an emerging outbreak. spatial-temporal modeling of health events can be seen as the final stage of the analysis. it is different from statistical modeling. despite using risk factors, it considers the epidemic phenomenon as a whole, taking into account the spatial relationships between agents (hosts, vectors, reservoirs, and pathogens), between individuals, and relationships between individuals and their environment. this model is thus useful for understanding and anticipating the epidemics, and can be generally used to classify individuals in different states (susceptible, infected, sick healed, immune) and to model the major phenomena that can change the state of an individual. however, when a model takes into account many phenomena, it can quickly become very complex. the vast majority of models are simplifications of assumed reality. two broad categories of methods are usually developed in modeling: -a deterministic approach, based on differential equations whose coefficients are adjusted from observed data, or monitoring data from epidemics. in this model, one can introduce stochastic types of components in the coefficients, studying the variability of observed data. taking no account of spatial relationships is difficult in these models, which deal in general populations, not individuals. -a nondeterministic approach, which is based on agents whose behavior is described by expertly determined rules (multiagent models). the status of each agent is calculated at each time step, from its behavior, environment, and relations between the agent and all other agents. these models take into account a more realistic description of the phenomenon, near the complex system finely describing reality. they allow us to consider spatial relationships in each time step. these models require intensive calculation, and their use is made possible by development of the power of computer calculations. let us first honestly address the fundamental questions about epdimeics and preparedness: what did we learn from all the past epidemics, what will we remember in times of need? are we prepared for the worst of these hypothetic pandemics abundantly illustrated in the cinema and unfortunately sometimes overwhelmed when reality goes beyond fiction? certainly, we are not "globally" prepared, unfortunately, at that scale, the immense natural and human disparities do not permit it, but we do our best in our own societies. the concept of disease emergence, born only at the end of the twentieth century, is a societal marker, our desire to be on alert, understand and predict epidemics. ultimately, there are a few, but necessary and difficult goals to reach for the prevention and control of any epidemic, also these goals are part of the development of our societies, as well as for education, they become part of the wellbeing for all: first, beyond understanding transmission, is needed a clear understanding of the epidemiological pattern and the spread of a given disease, before it is too late; then, which is certainly one of the more complex and costly things to achieve, is having an efficient health system to respond to an epidemic and an operational network to respond at the regional and global levels; and last but certainly not a least, having identified funding for any public health emergency will be crucial to changing our world. perhaps, in a shrinking global community, after too many ebola virus disease outbreaks, we will learn and be prepared for future epidemic challenges? the progress made, mostly by computer sciences in the overall analysis of health data, should serve as a tool in the prevention of major epidemics. let us ultimately use our predictions of pandemic risk to meet and unite beyond the current frontiers of political and social wills. epidemic predictions in an imperfect world: modelling 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epidemiology - the chikungunya epidemic on la réunion island in - : a cost-of-illness study global health risk framework: pandemic financing: workshop summary african risk capacity. executive perspective: outbreak and epidemic insurance, new solution to an old problem. the rockefeller foundation from the ebola river to the ebola virus disease pandemic: what have we learned? using web search query data to monitor dengue epidemics: a new model for neglected tropical disease surveillance evaluation of internetbased dengue query data: google dengue trends biosurveillance enterprise for operational awareness, a genomic-based approach for tracking pathogen virulence bioinformatics for biodefense: challenges and opportunities biosurveillance of emerging biothreats using scalable genotype clustering optimizing biosurveillance systems that use threshold-based event detection methods biodefense oriented genomic-based pathogen classification systems: challenges and opportunities biosurveillance observations on biowatch generation- and other federal efforts: testimony before the subcommittees on emergency preparedness, response, and communications and cybersecurity, infrastructure protection, and security technologies, committee on house homeland security, house of representatives congress. house ( ) committee on homeland security. subcommittee on emergency preparedness response and communications., united states. congress. house. committee on homeland security. subcommittee on cybersecurity infrastructure protection and security technologies., united states. government accountability office: biosurveillance observations on biowatch generation- and other federal efforts: testimony before the subcommittees on emergency preparedness, response, and communications and cybersecurity, infra structure protection, and security technologies, committee on house homeland security, house of representatives acknowledgments w.a. valdivia-granda has been funded by the department of homeland security and the department of defense. we are greatfull to sarah cheeseman barthel, director, data acquisition & management metabiota, inc., for her review and input of the section on "global surveillance and data collection." key: cord- - xiqz w authors: song, daesub; moon, hyoungjoon; kang, bokyu title: porcine epidemic diarrhea: a review of current epidemiology and available vaccines date: - - journal: clin exp vaccine res doi: . /cevr. . . . sha: doc_id: cord_uid: xiqz w porcine epidemic diarrhea virus (pedv), an alphacoronavirus in the family coronaviridae, causes acute diarrhea, vomiting, dehydration, and high mortality rates in neonatal piglets. pedv can also cause diarrhea, agalactia, and abnormal reproductive cycles in pregnant sows. although pedv was first identified in europe, it has resulted in significant economic losses in many asian swine-raising countries, including korea, china, japan, vietnam, and the philippines. however, from april to the present, major outbreaks of pedv have been reported in the united states, canada, and mexico. moreover, intercontinental transmission of pedv has increased mortality rates in seronegative neonatal piglets, resulting in % loss of the us pig population. the emergence and re-emergence of pedv indicates that the virus is able to evade current vaccine strategies. continuous emergence of multiple mutant strains from several regions has aggravated porcine epidemic diarrhea endemic conditions and highlighted the need for new vaccines based on the current circulating pedv. epidemic pedv strains tend to be more pathogenic and cause increased death in pigs, thereby causing substantial financial losses for swine producers. in this review, we described the epidemiology of pedv in several countries and present molecular characterization of current strains. we also discuss pedv vaccines and related issues. throughout europe. however, during the s and s, the number of ped outbreaks decreased markedly in the re gion. only a few severe outbreaks have been reported since the s in europe. however, ped has become an endemic disease in asian pig farming countries, such as korea, china, vietnam, japan, the philippines, taiwan, and thailand [ ] . until , ped was thought to have been restricted to asian countries. however, an outbreak of pedv infection occurred in the united states in iowa in april , and within year, pedv had spread to canada and mexico [ ] , which share borders with the united states. additionally, ped outbreaks occurred in korea and japan, across the pacific ocean, also within year of the us outbreak [ , ] . the pedv strain iso lated in the united states was genetically related to the chi nese pedv strain reported in [ ] . interestingly, the ko rean and taiwanese pedv strains isolated after the us out break were genetically related to the us pedv strain [ ] . after spring , ped was no longer found only in asia. us scientists who had not researched pedv began to study this disease, which had previously not been a problem in ame ri can. from this, a ped vaccine reflecting the genetic charac teristics of the pedv strain isolated during the us outbreak was commercialized [ ] . moreover, many veterinary scien tists have focused on the development of more effective ped vaccines because of the major economic losses associated with ped outbreaks. after the us outbreak, sporadic ped out south korean, piglets < week of age died from severe watery diarrhoea after showing signs of dehydration. after the acute outbreak, piglets were anorectic, depressed, vomiting, and producing water faeces that did not contain any signs of blood. (c) necropsies of deceased piglets from the gimpo outbreak uncovered gross lesions in the small intestines, which were typically fluidic, distended, and yellow, containing a mass of curdled, undigested milk. atrophy of the villi caused the walls of the small intestines to become thin and almost transparent. (d) yellowish watery diarrhea in sucling piglets after acute infection of pedv. breaks occurred in germany. therefore, european countries were not isolated from the spread of the us pedv [ ] . thus, the us outbreak was important turning point in ped research, and ped research can be said to be divided into two eras: be fore and after . this review covers the vaccine, epidemiology, genetic struc ture, and characteristics of ped/pedv after . this report may improve our understanding of this disease, which is cur rently the most fatal disease in pigs and one of the most costly health issues in animals. furthermore, this review may pro vide insight into important topics for investigation in ped re search. the genome of pedv is positivesense, singlestranded rna. the size of pedv genomic rna is about kb. the organiza tion of the pedv genome is presented in table . from the ′ cap to the ′ poly a tail, ped genomic rna contains seven open reading frames (orfs) encoding viral proteins. orf a and orf b encode the viral polymerase. orf encodes a non structural protein with an unknown function; this protein is thought to be related to viral pathogenicity [ ] . additionally, the other orfs have specific names according to the proteins encoded in these regions, i.e., spike (s), envelope (e), matrix (m), and nucleocapsid (n) proteins [ , ] . table presents the characteristics of the pedv proteins as described in pre vious articles. of the pedv proteins, the s protein is considered the most antigenic. as summarized in table , the s protein is respon sible for the interaction with host cellular receptor molecules [ , ] . this interaction is crucial for the entry of the virus and is related to induction of neutralizing antibodies against the virus [ , , ] . additionally, these critical characteristics of the s protein are used for analysis of the molecular epidemi ology of pedv. thus, pedv researchers have started to analyze the geno types of pedv using the s gene [ ] . while other genes, such as the gene encoding the m protein and the gene encoded in orf [ ] have been used for phylogeny or molecular epi demiological studies, genetic diversity of the s gene is the fo cus of this review. one of the most interesting characteristics of the s gene is the diversity in this gene that has occurred from the end of s to the present. genotypes in the s gene of pedv could be important because this gene may affect the pathogenicity of novel ped outbreaks based on variations in the s gene [ , , , ] . moreover, the chinese ped out break in involved the presence of new variants based on the nucleotide similarities in the s gene. this variant pedv exhibited % similarity with the cv prototype pedv strain in the s gene [ ] . moreover, the pedv isolated after the us outbreak also exhibited % % similarity with the s protein of cv [ , ] . phylogenetic analyses of pedv rna have been reported in many previous studies [ , , , , ] . whether the % nucleotide difference often observed in the s gene can affect the pathogenesis of pedv has not been clarified. however, the similarities in the s gene, which is re sponsible for the host interaction and normalization, the s region in particular could be important in vaccine efficacy and development strategies [ , ] . neutralizing epitopes of the pedv s protein have been investigated [ ] . in particular, the co k equivalent (coe) is a neutralizing epitope within the co k collagenase fragment in transmissible gastroen teritis virus (tgev) [ , ] . in the prototype pedv (cv ) and vaccine strains, certain coes are different from field iso lates that were isolated after . the different coes are t and g in the prototype and vaccine strains, respectively (table ) ; however, other coes that differ from that of cv have been shown to be identical to the vaccine strains p th or attenuated dr [ ] . in pedv isolates acquired af ter in china, these amino acids were changed to serine; similar observations were made for the pedv strain from the us outbreak [ ] . the new variant pedv strains have similar mutational patterns for the neutralizing epitope. in contrast, pedv strains isolated from to exhibit different pat terns in t and g compared to strains isolated after . interestingly, at amino acid position , some strains exhibit no changes; however, in most strains, amino acid is chang ed to arginine (r). additionally, most strains exhibit a change from g to s at amino acid position , similar to current stra ins [ ] . in order to elucidate the positive correlations between chan ges in the s protein and virulence or vaccine efficacy, further studies involving animal models are needed. in addition to the changes in the s protein described above, more variations have been discovered. for example, park et al. [ ] reported large deletion in the s protein from amino acid to amino acid , within the s and s domains. this virus was detected in , and other regions of the s protein share . % . % amino acid identity in the partial s domain with other strains isolated in korean in and . in the united states, a deletion in the s gene was also reported after the united states outbreak. in december , a strain with deletion of the s gene was detected and isolated in ohio [ ] . this strain exhibited patterns that were different from those of the korean strain with the s gene deletion. the us deletion mutant contains a large deletion ( amino ac ids in length, from amino acid to amino acid ) in the s domain [ ] . the effects of deletion in the s protein should be further investigated and are reminiscent of porcine respirato ry coronavirus arising from s protein deletion in the genome of tgev [ , ] . through pedv research, unique genetic characteristics other than those in the s gene have been reported. fulllength analysis of the orf gene of pedv revealed a bp deletion in the cellattenuated pedv strain dr [ ] . this deletion in the orf gene has not been identified in wildtype pedv; however, in addition to the attenuated pedv dr strain, live pedv vaccine strains available in korea exhibit similar dele tion patterns by reverse transcription polymerase chain reac tion (rtpcr) comparisons [ ] . this deletion pattern is clin ically useful for differentiation of live vaccine strains from wild type pedv casing diarrhea. the final genetic mutation we will discuss is deletion of the e gene in the cellattenuated pedv strain dr . genetic anal ysis has focused on the s, n, and m genes. from analysis of the e gene, a unique deletion was found. moreover, compar ed to other pedv strains, including the wildtype and vaccine strains, only the attenuated pedv strain dr has been shown to have a bp deletion in this gene [ ] . the e protein of the coronavirus is responsible for the assembly of the virus and cell stress responses [ ] . the effects of the e gene deletion are under investigation. in the czech republic, rodak et al. [ ] reported that out of fecal samples from diarrheic piglets (< days old) were positive for pedv. this outbreak occurred between may and june in an area densely populated with pigs in the po valley in northern italy [ ] . some pedvpositive farms ( out of ) were detected between mid and the end of ; however, the disease progressively disappeared [ ] . during the period from to , mild clinical signs were report in pigs of all ages, and mortality was observed in pig lets only in pedvpositive farms [ ] . [ ] , and the southern prov inces of vietnam [ ] . in october , a largescale outbreak of pedv was reported in several provinces in southern china. pedv also spread to other regions of the country, particularly in northwest [ ] . pedv is now circulating in at least chi nese provinces [ ] . in october , japan reported a pedv outbreak to the world organization for animal health (oie) [ ] after a period of years without an outbreak. according to the information provided by japan's national institute of animal health, pedv isolates from this outbreak are geneti cally related to the pedv isolates recovered from china and the united states in . in addition, in late , pedv out breaks were reported in south korea and taiwan [ , , ] . the us pedv strains identified during the us outbreak were genetically related to the chinese strains (china/ /ah ) reported in [ , ] . pedv was first identified with in the united states in iowa in may , although testing of historical samples showed that pedv occurred the month before in ohio. pedv rapidly spread throughout the country and was confirmed on farms from states, including ohio, indiana, iowa, minnesota, oklahoma, illinois, and north car olina, by the end september [ ] . pedv was detected in mexico for the first time in july [ ] . in october , pedv was identified for the first time in peru [ ] . in novem ber , pedv was also identified as the cause of outbreaks of diarrhea in farms in the espaillat province, dominican re public. by september , ped outbreaks were reported in seven of the provinces in the dominican republic [ ] . in april , canada reported outbreaks of pedv to the oie; these outbreaks started in january and affected herds in four provinces [ ] . an acute outbreak of diarrhea and death in lactating piglets was observed in columbia in march . by september , samples from six departments were confirmed via laboratory testing [ ] . several reports have described the development of rtpcr as a diagnostic technique for detection of both laboratory and field isolates [ ] . primers derived from the m gene can be used in an rtpcr system to obtain pedvspecific fragments [ ] , and duplex rtpcr has been used to differ entiate between tgev and pedv [ ] . within the past few years, several useful modifications of the basic rtpcr meth od have been reported. for example, it is possible to estimate the potential transmission of pedv by comparing viral shed ding load with a standard internal control dna curve [ ] and by multiplex rtpcr to detect pedv in the presence of various viruses [ ] -a technique that is particularly useful for rapid, sensitive, and costeffective diagnosis of acute viral gastroenteritis in swine. the commercial dual priming oligo nucleotide system (seegene, seoul, korea) (fig. ) has been developed for the rapid differential detection of pedv. this system employs a single tube onestep multiplex rtpcr with two separate primer segments to block nonspecific priming [ ] . recently, a proteinbased enzymelinked immunosor bent assay (elisa) system was developed to detect pedv. using this technique, a polyclonal antibody is produced by immunizing rabbits with purified pedv m gene after its ex pression in escherichia coli. immunofluorescence analysis can then be carried out with the antipedvm antibody in order to detect pedvinfected cells among other enteric vi ruses [ ] . another useful reverse transcriptionbased diagnostic tool is rt loopmediated isothermal amplification. this assay, which uses primers that recognize regions of the tar get dna, is more sensitive than gelbased rtpcr and eli sa, largely because this method produces a greater quantity of dna [ ] . immunochromatographic assay kits can be used at farms in order to detect the n (nucleocapsid) protein of pedv with % sensitivity and % specificity. moreover, a rapid technique for differential detection of pedv and por cine rotavirus (rv) has recently been commercialized and is now widely used in the field (fig. ) . this technique is less sensitive than rtpcr, but allows for diagnosis within min utes. thus, it is particularly effective for quickly determining quarantine or slaughter policies in the field. interestingly, some reports have commented on the detec tion of pedv genomic dna in sera. genomic detection in gno tobiotic piglets has been reported for serum viral rna con centrations ranging from . to . log genomic equivalents (ge)/ml after inoculation of the us pedv strain. similar de tection of the pedv genome has been observed in diarrheic pigs at age weeks ( . . log ge/ml) [ ] . however, no infectious pedv has been recovered from genomeposi tive sera samples. unfortunately, after intensive screening and trials to isolate the pedv genome from serum samples, we have not succeeded in this endeavor (data not shown). enteropathogenic viruses can be divided into two types (type i and ii) according to their infection site in the intestine [ ] . viruses infecting villous enterocytes, including tgev, pedv, and rv, are type i viruses and can be suppressed by local gut associated immunity. diseases caused by type ii viruses, which infect crypt enterocytes basolaterally (e.g., canine parvovirus), can be prevented by inducing systemic or mucosal immuni ty. in this review, we discuss control strategies for reducing viral shedding, mortality, and the transmission of pedv in swine herds, such as transmission occurring from artificial oral exposure (i.e., the feedback method) and vaccines. in naïve swine herds, ped is characterized by vomiting and acute diarrhea and results in high mortality rates in piglets less than weeks of age. neonatal pigs are born without ma ternal antibodies if they are not infected in utero, and they should receive passive lactogenic immunity (igg and iga) through intake of colostrum and milk to promote survival af ter birth. therefore, maternalderived immunity at an early age is critical for passive protection of neonatal pigs; for this purpose, immunization of the dam preparturition has been used successfully [ ] . igg is the major immunoglobulin com ponent in pig colostrum, consisting of more than % of all immunoglobulins, but is not found in milk. iga accounts for a substantially reduced percentage of colostrum immunoglob ulin content; however, iga is more effective than igg or igm at protecting animals from orally infected agents because it is more resistant to the activity of proteolytic enzymes in the in testine and has a higher neutralizing ability than igg and igm [ ] . bohl et al. [ ] and saif et al. [ ] demonstrated that oral inoculation of seronegative sows with live virulent tgev re sults in high rates of protection in suckling piglets. in these sows, passive protection is associated with high titers of se cretory iga (siga) in colostrum and milk. this investigation suggested the presence of a gutmammary glandsiga axis; that is, iga plasmablasts stimulated in the gut by virulent path ogens migrate to the gut lamina propria and mammary glands. several highly attenuated oral tgev vaccines, which repli cate lower in the gut, induce poor milk siga titers compared with virulent tgev in sows and result in lower protective effi cacy in piglets [ , ] . this research could be employed to maternal immunization strategies for pedv. in areas where no effective ped vaccines are available, some veterinarians have recommended artificial infection of sows (i.e., the feedback method) during pregnancy to supply lacto genic immunity to their piglets [ ] . the recommended feed back material is pooled feces collected from infected piglets during the first hours of infection. every sow on the farm should be simultaneously administered feces containing high titers of pedv, allowing all sows and gilts to recover at approx imately the same time and stop shedding the virus. one of advantage of this type of feedback method is strong stimulation of mucosal immunity in the gut and a quick re sponse after immunization. after successful feedback, the piglets will be protected during the first few days after birth by passive antibodies through colostrum and milk. however, there is a potential risk of transmission of the contaminated viral or bacterial agents in the inoculum (e.g., porcine circovi rus type [pcv ] infection, porcine reproductive and respi ratory syndrome virus [prrsv] , and salmonellosis) [ , ] . additionally, it is possible that pedv may spread rapidly in pigs of all ages in the index farms. the severity of the disease may vary with unknown factors, such as stress, nutrition, or coinfection. in addition, there is a risk that the virulent virus used for feedback materials may spread to and produce dis ease in other herds. irregular immune responses in sows after feedback may also be a major concern for optimal induction of herd immunity for protection. all of these possibilities em phasize the need for a safe and effective pedv vaccine to pro tect both sows and piglets. for the prevention of pedv infection, several vaccines have been reported in asian countries; the predominance of vac cines in asian countries, but not in europe or america, is thou ght to be related to the occurrence of severe ped outbreaks and major economic losses in asia [ ] . commercial pedv vaccines include live attenuated vaccines and binary ethyl enimine (bei) inactivated vaccines. some of these vaccines have been combined with vaccines for tgev (a bivalent vac cine) and porcine rv (a trivalent vaccine) and used in china and south korea [ , ] . moreover, an attenuated virus vac cine using cell cultureadapted pedv has been administered to sows in japan since . oral vaccination with a cellat tenuated vaccine has been used in south korea since and in the philippines since [ ] . although these commer cial vaccines are considered effective and have been widely used, not all animals develop solid lactogenic immunity. sev eral factors are thought to be associated with the poor lacto genic immunogenicity of the commercial vaccine, including the immunizing route of the vaccine. song et al. [ ] demon strated that oral inoculation of pedvseronegative pregnant sows with live attenuated pedv reduces the mortality of suck ling piglets more effectively rather than injection after chal lenge, and this protection is associated with elevated iga con centrations in colostrum and milk. despite the reduction in mortality rates in piglets delivered from orally vaccinated sows, there was no shortening of the duration of virus shedding and no reduced severity of diarrhea after challenge between vac cinated and control pigs. thus, some researchers may con clude that passive immunity by vaccination with the highly attenuated pedv strain dr does not prevent virus shedding after challenge. protection against virus challenge in conven tional pigs is related to the inoculation dose of the virus in the vaccine and the challenge dose of the virulent virus. at low doses of the attenuated pedv, % of pigs are protected against pedv challenge; however, this proportion increases to % when pigs are inoculated with a dose times higher [ ] . moreover, loss of body weight and the content of viral shed ding decrease in orally vaccinated pigs compared with those in intramuscularly vaccinated and unvaccinated pigs follow ing challenge with a low dose of virulent virus ( ld , . tcid /dose). additionally, the lethal dose of pedv changes depending on the body weights of the infected piglets and in fection of sows with the challenge virus (data not shown). however, several publications have questioned the efficacy and/or safety of pedv vaccines used in asia [ , , , , ] . in particular, after the us outbreak, the efficacy of commer cial ped vaccines in korea became controversial, and simul taneously, there was an urgent need for a new vaccine in or der to establish solid immunity in sow herds prior to farrow ing to protect piglets. furthermore, many groups have debat ed the appropriate standards for evaluation of the efficacy of vaccines after official challenge tests using currently available pedv vaccines in south korea in . information on pedv mucosal immunity is limited. moreover, due to the complex characteristics of mucosal viral diseases, simple criteria, such as serum neutralizing antibodies, severity of diarrhea, and mortality after virulent challenge, are insufficient for the ac curate and optimal evaluation of pedv vaccine efficacy. for detailed identification of standards for the evaluation of pedv vaccines after virulent challenge, the following criteria, which may not be controllable, should be taken into consideration: characteristics of piglets used in the challenge test: con ventional or specific pathogenfree piglets, weight of pig characteristics of sows: parity number, existence of aga lactia or coinfection with other viral and bacterial patho gens, number of delivered piglets quantity of challenged virus: amount of viral load for the challenge virus may result in discrepancies in the observ ed mortality rates of piglets cohabitation with sows: the conditions of piglets challeng ed with virulent virus could be affected by the occurrence of viral shedding by sows duration of the challenge test the vaccine strains commonly used in korea display a max imum difference of % at the amino acid level compared with field viruses. additionally, using sn assays, the sm vaccine strain was shown to exhibit variable crossreactivity with several antisera against other vaccines and field viruses, implying that these vaccines would confer protection against the vaccine prepared using wildtype pedvs from the field [ ] . however, the crossprotection between vaccine strains and field viruses should be elucidated through animal exper iments, which can show protection based on lactogenic im munity after vaccination. for the ideal development of pedv vaccines, new vaccine strains that are genetically related to field viruses are critical. furthermore, several criteria, includ ing factors related to the reduction in virus shedding and loss of body weight in piglets as well as the details of mucosal im munity and the relationships between protection and immu nity, should be considered and identified during the develop ment of nextgeneration ped vaccines. pedv research has become a hot topic in veterinary virology since the us outbreak in . ped had been a regional dis ease primarily found in asian countries. however, ped was transmitted to the united states and subsequently to neigh boring countries, including mexico and canada. european countries have also encountered pedv. accordingly, with the spread of the ped outbreak area, research on pedv has in creased rapidly. veterinarians and veterinary scientists are striving to breakthroughs to combat current ped outbreaks worldwide, and remarkable advances have been made in the relatively short time after the outbreak. therefore, reasonable methods for ped vaccine evaluation, along with the development of new vaccines, are urgently need ed, and this complicated process could provide valuable in formation on pedv, immune responses to pedv infection, and pedv pathobiology. furthermore, rational evaluation procedures can help swine farmers understand and control ped more efficiently. a new coronaviruslike particle associated with diarrhea in swine isolation of porcine epidemic diarrhea virus in porcine cell cultures and experimental infection of pigs of differ ent ages outbreak of porcine epidemic diarrhea in suckling pig lets letter to the editor cloning and sequence analysis of the m gene of porcine epidemic diarrhea virus ljb/ isolation and se rial propagation of porcine epidemic diarrhea virus in cell cultures and partial characterization of the isolate porcine epidemic diarrhoea virus: a com prehensive review of molecular epidemiology, diagnosis, and vaccines isolation of porcine epidemic diarrhea virus (pedv) in korea an outbreak of swine diarrhea of a newtype associated with coronaviruslike particles in japan distinct charac teristics and complex evolution of pedv strains complete genome sequence of k jb , a novel variant strain of por cine epidemic diarrhea virus in south korea uslike strain of por cine epidemic diarrhea virus outbreaks in taiwan origin, evolu tion, and genotyping of emergent porcine epidemic diar rhea virus strains in the united states ped vaccine gains conditional approval sci entific opinion on porcine epidemic diarrhoea and emerg ing porcine deltacoronavirus genetic variabil ity and phylogeny of current chinese porcine epidemic diarrhea virus strains based on spike, orf , and mem brane genes porcine epidemic diarrhea virus infection: etiology, epidemiology, pathogenesis and immunopro phylaxis the coro navirus spike protein is a class i virus fusion protein: struc tural and functional characterization of the fusion core complex the gprlqpy motif located at the carboxyterminal of the spike protein induces antibo dies that neutralize porcine epidemic diarrhea virus identification of the epit ope region capable of inducing neutralizing antibodies against the porcine epidemic diarrhea virus major recep torbinding and neutralization determinants are located within the same domain of the transmissible gastroenteri tis virus (coronavirus) spike protein sequence analysis of the partial spike glycoprotein gene of porcine epidemic diar rhea viruses isolated in korea cloning and further sequence analysis of the orf gene of wild and attenuatedtype porcine epidemic diarrhea viruses molecular characteriza tion and phylogenetic analysis of membrane protein genes of porcine epidemic diarrhea virus isolates in china molecular epidemiology of porcine epidemic diarrhea virus in china isolation and characterization of porcine epidemic diarrhea viruses associated with the disease outbreak among swine in the united states evaluation on the efficacy and immunogenicity of recombinant dna plasmids express ing spike genes from porcine transmissible gastroenteritis virus and porcine epidemic diarrhea virus complete ge nome sequence of a highly prevalent isolate of porcine epidemic diarrhea virus in south china new variants of porcine epidemic di arrhea virus, china molecular epidemiology and phylogenetic analysis of porcine epidemic diarrhea virus (pedv) field isolates in korea anti genic structure of the e glycoprotein from transmissible gastroenteritis coronavirus four major antigenic sites of the coronavirus transmissible gas troenteritis virus are located on the aminoterminal half of spike glycoprotein s bioinformatics insight into the spike glycoprotein gene of field porcine epidemic diarrhea strains during novel porcine epidemic di arrhea virus variant with large genomic deletion cell culture isolation and sequence analysis of genetically diverse us porcine epi demic diarrhea virus strains including a novel strain with a large deletion in the spike gene the coronavirus e protein: as sembly and beyond timized for porcine epidemic diarrhoea virus detection in faeces epidemic of diarrhoea caused by porcine epidemic diarrhoea virus in italy comparison of enzymelink ed immunosorbent assay and rtpcr for the detection of porcine epidemic diarrhoea virus diagnosis and investiga tions on ped in northern italy genetic di versity of orf and spike genes of porcine epidemic diar rhea virus in thailand chineselike strain of porcine epidemic diarrhea virus impact of porcine epidemic diarrhea virus infection at different periods of pregnancy on subsequent reproductive perfor mance in gilts and sows one worldone health: the threat of emerging swine diseases. an asian perspective emerging and re emerging diseases in asia and the pacific with special em phasis on porcine epidemic diarrhoea heterogeneity in spike protein genes of porcine epidemic diarrhea viruses isolat ed in korea genetic characterization of porcine epidemic diarrhea vi rus (pedv) isolates from southern vietnam during outbreaks outbreak of porcine epidemic diarrhea in piglets in gansu province the updated epidemic and controls of swine en teric coronavirus in china outbreakrelated porcine epidemic diarrhea virus strains similar to us strains, south korea comparative genome analy sis and molecular epidemiology of the reemerging por cine epidemic diarrhea virus strains isolated in korea two cases report of ped in different states in méxico porcine epidemic diarrhea outbreak in peru diarrea epidémica porcina (dep) en republica dominicana situacion de la diarrea epidemica porcina en colombia direct and rapid detection of porcine epidemic diarrhea virus by rt pcr rapid diagnosis of porcine epidemic diarrhea virus infection by polymerase chain reaction pedv leader sequence and junc tion sites identification and characteriza tion of new and unknown coronaviruses using rtpcr and degenerate primers differential detection of trans missible gastroenteritis virus and porcine epidemic diar rhea virus by duplex rtpcr fecal shedding of a highly cellcultureadapted porcine epidemic diarrhea virus af ter oral inoculation in 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class es of transmissible gastroenteritis viral antibodies exposing sows to pedv to build herd immunity national hog farmer detec tion of porcine circovirus in mammary and other tissues from experimentally infected sows colostral transmission of porcine circovirus (pcv ): reproduction of postweaning multi systemic wasting syndrome in pigs fed milk from pcv in fected sows with postnatal porcine parvovirus infection or immunostimulation oral efficacy of vero cell attenuated porcine epidemic diarrhea virus dr strain mucosal and systemic isotypespecific antibody responses and protec tion in conventional pigs exposed to virulent or attenuat ed porcine epidemic diarrhoea virus isolation and characterization of a variant porcine epidemic diarrhea virus in china molecular characterization and phylogenetic analysis of new variants of the porcine epidemic diarrhea virus in gansu genetic characterization of porcine epidemic diarrhea virus in korea from key: cord- -u rkn uh authors: dimaschko, j. title: superspreading as a regular factor of the covid- pandemic: ii. quarantine measures and the second wave date: - - journal: nan doi: . / . . . sha: doc_id: cord_uid: u rkn uh within the framework of a two-component model of the covid- epidemic, taking into account the special role of superspreaders, we consider the impact of the recovery factor and quarantine measures on the course of the epidemic, as well as the possibility of a second wave of morbidity. it is assumed that there is no long-term immunity in asymptomatic superspreaders who have under- gone the infection, and the emergence of long-term immunity in those who have undergone severe illness. it is shown that, under these assumptions, the relaxation of quarantine measures leads to the resumption of virus circulation among asymptomatic superspreaders. depending on the charac- teristics of the quarantine, its removal may or may not lead to a renewed wave of daily morbidity. a criterion for the occurrence and repeated wave of morbidity is proposed based on the analysis of the final phase of the first wave. based on this criterion, the repeated wave of the epidemic is predicted in new zealand. a natural explanation is given for the decrease in lethality among the infected against the background of an absolute increase in their number. in previous work [ ] , a two-component model of the covid- epidemic was proposed. the model is based on the selection of two immunologically different groups of the population -superspreaders and sensitive. superspreaders carry the infection without visible symptoms, so they spread it. sensitive, having received an infection, fall ill, are isolated and therefore cannot spread it further. a few relevant examples have shown that the model adequately describes the course of the covid- epidemic. at the same time, the two-component model describes only the spread of the virus and does not consider the recovery processes. further, it does not consider quarantine measures during the epidemic and the impact of these measures on the course of the epidemic itself. in this paper, we will include these factors in the twocomponent model and examine their impact on the final phase of the epidemic. in particular, the possibility of a second wave of the epidemic will be considered, and the conditions for its appearance will be determined. the article is structured as follows. in its second part, we consider the impact of recovery processes on the dynamics of the epidemic in the framework of the two-component model, as well as the impact of the quarantine as a factor affecting the spread rate. in this part, we introduce both factors into the dynamic equations of the two-component model and find an analytical solution under conditions of permanent quarantine. the third part examines the phases of the epidemic. in particular, the effect of lifting the quarantine in the final phase is being investigated. the effect is to re-increase the endemic equilibrium number of asymptomatic superspreaders. this, however, does not mean * electronic address: dimaschko@gmx.net an automatic re-increase in the incidence, if the proportion of those who have been ill and who have received immunity among the sensitive is already large enough. in the fourth section, we formulate a criterion for predicting the presence of a re-wave based on the analysis of the final segment of the first phase of the epidemic. next, we compare the results obtained with the current course of the epidemic in a few countries and territories. the final section summarizes the application of the model to the course of the current covid- pandemic and provides a natural explanation for the decrease in mortality resulting from the two-component model. the dynamic equations of the two-component model [ ] describe the change in the number of infected sensitive (n out of their total number n ) and the number of infected superspreaders (n out of their total number n ) over time: in this model, only superspreaders spread the infection, see fig. . equations ( , ) take into account only the process of infection spread and do not take into account the recovery processes. in addition, they do not take into account the quarantine measures that have a direct impact on the spread rates of g and g . to consider this effect, we introduce the quarantine factor q, which takes a value from to . the effect of fig. : scheme of the two-component epidemic model quarantine on the dynamics of the spread is reduced due to the same decrease in the spread rates g and g : when considering the recovery processes, we will proceed from the assumption that after suffering a disease with severe symptoms, a person acquires absolute immunity. thus, he is deprived of the opportunity to be re-infected and, from the point of view of the model, is no different from a simple patient -both during the illness and after it, a person from the sensitive group cannot spread the infection. therefore, such a restoration does not affect the dynamics of the two-component model. in contrast, recovery processes in asymptomatic infected individuals have a direct impact on the spread of the virus. we will assume that asymptomatic infected are deactivated with a recovery rate of γ. however, they do not acquire any lasting immunity and can be re-infected. this creates a circulation of infection among the superspreaders, leading to endemic equilibrium. considering the factors of quarantine q and the recovery rate γ, the equations of the two-component model take the form after switching to new variables it is reduced to a simple form: here the value is the ratio of the spread rates g ≡ αg and g ≡ g. in the case of a long-time permanent quarantine, q = const, this system of equations has an exact solution where τ ≡ qgt is dimensionless time and -dimensionless parameter of superspreaders deactivation rate. as in the absence of the quarantine (q = ) we have an epidemic occurs, the epidemic criterion is met (µ < ). consequently, the ratio of the recovery (γ) and spread (g) rates is also less than one: the found solution ( , ) meets the initial conditions that is, at the beginning of the epidemic, there are already infected people, but no sick ones yet. a stable endemic equilibrium among superspreaders is the state of in accordance with ( , ), at a sufficiently small value of q, i.e. with a sufficiently strict quarantine leading to the case of µ ≥ , s = -all superspreaders are deactivated. in the opposite case of non-strict quarantine, when the value of the quarantine factor q is not small enough and the parameter µ is less than one (µ < ), an endemic equilibrium takes place with a certain proportion of active infected superspreaders, s > . in such a solution the proportion of cases sensitive s continues to grow until it reaches the limit value s = . it is this condition that corresponds to the end of the epidemic and the vanishing of the daily incidench among superspreaders the infection continues, as at the beginning of the epidemic, to circulate at the stationary endemic level. the course of the epidemic according to the found solution ( , ) is shown in fig. . thus, in the two-component model, the quarantine factor does not affect the reproductive number, which determines the exponential growth rate of the incidence, but rather the endemic equilibrium number of asymptomatic superspreaders. the daily incidence is directly proportional to this number. in addition, it is proportional to remix, or adapt this material for any purpose without crediting the original authors. preprint (which was not certified by peer review) in the public domain. it is no longer restricted by copyright. anyone can legally share, reuse, the copyright holder has placed this this version posted august , . . https://doi.org/ . / . . . doi: medrxiv preprint fig. : course of an epidemic within the two-component model. filled areas show share of infected sensitive s (t) (orange) and superspreaders s (t) (blue). when t → ∞, the share of infected sensitive s (t) tends to , the share of infected superspreaders s (t) tends to the endemic equilibrium value of ( − µ). the proportion of those who do not recover among sensitive, which decreases during the epidemic. the end of the epidemic in this model does not correspond to the disappearance of infected superspreaders, but to the exhaustion of the number of still not infected sensitive individuals, which constitute only a relatively small part of the total population. the whole course of the epidemic in the two-component model is shown in fig. . in the general case, the value of the quarantine factor q is some function of time q(t), determined by the sequence and severity of quarantine measures. a typical course of the function q(t) is shown in fig. . natural boundary conditions for it are at the beginning of the epidemic, there is no quarantine and the quarantine factor is close to one, which corresponds to the boundary condition q( ) = . as the epidemic develops, quarantine measures are taken, which are responsible for reducing the value of the q factor. as the incidence decreases, the quarantine measures are removed, and the quarantine factor returns to the initial value. this corresponds to the second boundary condition q(∞) = . for an arbitrary dependence q(t), the dynamic equations ( , ) have no exact solution. however, taking into account the boundary conditions ( ), it turns out to be possible to carry out a qualitative analysis of the course of the epidemic corresponding to the real dependence q(t). in this analysis, it is convenient to divide the entire course of the epidemic into phases. a) the epidemic phase itself. at the beginning of the epidemic, there is no quarantine,q = . at the same time, the number of the superspreaders is growing exponentially, s ∝ e (g−γ)t . the daily incidence among sensitives is directly proportional to the number of superspreaders ds /dt ∝ s and therefore also grows exponentially. b) quarantine start phase. in this phase, the spread rates are suppressed by quarantine measures with a factor of q < , the relative number of the superspreaders reaches the endemic equilibrium value s = − γ/(qg) and stops growing. therefore, the daily incidence ds /dt, which is directly proportional to the number of superspreaders, also stops growing. in this phase, the daily incidence reaches its maximum. c) endemic phase. in conditions of constant quarantine and, accordingly, an endemic constant number of the superspreaders, the daily incidence is gradually decreasing due to a decrease in the proportion of those who have not been cured among sensitive, ( − s ). ideally, by the end of this phase, this proportion is already small, − s . d) quarantine release phase. after the quarantine is released, the equilibrium number of the superspreaders increases from the value s = −γ/(qg) established after the quarantine is turned on to the maximum possible value s = − γ/g. thus, even if the endemic equilibrium number of the superspreaders was significantly reduced during quarantine, after the quarantine was lifted at the end of the epidemic, it again increases to its maximum value. if the proportion of those who did not recover among the sensitive by the time the quarantine was lifted is already small, − s , then this does not lead to a noticeable increase in the daily incidence at the end of the epidemic. if this share has not yet managed to become sufficiently small, i.e. a significant part of the sensitive, then the release of quarantine leads to a noticeable increase in the daily incidence, i.e. to the second wave. to illustrate the possibility of the emergence of the second wave, let us consider the course of the epidemic at remix, or adapt this material for any purpose without crediting the original authors. preprint (which was not certified by peer review) in the public domain. it is no longer restricted by copyright. anyone can legally share, reuse, the copyright holder has placed this this version posted august , . . https://doi.org/ . / . . . doi: medrxiv preprint different values of the quarantine factor q, shown in fig. . factor q controls the endemic equilibrium number of the superspreaders during quarantine. at q = (absence of the quarantine), q = . and q = . (soft or moderately strict quarantine), the equilibrium endemic number of the superspreaders differs from zero. in these three cases, superspreaders continue to spread the infection during quarantine, and the incidence decreases relatively slowly due to a decrease in the number of sensitive who have not been ill. as can be seen from the first three graphs, here the release of quarantine after a significant decrease in the incidence does not lead to the appearance of a noticeable second wave, since by this moment the vast majority of the sensitive have already been ill. if q = . (very strict quarantine), as shown in the fourth graph, then the endemic equilibrium number of superspreaders during quarantine becomes zero. on the one hand, this leads to a rapid zero morbidity during quarantine. however, it is for this reason that most sensitive do not have time to get sick during quarantine. after the quarantine is released, the number of the superspreaders returns to the former endemic equilibrium non-zero value, and a new wave of infected people appears among the sensitive. it represents the second (residual) wave of morbidity thus excessively strict quarantine that deactivates all carriers of the virus is harmful. the reason for this is that in the absence of the virus, the sensitive are completely deprived of the opportunity to acquire immunity during the course of the disease. when active infected superspreaders reappear after the quarantine has been lifted, this still inevitably leads to the infection of the sensitive, deprived of immunity, to the appearance of a second wave of the epidemic and, thereby, to an increase in its duration. since the severity of quarantine can be assessed only by its consequences, it seems reasonable to find a criterion for the possibility of a second wave after quarantine is removed (corresponds to the phase of quarantine d in fig. ) based on the analysis of the current course of the epidemic, i.e. before the quarantine was lifted (corresponds to the beginning of quarantine phase b and endemic phase c in fig. ) . the forecast of the second wave will be based on the course of the epidemic immediately before and after the first maximum. in accordance with the exact solution ( , ), before reaching the first maximum, the increase in the incidence rate under quarantine conditions with factor q occurs with an exponential rate ∝ e (qg−γ)t . after reaching the first maximum, the incidence rate decreases exponentially ∝ e −(qαg+γ)t . the ratio of the fig. . the appearance of the second wave with a decrease in the quarantine parameter q (i.e., with an increase of the quarantine). sections a, b, c, d correspond to different phases of the epidemic: athe epidemic phase itself, b -the phase of the beginning of quarantine, c -the endemic phase, d -the phase of quarantine lifting. the dotted line shows the quarantine factor q(t) as a function of time. solid -daily incidence. for comparison, the course of morbidity is shown in the complete absence of quarantine measures, q= . in this case, the maximum incidence would exceed the maximum scale of the graph by about . times. the minimum value of the quarantine factor q= . conditionally corresponds to moderate quarantine measures, q= . -strict, q= . -extremely strict. remix, or adapt this material for any purpose without crediting the original authors. preprint (which was not certified by peer review) in the public domain. it is no longer restricted by copyright. anyone can legally share, reuse, the copyright holder has placed this this version posted august , . . https://doi.org/ . / . . . doi: medrxiv preprint increment of increase and decrement of decrease is the value in the epidemic limit γ/(qg) , when the recovery constant can be neglected, this ratio is equal to /α. in [ ] , we showed, using the example of a number of countries, that this value has a numerical value of in other words, this means that for most countries and territories, the value of a is close to . a significant deviation from this value towards a decrease should indicate excessively strict quarantine measures, which can lead to the appearance of a noticeable new wave -even after almost complete attenuation of the first. the lower the value of the parameter a, the more likely the second wave. examples of this kind are israel (a= . ) and serbia (a= . ), where there is a significant second wave. the course of the epidemic in these countries is shown in fig. . the value of the critical parametera is determined by the section of the graph at half the maximum height and the projection of the top of the graph onto this section. the value of parameter a in this and subsequent graphs is estimated as the ratio of the lengths of the right and left segments of this section. a very interesting situation shown in fig. is observed in australia and new zealand. the first peak of the epidemics in both neighbouring countries is similar, observed in the same time and satisfies the second wave criterion: a= . in australia and a= . in new zealand. in australia we already observe the second wave with maximum about cases per day. the value of a= . indicates the emergence of a similar second wave in new zealand in the near future. counterexamples of countries with moderate values of a are germany (a= . ) and italy (a= . ), where the signs of the second wave are very weak. the course of the epidemic in these countries is shown in fig. . in addition to the excessively strict quarantine, the reason for the appearance of the second wave can obviously be its premature weakening. in this case, the endemic equilibrium number of superspreaders increases against the background of a significant proportion of sensitive individuals who have not recovered and have not yet received immunity. this will lead to an immediate increase in the incidence, as appears to have happened in iran and the united states. the course of the epidemic in these countries is shown in fig. . note that in terms of the criterion of severity of quarantine, iran is equivalent to germany, and the united states is equivalent to italy (fig. ) . this indicates that in both cases, extending the quarantine until the end of the first wave would have avoided the appearance of a second wave. thus, the two-component model not only provides an adequate description of the course of the covid- epidemic, but also allows one to assess the impact of the severity and duration of quarantine measures on the course of the epidemic. it results a simple criterion for predicting the possibility of a second wave of the epidemic after the quarantine is weakened. based on this criterion, we can predict the repeated wave of the epidemic in new zealand. further, the two-component model provides a natural explanation for the observed decrease in mortality among those infected. it is important to understand that, due to the individual differences in the immune response, the concepts of "infected" and "sick" are not equivalent: infection leads to disease only in sensitive and does not lead to disease in superspreaders. the increase in the number of infected in the final phase of the epidemic may largely occur not due to an increase in real morbidity, but due to an increase in the number of asymptomatically infected superspreaders found during testing. since those who have recovered from the sensitive acquire immunity, an increasing proportion of those infected are superspread-remix, or adapt this material for any purpose without crediting the original authors. preprint (which was not certified by peer review) in the public domain. it is no longer restricted by copyright. anyone can legally share, reuse, the copyright holder has placed this this version posted august , . . https://doi.org/ . / . . . doi: medrxiv preprint ers. that is why, according to the two-component model, there is a decrease in mortality among the full array of infected people, which consists of two parts: sick -infected sensitive, and asymptomatically infected superspreaders identified during testing. for this reason, data on absolute mortality from covid- are more adequate for model verification than data on the number of infected. it is these data that were predominantly used to evaluate the re-wave criterion in finally, note that the two-component model ignores the spatial heterogeneity of population density. this circumstance is important for countries with a large territory and an extensive system of regions and megalopolises (russia, usa). for such countries, the epidemic acquires a multifocal character, and its spread to the entire territory of the country takes a longer time. taking this circumstance into account requires considering the spatial distribution and corresponding modification of the model in the spirit of [ ] . superspreading as a regular factor of the covid- pandemic: i. a two-component model spatial models and biomedical applications i am deeply indebted to prof. mykola iabluchanskiy and dr. vladimir shlyachover for valuable remarks and discussions, and to dr. daniel genin for help in use of mathematika tools. i express my gratitude to dr. matteo ferensby and to dr. giovani vasconcelos for fruitful discussion of the results. key: cord- -wkz axo authors: baud, grégory; brunaud, laurent; lifante, jean christophe; tresallet, christophe; sebag, frédéric; bizard, jean pierre; mathonnet, muriel; menegaux, fabrice; caiazzo, robert; mirallié, Éric; pattou, françois title: endocrine surgery during and after the covid- epidemic: expert guidelines in france date: - - journal: j visc surg doi: . /j.jviscsurg. . . sha: doc_id: cord_uid: wkz axo abstract the covid- pandemic commands a major reorganization of the entire french healthcare system. in france, general rules have been issued nationally and implemented by each healthcare center, both public and private, throughout france. guidelines drafted by an expert group led by the french-speaking association of endocrine surgery (afce) propose specific surgical management principles for thyroid, parathyroid, endocrine pancreas and adrenal surgery during and after the covid- epidemic. the ongoing covid- pandemic commands a major reorganization of the entire french healthcare system ( ) . to respond to the present and expected influx of patients needing a period of intensive care ( ) , the short-term priority has been directing available material and human resources toward sectors dispensing care for covid- patients ( , ) . this policy has entailed the almost complete de-scheduling of non-urgent surgery ( ) . more than a month now after the start of the epidemic, there is a pressing need to manage other health disorders not linked to covid- but for which deferral of surgery until after the epidemic is over could worsen prognosis or be life-threatening. it is also important to be thinking now about the conditions under which surgery can be resumed at a normal pace after the epidemic. general rules have been put out nationally and implemented by each healthcare center, both public and private, throughout france. specific guidelines have been proposed for visceral surgery ( ) . likewise, to meet their need for specific guidelines, the frenchspeaking association of endocrine surgery (afce) brought together a group of experts to propose principles for the surgical management of thyroid, parathyroid, endocrine pancreas and adrenal pathologies during the covid- epidemic and afterwards, when surgical activity will be able to return gradually to its normal pattern. these guidelines were drafted in the light of the existing literature. they will be updated as knowledge advances. four scheduling levels were defined to help prioritize patients (these levels may change according to how the epidemic setting evolves): urgent surgery that must be carried out as soon as possible because even a short deferral would be life-threatening. (ii) semi-urgent surgery that can be deferred for a few weeks but not beyond months without threat to life or adverse effects on cancer or functional prognosis. (iii) high-priority elective surgery that can wait for several months but must be given scheduling priority as soon as the epidemic is over. (iv) distant elective surgery that can be deferred until well after the epidemic is over, even more than months, without compromising the indication. for urgent surgery, the ratio of the benefit expected from surgery to the risks incurred by scheduling it during the epidemic must always be evaluated according to how both the national and local contexts are evolving, in particular the resources available: operating room, consumables and hospital capacities, particular if intensive care may be needed. when surgery is prescribed in the epidemic setting, short hospital stays or outpatient care are recommended ( ) , provided this does not increase the risk of rehospitalization. to limit operating time and the risk of post-operative complications, the surgery should also be performed by one or more experienced surgeons. even if no symptoms of covid- are apparent, the risk of infection should be assessed beforehand as it may be associated with unfavorable prognosis ( , ) . any surgery on a patient infected or suspected of being infected must be performed according to the rules laid down by the hospital's hygiene teams and infectiologists ( ). a. thyroid cancers (fig. ) control those of thyroxine (t ) at the time of surgery. non-suspect goiters responsible for severe compressive symptoms (inspiratory dyspnea due to tracheal compression, dysphagia due to esophageal compression, superior vena cava syndrome due to deep vein compression) must also be scheduled for semi-urgent surgery before the epidemic ends. c. hyperparathyroidism (fig. ) surgical treatment of primary hyperparathyroidism (hpt) is generally not urgent ( ) . in the covid- epidemic setting, its scheduling depends on the presence or absence of severe hypercalcemia, defined by a very high level of blood calcium > . mmol/l ( mg/l) ( ) , and/or the presence of clinical complications -acute pancreatitis secondary to hpt, brown tumor, calciphylaxis, fracture osteopenia, heart rhythm disorders (qt shortening on ecg, bradycardia with risk of asystole) with cardiac insufficiency ( ) ( ) ( ) ( ) . in all cases, hypocalcemia treatment must first be given. in the epidemic setting, the use of cinacalcet is recommended ( ) . in cases of severe hypercalcemia, surgery must be scheduled as semiurgent, without waiting for the epidemic to end, or as urgent when it escapes control by the medical treatment. if there is no severe hypercalcemia, surgery can be deferred without risk until the epidemic is over. these guidelines are valid for cases of genetically determined primary hpt. for tertiary hpt, the blood calcium threshold defining severe hypercalcemia must be lowered to . mmol/l to protect renal grafts (nephrocalcinosis, acute tubular necrosis, lithiasis) and bone and vascular impact ( , ) . for secondary hpt, surgical treatment is not recommended during the epidemic because of the higher risk of covid- infection in dialyzed patients ( ) . when indicated, surgery must be scheduled as a priority in the three months following the epidemic in cases of disabling bone pain, brown tumor or temporary contraindication for renal transplant ( ). uni-or bilateral cervicotomy is the approach recommended for the surgical treatment of thyroid or parathyroid pathologies in the epidemic setting, so as to limit operating time and complication risk ( ) . surgery requiring a thoracic or mediastinal approach and/or postoperative intensive care ( ) in the epidemic setting, the indication for the surgical treatment of a neuroendocrine tumor of the pancreas must be discussed in an mdt meeting to assess the balance between the risks of surgery and its oncological and/or secretory benefits ( ) . the management of ( ) . a pancreatectomy may be indicated when a curative resection can be considered after clinical and morphological reassessment ( ) , in which case surgery is scheduled as semi-urgent before the epidemic has ended. patients with a well-differentiated neuroendocrine tumor of the pancreas (grades g , g or g ) that is nonsecretory can be deferred until well after the epidemic is over. if there is an associated secretory syndrome, a medical treatment should first be given ( ) . if this treatment fails to control the secretory syndrome satisfactorily, pancreatectomy must be scheduled as semi-urgent before the end of the epidemic. if the medical treatment is effective, surgery can be deferred until well after the epidemic has ended. when technically possible, laparoscopy is recommended for left pancreatectomies and enucleations to minimize postoperative impact on respiratory function and hospital length of stay ( ). in the epidemic setting, the indication for the surgical treatment of an adrenal lesion must be discussed at an mdt meeting to assess the balance of risk and its oncological and/or secretory benefits. lesions suspected to be malignant (cortico-adrenaloma, metastases) must undergo surgery when they are considered resectable ( , ) . in cases of secretory syndrome, prior management by a medical treatment is recommended (metyrapone, ketoconazole). surgery must be scheduled as semi-urgent, before the end of the epidemic, in an expert center ( ). chromaffin lesions (pheochromocytoma and/or paraganglioma) must first receive an appropriate antihypertension treatment (alpha-blocking agents, beta-blocking agents, calcium inhibitors), and be monitored by an experienced care team ( ) . if this treatment controls the secretory syndrome, close monitoring can be continued until the for other secretory adrenal lesions (in particular, hypercorticism and hyperaldosteronism), an appropriate medical treatment (steroidogenesis inhibitors, antialdosterone) must first be implemented. if the secretory syndrome is not controlled or if impact is marked, adrenalectomy can be scheduled as semi-urgent during the epidemic. in other cases, adrenalectomy can be scheduled well after the epidemic has ended. during the epidemic, laparoscopy remains the preferred approach for adrenalectomy. conversely, for suspect lesions and/or those larger than cm, laparotomy is recommended ( ). post-operative follow-up consultations must be maintained during the epidemic. teleconsultation is recommended to ensure continuity of care while limiting the risks of coronavirus propagation in healthcare centers. for a consultation in which a diagnosis of cancer or a therapeutic strategy is to be announced, some form of video exchange is recommended. whenever possible, blood tests and imaging must be performed outside hospitals. in a situation where medical drugs of major therapeutic importance may be in short supply, patients who are dependent on a hormone substitution treatment should be reminded never to interrupt their treatment longer than h for corticoids ( ) , longer than h for calcium ( ) , and longer than one week for thyroid hormones ( ) . * steroidogenesis inhibitors (metyrapone, ketoconazole), anti-hypertensive agents (alphablocking drugs, beta-blocking drugs, calcium inhibitors), antialdosterone diuretics, (ttt med = medical treatment, pheochr = pheochromocytoma) covid- : what is next for public health? high prevalence of obesity in severe acute respiratory syndrome coronavirus- (sars-cov- ) requiring invasive mechanical ventilation critical care utilization for the covid- outbreak in lombardy, italy: early experience and forecast during an emergency response blueprint for restructuring a department of surgery in concert with the health care system during a pandemic: the university of wisconsin experience covid- : all non-urgent elective surgery is suspended for at least three months in england strategy for the practice of digestive and oncological surgery during the covid- epidemic at last a step forward toward ambulatory care for endocrine surgery in france? clinical characteristics and outcomes of patients undergoing surgeries during the incubation period of covid- infection cancer patients in sars-cov- infection: a nationwide analysis 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thyroid surgery with monitoring loss of signal randomized controlled trial of alfacalcidol supplementation for the reduction of hypocalcemia after total thyroidectomy enets consensus guidelines update for gastroduodenal neuroendocrine neoplasms covid- epidemic: proposed alternatives in the management of digestive cancers : a french intergroup clinical point of view enets consensus guidelines for high-grade gastroenteropancreatic neuroendocrine tumors and neuroendocrine carcinomas pancreatic neuroendocrine tumors: the impact of surgical resection on survival enets consensus guidelines for the management of patients with digestive neuroendocrine neoplasms: functional pancreatic endocrine tumor syndromes european society of endocrine surgeons (eses) and european network for the study of adrenal tumours (ensat) recommendations for the surgical management of adrenocortical carcinoma adrenocortical carcinoma: impact of surgical treatment adrenalectomy risk score: an original preoperative surgical scoring system to reduce mortality and morbidity after adrenalectomy long-term survival after adrenalectomy for stage i/ii adrenocortical carcinoma (acc): a retrospective comparative cohort study of laparoscopic versus open approach adrenal insufficiency hypocalcemic emergencies combined levothyroxine plus liothyronine compared with levothyroxine alone in primary hypothyroidism: a randomized controlled trial key: cord- -iu wg ik authors: hoang, hai; killian, mary l.; madson, darin m.; arruda, paulo h. e.; sun, dong; schwartz, kent j.; yoon, kyoungjin j. title: full-length genome sequence of a plaque-cloned virulent porcine epidemic diarrhea virus isolate (usa/iowa/ / ) from a midwestern u.s. swine herd date: - - journal: genome announc doi: . /genomea. - sha: doc_id: cord_uid: iu wg ik porcine epidemic diarrhea (ped) was recognized in u.s. swine for the first time in early . a plaque-purified ped virus (pedv) isolate (usa/iowa/ / ) was obtained from a diarrheic piglet. the isolate is genetically close to other previously reported u.s. pedvs and recent chinese pedvs and was virulent when inoculated into neonatal pigs. genus alphacoronavirus ( ) ( ) ( ) , was first identified in england in and later in other countries, such as belgium, china, hungary, italy, japan, korea, and thailand ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) . in april of , ped emerged in u.s. swine ( ) and was detected in swine herds in u.s. states by the end of october (http://www.aasv.org/pedv /pedv_weekly_report_ .pdf), causing considerable economic losses. an isolate of ped virus (pedv) was sought for use in studies to address concerns regarding diagnosis, transmission, pathogenesis, and vaccination. virus isolation was attempted from field samples submitted to the iowa state university veterinary diagnostic laboratory that were positive for pedv by a real-time reverse transcriptase pcr (rt-pcr) assay ( ) using vero cells (atcc ccl- ), as previously described ( ) . a cytopathic virus with coronavirus morphology was isolated from intestinal tissues collected from a . week-old piglet from a swine farm in iowa. in the cells that were inoculated with the virus, the virus induced syncytia and eventually cell death. the presence of pedv in the inoculated cells was confirmed by immunofluorescence microscopy using a pedvspecific monoclonal antibody, c ( ) . after cell culture passages, the primary isolate was subjected to plaque purification. a plaque-cloned virus isolate was further propagated in the cells for more passages, for a total of cell passages (p ). the plaque-cloned pedv p isolate (usa/iowa/ / ) was able to cause cytopathic effects at to h postinoculation (hpi) and reach a titer of . pfu/ml within hpi. caesareanborn colostrum-deprived piglets orally inoculated with the isolate at a rate of pfu/ml developed severe watery diarrhea and dehydration within hpi and eventually died. microscopically, intensive immunohistochemical staining of almost all enterocytes for pedv was observed at hpi, leading to severe villous atrophy at a later time. the entire genome of the isolate usa/iowa/ / was sequenced using next-generation sequencing technology on the ion torrent platform (life technologies, austin, tx) as per the manufacturer's instructions, and the data were assembled using dnastar ngen based on known pedv sequences. the genomic rna of the isolate is , nucleotides long, excluding the = poly(a) tail. the genomic organization of the isolate is similar to what was previously described ( , , ) and includes a = untranslated region ( = utr), open reading frame a (orf a)/ orf b, s, orf , e, m, n, and a = utr with a slippery sequence ( tttaaac ) in orf . there is an insertion between nucleotides and in orf that causes a reading frameshift, shortening the replicase polyprotein ab ( , amino acids long). phylogenetically, the isolate is . to . % similar to other u.s. pedvs reported earlier ( , , ) , . to . % similar to recent chinese pedvs ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) , with ah (genbank accession no. kc ) being the closest, and . % similar to the prototype pedv strain cv ( ). in conclusion, the pedv isolate usa/iowa/ / is a virulent strain with a genetic profile similar to those of other u.s. pedvs reported to date. such a representative purified virulent pedv isolate can be a valuable reagent for studying the pathogenesis and immunobiology of pedv and developing diagnostic reagents and kits, as well as effective vaccines. nucleotide sequence accession number. the complete genome sequence of pedv strain usa/iowa/ / was submitted to genbank under the accession no. kf . we are grateful to practicing swine veterinarians for submitting samples from suspect cases to the iowa state university veterinary diagnostic laboratory and procuring additional samples. we also thank drew magstadt (veterinary diagnostic laboratory, iowa state university, ames, ia) and john neil (ruminant diseases and immunology research unit, national animal disease center, usda/ars, ames, ia) for assistance in animal work and laboratory support, respectively. the study was supported in part by funding from the iowa pork producers association (npb no. . sequence determination of the nucleocapsid protein gene of the porcine epidemic diarrhoea virus confirms that this virus is a coronavirus related to human coronavirus e and porcine transmissible gastroenteritis virus genome organization of porcine epidemic diarrhoea virus sequence analysis of the nucleocapsid protein gene of porcine epidemic diarrhoea virus letter to the editor a new coronavirus-like particle associated with diarrhea in swine molecular characterization and phylogenetic analysis of membrane protein genes of porcine epidemic diarrhea virus isolates in china enterotoxigenic escherichia coli, rotavirus, porcine epidemic diarrhoea virus, adenovirus and calicilike virus in porcine postweaning diarrhoea in hungary epidemic of diarrhoea caused by porcine epidemic diarrhoea virus in italy an outbreak of swine diarrhea of a new-type associated with coronavirus-like particles in japan prevalence of porcine epidemic diarrhoea virus and transmissible gastroenteritis virus infection in korean pigs chinese-like strain of porcine epidemic diarrhea virus emergence of porcine epidemic diarrhea virus in the united states: clinical signs, lesions, and viral genomic sequences multiplex real-time rt-pcr for the simultaneous detection and quantification of transmissible gastroenteritis virus and porcine epidemic diarrhea virus propagation of the virus of porcine epidemic diarrhea in cell culture complete genome sequence of porcine epidemic diarrhea virus strain usa/colorado/ from the united states porcine epidemic diarrhoea virus: a comprehensive review of molecular epidemiology, diagnosis, and vaccines origin, evolution, and genotyping of emergent porcine epidemic diarrhea virus strains in the united states complete genome sequence of porcine epidemic diarrhea virus strain aj isolated from a suckling piglet with acute diarrhea in china complete genome sequence of a chinese virulent porcine epidemic diarrhea virus strain complete genome sequence of a porcine epidemic diarrhea virus variant complete genome sequence of a novel porcine epidemic diarrhea virus in south china phylogenetic analysis of porcine epidemic diarrhea virus field strains prevailing recently in china complete genome sequence of a recombinant porcine epidemic diarrhea virus strain from eastern china complete genome sequence of a highly prevalent isolate of porcine epidemic diarrhea virus in south china complete genome sequence of a variant porcine epidemic diarrhea virus strain isolated in central china complete genome sequence of novel porcine epidemic diarrhea virus strain gd- in china complete genome sequence of a vero cell-adapted isolate of porcine epidemic diarrhea virus in eastern key: cord- - olapsmv authors: xu, zhijie; ye, yuanqu; wang, yang; qian, yi; pan, jianjiang; lu, yiting; fang, lizheng title: primary care practitioners’ barriers to and experience of covid- epidemic control in china: a qualitative study date: - - journal: j gen intern med doi: . /s - - - sha: doc_id: cord_uid: olapsmv background: the coronavirus disease (covid- ) emerged in december and posed numerous challenges to china’s health system. almost million primary care practitioners (pcps) participated in controlling the outbreak. however, pcps’ barriers to and experience of the epidemic control remain unknown and are essential for improving countermeasures. objective: to better understand the barriers pcps faced in covid- epidemic control and their psychological and occupational impacts, and explore potential solutions. design: this qualitative study was conducted through semi-structured, in-depth interviews from february , to march , . participants: a purposive sample of frontline pcps affiliated with either community health centers or township health centers in four provinces of china were recruited. approach: interviews were conducted by telephone, and then recorded, transcribed, and content analyzed. themes surrounding pcps’ barriers to covid- epidemic control, their experience, and potential solutions were iteratively identified using the constant comparative method. key results: of the pcps interviewed, ( %) were women and ( %) worked in rural areas. barriers to epidemic control in primary care included inappropriate pcp scheduling and role ambiguity, difficult tasks and inadequate capacities, and inexperienced community workers and insufficient cooperation. some pcps perceived respect and a sense of accomplishment and were preoccupied with the outbreak, while others were frustrated by fatigue and psychological distress. pcps reported potential solutions for improving countermeasures, such as improving management, optimizing workflows, providing additional support, facilitating cooperation, and strengthening the primary care system. conclusions: due to their roles in controlling the covid- epidemic, pcps in china faced a series of barriers that affected them physically and mentally. support for pcps should help them to overcome these barriers and work efficiently. the current findings provide insight into the challenges and potential solutions for strengthening the preparedness and response of china’s primary care system in future disease outbreaks. electronic supplementary material: the online version of this article ( . /s - - - ) contains supplementary material, which is available to authorized users. i n december , a novel coronavirus was detected from a series cases of pneumonia of unknown cause in wuhan, china, which was subsequently named the coronavirus disease (covid- ) by the world health organization (who). [ ] [ ] [ ] as of june , , , cases including deaths had been confirmed in china, and a global pandemic had emerged. in addition, a total of countries had reported over , , confirmed cases and , deaths, and the numbers continue to grow. [ ] [ ] [ ] primary care practitioners (pcps) are essential in confronting the pandemic. for example, almost million pcps in china participated in covid- epidemic control. they worked in collaboration with the community workers and community police in a "joint defense team" led by the neighborhood committee. pcps were responsible for screening suspected cases, visiting residents in quarantine, contact tracing and monitoring, and surveillance at checkpoints, while community workers and community police provide nonmedical support to residents in quarantine. pcps regularly recorded work-related information on forms and uploaded the forms to the neighborhood committee and health administrative departments. similar procedures were undertaken by pcps in singapore. numerous studies have focused on barriers to epidemic control in primary care. a systematic review identified challenges faced by pcps in different countries during previous pandemic response, such as a shortage of personal protective equipment (ppe), limitations of provided information, and insufficient training. a qualitative study showed that pcps experienced difficulties in translating pandemic guidelines into practice. however, the barriers pcps encountered in covid- epidemic control and their solutions have not been explored. another research focus has been the impact of epidemic control on pcps and their experiences. a recent survey showed that general practitioners (gps) in shanghai displayed psychological health problems of varying severity during epidemic control, and . % of gps felt stressed. similarly, previous studies demonstrated that the pandemic outbreak changed pcps' work environment and lifestyle, and led to a series of negative emotions, such as depression, anxiety, and fear. they could also experience symptoms of acute stress disorders or post-traumatic stress disorder (e.g., intrusion, avoidance, and hyperarousal) after the outbreak. therefore, pcps' experience in covid- epidemic control deserves closer attention to inform improvement efforts. to understand pcps' perceived barriers to and experience of performing their tasks in epidemic control, we recruited frontline pcps in china and conducted in-depth interviews using a qualitative design. we aim to understand pcps' perspectives on their work and explore the strategies for improving countermeasures in primary care. from february to march , , we conducted a descriptive qualitative study involving semi-structured, in-depth interviews with purposive samples of pcps. interviews were conducted by telephone because of the nationwide traffic restriction, and they lasted a mean of minutes (range: - minutes). all participants provided verbal informed consent before the interviews began and were not compensated for their participation. the study was approved by the sir run run shaw hospital ethics committee and adhered to the declaration of helsinki. we used wechat, an instant messaging app, to invite pcps to participate in the interviews, using the principle of maximum variation. three family physicians refused to participate because they were not responsible for tasks in epidemic control. participants were affiliated with local government-owned community health centers in urban areas (zhejiang and guangdong province) or township health centers in rural areas (shaanxi and hunan province). participants knew the investigators prior to the interview, but none had worked with the investigators. the sample size was determined using thematic saturation: two investigators (z.x. and y.y.) analyzed the transcripts and notes for newly emergent themes after the first in-depth interviews, and after every or thereafter. we stopped scheduling interviews when additional interview data created little or no change to the codebook and no new patterns or themes emerged. , repeat interviews were not carried out. the interview guide was adapted from relevant qualitative studies involving healthcare workers in infectious disease outbreak, , and was refined through pilot interviews with three pcps to improve appropriateness and clarity (eappendix ). each interview began with a question about the types of tasks participants had performed in epidemic control. probing questions were then used to encourage participants to describe tasks in which they felt their performance was deficient and whether they encountered any barriers to task performance (e.g., how did the barriers or difficulties affect your work?). probing questions also elicited details of pcps' experiences and the occupational and psychological effects of epidemic control (e.g., have you experienced any positive or negative emotion?). at the end of the interviews, investigators encouraged pcps to talk freely about their perspectives regarding strategies that could contribute to improved control measures in primary care. information regarding participants' characteristics was collected before the interviews, which were independently audio recorded and transcribed verbatim by two male general practitioners as interviewers (z.x. and y.y.) who had received training on qualitative interviewing. the interviewers made field notes during the interview when necessary. they independently identified major themes and subthemes via thematic content analysis and developed a preliminary codebook for data analysis based on the first three transcripts. they reviewed transcripts continuously using the constant comparative method to expand existing themes and identify new ideas or themes. the codebook was iteratively refined and finalized via internal consensus until % agreement was reached. maxqda (version . . ) was used in the data analysis and retrieval. transcripts were not returned to participants for comment or correction, but we randomly selected three participants and sent them our main findings via e-mail. they agreed with the themes without modification. we recruited eligible pcps ( family practitioners, internists, surgeons, and pediatrician) from practices ( community health centers and township health centers). of the participants, ( %) were women, and ( %) participants undertook administrative tasks in their medical practice. the mean age of participants was years (range: - years), and the mean duration of practice was years (range: - years) (eappendix ). inappropriate pcp scheduling and role ambiguity. participants described numerous barriers to epidemic control (table ) . some felt overburdened and assigned to unsuitable positions. one family physician explained this feeling using a surprising example: "there were residents [to be quarantined] that day, but the community health center only assigned physicians [to visit them]." others felt confused, as they were asked by the leaders of their community/township health centers to perform low-skilled work and believed they needed an additional supportive workforce. the confusion was described by an internist as follows: "when i came back [from the home visits], i was not free until i disinfected the ambulance. but why not employ a cleaner?" some policies were considered inflexible and pcps felt they limited effective scheduling. for example, the quarantine duration was fixed for everyone leaving the epidemic area, regardless of whether self-quarantine had already been undertaken. one participant commented, "[there is] a one-size-fitsall approach that we need to follow, and it took much more time to address the consequences." these inflexible policies not only increased the unnecessary workload but also may have reduced residents' trust in epidemic control. another reported barrier was excessive inspection and meetings. the government officials and medical experts irregularly visited the community/township health centers and inspected pcps' daily practice of epidemic control, including the material preparation and arrangement, and held meetings to discuss the existing problems and potential solutions with pcps. one participant stated, "it really troubled me that i had to accompany those supervisors, maybe to times a week, and show them what we had done with countless papers and forms and photos." some instructions distributed to pcps by supervisors were perceived as "scratching the surface". in addition, the frequent modification of guidance regarding epidemic control confused pcps. difficult tasks and inadequate capacities. although routine care was largely canceled in many primary care practices, participants frequently noted the deficiencies of the workforce and that they worked for extended hours during epidemic control. pcps were on call hours per day to visit newly quarantined residents. online consultation with residents increased workload during time off. one family physician stated, "i often kept an eye on my mobile phone because the residents often left a message of inquiry in the wechat group waiting for my reply." all participants had limited experience in working during a pandemic and more than half perceived their professional training as inadequate and not tailored to their work of epidemic control in the community. in addition, most institutions lacked ppe (particularly masks and gowns) and pcps generally compromised their safety by reusing ppe. cooperation. pcps in china performed home visits for quarantined residents in cooperation with community workers. a few participants complained that community workers were sometimes inactive in terms of participation in epidemic control: "the home visits should be implemented by a group of family physicians and community workers, but sometimes they arrived late." another barrier pcps encounter was that community workers received inadequate training in epidemic control. as one internist commented, "the temporarily recruited [community workers] had no clinical background; they might fall in a rut and fail to deal with things case by case." participants also described a lack of cooperation between pcps and community workers. one family physician stated, "it might cause a delay if there was any error of communication. sometimes the community workers isolated the resident or days before i received the notice. but [the resident] still needed to stay at home for days." a possible explanation for the miscommunication was that orders were released by different administrative departments with limited previous interaction or experience of cooperation. preoccupation. the heavy tasks and work stress involved in epidemic control resulted in pcps devoting additional energy and effort to their daily practice. one source of pcps' preoccupation with epidemic control was the culture of commitment and sacrifice in the healthcare workforce. one participant expressed his pride in participating in epidemic control: "in my school days, i witnessed the outbreak of sars in and was impressed by the sacrifice of angels in white…so i feel proud to have the opportunity to control the outbreak on the frontline." sense of respect and accomplishment. all participants expressed a sense of respect for epidemic control, which enhanced their relationship with residents. pcps received increased emotional support and appreciation, and their efforts were recognized by residents in the community. participants also expressed satisfaction with the insurance and compensation provided by the government. some pcps felt a sense of accomplishment when the quarantine expired, and the residents they managed were not infected. others were inspired to have greater solidarity with colleagues, described as follows: "it's impressive to see my colleagues bearing the hardship…our cohesion is greater than before and makes it all worthwhile." fatigue. more than half of the participants claimed they experienced fatigue as a result of participating in epidemic control. some participants complained that the work content was beyond their capacity and the requirements were incongruous with their training. the intensive work and tough tasks were described as the main factors affecting fatigue. insomnia was cited as another cause of fatigue. one participant reported that the overwhelming work stress deteriorated his sleep quality, which led to inadequate rest and intensified his experience of fatigue. many other symptoms, such as "memory decline," "weight loss," and "inappetence," were reported as common concomitant manifestations of fatigue. psychological distress. participating in epidemic control made pcps a vulnerable group susceptible to psychological distress ( table ). some experienced fear of being infected, and this fear was intensified by the inadequate supply of ppe and prolonged frontline work. pcps frequently experienced anxiety because they needed to adapt to a fast-paced, highly efficient working environment. some participants felt anxious about errors of omission and residents' complaints. most pcps experienced frustration with the paperwork required for reporting, which was deemed as time-consuming but scarcely conducive to practice. another reason for their frustration was that their efforts and contributions were not always recognized by supervisors. pcps would become angry when residents refused to comply with the quarantine and were offended by scurrilous remarks. however, all participants denied persistent or severe depressive symptoms (e.g., feeling hopeless or suicidal thoughts). most participants found psychological support from their colleagues for their psychological distress, but all participants described a lack of external support, and the reasons were "no available professional psychological support," "too busy to seek for help," and "won't help things at all." "i was constantly taking on new tasks and adapting to new requirement, dealing with things that might come up. i was very anxious at that time." frustration "the guidance was problematic at the early stage of epidemic control, but we had no voice to make a change…i felt helpless and powerless." anger "some villagers were frightened of virus transmission through us physicians and hurled insults at me…i choke down their acrimony…it's very annoying." improving management and supervision. to solve certain problems, such as improper task allocation and inflexible policies, participants generally suggested that administrative departments should develop measures that were more personcentered and based on specific contexts. one participant stated, "i appreciate those officials who listened to our voices, sympathized with our dilemmas, and were capable of providing practical strategies." moreover, streamlining excessive inspection and meetings was suggested by some participants. one surgeon remarked, "…facing a succession of inspec-tions…then i became unmoved. i didn't care about what they asked anymore." optimizing workflow. many participants expressed a wish to work efficiently. for example, paperwork and reporting were frequently mentioned as a barrier to epidemic control and occupied much of pcps' time. strategies involved rational workforce arrangement and internal coordination. as one participant stated, "[the medical institution] could recruit full-time medical assistants to perform the low-skilled tasks, such as the daily statistical report." in addition, participants proposed the option of streamlining the procedures for reporting using an intelligent approach. one physician admitted, "the task of surveillance [at the checkpoints] is getting easier because now we have an identity database to screen the contact history for the travelers." providing necessary support. most participants emphasized an imperative of increasing the supply of ppe to pcps, although they all understood the shortage. one suggested strategy was to "use ppe in a planned way" to ensure the security of the frontline healthcare workforce. other options included "collecting ppe from the public" and "centralized purchasing." some participants thought they lacked the experience of coping with major infectious diseases and needed more professional training. one participant commented, "the online education program helped me gain much knowledge of covid- , but we need lessons more tailored for primary care." facilitating cooperation. participants described the need to reinforce cooperation with community workers. participants noted that it was necessary to identify the division of responsibilities for both sides and strengthen the training and supervision of cooperation. an effective approach would be to establish a mechanism of interaction and communication. as one participant stated, "tacit cooperation cannot be expected in one stroke…if the effect of communication was not significant, then we must try again." strengthening the primary care system. participants unanimously agreed that the covid- outbreak was a challenge to the chinese primary care system. to strengthen this system, participants' recommendations ranged from "increasing investment in primary care institutions" and "developing information technology" to "improving the capacity of healthcare personnel." participants expected a system that was "more resilient", "offered universal coverage down to the community level," and "provided integrated care for residents." primary care is the first line of defense in controlling an epidemic at a community level, but the susceptibility of pcps to tasks and the serious consequences were not fully recognized. to enhance understanding of the current status of covid- epidemic control in primary care, we characterized pcps' perceived barriers and experience. we also examined pcps' perspectives on the solutions that could potentially benefit the primary care system in coping with major infectious diseases. to our knowledge, this was the first qualitative study to explore pcps' work in major infectious disease control in china. the pcps described a series of barriers to epidemic control. aside from the extreme workload, rapidly evolving practice environment, ppe shortage, and inadequate training, which are consistent with international reporting, , participants emphasized specific concerns about inappropriate pcp scheduling and role ambiguity, which complicated their routine work, and insufficient cooperation with community workers, which reduced their work efficiency. these findings highlight new problems within and beyond the primary care system during emergency emergencies. therefore, a feedback channel between pcps and leaders should be established to detect problems in epidemic control. implementation of epidemic control had varied occupational and psychological effects on pcps. some pcps responded to the epidemic proactively because of inner motivation or external pressure, whereas others felt fatigued and expressed psychological distress. evidence suggests that frontline healthcare workers are generally vulnerable to the emotional impact of epidemics. [ ] [ ] [ ] in this study, we inductively identified manifestations of psychological distress among participants-fear, anxiety, frustration, and anger ( table )-most of which were reported as mild in degree and short in duration, and seldomly the cause of absenteeism or disease. our findings provide insights into the factors affecting emotions that primary care managers should acknowledge. for example, pcps felt frustrated with the paperwork of reporting surveillance data not only because it was time-consuming or complex but also it was of little practical value. remarkably, most participants found support from their colleagues, but none received external psychological support, suggesting potential gaps in mental health services for pcps during emergencies. although many studies have reported that positive professional relationships, including dialogue and emotional support, were an essential protective factor for preventing physician burnout, our findings support and expand on the existing knowledge regarding the essential role that the peer support plays in pcps' psychological support during a time of pandemic and workforce scarcity. strategies to help pcps overcome challenges and prevent the primary care system from being overwhelmed are urgently needed. first, health authorities and institutional leaders were expected to provide specific support in terms of material, technology, and mental care to make pcps equipped for epidemic control. it is worth noting that leaders must listen to pcps' concerns and encourage them to ask for help, instead of blaming or criticizing them. an array of feedback channels, such as listening sessions and email suggestion box, could be considered to make pcps' voice be part of the decision-making process. second, the burden of unnecessary work could be reduced to maximize the capacity of pcps during this turbulent time. pcps wished to be freed from non-essential tasks and meetings to perform to their full potential and provide integrated care for residents in the community. it is advisable to consider innovative ways proposed by participants in our study to reduce workload and streamline procedures, such as rational workforce arrangement, effective internal coordination, and establishing an intelligent system of communication and surveillance. third, professional training could be provided to community workers to help facilitate their cooperation with pcps. current healthcare systems in many countries are under extreme pressure, and the use of community workers for the covid response would fill gaps in routine primary care. there is a potential to improve community workers' capacity to deliver a wider range of care for the residents. for example, community workers receiving a basic training program might help pcps manage older people in terms of drug delivery and collection of medical information, and this idea should be investigated in a future study. fourth, steps should be taken to build a more peoplecentered primary care system. several long-standing limitations to china's primary care system, particularly the shortage of professional human resources, substantially increased the difficulty of epidemic control in the community. pcps in china are paid low wages and minimal benefits, receive inadequate training, and experience high rates of occupational burnout, which impede pcps' delivery of integrated and highquality care. therefore, the primary care system should ensure an adequate total income and strengthen the career development opportunities for pcps. there are several limitations in our study. first, the results may not be generalizable to other regions of china because we only interviewed pcps in four provinces. second, pcps other than clinicians (e.g., nurse practitioners) were not included in our study because their scope of responsibilities was narrower than that for clinicians. third, our study was not designed to compare the differences between urban and rural areas. finally, we were unable to triangulate the results with those from other stakeholders, such as policymakers and community workers, but we will consider this in future studies. pcps in china perceived a series of barriers in confronting the covid- epidemic, which had positive and negative effects on their physical and mental health. therefore, effective approaches are urgently needed to help pcps overcome these barriers and work in an orderly and efficient manner. the current findings offer important lessons for policymakers and leaders for improving future control measures. in addition, they highlight the importance of developing the primary care system to strengthen preparedness and response to upcoming health challenges. emerging understandings of -ncov coronavirus infections-more than just the common cold latest data on novel coronavirus who strategic and technical advisory group for infectious hazards. covid- : towards controlling of a pandemic responding to covid- -a once-in-a-century pandemic? national health commission of the people's republic of china. nearly million primary care practitioners are participating in prevention and control of the epidemic outbreak contributions and challenges of general practitioners in china fighting against the novel coronavirus crisis covid- : notes from the frontline, singapore's primary healthcare perspective response of general practitioners to infectious disease public health crises: an integrative systematic review of the literature challenges of the pandemic response in primary care during prevaccination period: a qualitative study survey on the difficulties, needs and psychological status of general practitioners in community-based prevention and control of the covid- epidemic primary care physicians in hong kong and canada-how did their practices differ during the sars epidemic? how infectious disease outbreaks affect community-based primary care physicians: comparing the sars and h n epidemics post-sars 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thematic analysis covid- : gps call for same personal protective equipment as hospital doctors covid- : don't forget the impact on us family physicians supporting the health care workforce during the covid- global epidemic timely mental health care for the novel coronavirus outbreak is urgently needed factors associated with mental health outcomes among health care workers exposed to coronavirus disease occurrence, prevention, and management of the psychological effects of emerging virus outbreaks on healthcare workers: rapid review and metaanalysis online mental health services in china during the covid- outbreak understanding and addressing sources of anxiety among health care professionals during the covid- pandemic national uk programme of community health workers for covid- response early appraisal of china' s huge and complex health-care reforms the primary healthcare system in china acknowledgments: the authors would like to thank frontline primary care practitioners who participated in this study for their timely feedback and contributions to the epidemic control. the authors declare that they do not have a conflict of interest.open access this article is licensed under a creative commons attribution . international license, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the creative commons licence, and indicate if changes were made. the images or other third party material in this article are included in the article's creative commons licence, unless indicated otherwise in a credit line to the material. if material is not included in the article's creative commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. to view a copy of this licence, visit http://creativecommons. org/licenses/by/ . /. key: cord- - x kdv authors: fu, you-lei; liang, kuei-chia title: fuzzy logic programming and adaptable design of medical products for the covid- anti-epidemic normalization date: - - journal: comput methods programs biomed doi: . /j.cmpb. . sha: doc_id: cord_uid: x kdv background: the covid- prevention and control constantly affects lives worldwide. in this paper, household medical products were analyzed. considering the household anti-epidemic status, economic and environmental benefits, the adaptable design method of anti-epidemic products in the vestibule was proposed. the measure of adaptable design method still have shortcomings. therefore, an improved method that is based on fuzzy logic programming is required. method: firstly, common medical product types used in vestibules and household anti-epidemic products were identified and summarized into product sets through the literature review, focus groups and questionnaires. then matching degree matrix was obtained by functional configuration decomposition and matching calculations. secondly, experts were invited to evaluate the paired comparative probability matrices and linguistic variables, and the evaluation data were converted by trapezoidal membership functions, fuzzy numbers and the defuzzification method to obtain the usage probability values for product functions. finally, the matching degree value and the product function were calculated by adaptability measure formula, and product function, the adaptability factor and the adaptability were obtained. results: our results show that the degree of adaptability of each product function in the product set. the higher value of the product function, the more it can be prioritized for design development with functional cost savings, simplification or clustering. conclusion: this study proposes an adaptable design method based on fuzzy logic programming. the data results in this study can guide the development and programming of the vestibule anti-epidemic products. the higher adaptability value of a product function indicates that it is more capable of being simplified, clustered, and adapting to changes in the product set. since , coronavirus (covid- ) has spread to many countries［ ］［ ］. during the covid- epidemic, "social distancing measures" is still recognized as the most effective approach［ ］［ ］ in the absence of any vaccine or treatment. considering the epidemic situation, "home quarantine" was recommended as a preventive measure to protect both oneself and others by physically isolating the infected from communities and preventing second-and third-generation cases development［ ］. "self-quarantine" was originally proposed, namely covid- infected individuals were prevented from contacting with others; eventually it evolved to that all public "stays at home" for quarantine as much as possible to prevent epidemic spread, regardless of a person with or without infected symptoms of since , the number of confirmed covid- cases in china has been on a downward trend. the government has begun to coordinate epidemic prevention and control with economic social development efforts. china began to fully promote work and production resumption under the anti-epidemic normalization. the concept of "new normalization" is introduced and discussed by numerous social media posts, online newspapers, portals and forums, and academic platforms［ ］. the "normalization" concept will eventually become a stable reality and normality state, influencing the future lives and work of the public. however, due to the sudden outbreak of the covid- epidemic, the preparation in the households is not adequately made for home self-quarantine and residential spaces are not designed for epidemic prevention factors. as a result, anti-epidemic supplies are temporarily placed in specific locations in the house during the epidemic period; there is a lack of standard design patterns for placement and usage due to different types and conditions of residential spaces. under the "covid- anti-epidemic normalization" concept, the placement and usage of household anti-epidemic items need to be improved from the perspective of the long-term usage. as a connecting area with outdoor, the vestibule is an important separating part from outdoor with protective and purifying characteristics. in this study, the residential vestibule space is used as an important area for home epidemic prevention, and a design and development method is proposed, in which general household anti-epidemic products are combined with common products used in residential vestibules. finally, epidemic prevention functions are integrated into houses to extend the usage time and application of anti-epidemic products. besides, an improved adaptable design methodology is used for the design development of household anti-epidemic products at vestibules. previous method of evaluating usage probability or frequency of the product functions, which is predicted by specific information such as previous sales records and market research. many decision-making methods, such as the analytic hierarchy process (ahp), elimination et choice translating reality (electre) and borda count method, are based on paired comparative judgment matrix. in other words, these methods greatly rely on the decision maker's intuitive judgment to evaluate things that cannot be physically measured. with the decision maker's relevant knowledge and experience, the real situation could be reflected［ ］［ ］. since the usage probability of product functions is influenced by lifestyle and culture, there is randomness and fuzziness in pf usage. in usage probability of multiple products often is uncertain and imprecise. the use of fuzzy theory allows uncertain and subjective probabilities to be evaluated. fuzzy set theory, and probability theory are no substitutes, but they complement each other. although fuzzy set theory has quite a number of "degrees of freedom" in the intersection and union operators, different kinds of fuzzy sets (membership functions), probability theory is well-developed and uniquely defined in the operation and structure. fuzzy set theory seems to be more adaptable to different contexts. this, of course, also implies the need to adapt the theory to a context if one wants it to be an appropriate modeling tool. therefore, in this study, the paired comparison judgment matrix technique in the usage decision-making method is proposed and combined with fuzzy theory to obtain the usage probability value of pf through expert evaluation. linguistic variables, trapezoidal membership functions, and fuzzy sets of the probability are selected. experts use the linguistic variable of the probability to evaluate, and then translate the values into fuzzy numbers, and finally defuzzification is carried out. the linguistic variables provide a basis for dealing in a systematic fashion with systems that are too complex or too ill-defined to be amenable to analysis by conventional probability-based methods. the concept of a linguistic variable reflects the fact that most of human reasoning is approximate rather than exact, and that the values of variables in human discourse are usually expressed in words rather than numbers. linguistic variable takes words in the natural language as values, providing appropriate subjective judgment expressions. linguistic variable is used to process complex, unclear or ambiguous information to express the computable "possibility"［ ］. since subjective expressions have a considerable degree of ambiguity, the fuzzy logical concept can be employed to describe the usage probability of product functions. van laarhoven and pedrycz applied the fuzzy concept to paired comparison matrix to deal with subjectivity, inaccuracy and ambiguity in decision-makers' judgments［ ］. buckley used ladder fuzzy numbers transforming expert opinions into a fuzzy matrix［ ］. zimmerman proposed a classical set of "probabilistic" linguistic variables examples based on zadeh's fuzzy logic and fuzzy probability, such as: {almost impossible, not very probable, very probable, almost certain}［ ］. halliwell proposed a linguistic bayesian network method to measure the linguistic probability and fuzzy numbers, such as: {impossible, very unlikely, nearly impossible, quite unlikely, even chance, very likely, quite likely, nearly certain, certain} ［ ］. lower et al. proposed the probability affiliation function of the semantic variable for event occurrence and the use of degree adjective language expressions, like: {extremely improbable, very rare, average, probable, frequent} ［ ］ , allowing assessors to use semantic vocabulary to judge the probability occurrence degree. the trapezoidal membership functions is to solve the problem in uncertain environment. in the study shall characterize some transformation functions between the linguistic and numerical expression domains. any linguistic label has its associated fuzzy number. in this study, the probability of product function (pf) usage is determined, the fuzzy set corresponding to the semantic variable is denoted using trapezoidal membership functions with parameters (a, b, c, d) . as shown in figure , the positive trapezoidal fuzzy number is defined as n , and n = (a, b, c, d), and its membership function［ ］ is defined by the following formula: ( ) according to the nature of trapezoidal membership functions and the expansion principle［ ］, it is assumed that there are two trapezoidal fuzzy numbers n = (a , b , c , d ) and n = (a , b , c , d ), which are calculated as follows: the semantic variables and trapezoidal fuzzy numbers used in this study are shown in table . delgado et al. defined a linguistic-numerical transformation function, which obtains a numerical value from a given label. the process of converting fuzzy numbers to clear values is called "defuzzification"［ ］. therefore, the method of defuzzification is the value of a fuzzy number. from the overall perspective of a positive trapezoidal fuzzy number, the central part is the region expressing the best importance, and the fuzzy assessment value ij n % = (a ij , b ij , c ij , d ij ) can be defuzzied (in terms of ij n r ) by the center-value method formula as follows: home self-quarantine behaviors can effectively delay virus transmission［ ］ ［ ］. although covid- transmission risk between individuals is much greater than that through surfaces, using cleaning products such as disinfectant wipes or disinfectant sprays to clean and disinfect high-frequency contacted surfaces at least once every day (even if you do not go outdoors) is recommended by the center for disease control and prevention (cdc)［ ］. the recommendations of anti-epidemic products proposed by world health organization's (who) are as follows: ( ) clean hands regularly and thoroughly with alcohol-based hand sanitizer, or wash hands with soap and water; ( ) avoid contact with eyes, nose and mouth; ( ) ensure that you and people around you maintain good respiratory hygiene; ( ) seek medical attention if you suffer from any fever, cough, and difficulty breathing, call in advance if possible and follow the instructions of local health authorities. household anti-epidemic products［ ］ include thermometers, disposable medical masks, medical-surgical masks or n /kn masks, and household disinfection products, etc. this study presents the definition of household anti-epidemic products. firstly, according to the recommendations of anti-epidemic products proposed by world health organization's (who) and center for disease control and prevention (cdc). secondly, obtain data of product selection through online survey. finally, major household anti-epidemic products were analyzed by the chi-square test. in practice, residential space usage is defined by resident preferences［ ］. it is not just a structure but a space created for a set of complex purposes［ ］ . with the change of cultural values and practices, the psychological needs and the residential function are changing［ ］. abercrombie believes that an architecture entrance is both a physical and psychological turning point, which brings out people's memory of indoor and outdoor environment here, and the psychological expectations based on this memory［ ］. the east asian traditional residential entrance is a transitional area between indoor and outdoor, generally known as the vestibule in china［ ］, "genkan" in japan, and "hyun-gwan" in korea［ ］. after the introduction of western architectural forms into china in the th century, vestibule space in modern chinese houses remains the progressive concept of barrier and protection. besides, influenced by japanese genkan the additional purifying function, vestibule functions that blend eastern and western living styles are gradually developed. at present, functionality is more emphasized by vestibule, and vestibule is connected with purification rituals to remove "impurities from outdoor". for example, before entering vestibule, you may need to remove your shoes, jacket and hat, making sure the clothes are neat and tidy. therefore, the selected product is related to concept of barrier, taking off shoes and clothes. adaptable design was proposed by gu for efficient and effective products design for functionality, manufacturing, customization and environment. adaptable design is a design model that balances economic and environmental benefits. the basic idea of adaptable design is to design products with adaptability to meet new demands, or to reuse products and designs as the environment changes, and adaptability is defined as an extension of the product's utility (service) ［ ］. the principle of existing solutions remain essentially unchanged, and local changes are made to existing products to extend the product life or to expand products' applications. "adaptable design" achieves "saving" by adapting and reusing existing products based on their functionality, and comparative analysis in the design decision process can be made in a quantifiable way along with other design criteria. adaptable design includes both design adaptability and product adaptability. design adaptability aims at reusing the same "design" for the creation of different products. product adaptability refers to the ability of a product to be adapted to various usages or capabilities. sand and gu developed modular and upgraded planning methods for the adaptable design, and applied them by examples ［ ］. fletcher et al. proposed a quantitative calculation method for adaptability［ ］. xu et al. proposed an adaptable redesign and improved the metrics by quantifying the structural similarity and performance brought by adaptable design［ ］. since the adaptable design theory concept was proposed, many adaptable design methods and applications have been further developed and improved in the past decade ［ ］ . to quantitatively evaluate the resource-saving effect of product platform design, chen et al. proposed an adaptability-oriented parametric product platform construction method［ ］. based on the similarity analysis, chen et al. combined the information entropy concept with the product modularity principle, and proposed an improved adaptability calculation using the adaptable information entropy function to characterize the product boom complexity and uncertainty［ ］. adaptable design method is the process of "adapting" an existing design, usually results in savings in development time, design and production costs. if the product itself is adaptable, it benefits the user by replacing several products with one or by providing more functionalities. in any case, there are also environmental benefits based on the fact that adaptable design encourages the reuse of existing entities. the adaptable design is often used for discrete products. since vestibule anti-epidemic products consist of multiple sub-products, each sub-product is independent and related to each other, and has the characteristics of discrete products, it is suitable to use the adaptable design method for design and development. in order to integrate anti-epidemic products into the vestibule, while reducing the cost and time of design development and extending the life cycle of the products, and thus, they are able to adapt to the changes in the covid- anti-epidemic normalization and the social environment. firstly, the recommendations for household epidemic prevention and the characteristics of residential vestibules are explored through the literature review in this study. then a combination of literature and questionnaires is used to summarize the categories of household anti-epidemic supplies and products commonly used in the vestibule, and the two product categories are aggregated into a target adaptable set. secondly, the functional configuration of each product is then separated one by one. finally, the adaptability metric is then carried out, and adaptable design applications are developed based on the adaptability value level of the pf (figure ). a survey was designed based on who, cdc and expert recommendations for anti-epidemic, combined with a focus group approach to further identify acceptable household anti-epidemic products for families. focus groups are becoming increasingly popular in health research for exploring what individuals believe or feel as well as why they behave in the way they do.it can be used to understand, and explain, the meanings, beliefs and cultures that influence the feelings, attitudes and behaviours of individuals. properly conducted focus groups are not necessarily inexpensive; unless one is in the business of conducting and analyzing focus groups, the time saved in interviewing may be lost in recruitment, logistics, and trying to make sense out of data that are complex and messy. krueger and casey suggested that focus groups can be used to assess demands and assets, develop social marketing efforts, pilot-test ideas and products, and evaluate services or programs［ ］. group members linked their experiences and reflection, and some common reference frames may emerge among members［ ］. the number of focus group members is usually - , as smaller groups show greater potential ［ ］. eight criteria for focus groups work based on krueger's research was proposed by rabiee［ ］, serving as the main basis for the implementation of the focus group approach in this study. eight criteria are as follows: words, context, internal consistency, frequency, intensity of comments, specificity of responses, extensiveness, and big picture. the focus groups consists of members (n= ) with design-based backgrounds including health attendant, medical product engineer, medical doctor, nurse and medical trainee ( table ). the purpose was to discuss the influencing factors of "household anti-epidemic" from multiple perspectives, so as to develop a questionnaire. after three rounds of discussion, a consensus was reached as follows: factors such as family members, living conditions, knowledge of epidemic prevention information, disinfection habits and acceptable cost of epidemic prevention have a great influence on household epidemic prevention. therefore, a questionnaire on "household anti-epidemic condition" was drafted in four parts including " participants' personal information", "knowledge of epidemic prevention", "household epidemic prevention habits" and " household anti-epidemic products consumption". besides, the descriptive language was used to make it easier for participants to make judgments based on their actual situations. through the "questionnaire star" software, the online survey was conducted between april and may , . based on the adaptable design theory proposed by gu［ ］, an improved adaptability measure is developed by combining the paired comparison matrix technique and fuzzy theory in this study. the formula for matching adaptability factors to product functionality is as follows: in equation ( ), tp=pf i |pf j denotes a tp, pf denotes a product function unit with a functional configuration set, and tp is the conversion of the product from pf j to pf i through an adaptable process. p (pf i |pf j ) denotes the functional configuration matching degree when converting pf j is converted to pf i through an adaptable process. pr (pf i |pf j ) denotes pfi usage probability when users have pf j , and is the weighted value for the functional configuration matching degree. as the adaptability factor (af) of tp, af (tp) is defined as the degree of adaptable conversion from pf j into pfi, i.e. the product of pfi matching degree and pf i usage probability. note that p denotes the functional configuration matching degree when converting pf j is converted to pf i through an adaptable process. p is the summed average of the column entries in the p tp matrix. in equation ( ), pf i ∩pf j represents the pf i and pf j shared functional configurations set; inf (pf i ∩pf j ) represents the sum of generalized costs of pf i and pf j shared functional configurations set, i.e. the resources sum consumed by shared functional configurations set; these shared configurations cost is preserved during the pf j to pf i conversion; inf (pf i ) represents the sum of broad costs of all functional configurations of pf i , i.e. the sum of resources consumed in designing the product. af (tpi)=af (pf i |pf j ) indicates that the adaptable capacity of pf i to become pf j . similarities in function or constraints between pf i and pf j can be one or more. the adaptability factor (af) has a value range of [ , ]. if af = , then pf i has no common part at all and the pf j and the pf i cannot be reused by modifying the pf j ; if <af< , pf i and pf j have common parts, and partial pf i can be reused in pf j through modification; if af= , pf i and pf j are the same, and no modification is needed. the summed average of the adaptability factors for each pf j transformed into a pf i within the tp is the adaptability for each pfi, given by the following formula: in equation ( ), a (pf i ) denotes the pf i adaptability, the larger the value, the better the adaptability of the pf i . the "vestibule anti-epidemic products set" gathered from literature and questionnaires is defined as " target adaptable set " and then adaptability metric, specific steps are conducted as follows: . definition of adaptable design objectives and products: the types of products commonly used in the vestibule and household anti-epidemic products are determined according to customers' demands. . solution planning for product function configuration: customers' requirements are matched with corresponding functions to determine the main functions and restraints of target products, and functional configuration is established through case studies. . commonality check of the functional configuration: compare and analyze the commonalities between "product functions", including the similarities between functions and usage states. the determination of these commonalities can be used to develop shared or clustered content for new product designs. . judgment of the product usage probability: based on the expert evaluation method, the usage probability of "product functions" with each other is judged to get usage frequency of each product in the whole system, which is as the weight of the common functions for the function configuration. . adaptability measurement and design: the adaptability value of the " vestibule anti-epidemic products set" is calculated, and the results are ranked according to the adaptability degree. the "product function" which should be prioritized for adaptable design is determined to save costs and adapt to demand. literature and questionnaires were used to obtain basic types of vestibule products and household anti-epidemic products, as the basis for establishing the image relationship between products and functions. a function-based design process model was developed, which was derived from a process model similar to the axiomatic design proposed by suh［ ］. axiomatic design categorizes design activities into customer domain, functional domain, physical domain and process domain, which provides a framework for mapping between the function-structure of a product, and parametric techniques, which combine to provide a model for rapid product design. in this study, the function and anti-epidemic requirements of a residential vestibule correspond to customer domain, the required product types correspond to the functional domain, and the function configuration consisting of numerous functions and constraints corresponds to physical domain. the function configuration expression is defined as a functional structure consisting of matter, energy, and signal ［ ］ , ［ ］ . the transfer of matter, energy and signal of a product is an inherent property of its physical functions, which is used to identify the product's operational activities and utilities, and the function is achieved through its physical structure［ ］. figure shows the functional configuration decomposition of product. in equations ( ) and ( ), pr (pf i |pf j ) is the usage probability or frequency of the product functions, which is predicted by specific information such as previous sales records and market research. in this study, the usage probability of product functions is expressed as the probability of needing pf i when using pf j , however, the usage probability of the vestibule anti-epidemic product functions is difficult to be predicted by this method. therefore, the usage probability of a product is obtained by comparing pairs of products and is suitable for the use of the paired comparison judgment matrix technique. many unmeasurable objects or phenomena can be understood and judged with a precise and reliable relative scale, which can be ensured by integrating the experience of several experts. a focus group of experts was formed to assess the usage probability of vestibule anti-epidemic product functions. since the study involved the requirements of household usage and epidemic prevention measures, experts with professional and technical experience in design and health care were gathered, ensuring the relative high validity of the assessment results for the interoperability probability of product functions. group discussion was performed to promote the consensus of judgment, ensuring the high confidence of the results. moreover, the consensus of judgment was promoted with high results reliability. in the group discussion, the purpose and content of this study were introduced, the evaluation method was explained, as well as the product functions, usage scenarios and states. after discussion, the assessment was carried out using probabilistic semantic variables and paired comparison matrixes, and the assessment probability value was combined with fuzzy theory to obtain the probability value of pf usage in the end. the values of usage probability assessments for product functions were transformed into a matrix of probabilistic semantic variables, and then transformed into fuzzy probabilities, as shown in table . the geometric mean algorithm was used to synthesize experts' fuzzy probability matrix equation ( ). and finally the central value method (equation ) was used to obtain the probability judgment value ij n r for defuzzification. in this study, ij n r is defined as pr (pf i |pf j ) to obtain the likelihood of defuzzification of the usage probability for vestibule anti-epidemic products. where pr n is the fuzzy probability matrix for integrating the kth member; k pr n is the fuzzy probability matrix evaluated by the kth member; and k is the number of members. in the context of china, the main participants of this survey were concentrated in fujian ( . %) and jiangsu ( . %), followed by beijing ( . %) and zhejiang ( . %). because the epidemic was stabilized earlier in jiangsu and fujian, and also the work and production resumption started earlier, thereby giving respondents in both regions a higher level of understanding of the normalization of the epidemic. participants were involved, among which completed it. the majority of the respondents were between and years old ( . %), with the majority of the female, and their basic information is shown in table . more participants have selected "simple disinfection before entering the house" ( . %). . % of participants were disinfected for - minutes daily and . % were willing to disinfect once a day. in contrast, % were willing to disinfect - times a week. participants' price acceptance range for household anti-epidemic products was more likely to be within usd, and more households during the survey period have spent between - usd ( . %), followed by - usd ( . %), as shown in table a . in summary, more women than men have participated in the questionnaire survey, lived with their elders in three-bedroom houses, known more about personal epidemic prevention measures, and paid more attention to the daily epidemic changes in the city. most participants have simple disinfection behaviors at the door side when entering houses, and are willing to spend - minutes for disinfecting once daily or - times a week. there is also a consensus among the participants that three main types of products should be available at home: masks, disinfectants and thermometers. chi-square test was conducted for gender using software (figure ) . the results show that there is no significant difference between men and women in the question of necessary anti-epidemic products stocking at home ( = . , p= ( . > . ); in addition, chi-square test of different ages reveals that there is a significant difference between ages in the question of the necessary anti-epidemic products stocking at home ( = . , p= ( . < . ). however, after performing a chi-square test for different ages for the three generally accepted types of anti-epidemic products, it is learned that there is no significant difference ( = . , p= . > . ) ( figure ). to test for differences in the types of household anti-epidemic products demanded by different genders and ages. if there are no differences, this indicates that the subjects have a consensus on the choice of household anti-epidemic products. by comparing the price acceptance of anti-epidemic products with the current spending of households on that, it can be judged that most of them can accept less than usd. vestibule anti-epidemic products based on the literature and recommendations of experts (who and cdc), a commonly used and inexpensive product was chosen as the prototype for this study. the main household anti-epidemic demands are as follows: hand cleaning and disinfection, cleaning and disinfection of frequently contacted surfaces, respiratory hygiene, close attention to symptoms such as fever, and maintaining social distance. corresponding to anti-epidemic demands, the items are disinfectants, masks and thermometers. the disinfectants include products derived from disinfectant wipes and disinfectant sprays, and thermometers are the common handheld infrared ones (table a ) . based on the literature, the basic functional needs of the vestibule include: removal of shoes, coats and hats, social interaction between hosts and guests, and space blocking. common products corresponding to the vestibule functions are: shoe cabinets, shoe pullers, shoe changing stools, coat racks, doorbells, and partitions (table a ) . product is originally a single entity, but in this study, product is defined as a product function (pf) that consists of multiple functional configurations. since it was known from the survey that affordable and practical anti-epidemic products are more popular, vestibule anti-epidemic products ( table a and a ) are defined as tp, and each product was defined as product functional unit (pf) in this study. based on the principle of basic (essential) functional requirements, the corresponding product prototypes are selected from the market and the functional separation is carried out in terms of energy, matter and information. figure shows the functional configuration structure of the disinfectant wipes. this is an abstract and direct way to translate requirements into functional configurations, and the remaining nine products are constructed by this method to perform the adaptability measurement. the configuration construction of pf is conducted by two steps: ( ) decompose the elements or constraints that constitute the pf, and ( ) express them in common terms. multiple pfs can be decomposed through configuration analysis into configurations consisting of energy, matter, and signal. but since each pf is different, the described configurations also differ. therefore, describing similar types of configurations using common words allows for easy consistency, quantitative analysis and comparison of pf configuration expressions. as a result, the consistency of functional description is ensured, and the easy design analysis and quantification are realized. meanwhile, different types of product functions can be compared to find the similarity of design concepts from the essence. common words are used to express the configuration and draw a functional configuration matrix. the amount of configuration information is expressed as the numbers " " and " ". " " indicates that pf does not have this configuration, while " " indicates that the pf has this configuration ( table a ). according to the table, equation ( ) is applied to calculate the matching degree between the functions of each product. after calculation, the matching degree matrix p (tp) is obtained. from the table, we can see that "pf " is disinfectant wipes, pf ={ pinch , draw , unfold , press , cloth , plastic , liquid , stand , sit , squat , . m≤h≤ m , m≤h≤ m , flat , visual , tactile }; "pf " is disinfectant spray, pf = hydraulic , pneumatic , pull , press , grip , plastic , liquid , stand , sit , squat , . m≤h≤ m , m≤h≤ m , flat , standing , visual , tactile }. the p-values of "pf " and "pf " are derived and calculated as follows: ( ) table shows the function match matrix for the product categories, indicating the matching degree between pf j and pf i when "pf j " is adaptable transformed into "pf i ". the higher value, the better match of the functional configuration. p is the summed average of the column entries in the matrix, a higher value indicates a higher similarity that the pf is to other pf in this set. p is between . and . , and the larger the value, the more appropriate the matching of pfj to the functional configuration of pfi. it can be seen that the functional configurations of the products for different applications match each other differently. for example, p-value is . if pf (disinfectant spray) is converted to pf (disinfectant wipes), but p-value is . for the conversion of pf to pf . it indicates that the functional configuration of the disinfectant spray can be more adaptable when converted to disinfectant wipes. when hand sanitizing, it is necessary to get antiseptic wipes or disinfectant spray from a shoe drawer, or get them while sitting on a shoe changing stool. hence, there is a usage correlation between the need for hand sanitizing and the use of multiple products. in this study, a paired comparison matrix of product functions is used to evaluate usage probability through the re-use of focus groups. the group consists of experts in both design, engineering, medical and health care fields with years of experience in practice, research and education (table a ) . firstly, experts with experience in vaccination work are selected. secondly, focus groups are used so that the experts have a good understanding of the problem, and finally, multiple discussions are held before making an assessment. the focus group discussion was conducted in the context of the anti-epidemic normalization in family life, focusing on prevention and maintenance of personal hygiene and safety in thoughts and behaviors. group members were asked to make initial judgments based on their professional experience. usage probability semantic variable (table ) determines the likelihood (probability) that "pf i " will be used when "pf j " is used. instead of probabilistic semantic variables, members make assessments using values of " , , , , " to express the probability. for example, when "pf j " is used, the need to use "pf i " is straightforward and frequent, the number " " is used; when the needing is average, " " is used; when it is extremely improbable to be used at all, " " is used. after group discussion and evaluation, there were paired comparisons with a cronbach α coefficient = . , indicating the high quality of the study data confidence level. after analyzing the variation degree assessed by members, the standard deviation was found to be between . and . , with a standard deviation < . there were comparisons and comparisons with standard deviations ≥ ( table a ) . the values of usage probability assessments for product functions were transformed into a matrix of probabilistic semantic variables, and then transformed into fuzzy probabilities ( table ). the geometric mean algorithm is less influenced by extreme values, so it is reasonable to use this method to respect the views of the experts and synthesize their assessments hierarchically. the geometric mean algorithm was used to synthesize experts' fuzzy probability matrix equation ( ), and finally the equation ( ) was used to obtain the probability judgment value ij n r for defuzzification. in this study, ij n r is defined as pr (pf i |pf j ) to obtain the likelihood of defuzzification of the usage probability matrix pr tp ( table ) for vestibule anti-epidemic products. finally, pr is the summed average of the column entries in the matrix. the pr value of "pf" is . - . . a higher value indicates a higher probability that the pf will be used in the set. according to equation ( ), the adaptability factor af (pf i |pf j ) is the product of product function usage probability pr (pf i |pf j ) and the matching degree p (pf i |pf j ). in this study, pr (pf i |pf j ) is replaced with the probability judgment value of defuzzification, so af(pf ) is calculated as in equation ( ). af tp matrix is derived ( table ) , from which the adaptability factor of the target adaptable set is known, and the higher value indicates the higher feasibility when pf j is transformed or clustered into pf i . according to equation ( ), the adaptability a (pf i ) is . - . , the higher the value, the higher the adaptability of pf. the highest value of adaptability in the set is pf (a= . ) and the lowest probability is pf (a= . ). in this study, the functional decomposition of matter, energy and information in the product is based on the input and output case, and the matching degree p-value is calculated based on the segmentation of functional configuration, and the product functional matching degree matrix (p tp ) is obtained. the usage probability of product functions in space is a rather vague concept, and there are independence and connectedness in various product usage. to accurately explore the interconnectedness of product use, a focus group approach is proposed by the paired comparison matrix technique in this study to assess pf usage probability. subsequently, a focus group approach is combined with fuzzy theory to obtain more accurate probability values and matrices of product use. finally, the probability matrix and the matching degree matrix are multiplied to obtain the adaptable factor matrix (af tp ), and adaptability a values (figure ). if the functional configuration between all products in the set is the same (p= ) and the usage probability is also the highest value (pr= ), then af= , the ideal maximum a value for the set should be . however, the highest a value in the set of actual product functions is . , which is a large difference from the ideal maximum a value, indicating that the similarity of the product functional configurations in a set and their mutual use are not strong. since the relative adaptability values among the products are mainly investigated in this study, the higher a value of a product indicates that it is more capable of being simplified, clustered, and adapting to changes in the set. based on adaptability (a) values, prioritized product functions for simplifying or clustering in design thinking can be determined by a comparative analysis. the most adaptable one in this set is pf , followed by pf , and the third ones are pf , pf , pf and pf , indicating that they are simplified or clustered with other products to a high degree. therefore, disinfectant sprays can be prioritized for adaptable design development. this study is based on chinese households and respondents, but the vestibule anti-epidemic products selected are internationally available. the fuzzy logic programming and adaptable design method proposed in this study are not limited by regions and can be applied to other countries and regions. previous research on adaptable design methods has been applied to single products, modular products, and product families. in this study, an adaptable measure of products set within a specific functional space is innovatively proposed and a new method for assessing the functional product usage probability is introduced. besides, focus group method was used twice: ( ) the first use for discussing and developing a questionnaire on the "household anti-epidemic state"; designers, researchers and educators with design backgrounds were involved to generate additional concepts; ( ) the second use for improving the assessment of pf usage probability in the adaptability metric; experts from design and health care backgrounds were involved to obtain accurate and broad-valued probability results. however, the results produced by the focus group method are limited by the professional background, experience and cultural factors of the members. since the adaptable design method in this study is based on the existing products and requirements, reuse of the existing product functional configurations for developing new designs, there are some limitations on the presumption of new product functional development. moreover, in the calculation of the adaptability degree, a detailed degree of decomposition for product functional configuration will affect the adaptability degree and design development. the adaptable design in this study is aimed at design adaptability. therefore, considering that specific physical parameters can constrain the diversity and possibilities of design thinking, the pf configuration analysis is not refined to specific physical parameters in order for the results to guide design ideas and make the product more creative. based on the basic configuration and product functions usage probability, physical attributes such as quantity, size, and form corresponding to the functional configuration are not evaluated. in future studies, product parameters can be refined and taguchi methods can be used to conduct product optimization design through the experimental process. the authors declare that there is no conflict of interests. table a . household anti-epidemic habits and consumption. table a . household anti-epidemic products and common products in the vestibule. table a . vestibule anti-epidemic products set -legend of product types. table a . vestibule anti-epidemic products set (based on this research). table a . product set function configuration matrix (mtp). table no. table no. doorbell (d) the control signal generated by the button drives the electrical energy to make the doorbell sound. a chair for changing shoes in a sitting position. screen (s) an object used to keep out the wind, to separate or to block the line of sight. diagnosis and treatment for covid- (trial version ) covid- timeline, uk perspectives by flora holmes using social and behaviour al science to support covid- pandemic response isolation, quarantine, social distancing and community containment: pivotal role for old-style public health measures in the novel coronavirus ( -ncov) outbreak first-wave covid- transmissibility and severity in china outside hubei after control measures, and second-wave scenario 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analysis. fuzzy sets and systems fuzzy logic and approximate reasoning. fuzzy set theory and its application linguistic probabilities: theory and application analysis of air traffic incidents using event trees with fuzzy probabilities. fuzzy sets and systems introduction to fuzzy arithmetic: theory and applications fuzzy sets and fuzzy logic theory and applications combining numerical and linguistic information in-group decision-making covid- ) advice for t he public emotional responses to prosocial messages increase willingness to self-isolate during the covid- pandemic. p syarxiv ［ ］center for disease control and prevention. cleaning and disinfection fo r households polyvalence, a concept for the sustainable dwelling house form and culture culture and the self: implication for cognition, emotion, and motivation boundaries and openings: spatial strategies in the chinese dwelling constructing the colonized land: entwined perspectives of east asia around wwii adaptex: extending product life cycles through strategic product upgrades product and design adaptability quantification adaptable design of machine tools structures adaptable design: concepts, methods and applications adaptability-oriented parametric product platform design. computer integrated manufacturing systems measurement method and application of adaptability for mechanical products focus groups: a practical guide for applied research getting the focus and the group: enhancing analytical rigor in focus group research focus-group interview and data analysis a reverse engineering and redesign methodology for product evolution functional analysis: a fundamental empirical study for reverse engineering, benchmarking and redesign. proceeding of the design engineering technical conferences product design:techniques in reverse engineering and new product development. beijing: publishing house of electronics industry the authors would like to thank the department of mathematics of national taiwan normal university for helping to analyze and verify the accuracy of fuzzy logic applications in their paper. key: cord- -r k ob authors: raina macintyre, c.; engells, thomas edward; scotch, matthew; heslop, david james; gumel, abba b.; poste, george; chen, xin; herche, wesley; steinhöfel, kathleen; lim, samsung; broom, alex title: converging and emerging threats to health security date: - - journal: environ syst decis doi: . /s - - - sha: doc_id: cord_uid: r k ob advances in biological sciences have outpaced regulatory and legal frameworks for biosecurity. simultaneously, there has been a convergence of scientific disciplines such as synthetic biology, data science, advanced computing and many other technologies, which all have applications in health. for example, advances in cybercrime methods have created ransomware attacks on hospitals, which can cripple health systems and threaten human life. new kinds of biological weapons which fall outside of traditional cold war era thinking can be created synthetically using genetic code. these convergent trajectories are dramatically expanding the repertoire of methods which can be used for benefit or harm. we describe a new risk landscape for which there are few precedents, and where regulation and mitigation are a challenge. rapidly evolving patterns of technology convergence and proliferation of dual-use risks expose inadequate societal preparedness. we outline examples in the areas of biological weapons, antimicrobial resistance, laboratory security and cybersecurity in health care. new challenges in health security such as precision harm in medicine can no longer be addressed within the isolated vertical silo of health, but require cross-disciplinary solutions from other fields. nor can they cannot be managed effectively by individual countries. we outline the case for new cross-disciplinary approaches in risk analysis to an altered risk landscape. few precedents or analytical tools. these technologies are increasingly available to hostile states and non-state terrorist groups. the rapidly evolving landscape of dual-use risks illustrates how societal preparedness for new challenges in health security can no longer be addressed within isolated vertical siloes. nor can they cannot be managed effectively by individual countries. well-recognised threats in the areas of biological weapons, surveillance for bioterrorism, laboratory security and antimicrobial resistance are discussed. we also highlight emerging new areas of threat in the intersection of health security and cybersecurity and enabling of precision harm through big data in medicine. against this backdrop, we outline below the need for new governance and risk analysis approaches that are global and cross-disciplinary. it has been possible since to create synthetic viruses in a laboratory, when researchers at the state university of new york at stony brook published the synthesis of the poliovirus in science (cello et al. ). there are now over private companies in synthetic biology (global engage ), which are self-regulated with voluntary codes of conduct (samuel et al. ). whilst prior biosecurity efforts focused on the biological materials themselves and the inherent challenges of securing and accounting for these materials within laboratories, genetic code can now be transmitted rapidly and used to create new or modified infectious pathogens (kelle ). in the specific case of synthetic infectious agents, the unique characteristic of transmissibility from person-to-person raises special concerns about health security. a virus manufactured in one location may spread worldwide and has a major population impact, thus requiring a global risk mitigation approach. the global regulation of synthetic biology pertaining to communicable diseases is challenging, with many models proposed . the tapic (transparency, accountability, participation, integrity and policy capacity) framework provides a guide to good governance (trump ) , but there is no enforceable global governance system in place as yet. the many private synthetic biology companies worldwide remain self-regulated, with voluntary guidelines about reporting of suspicious orders. a case in point is smallpox, for which the genome is fully sequenced and publicly available. in a report, the who (world health organization d) concluded that destroying existing stocks of smallpox in the usa and russia would serve no purpose because the virus can be created using synthetic biology. whilst it is theoretically possible for smallpox to be synthesised in a laboratory, experts have believed this to be a complex task. however, in , canadian scientists synthetically created an extinct poxvirus, closely related to smallpox, for $ , in a laboratory using mail-ordered genetic sequences (koblentz ) , illustrating the very real risk of synthetic smallpox emerging as the cause of a pandemic. in addition to synthetic biology, viruses and bacteria can be engineered for enhanced pathogenicity. a revolutionary new precision tool for gene editing, clustered regularly interspaced short palindromic repeats (crispr cas ) associated nuclease cas , raises concerns about dual-use potential (ran et al. ) . whilst crispr cas offers the prospect of cures to major diseases, it also enables the precision design and construction of engineered microorganisms as potential weapons of mass destruction. in , the us director of national intelligence rated crispr cas as a leading weapon of mass destruction threat (mit technology review ). yet global planning for bioterrorism preparedness is still largely framed by cold war concepts and is largely limited to scenarios involving agents such as smallpox and anthrax in a twentieth-century context. however, contemporary biology presents an expanded threat spectrum with an unlimited array of possible engineered agents that transcend the scope of traditional concepts of biosecurity surveillance, preparedness and counter-measures. the convergence of security threats is illustrated by the use enabling technologies such as the dark web for trade in biological weapons and planning of bioterrorist attacks (macintyre ). a natural epidemic is one which arises in nature, without intervention by humans. unnatural epidemics are those which are caused by human intervention and may be deliberate or accidental release of either naturally occurring or altered pathogens. bioterrorism is the deliberate release of such pathogens to cause harm (venkatesh and memish ) . bioterrorism differs from other forms of terrorism in that a bioweapon is microscopic and invisible, and release of a bioweapon is not always recognisable as a deliberate attack (macintyre and engells ). all category a bioterrorism agents except smallpox also occur in nature. for example, anthrax occurs more frequently in nature (such as through humans handling infected animal carcasses) than as a bioterrorism attack (fong and alibek ) . planning for bioterrorism is underpinned by the assumption that attacks will be recognised as unnatural, but no public health systems exist to differentiate the aetiology of epidemics. tools such as the grunow and finke ( ) criteria are not well known in public health and have low sensitivity for detecting unnatural epidemics when tested against historical events (chen et al. ; macintyre and engells ) . public health agencies do not routinely use such tools and default to the assumption that they all epidemics are natural (macintyre ). there has been an unprecedented increase in the frequency of serious global epidemic risks such as ebola, avian influenza, mers coronavirus and zika virus in recent years (sands et al. ). this cannot be explained solely by environmental and ecological factors, which have changed at a slower rate than the increase in emerging infections. in a recent analysis , we documented that the rate of emergence of new strains of influenza virus infecting humans is escalating at an unprecedented rate, thereby increasing the probability of a pandemic. changes in climate, urbanisation and agricultural practices as well as improved global surveillance may have some role in this phenomenon, but have not changed at the same rapid rate as virus evolution. whether some of these new outbreaks involve engineered agents is unknown and has not been publicly analysed. historically, unnatural epidemics have not always been recognised at the time. for example, the rajneesh salmonella attack in oregon in was not only undetected as a bioterrorist attack, but when a local politician suggested bioterrorism, he was ridiculed by public health officials (mac-intyre ; török et al. ) . operation seaspray, which caused a serratia marcescens outbreak in san francisco in , was not recognised at the time as an open-air test by the us military, which was later disclosed in (wheat et al. ) . the accidental anthrax release in sverdlovsk, soviet union, , was investigated by us experts, who initially incorrectly believed the soviet explanation that it was a natural outbreak (the atlantic ). there are many other examples of failure to correctly identify unnatural epidemics (tucker and zilinskas ) . at a time when genetic engineering and synthetic biology contribute to increased risk of biological attacks, there is a need for new tools and risk analysis methods to rapidly identify unnatural epidemics. yet the grunow-finke criteria despite low sensitivity (macintyre and engells ) remain the best available tool. other tools have been developed but are even less known and used than the grunow-finke criteria (chen et al. ). in addition to risk analysis tools, rapid surveillance methods are required to detect unnatural epidemic signals. new methods for data mining of opensource unstructured data such as social media show promise for rapid epidemic intelligence (the conversation ) but have not yet been utilised for biosecurity (yan et al. ). laboratory safety has been highlighted as a key area of concern, with multiple breaches involving security sensitive pathogens in leading laboratories occurring in recent years (science ). research staff have the unique privilege of working with biological select agents and toxins and possibly the broader group of valuable biological materials (world health organization ), yet insider threat and laboratory accidents are known risks. a related issue is practical impacts of the emerging field of biorisk management in which the previously separate disciplines of biosafety and biosecurity are merged into a singular approach of laboratory biorisk management (cook-deegan et al. ; salerno and gaudioso ) so as to achieve the mutual goal of keeping these materials safe and secure within those areas designated for use and storage. several entities are proposing this combined approach to enhance the risk management process and produce safer laboratories and more secure practices for these materials (association of public health laboratories ). a far too common situation at advanced biomedical research laboratories is a problematic relationship between the researchers and security staff. those relationships must change to reflect a new reality-one in which the research scientist and the law enforcement official are considered members of the same team striving for a mutual goal. those working in laboratories should monitor each other to create a rigorous form of professional self-governance (garrett ) . the implementation of that change will be strategic, for it changes the focus from the substances (biological materials), which because these are alive can be freely found outside the laboratory and continue to defy accurate longterm measurement, to a focus on the behaviours of those who work with these substances-biomedical research scientists, public health officials, clinical laboratorians and others (aquino ) . another threat is a new facet to the insider threat-the potential for radicalisation of health care workers and researchers, for violent extremists continue to defy precise categorisation or predictable profiles and to infiltrate research institutions (macintyre and engells ). in the current age, we must move past our previous solutions dominated by guns, gates and guards and move to a new age in which enhanced personnel security practices through innovative uses of psychology and organisational dynamics will enhance individual and small group accountability and produce a safer laboratory and community at large. doit-yourself biology and biohacker labs fall outside of such systems of governance and are presently self-regulated, but the technology is easily accessible for terrorist groups to establish clandestine labs. no systems exist to detect such laboratories. the risk of emerging infections is increasing, whilst our ability to treat infections with antibiotics is decreasing. antibiotics represent one of the major public health achievements of the twentieth century, which together with vaccines are responsible for the dramatic reduction in morbidity and mortality caused by infections. whilst antimicrobial resistance is not new, its cascading global impact and threat to national and global security are considerable. within a decade, antimicrobial resistance, driven by prolific misuse in animals, humans and food production, and limited development of new antimicrobial options, will present a significant threat to humanity in the twenty-first century. a key solution is to judiciously use our remaining antibiotic options, yet even in relatively well-off organisation for economic cooperation and development (oecd) nations, antibiotic misuse continues virtually unabated in both the human and veterinary sectors (world health organization b). the world health organization ( b) and other key stakeholders have indicated the critical need for immediate global antimicrobial optimisation, reduction in unnecessary usage, and the roll-out of stewardship across health and agriculture sectors. for example, there has been a % global increase in use of last resort antimicrobials (carbapenems) over the last years, and both low-income countries and high-income countries are using substantially more antibiotics per capita than in previous decades (review on antimicrobial resistance ). as with other infectious diseases threats, a global response to this threat is urgently required, with human movement across national borders, threatening antimicrobial viability, even in countries with active surveillance and control programmes. the vertical management of antibiotic use in the human and animal sectors as well as in agriculture and food production must also be addressed in an integrated way, as the volume of use is much higher in these other sectors. a key strategy, in terms of policy, will be the adoption of the one health model for amr supported by who ( a), the eu, and the usa (centers for disease control and prevention ). whilst policy and regulation have progressed considerably in health care environments, a parallel set of strategies will need to be implemented in farming, agriculture and veterinary medicine, which account for around % of antibiotic use (food and drug administration ). thus far, strategies utilised across contexts have largely failed to set national targets to reduce antibiotic use in animal agriculture and nor mandate the collection of antibiotic usage data (martin et al. ) . consumer-led strategies-for example, the marketing of antibiotic free products-are one such strategy that may be used to promote sustainable use of antibiotics in the non-health sector (doyle et al. ) . increasing public awareness of the connections between animal and human health-a cornerstone of the one health approach-will be central to this strategy. there is growing recognition of the costs and significance of amr. multi-resistant organisms are emerging at much higher rates than seen previously, with urgent attention needed to mitigate a risk which is predicted in one report to be the greatest global burden of disease (review on antimicrobial resistance ). one recent estimate indicates that by , infections from resistant bacteria may overtake cancer as the leading cause of death in the world and cost us$ trillion. this estimate has been questioned and likely an overestimate, but amr nonetheless causes a significant burden of disease (de kraker et al. ). the world is in urgent need of new strategies in the human, animal, agricultural and food industries. this includes reviewing how we price/value antimicrobials, incentives for new antimicrobial development and judicious use, and restrictions around use across sectors. in addition, serious amr could be engineered and released as an act of bioterrorism, given the availability of technology such as crisp cas (macintyre and bui ). a longer-term model of population risk (versus immediate individual risk of often minor infection) is required to guide everyday use and mitigate this global threat. whether a bioterrorist attack, pandemic or infections complicated by amr, the risk is increasing as outlined above. infectious diseases do not respect international borders and can spread rapidly around the world. the continued growth in large urban areas, and megacities in particular, in which high population densities represent optimum conditions for spread of infection merits significant attention in biosecurity. this risk is heightened for megacities in developing countries in which serious gaps exist in public health surveillance for early detection of epidemic threats, together with inadequate critical infrastructure and other preparedness resources. prevention, mitigation and control of these threats, therefore, require efforts at local, national and global levels. despite the call for a one health approach (rabinowitz et al. ) , there is no suitable system for governing use of antimicrobials across human health, animal health and food production, and often no coordination of efforts across these sectors. in considering new technologies such as crispr cas (bulletin of the atomic scientists ). the cartagena protocol was developed to address regulation of movements of living modified organisms (lmos) resulting from biotechnology from one country to another, but has focused on ecology and biodiversity and has not been utilised for human biosecurity. the tapic framework (trump ) is a good starting point for considering how existing regulations can be improved and enforced and how new ones could be developed globally. the key needs in risk analysis for biosecurity are timely surveillance and identification of biosecurity threats, risk analysis of impacts and differentiation of natural versus unnatural outbreaks. traditional disease surveillance lacks the timeliness required for rapid detection of emerging and re-emerging pathogens. current public health systems rely on validated data from sources health systems, such as hospital and laboratory data, which are important for analysing trends over time, but do not meet rapid epidemic intelligence needs for early detection of epidemics (yan et al. ). epidemics, defined by a reproductive number greater than one (macintyre and bui ), grow exponentially, so every day of delay in detection could substantially increase the morbidity and mortality burden. mathematical models, typically of the form of deterministic systems of nonlinear differential equations, are often used to gain insight into the transmission dynamics and impact of natural and unnatural emerging and re-emerging infectious diseases that threaten health security, such as disease pandemics (nuno et al. ; nuño et al. ; sharomi et al. ) and the deliberate release of agents of bioterrorism, such as anthrax (brookmeyer and blades ; mushayabasa ; pantha et al. ) and smallpox (banks and castillo-chavez ; del valle et al. ; kaplan et al. ; meltzer et al. ). these models, combined with robust health data analytics, computational and data visualisation techniques and numerical simulations provide a realistic, rapid real-time assessment of threats to public health security. furthermore, informing these models with data generated from modern diagnostic tools that are capable of detecting asymptomatic cases with high degree of sensitivity and specificity (such as peptide-based immune-signaturing or low-cost paper-based rna sequencing) (legutki et al. ; navalkar et al. ; pardee et al. ; stafford et al. ) , and using knowledge of prior bioterrorism attacks and natural disease outbreaks allow for a realistic proactive prediction of future threats before they are detected by the public health system. these approaches allow for a more proactive disease surveillance for human diseases as well as veterinary surveillance for zoonotic pathogens that can mutate and cause major burden in human populations. other modelling paradigms, such as agents-based and other datadriven statistical and stochastic modelling approaches (halloran et al. ; hu et al. ; kaplan et al. ; nuño et al. ) , are also being used for this purpose. a stochastic approach to risk analysis allows model inputs to exhibit a degree of uncertainty. in contrast to deterministic models, the inputs follow various forms of probability distributions. risk is computed by sampling these input distributions many times. therefore, the outcome of a stochastic risk model is a distribution of risk-rather than a single value. the key advantage is that in addition to analysing outcomes, it allows for an analysis of the probability of these outcomes. it also allows for easy scenario analysis and sensitivity analysis. these can all assist decision-makers in taking intervention measures and allocating resources. one such example is a stochastic risk model (hill et al. ) of zoonotic and pandemic influenzas, with a focus on human infection with avian influenza. however, there are few real-time models with applicability in operational public health, with most modelling occurring in academia without real-time applicability for disease control . end-users in the public health system do not have much knowledge or nor trust in modelling, and do not use it widely for disease control (muscatello et al. ) . availability of simple, transparent tools that can assist with pressing questions such as surge capacity planning during the influenza season is what stakeholders value (muscatello et al. ) . although mathematical modelling has enjoyed widespread popularity within the academic public health community in terms of using it to predict epidemics as well as to assess and propose effective containment strategies (newall et al. ) , the use of genetic data (despite its huge potential to provide much deeper insight) for predictive purposes has not yet become a mainstream tool in public health practice (dudas et al. ) . virus phylogeography and phylodynamics are methods developed to utilize viral dna sequences to explore the evolution of pathogens by estimating their ancestry. these methods also show promise for public health surveillance, but are not as well developed or used in public health practice. it has only been somewhat recent that more focus has been on combining descriptive phylogenetic approaches with other modelling methods that attempt to predict epidemics. phylogenetic and phylogeographic analyses can be combined with methods for epidemic modelling to analyse risk factors and predictors of risk in a geospatial and genetic context. geographic information systems (gis) provide a further platform for public health researchers to take a map of an area and add layers of information regarding demographics, disease prevalence and socio-economic status (mondini and chiaravalloti-neto ; rushton ) . when overlaying multiple types of information, relationships and correlations can be discovered, adding analytical value beyond traditional descriptive approaches (doku and lim ) . patient data distributions and timestamps are significant factors in determining the specifics of an epidemic disease. hence, gis techniques such as emerging hot spot analysis and grouping analysis (van steenwinkel et al. ) allow for risk analysis of healthrelated concerns as correlated to location. for example, emerging hot spot analysis (wang et al. ) can help monitor changes and trends of an epidemic disease, such as identifying locations representing new or intensifying hot spots. new risk analysis methods are required to flag epidemics for urgent intervention, as illustrated by the catastrophic consequences of inaction with the ebola epidemic in west africa (world health organization ). we have shown that a simple risk prediction tool can be developed which identifies regions at high risk of severe outcomes of epidemics (argisiri et al. ) . such a tool, which considers disease specific, geographic, political, social, situational and contextual factors, could be used to prioritise epidemic response in situations of limited resources and reduce the impact of serious events. finally, the vast quantities of publicly available, unstructured data such as news feeds, social media and other public information offer potential for rapid epidemic intelligence and early detection, but are not yet accepted in public health (yan et al. ) . google, twitter and other sources have shown early promise for rapid disease detection by using algorithms and natural language processing to detect signals for epidemics, but are still eschewed by traditional public health systems (schmidt ) . rapid epidemic intelligence tools based on social media and news feeds could supplement traditional health system based, validated surveillance systems by providing more timely signals for epidemics of concern (yan et al. ) . we have shown that the ebola epidemic of could have been detected months earlier than it was using a novel twitter-based tool (yan et al. ). in addition, risk analysis frameworks play an important role in biosecurity decision-making and policy. using the approach of multiple criteria based upon emerging biotechnologies such as synthetic biology, traditional risk assessment such as health and environmental data, and other characteristics such as the uncertainty, reversibility, manageability of risk and levels of public concern (cummings and kuzma ; trump et al. ) , can be integrated to provide evidence-based information to government, academia and non-governmental organisations. such risk analysis methods could assist decision-makers to rank policy priorities and to improve the governance of biosecurity. whilst new risk analysis methods and tools are continually developed, many of the established methods for risk analysis of emerging infections are used separately and in different contexts. with increasing biothreats in society, these methods could be better integrated to add value improve the capacity to predict and mitigate risk. biosecurity is affected by cybersecurity concerns, but planning for biosecurity often fails to consider critical dependencies with information technology and computing. for example, mitigation and prevention of bioterrorism require surveillance for trade in bioweapons. the dark web offers terrorists a platform for trade in weapons, including bioweapons. numerous dark web marketplaces such as silk road and alphabay have been shut down by us law enforcement in recent years, but new ones continue to emerge (business insider australia ). whilst such market places are better known for trading in drugs and weapons, in a new york university student was arrested for attempting to purchase a category b bioterrorism agent, ricin, on the dark web (new york post ) . this highlights the need for integration of cybertechnology as a tool in prevention and surveillance for bioterrorism. surveillance for planned bioterrorism is not as well advanced in this realm as it is for traditional forms of terrorism. law enforcement agencies employ surveillance of the dark web and social media to detect chatter about planned terrorism, but the focus has been far less on bioterrorism. for example, surveillance for purchase of genetic code to create dangerous viruses failed to pick up the canadian scientists who created an extinct poxvirus in the laboratory using mail-order dna (science ). the world first knew about this experiment only when the scientists announced it. whilst this group was legitimate and not engaged in bioterrorism, the same methods for procurement which they used could well be used by terrorist groups. therefore, surveillance is required to detect such activity and prevent bioterror attacks. it was reported in that the unique health records of all australians are available for sale on the dark web, a fact uncovered by a reporter, not by law enforcement or government, exposing authorities as completely unprepared (bickers et al. ) . cyberattacks and cybertheft affect all facets of society, from banking and health to critical infrastructure (the age ). in many cases, the outcome of a cyberattack is loss of money or assets. however, if critical infrastructure or health systems are attacked, human lives may be lost. for example, if the power grid of a city is compromised, this has many flow-on effects on health systems, such as loss of functioning of critical equipment in intensive care units or operating theatres, or even for home interventions that rely on power such as nebulisers or oxygen (lee et al. ) . hospitals rely on generators as backup, but these can fail in the event of a disaster (parson ; sifferlin ) . the escalation of ransomware attacks on hospitals, which are poorly prepared and easy targets, can bring whole health systems to standstill, as seen within the uk nhs and us hospitals (deane-mckenna ; gillett ; landi ) . the goal of most health systems is to achieve paperless operations, to which the electronic patient medical record is central. yet the zeal for electronic health (e-health) has progressed with very little consideration of cybersecurity, leaving hospitals vulnerable to ransomware attacks (cbsnews ). the aspiration of health systems towards the e-health record is driven by the desire to improve care, protect patient safety and reduce medical errors (australian digital health agency ). the e-health record (ehr) has also been embraced by researchers as a means to efficient health research through data linkage of large administrative databases (powell and buchan ) . for example, data linkage was used to show that ct scans are associated with childhood cancer (mathews et al. ) . whilst big data allows new ways of conducting medical research, the risk of hacking of the ehr has not been adequately mitigated in health care. education and training in hospital and health management does not routinely offer courses in cybersecurity, leaving health planners and hospital managers unaware of the risk and underprepared. participants in the us federal medicare ehr incentive program have to attest that they have a fundamental cyber security programme and have adopted certified ehr technology (the office of the national coordinator for health information technology ). hospitals attesting meaningful use are legally bound to meet specific standards, including protection of the her, and can be audited. however, even this system has not protected us hospitals from cyberattacks (cbsnews ), and many countries do not have any such safeguards. precision medicine has revolutionized medicine, with the ability to tailor treatments for individuals by combining detailed medical, genetic and other patient information. this, however, also leads to the possibility of the same information being used to tailor "precision harm". it is well recognised that individuals can be targeted by biological weapons (macintyre and engells ), but convergence of technology opens new avenues for precision harm of individuals. the catastrophic hacking of the us office of personnel management (opm) in (mukherjee ) exposed data on over million us federal employees. at the same time, anthem health, the largest provider of health insurance to these employees, was also hacked (tuttle ) . data linkage would allow the perpetrators to access the sensitive personal medical information of employees, identify their medical vulnerabilities and plan targeted attacks, such as medication tampering or hacking of digital medical devices. the risks posed by hacking digital medical devices such as pacemakers and insulin pumps are also cause for concern (francies ) . this includes more extreme scenarios in which individuals with high political profiles or other strategic value could be assassinated by manipulation of their medical devices, tampering with their medication regimen or the design of microbial agents matched to their individual genetic profile. former us vice president dick cheney had his pacemaker wireless function disabled to mitigate such risk (peterson ) . if hostile states, organised crime groups or terrorist gain digital medical information on defence or security professionals, government officials or judges, it may become a more attractive option to more obvious methods for causing harm. figure illustrates the potential for precision harm targeting high profile individuals, enabled by convergence of technologies. in the example provided, a federal judge could be targeted in several different ways, including biological weapons, hacking of digital medical devices, medication tampering, interference with scheduled medical procedures or use of toxins or immune modulators, once a roadmap for precision harm is created. this example could apply to linkage of data from the opm and anthem health hacks to create personalised medical profile for federal employees. these examples illustrate the convergence of cybersecurity and health security and the need for more integrated approaches to prevention and mitigation of emerging risks in health care. in summary, we face rapid advances in science and technology, a corresponding escalation of risk to biosecurity, and convergence of multiple security threats which have traditionally been addressed separately. the changing landscape in biothreats and convergence with other areas of security can no longer be addressed in the traditional narrow, healthcentric way. the solution requires a multidisciplinary, global approach to security, whilst meeting local government regulatory requirements. we need new methods to prevent, identify and mitigate threats to biosecurity, which require cooperative thinking across national and professional boundaries. globally, health, law enforcement, defence and intelligence agencies will need to collaborate and pool their information and expertise. new risk analysis methods and surveillance tools need to be developed, and old methods may need to be used in new ways. this must be addressed in a coordinated global way to ensure risk is minimised. radicalized health care 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coordinator for health information technology ( ) guide to privacy and security of electronic health information a large community outbreak of salmonellosis caused by intentional contamination of restaurant salad bars synthetic biology regulation and governance: lessons from tapic for the united states a decision analytic model to guide early-stage government regulatory action: applications for synthetic biology the smallpox epidemic in aralsk, kazakhstan, and the soviet biological warfare program cyberdisaster: how the government compromised our security assessing biosecurity practices, movements and densities of poultry sites across belgium, resulting in different farm riskgroups for infectious disease introduction and spread bioterrorism-a new challenge for public health measuring the deconcentration of housing choice voucher program recipients in eight us metropolitan areas using hot spot analysis infection due to chromobacteria; report of cases who, geneva world health organization ( ) report of the ebola interim assessment panel antimicrobial resistance world health organization ( b) global action plan on antimicrobial resistance world health organization ( c) international health regulations (ihr) world health organization ( d) who advisory committee on variola virus research: report of the eighteenth meeting utility and potential of rapid epidemic intelligence from internet-based sources the authors are affiliated with global security key: cord- -fhy qt authors: huang, he; chen, yahong; ma, yefeng title: modeling the competitive diffusions of rumor and knowledge and the impacts on epidemic spreading date: - - journal: appl math comput doi: . /j.amc. . sha: doc_id: cord_uid: fhy qt the interaction between epidemic spreading and information diffusion is an interdisciplinary research problem. during an epidemic, people tend to take self-protective measures to reduce the infection risk. however, with the diffusion of rumor, people may be difficult to make an appropriate choice. how to reduce the negative impact of rumor and to control epidemic has become a critical issue in the social network. elaborate mathematical model is instructive to understand such complex dynamics. in this paper, we develop a two-layer network to model the interaction between the spread of epidemic and the competitive diffusions of information. the results show that knowledge diffusion can eradicate both rumor and epidemic, where the penetration intensity of knowledge into rumor plays a vital role. specifically, the penetration intensity of knowledge significantly increases the thresholds for rumor and epidemic to break out, even when the self-protective measure is not perfectly effective. but eradicating rumor shouldn’t be equated with eradicating epidemic. the epidemic can be eradicated with rumor still diffusing, and the epidemic may keep spreading with rumor being eradicated. moreover, the communication-layer network structure greatly affects the spread of epidemic in the contact-layer network. when people have more connections in the communication-layer network, the knowledge is more likely to diffuse widely, and the rumor and epidemic can be eradicated more efficiently. when the communication-layer network is sparse, a larger penetration intensity of knowledge into rumor is required to promote the diffusion of knowledge. epidemics continue to trigger world alarms in recent decades [ , ] , and have become a serious threat to human health [ ] [ ] [ ] . currently, a new type of coronavirus (covid- ) is circulating worldwide [ ] , and its plateaus hasn't been reached up to the time of writing this manuscript [ ] . however, the world is still not fully prepared for the outbreak of an epidemic [ ] . there are many reasons behind this, including the widespread presence of viral vectors (such as mosquitoes) [ ] , virus mutation [ ] , low effect of treatment [ , ] , seasonal outbreak (such as influenza) [ , ] , etc. as a consequence, the global protection is not enough, and people are usually encouraged to strengthen personal protection to reduce the risk of being infected, and they are also willing to do that [ , ] . previous researches have discovered the important role of individuallevel self-protection in eliminating epidemics and saving human lives [ ] . wang et al. reviewed the researches on the coupled dynamics of behavior and epidemic, and summarized that people's precautions obviously affect the prevalence of an epidemic [ , ] . more importantly, the self-protective awareness will spread across the population [ ] , yielding an interdisciplinary research area: interaction between information diffusion and epidemic spreading [ ] . previous complex network models have found that information diffusion plays an important role in promoting the spread of self-protective measures during an epidemic [ , ] . however, in the era of information explosion, the accuracy of information is difficult to guarantee. the spread of incorrect information may mislead people to choose the measures of low effect or no effect. tai et al. reviewed in detail the rumors on protective measures during the outbreak of sars, such as fumigating vinegar [ ] . in addition, even if the correct information is spreading in social networks, rumors against it may discourage people from adopting it [ ] . one of the reasons for the inaccurate information to prevail in social networks is that, most people only have common sense and lack relevant professional knowledge to make accurate judgments. the professional knowledge is usually mastered by a few people. for example, prelec et al. conducted a survey on the knowledge of us state capitals [ ] . one question is "philadelphia is the capital of pennsylvania, yes or no?" the answer given by most respondents is "yes", which is incorrect. although the respondents are from world-class universities, they failed to give the right answer. to explore the reason behind, prelec et al. found that almost all respondents have the common sense that philadelphia is the largest city in pennsylvania, while the knowledge that "harrisburg is the capital of pennsylvania" is mastered by a few people. similarly, during sars, people may have the common sense that acetic acid has a certain bactericidal effect, but the knowledge is that the concentration of acetic acid in vinegar is not enough to kill the virus. in this research, we define inaccurate information as rumor and accurate information as knowledge. as what we learn from the study of prelec et al., rumor may spread more widely than knowledge, which is very harmful to controlling an epidemic. therefore, it is important to know how the diffusion of rumor affects the spread of an epidemic, and whether rumor and epidemic can be contained by the diffusion of knowledge. we adopt a two-layer network to model the processes of information diffusion (including rumor diffusion and knowledge diffusion) and epidemic spreading. in the communication-layer network, we adopt a ua a model to describe the competitive diffusions of rumor and knowledge. specifically, we propose a unidirectional transition probability from the rumor-believed state to the knowledge-believed state, which represents the penetration of knowledge into rumor. in the contact-layer network, we adopt an seis model to describe the spread of epidemic. the infected state is divided into two stages: infected but undetected (e), infected and detected (i). when infected nodes are detected, they will be quarantined immediately. previous epidemic models often assumed that the diffusion of information is driven by local risk information (e.g., whether the linked neighbors are infected [ ] ). however, in our epidemic model, the direct risk sources (i.e., unobserved infected nodes) are not detected, which makes the local risk information less "protective" [ ] . moreover, people prefer to making pre-protection, regardless of whether there is any infected neighbor [ ] . for instance, in the previously mentioned vinegar case, people's pre-protection is mainly induced by global risk information. as another example, since the covid- virus was proved to be infectious, the knowledge of wearing appropriate masks is widely spread on social networks of . billion chinese users. therefore, unlike previous models, we will focus on pre-protection and assume that once the infected node is detected globally, information diffusion will begin. when a node receives a piece of rumor or knowledge, s/he is likely to take corresponding protective measures. we use three methods to analyze the model: numerical prediction, agent-based simulation and mean-field analysis. the results of the three methods are very close. based on the results, we summarize three main findings. first , the diffusion of knowledge can not only eradicate rumor, but also help to eradicate the epidemic, and the penetration of knowledge into rumor plays a key role. we analyzed the relationship of the outbreak thresholds (of rumor and of epidemic) with the penetration intensity of knowledge into rumor. in the communication-layer network, when the penetration intensity of knowledge is increased, the rumor outbreak threshold is increased linearly, so that the rumor becomes easier to control. in the contact-layer network, no matter whether the self-protective measure is perfectly effective or not, the threshold of epidemic outbreak increases nonlinearly with the penetration intensity of knowledge, but only if the penetration intensity of knowledge is large enough to make the knowledge widely spread. second , it is not necessary to eradicate rumor in order to eradicate epidemic. eradicating rumor is undoubtedly helpful to contain the epidemic, but it may cost too much. when there are enough knowledge-believed nodes, the epidemic outbreak threshold will be increased greatly. our results show that when rumor and knowledge are diffusing simultaneously in the communication-layer network, the epidemic can also be eradicated by the diffusion of knowledge. however, it should be noted that when rumor is eradicated, if the effectiveness of self-protective measures is very low, the epidemic may not be eradicated. third , the topology structure of the communication-layer network is very important for eradicating epidemic in the contact-layer network. when more links are added to the communication-layer network, which allows people to receive information from more sources, knowledge is more likely to break out, and rumor and epidemic are more likely to be eradicated. in addition, in a sparse communicationlayer network, a higher penetration intensity of knowledge into rumor is required to diffuse the knowledge. the coupled dynamics of information diffusion and epidemic spreading have been extensively studied [ , , , ] . a typical method is to build a two-layer network, with one layer to model the diffusion of information, and the other layer to model the spread of epidemic [ ] [ ] [ ] [ ] [ ] . for this research, such method is more necessary because there are two competitive dynamics for information diffusion. the structure of the two-layer network is presented in fig. . the nodes in the two layers are the same, while the links are not exactly the same. wang et al. considered a case that the links in the two layers are uncorrelated [ ] . some other researches proposed a coefficient to denote the overlap (or correlation) of links in the two layers [ , ] . in this research, we propose a different overlapping method . we assume that the communication-layer network is the extension of the contactlayer network. it is because that the spread of epidemic is based on offline contact, while the diffusion of information can be induced by both online and offline communication. people may never have any face-to-face contact with some online friends. to build the two-layer network, we first create a random network of node count n and average node degree k using the classical watts-strogatz (ws) network model [ ] . the first created random network is the contact-layer network. next, the nodes and links in the contact network are mapped to the communication-layer network. moreover, the network is extended by letting each node randomly link with k other nodes, generating the second random network with the average node degree k = k + k . the second created random network is the communication-layer network. previous studies have successfully modeled the diffusion of rumor [ ] , and found that the denying of rumor affects the outbreak size and threshold of rumor [ , ] . but the denying of rumor in their studies is usually described by a constant probability, not driven by the diffusion of knowledge. during an epidemic, it is easy to discover the diffusion of knowledge against rumor. for instance, during the covid- epidemic, knowledge about the functions of different medical masks was widely spread on social media, which helps people to choose the appropriate masks [ ] . moreover, cyberspace administration of china (cac) builds a specialized zone for sharing knowledge and refuting rumor during the covid- epidemic [ ] . inspired by previous rumor models and combined with the findings of prelec et al., we propose a ua a model to describe the competitive diffusions between rumor and knowledge, extended from the sis model [ , ] . each node has three possible states: unknown (u), rumor-believed (a ), and knowledge-believed (a ). the transition of the three states are well presented in fig. . when an unknown node receives information from a rumor-believed (or knowledge-believed) neighbor, s/he may become rumor-believed (or knowledge-believed), as well. the "infectivity" of rumor (or knowledge) is α (or α ). after a considerable period of time, the rumor-believed (or knowledge-believed) node may forget the information and return to the unknown state [ ] [ ] [ ] . the expected period length is / f (or / f ). namely, the probability for the rumor-believed (or knowledge-believed) node to return to the unknown state is f (or f ). moreover, there is an important unidirectional transition between the rumor-believed (a ) state and the knowledge-believed (a ) state. when the rumorbelieved node receives information from a knowledge-believed neighbor, s/he is likely to become knowledge-believed. the "infectivity" of knowledge on the rumor-believed node is defined as α . apparently α denotes the penetration intensity of knowledge into rumor. it should be noted that a node can transit from the rumor-believed state to the knowledgebelieved state because the knowledge-believed nodes have the extra accurate information (namely knowledge). thus, the "infectivity" of knowledge may be lower than that of rumor because people have to take more time/efforts to learn such extra knowledge. besides, previous studies also suggested that rumor might be more contagious. for example, in the new york times, awe-inspiring tales are likely to be more contagious than the regular news [ ] . therefore, we set α < α . previous overlapping methods are also applicable in our model. here "u" denotes the state that people are unknown about rumor and knowledge. "a " denotes the state that people believe rumor, and "a " denotes the state that people believe knowledge. α and α denote the infectivities of rumor and knowledge. α denotes the penetration intensity of knowledge into rumor. f and f denote the forgetting probabilities of rumor and knowledge. we propose ϕ ( t ) and ϕ ( t ) to denote the probabilities of a randomly selected link pointing to a rumor-believed node and a knowledge-believed node [ ] . they are obtained as where a k ( t ) and a k ( t ) denote the densities of rumor-believed and knowledge-believed nodes among the nodes with degree k at time t. p ( k ) denotes the distribution function of the node degree. for ease of analysis, we assume that the communication-layer network is homogeneous and the nodes have similar degrees. thus, it can be approximately derived here a ( t ) and a ( t ) denote the densities of rumor-believed and knowledge-believed nodes, respectively. correspondingly, the probability that a node has n rumor-believed neighbors and n knowledgebelieved neighbors can be given by a trinomial distribution where k is the degree of node. the discrete-time information diffusion process can be described as follows where the discrete-time probabilities of state transitions are derived following the research of liu et al [ ] as blow when an unknown node receives information from a rumor-believed neighbor and a knowledge-believed neighbor at the same time, s/he is first affected by the knowledge-believed neighbor and then affected by the rumor-believed neighbor, as shown in eq. ( ) . namely, we set the priority of knowledge higher than that of rumor. based on the discrete-time probabilities of state transitions, we derive the continuous-time probabilities following wu et al. [ ] , as detailed in the appendix a- . the mean-field dynamic equations of information diffusion are then derived as below, we calculate the equilibrium of information diffusion, based on which we are able to derive the thresholds for rumor and knowledge to break out, as detailed in the appendix a- . the outbreak of rumor requires the following inequality to be satisfied here "s" denotes the state that people are susceptible to the epidemic, "e" denotes the state that people are infected but are not detected, and "i" denotes the state that people are infected and detected. β denotes the infectivity of epidemic. β denotes the infectivity of epidemic on the knowledge-believed nodes. γ denotes the detecting probability of the infected nodes. f denotes the recovery probability of the infected nodes. while the outbreak of knowledge requires the following inequality to be satisfied previous studies have extensively modeled the spread of epidemic in the contact-layer network [ ] [ ] [ ] [ ] . as shown in fig. , we adopt a transformed seis model (or siis model [ ] ), which is slightly different from the typical seis models [ , ] , to describe the spread of epidemic. when a susceptible node contacts with an undetected infected peer, s/he may become infected but is not detected (e.g., with mild symptoms). the infectivity of the epidemic is β . the undetected infected nodes are detected at rate γ . once detected (e.g., with severe symptoms), the infected nodes will be quarantined immediately and cannot infect other susceptible nodes. after a period of treatment, the detected infected nodes recover to the susceptible state at rate f . in addition, the diffusion of information has an important impact on the spread of epidemic. when the knowledgebelieved nodes take an effective protective measure, s/he will reduce her/his susceptibility to the epidemic. without loss of generality, we propose that the infectivity of epidemic on the knowledge-believed nodes changes to β . apparently, β < β . however, the rumor-believed nodes adopt an ineffective measure and the epidemic infectivity on them remains β . previous studies assumed that the spread of epidemic would continuously promote the diffusion of information, because the infected nodes were identified as risk sources for their neighbors [ ] . in this research, the detected infected nodes are quarantined and "of no risk", while the direct risk sources are undetected. as a result, the effect of local risk information on containing the epidemic is greatly reduced [ ] . moreover, we focus on pre-protection instead of local-risk protection (e.g., high-risk immunization [ ] ). therefore, we don't consider such local risk information in this research. we use ϕ e ( t ) to denote the probability of a randomly selected link pointing to an undetected infected node. it can be calculated as [ ] ϕ where e k ( t ) denotes the density of undetected infected nodes among the nodes with degree k at time t . the contact-layer network is a sub-network of the communication-layer network. we assume that it is also homogeneous. the node degree is set as k . it can be approximately obtained that ϕ e (t) = e(t ) . the probability that a node has m undetected infected neighbors can be given by a binomial distribution correspondingly, the discrete-time epidemic process can be described as follows where the discrete-time probabilities of state transitions are derived as similar to the analysis in the information diffusion model, we derive the continuous-time probabilities of state transitions based on the discrete-time probabilities, as detailed in the appendix a- . the mean-field dynamic equations of epidemic spreading are derived as below, we calculate the equilibrium of epidemic spreading, based on which we are able to derive the outbreak threshold of epidemic, as detailed in the appendix a- . specifically, the outbreak of epidemic requires the following inequality to be satisfied where the equilibrium density of the knowledge-believed nodes a ( ∞ ) is expressed in the appendix a- . when a (∞ ) = , the epidemic threshold degenerates to β = γ /k . to evaluate the model, we adopt three different methods including two numerical methods and one theoretical method. the two numerical methods are: prediction based on the discrete-time state transition equations (abbreviated as predicted results), and agent-based simulation (abbreviated as simulated results). the theoretical method is the mean-field analysis based on the continuous-time state transition equations (abbreviated as mean-field results). the predicted results are first compared with the simulated results for verification. and the mean-field outbreak thresholds are then presented with the predicted results to reveal more interesting findings. to get the predicted results, we adopt matlab to iterate the discrete-time state transition equations of information diffusion and epidemic spreading. for the simulated results, we adopt repast to perform a series of agent-based simulations. initially, rumor and knowledge are believed by only the minority. but rumor has a much larger "infectivity" than knowledge and diffuses much faster. the topology of the communication layer and the contact layer are set to be random network, with the average degree defaulted as k = and k = , respectively. some other parameters are defaulted as: compared with a neutral unknown node, a rumor-believed node is often less susceptible to knowledge. the concept of a popular decision model, that is belief decision model [ ] , can support this conjecture. according to the belief decision model, each node beliefs on three options: rumor-believed, knowledge-believed, and neutral (or hesitating). when a neutral node receives knowledge, her/his belief on knowledge will be quickly increased. while a rumor-believed node receives knowledge, her/his belief is first transferred from the rumor-believed option to the neutral option, and then transferred from the neutral option to the knowledge-believed option. apparently, the knowledge-believed belief of the rumor-believed node is less increased due to information fading during belief transfer. thus, the value of α is lower than the value of α . when α = , for example, the two information diffusion dynamics are completely separated. while α = α , the rumor-believed nodes have no reluctance against knowledge, and rumor is unable to affect the diffusion of knowledge. therefore, the value of α is vital for the competition between rumor and knowledge, and we select it as a key parameter for analysis. as shown in fig. , the equilibrium densities of the rumor-believed nodes a ( ∞ ) and the knowledge-believed nodes a ( ∞ ) over α are well presented. increasing α decreases the density of the rumor-believed nodes and increases the density of the knowledge-believed nodes. more importantly, the simulated results and the predicted results are consistent with each other. besides, from the results, we infer that both rumor and knowledge may have outbreak thresholds. specifically, the outbreak of rumor may require α to be smaller than . , while the outbreak of knowledge may require α to be larger than . . that is to say, when α is larger than . and smaller than . , rumor and knowledge will diffuse simultaneously. we select the infectivity of epidemic ( β ) to compare the predicted results and the simulated results of epidemic prevalence. as shown in fig. , the equilibrium density of the (undetected and detected) infected nodes over β is well presented. increasing β will undoubtedly increase the density of the infected nodes. moreover, the simulated results and the predicted results are very close to each other. besides, from the results, we can detect the epidemic outbreak threshold. it is important to study whether the diffusion of information (especially the diffusion of knowledge) could affect the epidemic outbreak threshold. to analyze the outbreak thresholds in the communication-layer network, especially to study whether and how rumor can be eradicated by the penetration of knowledge into rumor, we focus on the parameter space α − α to draw the heat maps of rumor-believed densities and knowledge-believed densities. the value of α is set as . , α is confined in the interval [ , . ], and α is confined in the interval [ . , ]. as shown in figs. and , the equilibrium densities of rumor-believed nodes and knowledge-believed nodes over α − α are almost complementary, reflecting the competition between them. increasing rumor infectivity ( α ) will increase the density of the rumor-believed nodes and reduce that of the knowledge-believed nodes, while increasing the intensity of knowledge penetrating into rumor ( α ) will reduce the density of the rumor-believed nodes and increases that of the knowledge-believed nodes. these two parameters could determine which wins in the competition, especially whether the rumor can be eradicated by knowledge. moreover, from the two figures, we observe the effects of α and α on the outbreak thresholds of rumor and of knowledge, and we compare the numerical predictions with the mean-field thresholds in eqs. ( ) and ( ) . it can be found that the numerical threshold of rumor is highly matched with the mean-field rumor threshold. as α (i.e., infectivity of rumor) increases, a larger α (i.e., penetration intensity of knowledge into rumor) is required to eradicate rumor. and the rumor outbreak threshold indicates that α should increase linearly with α , as shown below the numerical threshold of knowledge is also close to the mean-field knowledge threshold with the increase of α (i.e., infectivity of rumor), a larger α (i.e., penetration intensity of knowledge into rumor) is required for knowledge to diffuse. but it should be noted that the equilibrium density of the knowledge-believed nodes increases sharply with α . even if the infectivity of rumor is extremely high, a small α (e.g. α = . ) will make knowledge ineradicable. the knowledge outbreak threshold indicates that α increases nonlinearly with the increase of α , as shown below therefore, from the above results, we observe a three-phase phenomenon of information diffusion over α . when α < , knowledge starts to diffuse. as a result, rumor is gradually confined. when α > (α f − α f ) (kα − f ) , knowledge takes the dominant position and rumor is eradicated. thus, the value of α (i.e., penetration intensity of knowledge into rumor) is crucial to information diffusion. it largely determines whether rumor can be eradicated by knowledge. compared with rumor, the gap between the predicted thresholds and mean-field thresholds of knowledge is less negligible. it is largely due to two reasons. first, the mean-field analysis may lead to some bias. second, the bias becomes clear when the parameter α is confined in a very small range [ , . ] and the step is set as a very tiny value: . . to analyze the outbreak threshold of epidemic in the contact-layer network, especially to study whether the diffusion of knowledge helps to eradicate the epidemic, we consider two situations: perfect self-protection and imperfect self-protection. firstly, we focus on the parameter space α − β with the value of β set to (i.e., perfect self protection). α is confined in the interval [ , . ], and β is confined in the interval [ , ]. secondly, we fix the infectivity of epidemic ( β = . ) , and focus on the parameter space α − β , in order to explore how imperfect self-protection ( β ∈ [ , . ]) affects the spread of epidemic by knowledge diffusion. as shown in fig. , in the case of perfect self-protection, increasing the value of epidemic infectivity ( β ) will increase the density of the (undetected and detected) infected nodes, while increasing the penetration of knowledge into rumor ( α ) will decrease the density of the infected nodes. the finding verifies that the diffusion of knowledge helps to contain the epidemic. moreover, the numerical epidemic threshold is very close to the mean-field epidemic threshold in eq. ( ) . as epidemic infectivity ( β ) increases, a larger penetration intensity of knowledge into rumor ( α ) is required to eradicate the epidemic. the epidemic outbreak threshold indicates that the epidemic infectivity ( β ) can increase nonlinearly with the increase of α , as shown below as shown in fig. , in the case of imperfect self-protection, improving the effectiveness of self-protection (i.e., reducing β ) can significantly decreases the density of the infected nodes, but highly depending on the penetration intensity of knowledge into rumor ( α ). when the intensity of knowledge is insufficient to penetrate the rumor-believed nodes (e.g., α < . ), reducing β will not have much impact on the density of infected nodes. while α is large enough (e.g., α = . ), reducing β can eradicate the epidemic. moreover, the numerical epidemic threshold is compared with the meanfield epidemic threshold in eq. ( ) . with the increase of the penetration intensity of knowledge into rumor ( α ), a less effective self-protection, namely a larger β , can be enough to eradicate the epidemic. the epidemic outbreak threshold indicates that β can increase nonlinearly with the increase of α , as shown below it can be seen from the above results that information diffusion has significant influence on the epidemic spreading. as knowledge becomes more "penetrating" into rumor, rumor and epidemic are more likely to be eradicated. moreover, based on the outbreak thresholds in the communication-layer network, information diffusion can be divided into three phases. in this section, we try to explore the phase diagram of the whole two-layer system based on the outbreak thresholds in both layers. as shown in fig. , the two-layer system can be divided into five phases by α − β . first, information diffusion can be divided into three phases: "no knowledge ", "rumor vs. knowledge ", and "no rumor ". second, epidemic spreading can be therefore, it is not necessary to equate rumor eradication with epidemic eradication. when rumor cannot be eradicated, the epidemic can also be eradicated by the spread of knowledge. when rumor can be eradicated, the epidemic may be uneradicated when the effectiveness of self-protection is very low. moreover, the adjacent phases are interconvertible. for example, the "rumor vs. knowledge & no epidemic " phase can convert to the "no rumor & no epidemic " phase with the increase of α , and can convert to the "rumor vs. knowledge & epidemic outbreak " phase with the increase of β . based on the phase diagram, it is possible to find an optimal strategy to contain rumor or epidemic. for example, if the two-layer system is in the "rumor vs. knowledge & epidemic outbreak " phase (phase ii), the optimal strategy of containing the epidemic is to develop an effective self-protective measure to reduce β . the network structure highly affects the outbreak size and threshold of the spreading dynamics [ , ] . in a two-layer network, the overlap of the two layers is also important for the spreading dynamics [ ] . this research assumes that the communication-layer network is an extension of the contact-layer network. in the information age, the cost of communication is greatly reduced, and it becomes easier to extend the communication-layer network. it is interesting to know whether the extension of the communication-layer network helps to contain rumor and epidemic. therefore, in this section, we try to explore the evolution of the rumor-believed density and the infected density with the change of average node degree k in the communication-layer network. as shown in fig. , when k increases from to , the rumor-believed density will increase first and then decrease, while the knowledge-believed density will increase monotonically. obviously, rumor is more likely to break out in a sparse network than knowledge because rumor infectivity ( α ) is much larger than knowledge infectivity ( α ). however, when knowledge starts to break out (e.g., k = ), rumor will be confined immediately and the rumor-believed density will begin to decrease. it should be noted that a higher penetration of knowledge into rumor helps knowledge to break out in a very sparse network. moreover, when the knowledge-believed density starts to increase, the infected density begins to decrease. more importantly, with the increase of k , the infected density gradually decreases to , which indicates that extending the communication-layer network helps to eradicate the epidemic in the contact-layer network, consistent with eq. ( ) . besides, a larger α in the communication-layer network is also helpful to eradicate the epidemic. in summary, extending the communication-layer network is helpful to eradicate the epidemic, but it largely depends on the condition that knowledge is able to penetrate the rumor. when people can get information from diverse sources, s/he is more likely to get access to the accurate information (i.e., knowledge) and get rid of rumor. this will make her/him be better protected from the epidemic. besides, compared with reducing rumor infectivity or epidemic infectivity, the cost of widening information sources is usually lower. during an epidemic, individuals are usually willing to take protective measures to avoid being infected. however, the diffusion of rumor sometimes prevents them from choosing the effective measures. to make things worse, such rumor is often contagious and hard to be eradicated, making the epidemic difficult to contain. therefore, how to contain rumor and epidemic has become a critical issue to the human society. in this research, inferred from the study of prelec et al. and the practice of chinese authorities during covid- , we propose that the diffusion of knowledge is the key to controlling both rumor and epidemic. to model interaction between information diffusion and epidemic spreading, we adopt a two-layer network structure. the ua a model is adopted to describe the competitive diffusions of information and the seis model is adopted to describe the spread of epidemic. specifically, in the ua a model, we explicitly propose a unidirectional transition probability from a (rumor-believed state) to a (knowledge-believed state), which denotes the penetration of knowledge into rumor. three frequently used methods are used to evaluate the impact of knowledge diffusion on the spread of rumor and epidemic. the diffusion of knowledge is able to eradicate both rumor and epidemic, where the penetration intensity of knowledge into the rumor-believed nodes ( α ) plays a vital role. the rumor outbreak threshold increases linearly with α , while the epidemic outbreak threshold increases nonlinearly with α . in particular, even if the self-protective measure is not perfectly effective, increasing α is helpful to contain and even eradicate the epidemic. it is inappropriate to equate eradicating rumor with eradicating epidemic, although eradicating rumor is helpful to eradicate the epidemic. on one hand, when the density of knowledge-believed nodes increases, the outbreak threshold of epidemic will significantly increase, no matter whether rumor dies out or not. on the other hand, when rumor is eradicated, the epidemic may still prevail if the self-protective measure is not effective enough. the overlapping of the contact layer and the communication layer is a research focus in the two-layer network structure. we assume that the communication-layer network is an extension of the contact-layer network. when adding links to the communication-layer network, namely when people get information from more sources, knowledge is more likely to break out, while rumor and epidemic are more likely to be eradicated. moreover, a larger penetration intensity ( α ) makes knowledge more likely to break out in a sparse network. from the above conclusions, it can be obtained that information diffusion has significant influence on the epidemic spreading. increasing penetration intensity of knowledge or improving effectiveness of self-protection is helpful to eradicate an epidemic. therefore, for policy-makers, it is necessary to know which is more suitable for a specific case. the phase diagram provides lots of implications. first, it should be evaluated at which phase the present two-layer system is located. second, an effective strategy is the one that can convert the system from a bad phase (e.g., "rumor vs. knowledge " & "epidemic breakout ") to a nearby better phase (e.g., "rumor vs. knowledge & "no epidemic "). our research has several limitations, which can be extended in future studies. first, the dynamic impact of epidemic spreading on information diffusion is not fully considered. in particular, the spread of rumor may be dynamically affected by the severity of epidemic. for example, people's susceptibility to rumor may not be constant, but inversely related to the outbreak size of epidemic. in other words, when the epidemic outbreak size increases, the infectivity of rumor may increase, as well. we set the rumor infectivity to a very large value ( α = . ), but we didn't consider its dynamic feature. in a dynamic case, rumor and epidemic may be more easily contained at the early stage. second, the transition from the knowledge-believed state to the rumor-believed state is not considered, which is consistent with most of previous rumor models [ ] . in extreme cases, such transition may occur. for example, a wicked rumor may make people to abandon the effective practice [ ] . introducing such transition into our model may make the competition between rumor and knowledge more salient. third, the topology structures of the contact-layer network and the communication-layer network may be different, which may affect the spreading process. fortunately, although we only study the random network, this research can be easily extended to different network structures. world on alert for potential spread of new sars-like virus found in china a game theoretic approach to discuss the positive secondary effect of vaccination scheme in an infinite and well-mixed population epidemics and rumours in complex networks economic impact of dengue illness in the americas a systematic review of the social and economic burden of influenza in low-and middle-income countries clinical features of patients infected with novel coronavirus in wuhan forecasting covid- are we ready for pandemic influenza? evolutionary enhancement of zika virus infectivity in aedes aegypti mosquitoes optimal control of 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supplementary material associated with this article can be found, in the online version, at . /j.amc. . key: cord- -gi un authors: zhou, lingyun; wu, kaiwei; liu, hanzhi; gao, yuanning; gao, xiaofeng title: cird-f: spread and influence of covid- in china date: - - journal: j shanghai jiaotong univ sci doi: . /s - - - sha: doc_id: cord_uid: gi un the outbreak of coronavirus disease (covid- ) has been spreading rapidly in china and the chinese government took a series of policies to control the epidemic. therefore, it will be helpful to predict the tendency of the epidemic and analyze the influence of official policies. existing models for prediction, such as cabin models and individual-based models, are either oversimplified or too meticulous, and the influence of the epidemic was studied much more than that of official policies. to predict the epidemic tendency, we consider four groups of people, and establish a propagation dynamics model. we also create a negative feedback to quantify the public vigilance to the epidemic. we evaluate the tendency of epidemic in hubei and china except hubei separately to predict the situation of the whole country. experiments show that the epidemic will terminate around march and the final number of cumulative infections will be about (prediction interval, to ). by changing the parameters of the model accordingly, we demonstrate the control effect of the policies of the government on the epidemic situation, which can reduce about % possible infections. at the same time, we use the capital asset pricing model with dummy variable to evaluate the effects of the epidemic and official policies on the revenue of multiple industries. while coronavirus disease (covid- ) has been spreading rapidly in china and other regions, this virus outbreak has received substantial attention from the global public and was listed by the world health organization (who) as public health emergency of international concern (pheic). given this situation, there is an urgent need to predict the development of the epidemic. to control the epidemic, the chinese government took actions rapidly [ ] . they restricted the traffic, extended the spring festival holiday, and even closed wuhan and other cities in hubei. these measures are actually double-edged swords. if the measures are not strong enough, the virus transmission will become more difficult to control. under this circumstance, measures such as traffic control and regional closures are believed to have positive impacts on controlling the epidemic. however, the national economy may be impacted negatively. thus, some industries may be negatively impacted. therefore, studying and quantifying the effect of official policies can help us better understand these policies and prepare for the future. in general, we focus our research on the epidemic prediction and influence of official policies. traditionally, several existing models, such as cabin models based on propagation dynamics, individualbased models, and machine learning, can be used to predict the tendency of the epidemic. for example, the model of the susceptible, the exposed, the infected and the recovered (i.e., seir model) is a cabin model. it divides the population into the susceptible, the exposed, the infected and the recovered, using differential equations to explain the transmission of the virus between these groups. cellular automation is a commonly-used individual-based model [ ] . it sets detailed rules for population mobility, which accurately simulates the situation in a specific group of people. however, the former type for the predicting models always oversimplifies the epidemic, leading to inaccurate prediction, while the latter type is too meticulous to simulate the large-scale situation such as the nationwide prediction. furthermore, there are few related researches on the influence of official policies. most existing analyses focus on the impacts of the epidemic itself [ ] [ ] [ ] . also, some researches confuse the influence of official policies and the influence of the epidemic after the policies were published. it may give rise to some misunderstandings of the influence of official policies. in this paper, we give a reality-based analysis of the transmission process of covid- at first. the analysis considers four groups of people: the incubated, the infected, the recovered, and the dead. it also takes public vigilance to the number of infections and the capacity of virus transmission into consideration, which makes the analysis more concise than seir model. then we build four differential equations and one functional equation, which is called the model of the incubated, the infected, the recovered, the death and an infection function (i.e., cird-f model), to describe the transmission of the epidemic. using the data of cumulative infections, we can conduct regression by the least square method to quantify the public vigilance and the capacity of virus transmission. after that, we can draw curves to predict the number of future infections, incubations, recoveries and deaths. we also use a capital asset pricing model with dummy variable [ ] [ ] , which is called capm-dv model, to quantify the influence of official policies on different industries. we first set the value of the dummy variable according to the start time of the epidemic to quantify the influence of the epidemic [ ] [ ] . then, we set the value according to the day when the policies were published to quantify the influence of the epidemic after the policies. therefore, by subtracting the former influence from the latter, we can figure out how the policies influence different industries. in our experiments, we predict the tendency of the epidemic at first. we fit cird-f model in hubei and china except hubei separately. the results show that the situation in hubei is much more severe than the situation out of hubei. by combining the two situations, we draw curves to predict the tendency of the epidemic. then we analyze influence of official policies in two aspects. for one thing, we simulate the tendency of the epidemic without the closure policy. if wuhan and other cities in hubei were not closed, the situation of the whole country will be as severe as that in hubei. therefore, we use cird-f model for hubei to predict the tendency of the epidemic in china, which shows that the policies help reduce about % possible infections. for another, we use capm-dv model to quantify the economic influence of the policies on the healthcare, transportation, construction, entertainment and tourism industries. existing related work can be divided into three groups: epidemiological and clinical features of covid- ; mathematical methods of predicting the epidemic; influence of the official policies. epidemiological and clinical features existing researches are mostly based on cases [ ] [ ] and calculate medical parameters such as the cure rate, the mortality, the incubation period and the basic reproduction number. these data are an important basis for building mathematical prediction models. mathematic models [ , , ] the methods of modeling are used to predict the spread of the epidemic. these methods are also used during sars [ ] , ebola [ ] and so on [ ] . a commonly-used model is the cabin model based on propagation dynamics. one of the most basic models is seir model and its modification. this type of models divides people into different categories and describes the transmission of virus using differential equations. the accuracy of parameters and the description of the transmission determine the effectiveness of the model. another method is to use individual-based models like cellular automaton to simulate the transmission of virus [ ] , which is direct and vivid. however, it is difficult to simulate a domestic situation by models of this type. furthermore, machine learning is also used to conduct epidemic prediction [ ] . this method is based on big data. besides, a more mature model considers the public vigilance to the epidemic [ ] , using negative feedback. however, the model omits the people in incubation period, which oversimplifies transformation process of the infected population in different stages. influence of official policies for one thing, who and the global public fully affirm and praise the performance of the government in the epidemic prevention and control. for another, while some literature points out the negative economic effect of the epidemic [ ] , most chinese newspapers believe that the economy will not be greatly affected. more studies are focused on the influence of the epidemic rather than the effect of official policies. for example, ref. [ ] uses a capm-dv model to analyze the impact of the epidemic on economy during sars. in this paper, we use a cabin model based on propagation dynamics, which is modified from the model with negative feedback to predict the development of covid- [ ] . we also adopt the capm-dv model to analyze official policies in an innovative way. to solve the shortcomings of previous models, we build cird-f model and obtain more accurate prediction. cird-f model is actually a series of differential equations explaining the transformation process of the infected population in different stages. four stages of the infected population involve the incubation period, the infection period, the state of recovery from covid- , and the state of death due to covid- . cird-f represents incubation (c), infection (i), recovery (r), death (d) and a function (f) involving a feedback process to explain the public vigilance to the epidemic, as shown in fig. . transformation process of the infected population in different stages feedback process to simplify and formulate the transformation process of the infected population in different stages, we make some basic assumptions. first of all, since the chinese government rearranges the medical resources timely and has built two makeshift hospitals, there would be enough beds in the hospital and each patient would be quarantined immediately. therefore, we assume that the diagnosed patients will be immediately quarantined into the hospital, and then they will not be able to infect others. secondly, since there is no reported reinfection right now, we assume that the cured patients will not be reinfected and will no longer have the ability to spread the disease. finally, since there is no specific drug or available vaccine, we assume that the cure rate and the mortality rate remain unchanged in this paper. namely, we do not consider the occurrence of specific drugs for the time being. on the basis of the assumptions, we define the four stages of infected population more precisely. the incubation period is the first stage which a person experiences after he is infected. people in the incubation period show no symptoms and act like the healthy people. therefore, they may infect the healthy people and turn the healthy into those in the incubation period. according to the statistics recently collected [ ] , the length of incubation period is three days. the people in the infection period are those who have undergone the incubation period. people in the infection period show obvious symptoms, so they will be quarantined in the hospitals immediately and be not able to infect the healthy. since different patients get different therapeutic effects in the process of hospital treatment, some people in the infection period will die and others will survive, which corresponds to the state of recovery from covid- and the state of death due to covid- . people in the states of both recovery and death will not infect the healthy. we reckon that the cumulative number of confirmed cases (the total number of people in the infection period, the state of recovery and the state of death) will affect public vigilance to the disease. with the increase of the number of confirmed cases, public vigilance is constantly improved. because of the increased public vigilance, the same number of cases of persons in the incubation period will lead to fewer healthy people being infected than the previous situation. in other words, the growth of the confirmed cases decreases the growth rate of people in the incubation period, which is called a feedback process. the qualification of the feedback process will be explained later. figure shows the transformation process of the infected population in different stages with the feedback process, which is the basic idea of cird-f model. in this figure, we can see two types of lines, the dashed lines and the solid lines. the solid lines connect different stages of the patients and show the transformation process of the infected population in different stages. the growth rates of the people in the incubation period and the states of recovery and death remain unchanged, which will be later explained in detail. the dashed lines denote the feedback process describing the infection function. the infection function is the growth rate of people in the incubation period which is affected by the confirmed cases and affects the rate of incubated people infecting the healthy. based on the above analysis, cird-f model is shown as follows: where here, f represents the infection rate, n c represents the number of people in the incubation period, n i represents the number of real-time infections, n r represents the number of cumulative cures, n d represents the number of deaths, and t represents the outbreak duration; a represents the public vigilance to the number of infections, and b represents the capacity of virus transmission; α, β and γ represent the proportion of people becoming infected after the incubation period every day, the death rate and the cure rate, respectively; c t is the length of the incubation period. the subscript i represents the ith day after january , and t is the maximum value of i. what needs to be emphasized here is that f is a feedback function. the meanings of the five equations are explained as follows. as to the first equation, f is impacted by n r , n d and n i together. here, we set n i + n d + n r = n t , where n t is the number of the total infections (cumulative infections). with the increase of the total number of infected people, we believe that the government will take more stringent measures to control the epidemic, and the people will have a deeper understanding of the epidemic. therefore, with the growth of n t , f will decline, which represents that the infectious ability of disease in human society is gradually weakened. the second formula shows the law of population growth in the incubation period in unit time. some people in the incubation period become confirmed patients (infections), and the ratio of this process is α. some healthy people are still in the incubation period, which is directly affected by the infection index f . the third formula shows the increase in the number of diagnosed infections per unit of time. the proportion of people with a ratio of α changes from incubation period to confirmed patients. there are also a group of people cured and another died as a result of failed rescue efforts. the fourth and fifth equations are very simple, indicating that a certain number of patients will turn into healthy people and death cases under a certain cure rate and mortality in a unit time. we use the data from january to conduct the calculation. the initial values of n c , n i , n r and n d are set as follows: n i, , n r, and n d, are the numbers of the ones on january . since the incubation period is three days, n c, is the difference of the cumulative number of infections on january and january . in our fitting process, the sum of squares of residuals is required to be minimized to achieve the best result, so we use the least square method to fit. here are the strengths and weaknesses of cird-f model. in terms of strengths, our model takes the incubation period into account. therefore, the model is more accurate and closer to the reality. we set up a negative feedback function, in which a and b can well reflect the attitude of the government and people to the epidemic, making the later policy analysis more convenient. our model is not a traditional warehouse model, which requires less data and has higher accuracy. there are also some weaknesses of our model. in the modeling process, it is assumed that people would fully follow the instructions of the government. such a prediction may be more ideal than the real situation. in our calculation process, the calculation of cure rate and death rate is not very rigorous. in reality, both the cure rate and the death rate are functions of time, which is not reflected in the calculation process. through cird-f model, we can figure out the development of the epidemic and the effectiveness of official policies, but it is still difficult to quantify the economic impact of official policies. therefore, we need a capital asset pricing model with a dummy variable to solve this problem. traditional capital asset pricing model (capm) mainly studies the relationship between expected return of assets in the securities market and systematic risk [ ] . therefore, it shows how a certain capital asset is influenced in the background of a certain market. the dummy variable is a qualified independent variable [ ] , which is used to analyze the effect of abnormal factor. the model is where r e means the daily expected return of certain capital asset, r f means the daily risk-free interest rate, r m means the daily expected return of the certain market, ω is system risk which is defined in the traditional capm, is the disturbance, and λ is the influential factor. we need to fit ω and λ. the focus of this analysis is λ. if λ is significantly greater than , it indicates that the capital asset is influenced by the abnormal factor positively; if λ is significantly less than , it indicates that the capital asset is influenced by the abnormal factor negatively. recent study with auto-regressive distributed lag model shows that the increase and decrease in economic factors impact the stock returns, which are very sensitive, in china [ ] . furthermore, a study which focuses on several central and eastern european countries shows that there is a high level correlation between each country's gross domestic product (gdp) and its national stock exchange index [ ] . since the gdp or gdp per capita of most of these countries is similar to that of china, we infer that the result also applies to china. on the basis of these studies, we assume that there is a strong relationship between the stock market and the economy in china. therefore, we focus on the shanghai stock exchange and reckon that the stock indices in certain industry represent the economy situation of certain industry. in this way, "certain capital asset" of capm-dv model means "certain industry". "certain market" is referred to in particular as shanghai stock exchange in this paper. furthermore, we use the five-year government bonds to represent the risk-free interest. namely, r e,i means the daily income rate of the stock in certain industry on the ith day; r f,i means the daily income rate of five-year government bonds, which remains unchanged; r m,i means the daily income rate of shanghai composite index on the ith day. we use equal weight method to calculate the indices r e,i and r m,i of each industry separately. the complete calculations are where p i,j means the closing price of the jth stock in certain industry on the ith day, p e,i means the daily income of certain industry on the ith day, m means the number of stocks in certain industry, and p m,i means the closing price of shanghai composite index on the ith day. after we set the range of the subscript i and the dummy variable n d,i , which will be explained in subsection . . , we use linear regression to fit ω and λ. if n d,i equals to and before and after the epidemic broke out respectively, the absolute value of λ means the level of influence of the epidemic on certain industry and the sign of λ reflects whether the epidemic influences the industry positively or negatively. similarly, if n d,i equals to and before and after the government published official policies respectively, the absolute value of λ means the level of influence of the epidemic after official policies were published on the industry and the sign of λ reflects whether the influence on the industry is positive or negative. it should be noted that ω means the level of risk of the stocks in certain industry and it is not the focus of our research. we conduct several experiments to predict the tendency of the epidemic and evaluate the influence of official policies. in subsection . , we collect the cumulative number of infections from january to march from the national health commission of the people's republic of china. on the basis of these data, we use cird-f model to predict the tendency of the epidemic. in subsection . . , we use the result in subsection . to evaluate how many possible infections will be reduced by official policies. in subsection . . , we randomly collect closing prices of listed company stocks in shanghai stock exchange and shanghai composite index from january to february from china international capital corporation (cicc) wealth. according to these data, we evaluate the economic influence of official policies on five industries separately. in this section, we separate the procedure into two different parts: the data prediction of hubei and the data prediction of the whole country except hubei. the reason why we separate the procedure is that most cities in hubei have taken strict traffic control. also, hubei is a major epidemic area and the medical resources are saturated. therefore, the cute rate γ, the death rate β, the public vigilance a, and the virus transmission capacity b in hubei are evidently different from the ones in the other areas. after making the predictions separately, we figure out the trend of the epidemic of the whole country. for the data prediction of china except hubei, we use the total number of infections (i.e., n t ) from january to march to fit the parameters a and b. for hubei, since the government revised the diagnosis standard on february and the total number of infections that day increased by over ten thousand, we modify the range of data used for fitting accordingly. we assume that the reason why the government revised the standard was that as the epidemic developed, the old diagnosis standard lost its effectiveness. therefore, we reckon that the new standard after february is effective and the old standard stayed valid until february . on the basis of the assumption, we use the total number of infections from january to february and from february to march to fit the parameters a and b. using the corresponding data in hubei and china except hubei, we acquire the values of a and b separately. since we set the steps of a and b as × − and × − respectively, we also set the prediction intervals of a and b as ± ( × − ) and ± ( × − ) respectively. the values and the prediction intervals of the used parameters are shown in table . figure shows the tendency and changes of different populations (recovered people, death toll and so on) in hubei. figure shows the tendency in china except hubei. in the two figures, the solid line means the estimated number of infections in different stages, the shadow means the prediction intervals and the scatter means the data used to fit the model. through comparing the values of a and b in hubei and china except hubei, we find that the absolute value of a in china without hubei is significantly greater than that in hubei and the values of b in both regions are basically the same. the reason to the first fact is that the absolute value of a represents the public vigilance to the number of cumulative infections, and since the epidemic is more severe in hubei, the vigilance in hubei is weaker than that in china without hubei. the reason to the second fact is that the value of b represents the capacity of virus transmission which only depends on the virus itself and remains unchanged. we assume that the infected people are quarantined in hospitals. therefore, we define the end of the epi-demic as the day when the number of people in the incubation period drops to zero. according to our prediction, the number of people in the incubation period in hubei will drop to zero in the middle of march, about march . furthermore, if the situation in hubei is not taken into account, the national epidemic will end around march . in other words, the last patient in the incubation period in the country will be diagnosed and quarantined on march . the actual data of the number of infections can be used to prove the accuracy of our prediction. comparing the estimation interval of the total number of infections (the blue shadow) with the actual data (the pink scatters) in figs. and , we find that all the data predictions are in the estimation interval. we assume that the circulation of personnel in hubei and other areas of the country is seriously blocked, so we simply add the results of the previous two predictions and get the prediction of the whole country. the tendency of the epidemic is shown in fig. . figure shows the timeline of the development of the epidemic. from the figure, several important time nodes and corresponding data of the national epidemic can be obtained. as the reality, the peak of the national epidemic came around february , when the total number of infected people was about (prediction interval, to ). the national epidemic will end on march , which is the same as the end date of the epidemic in hubei. by that time, about (prediction interval, to ) people will be infected. we also calculate the goodness-of-fit of r for the models of hubei and china except hubei. we arrange the actual data of daily infection total (i.e., n i,i +n d,i + n r,i , recorded as n t,i ), which is defined in eq. ( ) and used for fitting, in chronological order as n t, , n t, , · · · , n t,k , where k means the total number of the samples. the coefficient of determination is where n t,k means the number of daily infection total of the kth sample,n t,k means the average of all the samples, andn t,k means the estimated number of daily infection total corresponding to the date of the kth sample. the values of r for the models of hubei and china except hubei are . and . respectively, which are both close to and show the high goodness-of-fit. however, while the actual number of the daily increased infections (n t,i − n t,i− ) in china except hubei remains between and for about ten days from february , the corresponding estimated numbers of daily increased infections decrease rapidly to zero. it shows that the model cannot describe the ending period of the epidemic very accurately. in this section, we consider the policy impact of the government from two aspects. these two aspects are the control of the epidemic and the impact on the economy. to analyze the impact of epidemic control, we use the previous model. as to the economic impacts, we will use a capm with dummy variable to assess the impact on different industries. since the chinese government mainly published its policies on january , we assume that the influence of official policies started from january . in the previous work, we have predicted the epidemic situations in hubei and china except hubei, and obtained some crucial parameters. since the epidemic in hubei is much more severe than that out of hubei, the government published a series of policies on january . if these policies were not published, the situation of the whole country would become as severe as that of hubei. to simulate the above situation, we use the values of the parameters α, β, γ, a and b in hubei and the initial numbers n c, , n i, , n r, and n d, in the whole country and solve the differential equations. the values of the parameters mentioned above are shown in table . figure shows the development of the epidemic if the policies were not published. as shown in fig. , the predicted number of cumulative infections greatly exceeds the actual number of cumulative infections, which means the control of the government is effective. if it is not controlled, there will be (prediction interval, to ) cases of infection at the end of the epidemic. the comparison between the simulation and the current situation shows that official policies decrease the number of possible infections by about %. moreover, we use the values of the parameters α, β, γ, a and b in china without hubei and the initial numbers n c, , n i, , n r, and n d, in the whole country and solve the differential equations. the values of the parameters mentioned above are shown in table . the above simulation reflects the situation that hubei acts like other regions in china. figure shows the situation that hubei implements strict control at the early stage of the outbreak. it can be seen that the total cumulative infections will be far lower than the current cumulative infections. if hubei takes actions like other regions, there will be only (prediction interval, to ) cases of infections at the end of the epidemic. the comparison between the simulation and the current situation shows that if the hubei takes action as quickly as the other regions, the number of possible infections will decrease by about %. time/d fig. situation of the whole country if hubei takes actions more timely from january to april in this section, we use capm-dv model to calculate the economic impacts of the epidemic and official poli-cies on different industries. the industries are healthcare, transportation, construction, tourism and entertainment. since the stock index can represent the performance of certain industry in a large economic environment, we randomly collect closing prices of listed company stocks in the five industries from january to february . the companies are all listed in shanghai stock exchange and located in all over the world. we list the stock code and its corresponding industry in table . after collecting the stock indices of the above stock codes from cicc wealth, we gain the values of r f,i , p m,i and p i,j . the usual closing price p m,i of shanghai composite index ranges from to , the usual closing price p i,j of each stock ranges from to yuan, and r f,i equals to . . the range of the subscript i will be explained later. assume that we have determined the range of i. on the basis of the above data, we use the equal weight method, which is described in section , to calculate the parameters r e,i and r m,i in capm-dv model. economic influence of the epidemic first, we analyze the impact of the epidemic on each industry by comparing the performances of the stock market before and after the epidemic broke out. therefore, the range of subscript i is from january to february and the dummy variable n d,i is set as: when i is later than december , n d,i equals to ; when i is between january and december , n d,i equals to . december , is the day when wuhan reported the epidemic. therefore, we can use linear regression to calculate the influential index λ for each industry separately. the results are shown in table . economic influence of official policies then, we analyze the impact of the epidemic on each industry when official policies were conducted by comparing the performances of the stock market before and after the policies were conducted. therefore, the range of subscript i is from december to february and the dummy variable n d,i is set as follows: when i is later than january , n d,i equals to ; when i is between december and january , n d,i equals to . january , is the day when the chinese government started publishing policies. similarly, we conduct the calculation for each industry and show the results in table . if we subtract the values of λ in table from the corresponding ones in table , we can calculate the economic impact of official policies. on the positive side, the policies bring . % additional income to the transportation industry. on the negative side, the policies cause . %, . % and . % additional losses to the healthcare, construction and tourism industries, respectively. there are some interesting points. although the epidemic stimulates the healthcare industry, official policies negatively influence this industry. possibly, the reason is that when the epidemic continues, public emotions have stabilized. thus, most people stay at home, no longer buying drugs blindly. although the epidemic negatively impacts the transportation industry, the policies show positive to this industry. possibly, the reason is that the epidemic has reduced the tourism, but the deployment of materials and personnel after the policies were conducted relatively stimulates the transportation industry. the model provides a universal method to calculate the impact on industries. as long as we get the stock indices of several companies in a certain industry, we can calculate the impact of the government on this industry quickly. more commonly, the dummy variable can be used to calculate the impact of a certain period on a certain industry. we can set different interval of i to determine when the dummy variable n d,i equals to and when it equals to . however, in this paper, we do not collect the data of all listed companies in certain industry, so errors probably exist. we provide cird-f model to analyze the spread and influence of covid- . we use different parameters to predict the trend of the epidemic in and out of hubei. the influence of official policies is divided into two parts: virus transmission, and economy. when predicting the tendency of the epidemic, we adopt the negative feedback to quantify public vigilance and consider the difference between people in the incubation and infection period. we also take different situations in and out of hubei into consideration. the results can be used to evaluate the possible infections which are reduced by official policies. when quantifying the economic influence of the policies on different industries, we calculate the influence of the epidemic and the influence of the epidemic after the policies were published. using these results, we can evaluate how the policies influence different industries. according to our calculation, the termination date of the epidemic in hubei are different from that of other parts of china. the former is around march , while the latter is around march . therefore, the epidemic in china will terminate on march . it means that the outbreak will not last long. according to the different situations in and out of hubei, we find that official policies are very helpful in reducing the number of infections. from the perspective of china, if the control is not timely, there will be about more infected people. if hubei acts like other regions in china, the number of infected people will be greatly reduced, which further confirms the importance of early prevention and control of the epidemic. furthermore, we use capm-dv model to calculate the economic impacts of the epidemic and official policies on different industries. the epidemic influences the healthcare industry positively and impacts the transportation, construction and tourism industries negatively. by contrast, the policies relatively influence the construction industry positively and impact the transportation, healthcare and tourism industries negatively. however, when using the cird-f model, we assume that the cure rate and the death rate remain unchanged to simplify the calculation. in the future work, we can treat the cure rate and the death rate as a function of time to give a more accurate prediction. novel coronavirus is putting the whole world on alert a cellular automaton model for the effects of population movement and vaccination on epidemic propagation outbreak of covid- : an urgent need for good science to silence our fears on the design of hyperstable feedback controllers for a class of parameterized nonlinearities: two application examples for controlling epidemic models clinical characteristics of coronavirus disease in china dummy variable regression model and two-stage nested design of agricultural variables a labor capital asset pricing model the mathematical principle of the spread of sars and its application on forcasting and controlling sars epidemic a new method for fuzzification of nested dummy variables by fuzzy clustering membership functions and its application in financial economy the epidemiological characteristics of an outbreak of novel coronavirus diseases (covid- ) in china epidemiological and clinical characteristics of cases of novel coronavirus pneumonia in wuhan, china: a descriptive study transforming clinical data into actionable prognosis models: machine-learning framework and field-deployable app to predict outcome of ebola patients nexuses between economic factors and stock returns in china the relationship between the stock market and the economy: evidence from central and eastern european countries key: cord- -caz fwl authors: yu, xinhua; duan, jiasong; jiang, yu; zhang, hongmei title: distinctive trajectories of covid- epidemic by age and gender: a retrospective modeling of the epidemic in south korea date: - - journal: int j infect dis doi: . /j.ijid. . . sha: doc_id: cord_uid: caz fwl objectives: elderly people had suffered disproportional burden of covid- . we hypothesized that males and females in different age groups might have different epidemic trajectories. methods: using publicly available data from south korea, daily new covid- cases were fitted with generalized additive models, assuming poisson and negative binomial distributions. epidemic dynamics by age and gender groups were explored with interactions between smoothed time terms and age and gender. results: a negative binomial distribution fitted the daily case counts best. interaction between the dynamic patterns of daily new cases and age groups was statistically significant (p < . ), but not with gender group. people aged - years led the epidemic processes in the society with two peaks: one major peak around march and a smaller peak around april , . the epidemic process among people aged or above was trailing behind that of younger people with smaller magnitude. after march , there was a consistent decline of daily new cases among elderly people, despite large fluctuations of case counts among young adults. conclusions: although young people drove the covid- epidemic in the whole society with multiple rebounds, elderly people could still be protected from virus infection after the peak of epidemic. the novel severe acute respiratory syndrome associated beta-coronavirus (sars-cov- ) of unknown origin, appeared in wuhan, china in late december and has swept the world over the past few months (anderson et al. ; li et al. a; zhu et al. ) , causing over , deaths worldwide (https://coronavirus.jhu.edu/map.html, accessed on june , ) and significantly disrupting both societal activities and person life (center ) . although several early studies described the dynamics of the epidemic process in details (li et al. a; wu and mcgoogan ) , many uncertainties remained. for example, diagnosis criteria varied significantly across countries. during the early epidemic in wuhan, china, patients were required to have serious pneumonia symptoms plus lab confirmed virus detection (huang et al. ; zhu et al. ) , thus missing most mildly symptomatic and all asymptomatic patients. as suggested in a modeling study, probably % of covid- cases might be undocumented in wuhan (li et al. b) . many epidemic measures such as basic reproduction number based on early epidemic in wuhan were questioned by later studies due to possible underestimating the true parameters (nishiura et al. ; zhao et al. a; zhao et al. b ). on the other hand, some countries such as south korea and singapore classified patients only based on lab tests, yielding a better picture of the epidemic. to fully understand the epidemic process of covid- , accurate and complete epidemic data are indispensable. data from south korea have been generally considered of highest quality, mainly due to two notable strategies adopted by the south korea government from the beginning of the epidemic: extensive contact tracing and massive testing to identify possible cases in addition to case isolation (shim et al. ) . south korea identified the first covid- case on jan , , and the outbreak started its exponential growth after feb , . in an outbreak j o u r n a l p r e -p r o o f occurred in a call center, , people were tested, were positive and confirmed (positive rate . %) (park et al. ) . after tracing all contacts of those cases, about % were tested positive (secondary attack rate). in addition, south korea also installed roadside testing stations to test any person who had concerns about his/her infectious status, in addition to those who had contacted known patients. such extensive controlling measures not only halted the epidemic successfully but also produced a more complete picture of the covid- epidemic. a striking phenomenon in covid- was that people aged or older suffered the heaviest burden of the disease (richardson et al. ; wu and mcgoogan ) and the proportion of cases was higher in men than that of women. according to a recent cdc report, about % of deaths occurred among elderly people, and those aged or above had almost % chance of dying if infected (cdc ; garg et al. ) . in our previous analysis based on florida covid- data, we found that people aged or older accounted for % of hospitalizations and % of deaths. the mortality rate was % among elderly people who were infected with coronavirus (yu a). furthermore, since may , , the covid- pandemic has been waning down across the world (https://coronavirus.jhu.edu/map.html), pressing many countries to consider re-opening the business. many public health experts warned a possible rebound of new cases if current interventions were relaxed (chowell and mizumoto ; ferguson et al. ; kissler et al. ). a recent model predicted that covid- epidemic might last more than a year and multiple waves of outbreaks were possible (kissler et al. ) . it is likely elderly people may still suffer the heaviest disease burden during the return of outbreak (hay et al. ). however, it was unknown whether and how the epidemic processes were different between young and old people. in this study, we aim to statistically learn the dynamics of the covid- j o u r n a l p r e -p r o o f pandemic based on data from south korea. in addition to identifying the best fit of the epidemic process, we explore gender-and age group-specific trajectories of covid- to facilitate our understanding of the disease and its impact on different populations, and inform the potential and severity of covid- rebound. the daily counts of confirmed new covid- cases and deaths were obtained from the open source (https://github.com/jihoo-kim/data-science-for-covid- , accessed on may , ), which were systematically gathered from korea center for disease control (kcdc) daily reports. all cases were verified against kcdc reports. the line list file included patient's age, gender and date of virus infection confirmation. however, the line list file excluded almost all cases occurred in the city of daegu (more than , cases), and thus cases from daegu were excluded from our study. we further excluded cases with missing confirmation date (n= ). age was grouped (in years) as - , - , - , and or above. those with missing gender information (n= ) or missing age information (n= ) were retained in the analysis for overall trajectories (total sample size n= ), but were excluded in the gender or age specific analysis. since our purpose in this study was not to predict new cases in the future but to model the epidemic process, we adopted a semi-parametric generalized additive model (gam) to obtain fitted daily case counts and also account for non-linear patterns of epidemic process (wood ) . the time was modeled as a continuous variable with smoothing terms (thin plate regression splines with knots). interactions between smooth terms and gender (or age group) j o u r n a l p r e -p r o o f were modeled as separate smoothing function for each group. specifically, for interaction models: where yij represents the observed case counts of day i and group j that follows a certain distribution. in this study, we focused on negative binomial (nb) or poisson distributions due to their robustness. we use variable timei to represent day starting from , ij( ) is an indicator variable ( / ) denoting if daily counts of new cases is for group j ( ) or not ( ), bk( ) represents a basis function for the k th term to smooth temporal trend, and j,k are regression coefficients for smooth term k and group j (representing group-specific effects). parameters were estimated via the restricted maximum likelihood (reml) approach. the generalized cross validation criterion with mallows' cp (gcv.cp) and maximum likelihood (ml) methods were also explored. therefore, the above gam framework allows us to compare different trajectories through examining the interactions between smoothed time term and age/gender groups with a focus on comparing the overall trajectories rather than point-wise comparisons. statistics r and percent of deviance explained by the models were used to identify the best fit model. r package mgcv was used to fit the gam model (wood ) . the data and programs are available online at https://github.com/jiasong-duan/covid- -epidemic-trajectories. from feb. to apr. , , there were , covid- cases ( , males, %) identified outside the daegu city. those with age - accounted for % (n= ) of total cases, and age j o u r n a l p r e -p r o o f - for % (n= , ), age - for % (n= , ), while those with age or above accounted for % (n= ) of total cases. as shown in figure , the epidemic outside the daegu city peaked around mar. , and declined afterwards except for a second small peak around march , . the fitted curves to the observed daily new cases were overlaid on the observed counts in figure . predictions from both nb and poisson models were indistinguishable. however, the confidence intervals from nb model were much wider than that of poisson model. as shown in the model comparison to be conservative, the model based on nb distribution was selected and implemented in the subsequent analyses. the confidence intervals from the fitted models were omitted in the subsequent plots to emphasize different overall patterns in the epidemic process. while there were two peaks in the epidemic process among people aged - years. in fact, the epidemic among people aged - led the whole epidemic process in the total population such that not only did young adults have more daily new cases than that of other age groups, but also the epidemic processes among people aged - and + years were trailing one to three days behind that of aged - . to further explore age and gender effects on the epidemic process, figure a -b presented the fitted epidemic curves by age groups for males and females separately. among males, people aged - had highest predicted daily counts and experienced two peaks over time, while those aged or older had much lower daily case counts and decreased consistently over time despite the large changes of epidemic in young adults. those aged - also experienced two peaks in the epidemic but were at a smaller scale than young adults. the patterns of epidemic processes by age groups among females were different from that of males. those females aged - and aged - had similar epidemic processes during the first peak of epidemic. the daily case counts among females aged - also increased after april , . females aged or above had smaller magnitude of epidemic but overall, similar to that of females aged - . in this study, we demonstrated different trajectories of covid- epidemic between gender and age groups based on south korea data. first, based on case reporting date and assuming similar incubation periods and reporting delays across all groups and over the whole study period, young people aged - years led the epidemic processes in the whole society and also had j o u r n a l p r e -p r o o f experienced two peaks about one-month apart, one major peak around march and a smaller peak around april , ; second, school age people (aged - ) had much smaller magnitude of epidemic overall; and finally, the epidemic process among people aged or above was trailing behind that of younger people, and the magnitude of epidemic was smaller than that of people aged - or - . after march , there was a steady decline of daily new cases among people aged or above, despite large fluctuations of case counts among young adults. our findings were consistent with other reports in which younger people accounted for most confirmed covid- cases (guan et al. ; wu and mcgoogan ; zhang et al. ). our empirical evidence from high quality data supported that covid- epidemic was driven by the infection among young adults. in addition, school age children had the least burden of disease, possibly due to early school closure and vacation breaks during that period. this pattern was different from that of typical respiratory infection diseases such as seasonal flu in which most cases were school age children. worldwide, people aged or above endured a disproportional burden of covid- disease (wu and mcgoogan ) . they had a higher risk of hospitalizations, and about % deaths occurred in this age group (garg et al. ). however, it was unclear whether elderly people were more likely to get infected, whether virus transmissibility was higher among elderly, or whether elderly people were merely more likely to have severe diseases than younger people (hay et al. ; zhang et al. ) . elderly people generally have weaker immune system than younger people. meanwhile, they have been exposed to many viruses over lifetime that may shield them from getting infected by a new virus, but there was no evidence for any prior immunity to the sars-cov . nonetheless, our findings provided some hope for mitigating the impact of epidemic on this vulnerable population. as demonstrated in figure b and a in addition, although overall gender difference in the covid- epidemic was moderate, age and gender specific analyses suggested that females (and to a less extent, males) aged - had similar experience of epidemic to that of people aged - . this might be because this age group often had close and frequent contacts with younger people in work or within households. though the risks of hospitalizations and deaths were low among this population, they were higher than that of regular respiratory infectious diseases such as seasonal flu. thus, the disease burden among this middle age group should not be neglected. there were some limitations in this study. first, our study excluded cases from the city of daegu (over cases) because detail information about cases from that city was not released to the public. although it was unlikely to bias our results, information from such a large outbreak could provide some additional insights on how the epidemic unfolded among people of different age and gender. however, during the early stage of epidemic, little gender and age stratified data j o u r n a l p r e -p r o o f were publicly available, and most individual level data from other regions were incomplete as well. second, we employed statistical methods to examine the trajectories of epidemic. there were two perspectives to model the epidemic process (hethcote ; unkel et al. ) . one common approach was to model the process based on the mechanisms of the epidemic. for example, the susceptible-exposed-infectious-removed (seir) model and its variants had been used to assess the dynamic of epidemic, obtain epidemic parameters, and evaluate the impact of various control measures on the epidemic (kucharski et al. ; peak et al. ; prem et al. ; yu b) . agent-based models were also used to simulate the epidemic process and assess the effects of various interventions (ferguson et al. ; ). the other perspective was based on traditional statistical models. non-linear models such as generalized logistic growth model (chowell ) were used to model the growth of the epidemic and estimate the growth rate of cases over time. in addition, some researchers directly modeled the epidemic curve with regression techniques, assuming daily counts follow some distributions such as poisson or negative binomial distributions. for example, models based on time series of count data were adopted to predict the covid- deaths in the us, such as those models from institute of health metrics and evaluation (ihme) (ihme ) and university of texas-austin (woody et al. ). our previous research also used vector autoregressive models to examine the risk interactions across age groups after the peak of covid- epidemic (yu c) . while there were many uncertainties among different gender and age groups about contact patterns, virus transmissibility and behavioral changes during the epidemic, since the epidemic data from south korea were more likely to be complete, it is possible to directly model the daily counts j o u r n a l p r e -p r o o f with regression models assuming a common distribution for count data. we believed that out models avoided many unfounded assumptions in the more complicated epidemic process models. third, we only have case reporting or lab confirmation dates in this study which were likely - days away from the actual virus infection date. the average incubation date for covid- was about days (lauer et al. ) and the report delay in south korea was unknown but likely very short due to extensive testing. thus, we make some untestable assumptions in comparing epidemic trajectories between age and gender groups. the incubation period and reporting delay were assumed to be the same across all groups and over the whole study period. this should be pertinent in south korea as they started mass testing and contact tracing from the beginning of the epidemic (shim et al. ) but may not be appropriate for the regions that testing is severely limited and delayed. finally, we only analyzed data from south korea. the epidemic processes of covid- in different countries were likely different due to different population structure and different interventions to mitigate the epidemic (anderson et al. ; chowell and mizumoto ; hay et al. ; lipsitch et al. ) . meanwhile, we expect our findings provided a general picture of the epidemic trajectories of covid- and can serve as a reference to other regions. in addition, as witnessed in the covid- epidemic, politics and ideology often overtook science and public health, so that effective interventions were sometimes implemented too late and incomplete, leaving the public at lost and public health practitioners in conundrum. the main strength of our study was our straightforward analyses to explore different epidemic processes based on high quality data. insights often emerge through such modeling exercise. we stratified the models by age and gender groups and discovered their different trajectories in the epidemic. recent studies had predicted a long-lasting epidemic for covid- and possible j o u r n a l p r e -p r o o f multiple waves of outbreaks after societal re-opening (kissler et al. ) . our findings were unique in providing empirical evidence for designing effective public health strategies to mitigate the impact of recurrent covid- epidemics and protect vulnerable populations. in summary, in south korea, and likely in other countries, covid- epidemic processes had distinctive dynamic patterns among age and gender groups. epidemic among young adults led the epidemic process in the whole population, and a second peak occurred in people aged - years. more importantly, during the post-peak period of the covid- epidemic and in the process of gradually returning the society and economy to normalcy, elderly people could be protected effectively though case isolation, contact tracing, mass testing, and proper personal protections, as exemplified in south korea. dr. xinhua yu was supported by fedex institute of technology, university of memphis for conducting this research. this study used only publicly available data and no human subjects were directly involved, thus deemed to be exempted from the approval of institutional review board. no informed consent was needed. all authors declared no conflict of interest in conducting this study. how will country-based mitigation measures influence the course of the covid- epidemic? severe outcomes among patients with coronavirus 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of the novel coronavirus disease (covid- ) during the early outbreak the basic reproduction number of novel coronavirus ( -ncov) estimation based on exponential growth in the early outbreak in china from to : a reply to a novel coronavirus from patients with pneumonia in china the authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. key: cord- -fq h i authors: yasir, ammar; hu, xiaojian; ahmad, munir; rauf, abdul; shi, jingwen; ali nasir, saba title: modeling impact of word of mouth and e-government on online social presence during covid- outbreak: a multi-mediation approach date: - - journal: int j environ res public health doi: . /ijerph sha: doc_id: cord_uid: fq h i although social presence plays an essential role under general conditions, its role becomes significant for societal protection during the quarantine period in epidemic outbreak. in this study, we attempted to identify the role of e-government and covid- word of mouth in terms of their direct impact on online social presence during the outbreak as well as their impacts mediated by epidemic protection and attitudes toward epidemic outbreaks. for this purpose, a unique multi-mediation model is proposed to provide a new direction for research in the field of epidemic outbreaks and their control. through random sampling, an online survey was conducted and data from participants were analyzed. partial least squares structural equation modeling was used to test the relationships between the variables of interest. the study results revealed that the roles of e-government and covid- word of mouth are positively related to online social presence during the outbreak. epidemic protection and attitude toward epidemic outbreak were found to positively moderate the impact of the role of e-government and covid- word of mouth on online social presence during the outbreak. the key findings of this study have both practical and academic implications. the flow of information in any matter is important and can considerably impact the situation during an epidemic outbreak. the role of e-government is also essential in any situation related to health protection, especially during an outbreak period. e-government (e-govt) is defined as "the use of information technologies that have the ability to transform relations with citizens, businesses, and other arms of government" [ ] . keeping people calm and focused is necessary during an epidemic and its quarantine period. if people are quarantined, the roles of e-govt and word of mouth (wom), especially message sharing through social media, increase in importance. now, with the current covid- outbreak, people are under quarantine until further notice, with many countries experiencing epidemic outbreaks. people have more time to use social media, which could be a source of rumors, anxiety, and, most important, knowledge for with physicians' online statements [ ] . this shows that women are more emotional about health conditions, especially during an epidemic outbreak. evidence was provided that rumors are spreading during the covid- outbreak in other countries, but in china, people were likely to improve their emotions in the fight against covid- and stay strong during the outbreak period by sharing positive posts on social media. as of the date of writing, march , we have been in quarantine since january , having direct experience with both normal life and quarantine. on social media, the importance of being online, especially during an epidemic outbreak, and the role of e-govt in the quarantine period shown in previous research, urged us to explore this phenomenon on a broader basis. positive awareness through the effects of covid- word of mouth ( -ncov-wom) and e-govt in the epidemic period has not been sufficiently explored. regardless of the important roles of -ncov-wom and e-govt in the epidemic outbreak, quantity of research is lacking. although online social presence is important at this time, scholars have not explored it sufficiently. from the literature, questions were raised whether online social presence increased the ability to obtain information about the safety measures and, with h of free time to use social media, if people might be more willing to spread safety information. on this basis, we tried to explore the direct effect of -ncov-wom and e-govt on online social presence, and tried to fill this gap using a cohesive methodology to identify the mediating effect of attitude toward epidemic outbreak and epidemic protection on online social presence. we used five constructs ( -ncov-wom, role of e-govt, attitude toward epidemic outbreak, epidemic protection, and online social presence in the outbreak) with a conceptual multi-mediation model. we explored a distinctive approach to answer two questions: is there any mediating effect of attitude toward epidemic outbreak and epidemic protection on online social presence? what is the best possible combination for the government to increase people's willingness to participate in quarantine with a psychological perspective? in the next section, we discuss our research model. based on the analysis, we discuss our study results in section . finally, consequences and practical implication of our research are given and future research is suggested in section . to fill these research gaps, we provide a new direction for research about epidemic outbreaks by discussing the role of e-govt and the effect of -ncov-womin relation to the use of social media and their mediating effect on long-term outbreaks. our research questions (rqs) were: rq : what is the association between social media, epidemic protection messages, and online social presence? rq : is there any mediating association between -ncov-wom and the role of e-govt in online social presence? people have perceptions about their government playing a role during an epidemic condition. perceptions are heightened during an outbreak period, as people are concerned about their protection, and their attitude toward an epidemic outbreak depends on this protection, to some extent. during a quarantine period, as people are isolated, the perceived role of e-govt may be increased and people might be motivated to play a role in epidemic protection after watching the involvement of e-govt. in our questionnaire, we asked about trust in e-govt, which might provide motivation to play an important role in epidemic protection. the literature shows that the role of government, especially governmental strategies and alertness messages, in any outbreak is progressively enhanced [ ] . communication and interaction with the government has increased in last few years, as the government is interested in engaging its people through social media [ ] . the abovementioned literature justifies that the government understands people's perceptions about the role of e-govt. people involved in policy-making are also inspired by social media [ ] . factors involved in sharing information are not described in this literature [ ] . attitudes and awareness is connected to the supposed efficiency of policy-making [ ] . improvement and development in chinese e-waste has been seen in the last six years [ ] .this might enhance the people perceptions about e-govt playing a role in an epidemic outbreak. in canada, social media was used as tool for facilitation of consumers by government officials [ ] . in latin america, research on e-govt is increasing and conflicting with what is occurring in the world [ ] . one reason we involved e-govt and online social presence in our research model is that a noteworthy difference was identified the in analysis of awareness about the use of mobile phones to seek health information during critical times [ ] . awareness promotion plays an important role in burn cases [ ] . universal and global research is needed in community health for the use of social media in e-govt [ ] . our study variables included capability of isolation, quarantine compartment, and interaction methods, which are responsible for occupancy rate isolation [ ] . to stop the transfer of infectious disease, isolating infected people from healthy ones is vital [ ] . the biggest outbreak of coronavirus, the middle east respiratory syndrome (mers), occurred in south korea in . the main spread of this virus occurred in south korea from and out of hospitals [ ] . as an independent variable, we added role of e-government in our study, because studies were lacking on the emotional influence of mers outbreaks [ ] . research showed that administration, media, and celebrities play important roles in health promotion on twitter [ ] because people are more attracted to celebrities. recommendations that are logically expressed have a strong impact on public [ ] . many governments are improving their use of social media in health departments and are trying to provide digital services to their people guidance; especially during outbreaks. to increase the theoretical literature on e-govt in the health sector, we aimed to fill this gap using a systematic review method to analytically evaluate, recognize, and create research evidence for the use of -ncov-womin connection with the role of e-govt in protection from covid- . we also tried to critically evaluate the role of social media and the willingness to undergo a long quarantine period for protection from this epidemic. here, per the literature, we take this variable of people's perception (perceived role) of the role of the chinese government, which was important because the government provided a plan to withstand the outbreak period. notably, this is the first critical review of the use of -ncov-wom and the role of e-govt in the covid- epidemic (as independent variables). given the above literature, we expected that e-govt plays a considerable role in the perception of epidemic protection and online social presence and in changing public attitudes toward an epidemic outbreak. therefore, we hypothesized the following: hypothesis a (h a): role of e-government considerably affects epidemic protection. role of e-government considerably affects online social presence during an outbreak. role of e-government considerably affects attitude toward an epidemic outbreak. wom provides new directions to people's thoughts and views about any condition, and especially during an epidemic outbreak. nowadays, the top trend is covid- epidemic conditions discussed in news and online social websites. many studies in the last years proved that there has been a large increase in the number of people willing to find health information on the internet. an increase in the number of social profiles providing health information was also observed [ ] . electroencephalography inter-subject correlation (eeg-isc) was improved by an increase in resilient health communication [ ] . the people of wuhan felt great confidence in sharing their views during data collection during the covid- epidemic outbreak quarantine. health promotions broadcast by the media are used to promote awareness. for young italian people, the messages were mostly about health and the environment [ ] . this is significant because health experts have been using it as a motivational tool during the treatment of patients [ ] and because histories of patients with similar symptoms are important for predictions [ ] . this may be helpful for the emotional treatment of patients in the future. conversely, the most important aspect of health promotions is increasing people's patience and keeping them calm during the quarantine period to avoid anxiety. the chinese government improved public endurance by their emotional awareness through message sharing, which encouraged people to share their views [ ] . it is a common for people to first think that social media information is only rumors during an outbreak; as such, people were at risk of being ignorant of health information shared by the government or by individuals. to provide better and urgent cure, people should know the signs and symptoms of corona viruses. many symptoms of the novel covid- -infected pneumonia (ncip) have been described by researchers; they include increased body temperature, dry cough, and body pain [ ] . the chinese government promoted awareness among people through social media, so that individuals showing signs of covid- would immediately understand and contact medical experts for treatment and minimize further spread of the virus. only online -ncov-wom was used for the quarantine period in china, especially in wuhan and anhui; some other countries soon after implemented quarantine measures. this means the chinese government played a positive role in the safety of people. the above-mentioned research demonstrated the importance of online -ncov-wom. so, we tried to explore the positive effect of -ncov-wom on online social presence in our research using exclusive mediating variables. we expected that -ncov-wom not only significantly affects perceptions of epidemic protection in terms of individuals' online social presence, but also influences changes in attitude toward the epidemic outbreak. so, we hypothesized the following: hypothesis c (h c): covid- word of mouth considerably affects attitude toward the epidemic outbreak. everyone is concerned with their protection in any condition, but particularly during an epidemic outbreak. the protection factor might affect social presence, but as people are isolated during quarantine, this factor changes the effect on online social presence in other ways. individuals' attitudes toward fitness is boosted by viewing health information posted on facebook in video form [ ] . people's responses to epidemic protection increase especially during quarantine because they are at home and have more free time. individuals with prolonged health problems acknowledged caretakers' guidance more than other adults in the u.s., but they did not obtain physical exercise guidance for good health [ ] . the covid- epidemic protection urged people to increase their online social presence to enhance public emotions for epidemic protection. the empirical studies mentioned above encouraged us to relate epidemic protection as a dependent variable due to obtaining specific information to protect online users during the quarantine period. here, we took this variable as people's perception to ensure their safety. china is more conscious about health due to the one-child policy, free internet to obtain information, and the perception of being safe through obtaining safety measures. therefore, we hypothesized the following: the literature discussed above indicated that assuming the role of e-govt in online social presence of the public is mediated by epidemic protection and -ncov-wom affects online social presence. however, we suspected that -ncov-wom is boosted by the psychological perception of epidemic protection. so, we hypothesized the following: hypothesis c (h c): epidemic protection mediates the association between covid- word of mouth and online social presence. hypothesis b (h b): epidemic protection mediates the association between role of e-government and online social presence. a study showed that people's attitudes toward an epidemic outbreak are more influenced by information on social media compared with physical discussion because source reliability has no impact on the health information provided online [ ] .people obtain information about the outbreak through social media and mobile health apps [ ] .however, a risk of client secrecy exists because online services are substantially affected by the happiness of clients [ ] .we took attitudes toward an epidemic outbreak as a mediating effect, meaning that attitudes toward an epidemic outbreak will promote or mediate the relationship of two independent variables and social online presence, as shown in figure . presence. however, we suspected that -ncov-wom is boosted by the psychological perception of epidemic protection. so, we hypothesized the following: hypothesis c (h c): epidemic protection mediates the association between covid- word of mouth and online social presence. hypothesis b (h b): epidemic protection mediates the association between role of e-government and online social presence. a study showed that people's attitudes toward an epidemic outbreak are more influenced by information on social media compared with physical discussion because source reliability has no impact on the health information provided online [ ] .people obtain information about the outbreak through social media and mobile health apps [ ] .however, a risk of client secrecy exists because online services are substantially affected by the happiness of clients [ ] .we took attitudes toward an epidemic outbreak as a mediating effect, meaning that attitudes toward an epidemic outbreak will promote or mediate the relationship of two independent variables and social online presence, as shown in figure . research showed that the availability of a vaccine for an epidemic affects people's attitudes toward the outbreak; for publicizing a vaccine, online sources are important. during epidemics, curiosity about a vaccine is more influenced by publicity, not by the epidemic conditions. however, vaccine uptake is also influenced by the epidemic condition when epidemic increases [ ] .recommendations by doctors, friends, and relatives stimulate people [ ] as they discuss their responses to epidemics. people who are isolated during an epidemic must recognize the importance of protection [ ] .research in toronto, canada, proved the willingness of people to participate in studies and the stress experienced by medical experts due to wearing of caring apparatus and being infected by disease in canada. as these medical experts were involved in attempting to cure a disease about which they had little knowledge, they were worried that they would be next targets when they saw their coworkers becoming sick and dying due to the epidemic [ ] . lack of trust in government was observed in the public in korea when attempting to control the mers epidemic [ ] . however, our focus was on the effect of -ncov-wom and the role of e-govt to protect the people during long-term outbreak, and to examine the response of people during the quarantine period. we supposed that public attitude toward epidemics affects their online social presence. in china, people are willing to share news and have positive attitudes when sharing the good news about protection. so, we hypothesized the following: research showed that the availability of a vaccine for an epidemic affects people's attitudes toward the outbreak; for publicizing a vaccine, online sources are important. during epidemics, curiosity about a vaccine is more influenced by publicity, not by the epidemic conditions. however, vaccine uptake is also influenced by the epidemic condition when epidemic increases [ ] . recommendations by doctors, friends, and relatives stimulate people [ ] as they discuss their responses to epidemics. people who are isolated during an epidemic must recognize the importance of protection [ ] . research in toronto, canada, proved the willingness of people to participate in studies and the stress experienced by medical experts due to wearing of caring apparatus and being infected by disease in canada. as these medical experts were involved in attempting to cure a disease about which they had little knowledge, they were worried that they would be next targets when they saw their coworkers becoming sick and dying due to the epidemic [ ] . lack of trust in government was observed in the public in korea when attempting to control the mers epidemic [ ] . however, our focus was on the effect of -ncov-wom and the role of e-govt to protect the people during long-term outbreak, and to examine the response of people during the quarantine period. we supposed that public attitude toward epidemics affects their online social presence. in china, people are willing to share news and have positive attitudes when sharing the good news about protection. so, we hypothesized the following: hypothesis b (h b): attitude toward epidemic outbreak considerably affects online social presence. the attitude of the public toward a situation impacts their online social presence and affects the role of e-govt and -ncov-wom on online social presence. this means that if the attitude of the public is positive, it mediates role of e-govt and online social presence. hence, we hypothesized that: hypothesis c (h c): attitude toward epidemic outbreak mediates the association between covid- word of mouth and online social presence. hypothesis b (h b): attitude toward epidemic outbreak mediates the association between the role of e-government and online social presence. according to social presence theory [ ] , social presence is about intimacy, feeling of closeness, familiarity, immediacy, and urgency to exchange information and motives in society. online social presence is important during epidemic outbreak quarantine periods. it not only plays an important role in the coordination of society but also in the creation of motives. online social presence is predicted by online streaming, mediating communal television pleasure [ ] . among the magnitudes of social presence (telepresence and social presence), online social presence indirectly plays a role in the mediating direction. findings encouraged innovative marketing policy through which participation can be optimistic by refining presence fundamentals [ ] . people are more attracted toward celebrities, which strengthens online social presence [ ] . so, if celebrities are active during outbreak periods, they can motivate people to increase their online social presence. in addition, human sympathy is apparent on online sites and especially social sites, representing their online social presence and recognizing their interactions and feelings [ , ] . the capability of a platform to deliver personal indications and increase online social presence willingness [ ] is interceded by useful commitments [ ] . every website provides specific confidentiality, which is expressively affected by online social presence [ ] . private platforms are facilitated by online social presence [ ] , so we predicted that they also affect the online response of people in quarantine during epidemics. sociability, pleasure, and belief are emotive reactions that reconcile social presence [ ] . these three responses were felt across the chinese nation during the covid- outbreak. people believe that we will overcome this deadly virus and people were seen to be more emotional and social during this pandemic. online social presence varies from their level of appointment, which reveals intellectual burden [ ] . contribution by people is inspired by their social value [ ] . addiction to social networking sites (sns) also improves online social presence and increases people's pleasure when interacting socially, also improving social communication and gratification [ ] . online social presence influences online engagement [ ] . we included two areas in our study: wuhan in hubei (all cities from this province) and anhui province. participants of our study were mostly from wuhan. anhui (hefei province) is the nearest city to wuhan, so we also considered anhui in our study. we were all in quarantine (except one doctor as a writer for medical terminology association but she is not living in china), directly experiencing the feelings of this situation. random sampling and snowball sampling techniques were used to collect the data. it was impossible for us to go to wuhan due to quarantine during the outbreak. we were quarantined by ourselves. to avoid this hindrance on data collection, we decided to collect data online. we sent our questionnaire to the people of wuhan and anhui provinces. data was collected during the covid- quarantine period, which has been in place for almost one month and continued during the research. most of the participants were chinese; however, we also included foreigners living in wuhan and anhui because of their presence. however, due to various countries' evacuation policies, we decided to exclude the foreigners' data. due to the mixed participants of our study, we used two versions of the questionnaire to overcome any language barrier. we used an english version for data collection from foreigners and a chinese version for the domestic population in wuhan and anhui. to increase interest and willingness of participants we sent them hongbao (lucky money) to the group owners of wechat through wechat (only owners, not the participants). we collected data from people (still ongoing, the corresponding author is willing to help any researchers with future research). in total, the participants included men and rest were women (we aimed to obtain participants equally from both sexes). due to online foreigners' evacuation during data collection, we excluded records during analysis and used valid samples for analysis. after the evacuation policy implementation, we decided to stop the collection from foreigners. the demographic characteristics of our research data are provided in table . moreover, the itemized sources of constructs used in the research are given in table . role of e-govt efforts of e-govt, trust in e-govt, support of e-govt [ ] -ncov-wom information,countries' status, -ncov-plan [ ] epidemic protection hand wash, mask, motivation to protect [ , ] attitude toward epidemic outbreak willingness to quarantine, health psychology, doctors' advice [ ] online social presence in outbreak more present in quarantine, present for social support, present to discuss covid- the steps in our methodology are reported in figure . role of e-govt efforts of e-govt, trust in e-govt, support of e-govt [ ] -ncov-wom information,countries' status, -ncov-plan [ ] epidemic protection hand wash, mask, motivation to protect [ , ] attitude toward epidemic outbreak willingness to quarantine, health psychology, doctors' advice [ ] online social presence in outbreak more present in quarantine, present for social support, present to discuss covid- the steps in our methodology are reported in figure . from onward, a noticeable increase in participation of partial least squares structural equation modeling has been reported [ ] . if not familiar with the data type or if the data have a common factor or are composite-based, findings illustrate that use partial least squares (pls) is the best choice for analysis [ ] . appraisal and review studies explained that in management research with multivariable analysis techniques, the application of partial least squares structural equation from onward, a noticeable increase in participation of partial least squares structural equation modeling has been reported [ ] . if not familiar with the data type or if the data have a common factor or are composite-based, findings illustrate that use partial least squares (pls) is the best choice for analysis [ ] . appraisal and review studies explained that in management research with multivariable analysis techniques, the application of partial least squares structural equation modeling (pls-sem) has been increased [ ] . pls-sem is being increasingly used in investigative and theory-based research [ ] . use of pls is increasing in different branches of management, especially research with one-variable-based techniques [ ] . past studies showed that pls-sem in different branches of management research have used multivariate analysis. as research in online user psychology is in its infancy and is not as developed as management research, the existing psychological studies about patients during pandemics during a sensitive time period (isolation)does not adequately explain the behavioral psychology of online users. as such, we applied pls-sem (smart pls) in our research [ ] . to assess our measurement model, we verified the concurrent validity, discriminate validity, and composite reliability (cr) [ ] . in addition to the square root values of the average variance extracted (ave), we compared constructs to determine the discriminate validity [ ] . factor loading values should be greater than . [ ] . for data validity and measurement, the value of the ave should be greater than . [ ] , cr > . [ ] , and rho > . [ ] . table provides the reliability and validity of our measurement scales and table provides the results of the fornell-larcker test used to check distinguished and divergent validity. to create intervals of confidence and t-values, we used bootstrapping ( re samples) to check for imagined associations between the concerned constructs of the planned structured model. streukens, s., et al. [ ] stated that bootstrap replications can vary considerably from a minimum of to a maximum of .in other words, statistic inconsistency is checked using the inconsistency of data using bootstrapping, which is a nonparametric resampling method, instead of using parametric statements to check the accuracy of approximation [ ] . efron, b., et al. [ ] proposed using more than bootstrap samples. the mediation effect is absent if the direct effect is not significant. figure illustrates the hypotheses testing of direct effects, which are also shown in table . table also provides the fit statistics. dependent variables indicate an important and positive precursor to their independent variables. particularly, the role of e-govt was a noteworthy predictor of epidemic protection. as can be seen from figure and table , all of the hypotheses were supported [ ] for the direct effect hypothesis at this step. to a maximum of .in other words, statistic inconsistency is checked using the inconsistency of data using bootstrapping, which is a nonparametric resampling method, instead of using parametric statements to check the accuracy of approximation [ ] .efron, b.et al. [ ] proposed using more than bootstrap samples. the mediation effect is absent if the direct effect is not significant. figure illustrates the hypotheses testing of direct effects, which are also shown in table . table also provides the fit statistics. dependent variables indicate an important and positive precursor to their independent variables. particularly, the role of e-govt was a noteworthy predictor of epidemic protection. as can be seen from figure and table , all of the hypotheses were supported [ ] for the direct effect hypothesis at this step. to check the importance of the structural path coefficients, we report the confidence interval [ ] . these were supported because we did not add up zero values in any confidence interval [ ] .at present, in standardized root mean square residual (srmr) pls path modeling, mostly model fit criteria are used. we checked the accuracy of the fit by using different tools like value of normed fit index (nfi), the non-normed fit index (nnfi), the comparative fit index (cfi), root mean square error of approximation (rmsea), and srmr. values equal to or higher than . in nfi, nnfi, and cfi indicate the best fit. sufficient adjustment was represented by rmsea and to check the importance of the structural path coefficients, we report the confidence interval [ ] . these were supported because we did not add up zero values in any confidence interval [ ] . at present, in standardized root mean square residual (srmr) pls path modeling, mostly model fit criteria are used. we checked the accuracy of the fit by using different tools like value of normed fit index (nfi), the non-normed fit index (nnfi), the comparative fit index (cfi), root mean square error of approximation (rmsea), and srmr. values equal to or higher than . in nfi, nnfi, and cfi indicate the best fit. sufficient adjustment was represented by rmsea and srmr with values less than . [ ] . for comparatively good fit between the hypothesized model and observed data, a cut-off value near to . for srmr and near . is best for rmsea; hu, l.t. et al. [ ] stated that a zero value for srmr indicates an ideal fit but if the value is smaller than . ,the fit is satisfactory fit [ ] . we investigated the standards of the coefficient of determination (r ) to verify the predictive strength of our structure model. collective consequences of exogenous contracts on endogenous constructs were indicated. the r of the endogenous latent variables is the vital decisive factor for this evaluation. this marker is used, from the perspective of a statistical model, to forecast future results or can be used to check the hypothesis on behalf of other related information. r also provides the results of the calculations and describes the practicality of the results [ ] . researchers can also use pls procedure to check their model's out-of-sample predictive power [ ] . in-sample predictive power, we also refer to the r [ ] . r varies from to and greater values show better descriptive power. substantial, moderate, and weak descriptive powers are indicated by r values of . , . , and . , respectively [ ] . pls-sem is less dependent on the model fit concept compared to cb-sem [ ] . as recommended [ ] rmsea cut-off values equal to or less than . using modification in r report effect size (f ) indicated that the effect of our dependent variables on independent variables was very satisfactory. the effect of the exogenous latent construct on the endogenous latent construct having three possible answers, i.e., substantial, moderate, and weak, was found using thef effect size. the blindfold method was used to check the strength of the research model. cohen's f is an identical measure of effect size that also permits checking the local effect size, which is the effect of one variable compared with the multivariate regression model [ ] . if the cross-validated redundancy (q ) is higher than ,then the model is related to predicting that factor [ ] . we focused on in-sample prediction more, compared to out-sample prediction, prognostic significance q , and relative relevance q , which are alternatives for evaluating a model's practical relevance, in addition to consulting r outcomes as a gauge of a model's predictive capabilities [ ] . r , q , path coefficients, and the effect size (f ) are the decisive factors we use for evaluation. in addition to this evaluation, researchers are required to check the inner model for potential co linearity issues. if the constructs are interrelated, then results approximated by the inner model are considered biased [ ] . a model's predictive accuracy is decided by the r . the r value also characterizes the combined consequence of exogenous variables on the endogenous variable(s). the effect ranges from to . a value of indicates complete predictive accuracy as can see in table . table . effect size and predictive relevance. cohen's f was calculated to check the effect size of each path model. when a construct was removed from the model, we calculated f while making no changes to r . researchers have to approximate two pls path models for computing f . the effect size of the omitted construct for a particular endogenous construct can be found by standard values: . for small, . for medium, and . for a large effect on the basis of the f value [ ] . this discussion supports the use of our mediators and variables in the model. in the pls path model, mediator variables absorb the effect of an exogenous construct on an endogenous construct; this absorption of effect is known as meditation [ ] . the mediation effect can be investigated using many tools, including pls-sem. though researchers use an older method to determine the mediation effect in pls-sem, the procedure that identifies the effect of a precursor variable on the findings and results is judged by mediation; in other words, mediation considers transitional variables [ ] . a mediating variable may have a transitional role in the association between dependent and independent variables, and engagement of this third variable is the important feature of the mediating effect [ ] . clarification and elaboration are the main effects of mediation [ ] . as such, we included multi-mediation concepts in the results of social presence theory and for psychological aspects during outbreaks (see table ). table . mediation analysis. table . multiple mediation paths outcomes and potency (level) of mediation effects are demonstrated in figures and . precise indirect effects were investigated by bootstrapping techniques with the help of the bias correction technique. the two independent variables (role of e-govt and -ncov-wom) affected online social presence; these effects support h b, h b, and h c in that order, as mentioned above. to determine whether h b, h b, h c, and h c are supported, we used the proposals by hair et al. [ ] . to finalize conclusions about the mediation effect; we calculated the amount and magnitude of mediation. we incorporated the variance accounted for (vaf) method to calculate the strength of mediation (figures and ). if vaf is less than . , there is no mediation; if vaf is less than or equal to . , there is a partial mediation; if vaf is greater than . , there is full mediation. the magnitude and strength of epidemic protection (h b: a b ) and attitude toward epidemic outbreak (h b: a b ) mediated the association between the role of e-govt and online social presence ( figure ). we found via comparison that epidemic protection has a partial mediation effect on the role of e-govt and online social presence because the vaf value was more than . , which indicated that there is a partial mediation effect. as such, h b is supported. attitude toward epidemic outbreaks mediated the association between -ncov-wom and online social presence; the vaf value was greater than . , which indicated the presence of mediation. therefore, we hypothesized imaginary harmonizing partial mediation because the effects of -ncov-womwere considerable both directly and indirectly and their products were positive [ ] . hair et al. [ ] concluded that complementary and competitive mediation can be differentiated if direct and indirect effects are more prominent. the condition in which direct and indirect effects work in the same direction is called complementary mediation. this means the outcome of the direct and indirect effect is positive. the magnitude and strength of the mediation effect of epidemic protection (h c: a b ) and attitude toward epidemic outbreak (h c: a b ) mediating the association of -ncov-womand online social presence is shown in figure . in comparison, the vaf value was higher than . , which indicated the presence and effect of mediation. due to the prominent direct and indirect effects of -ncov-wom, the complementary partial mediation was also positive. the comparison showed that the association between -ncov-wom and online social presence was mediated by attitude toward epidemic outbreak. the vaf value was higher than . , which indicated partial mediation, also supporting the multi-mediation hypothesis [ ] . int. j. environ. res. public health , , x for peer review of hair et al. [ ] concluded that complementary and competitive mediation can be differentiated if direct and indirect effects are more prominent. the condition in which direct and indirect effects work in the same direction is called complementary mediation. this means the outcome of the direct and indirect effect is positive. the magnitude and strength of the mediation effect of epidemic hair et al. [ ] concluded that complementary and competitive mediation can be differentiated if direct and indirect effects are more prominent. the condition in which direct and indirect effects work in the same direction is called complementary mediation. this means the outcome of the direct and indirect effect is positive. the magnitude and strength of the mediation effect of epidemic ipma, also called impact-performance map or priority map analysis, is a useful approach in pls-sem. ipma adds facets and measurements that consider the scores of latent variables reporting the path coefficient [ ] . approaches to determining the role of precursor constructs and their significance for management actions are offered by the pls-sem studies based on ipma. ipma compares the significance and recital (performance of the variables) [ ] . analysis dimensions are used to demonstrate the results of path coefficient approximation extended by ipma in figure . the advantage of ipma is the validation of total effects and a representation of their significance in a construct with an average score that indicates their performance. our main purpose with the construct was to find the most significant component in the construct. presence was mediated by attitude toward epidemic outbreak. the vaf value was higher than . , which indicated partial mediation, also supporting the multi-mediation hypothesis [ ] . ipma, also called impact-performance map or priority map analysis, is a useful approach in pls-sem. ipma adds facets and measurements that consider the scores of latent variables reporting the path coefficient [ ] . approaches to determining the role of precursor constructs and their significance for management actions are offered by the pls-sem studies based on ipma. ipma compares the significance and recital(performance of the variables) [ ] .analysis dimensions are used to demonstrate the results of path coefficient approximation extended by ipma in figure . the advantage of ipma is the validation of total effects and a representation of their significance in a construct with an average score that indicates their performance. our main purpose with the construct was to find the most significant component in the construct. online ratings are associated with higher enjoyment than negative reviews [ ] . to the best of our knowledge, the broader tasks and household behaviors of the community and family members in social media and role of e-govt have been relatively under-examined. we used an online questionnaire and proposed a unique conceptual model and multi-mediation model to achieve the objectives of our study. we constructed eight hypotheses for the direct effects(h a, h b,h c,h a,h b,h c,h a, and h b) and four hypothesis (h b,h b,h c, and h c) for the mediation effect of our dual mediators, i.e., epidemic protection and attitude toward epidemic outbreak, with their indirect effect between the role of e-govt and -ncov-wom on online social presence during outbreaks. our results are supported by mmijail etal. [ ] who concluded that local government affects the attitude and decision-making process of people with their e-government platforms. the results of our study showed that role of e-govt have a strong effect on the attitude of the public toward quarantine. our study results also showed that public relationship directly influences positive wom. our study results are supported by kim etal., who concluded that local government affects the social presence of community participants and the identified individuals' attitudes and community [ ] . our study results online ratings are associated with higher enjoyment than negative reviews [ ] . to the best of our knowledge, the broader tasks and household behaviors of the community and family members in social media and role of e-govt have been relatively under-examined. we used an online questionnaire and proposed a unique conceptual model and multi-mediation model to achieve the objectives of our study. we constructed eight hypotheses for the direct effects (h a, h b,h c,h a,h b,h c,h a, and h b) and four hypothesis (h b,h b,h c, and h c) for the mediation effect of our dual mediators, i.e., epidemic protection and attitude toward epidemic outbreak, with their indirect effect between the role of e-govt and -ncov-wom on online social presence during outbreaks. our results are supported by mmijail et al. [ ] who concluded that local government affects the attitude and decision-making process of people with their e-government platforms. the results of our study showed that role of e-govt have a strong effect on the attitude of the public toward quarantine. our study results also showed that public relationship directly influences positive wom. our study results are supported by kim et al., who concluded that local government affects the social presence of community participants and the identified individuals' attitudes and community [ ] . our study results revealed that attitude toward epidemic outbreak has a strong mediation effect between the role of e-govt and online social presence during outbreaks, indicating that other governments and organizations can follow china's safety model. the chinese government allowed full opportunity to be online and for online users to promote hand washing and mask wearing during the covid- outbreak. as for as effect of -ncov-wom and online social presence is concerned, our study findings are supported a the previous study [ ] in which human voice and wom were found to have a positive impact on social presence. our findings showed that -ncov-wom has a positive effect on online social presence. online social presence is increasing worldwide. social media has become increasingly important, especially for covid- information. in this study, we determined the impact of the role of e-government and covid- word of mouth on online social presence. we estimated the mediation impact of epidemic protection and attitude toward epidemic outbreaks on online social presence. the key results showed that the role of e-government and covid- word of mouth positively impacted online social presence. similarly, epidemic protection and attitude toward epidemic outbreak showed positive mediation impact on online social presence. from estimated results, we outline some implications and policy suggestions: during quarantine, people have more free time to participate in social media, which increases their desire to be present online. for themselves and society, they want to participate in disease protection and to provide suggestions to perform positively during the difficult time caused by covid- quarantine. people can obtain basic information and protection measures from e-government and obtain specifics about the issue. for practical implementations during epidemic outbreaks, the results suggest that the health authorities and government should pay more attention to managing the attitude toward outbreaks and its relationship with the role of e-government. people's perceptions about the government will help build their willingness toward long-term pandemic control. some limitations were unavoidable in our study. we used two sampling techniques: random sampling and snowball sampling; future research can be improved using different kind of sampling and data collection techniques. the second major limitation was the use of single type of role of e-govt. the reason behind this limitation was the ongoing quarantine, so it was impossible to compare the relationship of -ncov-wom in online social presence with offline discussion because personal meetings, face-to-face contact, physical interviews, etc. were prohibited. however, future research can be improved using different types of research variables, using web scraping and web mining of top trends complete protection analyses. however, our findings can be implemented to improve online social presence and increase emotive protection during epidemic quarantine periods. fourth, the data were collected online. therefore, we were unable to gauge the respondents' responses during data collection, although people were very motivated to share their answers to the questionnaire because of the involvement of the role of the government. more adequate research can be conducted by expanding the study area, e.g., people from other countries. our study was limited to two provinces because as of march, , these two provinces were still under quarantine. the study could also be further improved by focusing on recovered patients and comparing different countries affected by covid- using the proposed research model. further research on special issues is highly encouraged in other countries that have different isolation facilities, e.g., free internet, quiz competitions for children, etc., on the basis of the theoretical background, web scraping, and trends. maturity assessment of local e-government websites in the philippines communication channels and word of mouth: how the medium shapes the message when audiences become advocates: self-induced behavior change through health message posting in social media advice reification, learning, and emergent collective intelligence in online health support communities product patriotism: how consumption practices make and maintain national identity quantifying health literacy and ehealth literacy using existing instruments 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productive comments. we are also thankful to xiaojian hu and mengjiehu for the inspiration. the authors have no conflict of interest to declare. int. j. environ. res. public health , , key: cord- - d ge authors: ivanov, dmitry title: predicting the impacts of epidemic outbreaks on global supply chains: a simulation-based analysis on the coronavirus outbreak (covid- /sars-cov- ) case date: - - journal: transp res e logist transp rev doi: . /j.tre. . sha: doc_id: cord_uid: d ge epidemic outbreaks are a special case of supply chain (sc) risks which is distinctively characterized by a long-term disruption existence, disruption propagations (i.e., the ripple effect), and high uncertainty. we present the results of a simulation study that opens some new research tensions on the impact of covid- (sars-cov- ) on the global scs. first, we articulate the specific features that frame epidemic outbreaks as a unique type of sc disruption risks. second, we demonstrate how simulation-based methodology can be used to examine and predict the impacts of epidemic outbreaks on the sc performance using the example of coronavirus covid- and anylogistix simulation and optimization software. we offer an analysis for observing and predicting both short-term and long-term impacts of epidemic outbreaks on the scs along with managerial insights. a set of sensitivity experiments for different scenarios allows illustrating the model’s behavior and its value for decision-makers. the major observation from the simulation experiments is that the timing of the closing and opening of the facilities at different echelons might become a major factor that determines the epidemic outbreak impact on the sc performance rather than an upstream disruption duration or the speed of epidemic propagation. other important factors are lead-time, speed of epidemic propagation, and the upstream and downstream disruption durations in the sc. the outcomes of this research can be used by decision-makers to predict the operative and long-term impacts of epidemic outbreaks on the scs and develop pandemic sc plans. our approach can also help to identify the successful and wrong elements of risk mitigation/preparedness and recovery policies in case of epidemic outbreaks. the paper is concluded by summarizing the most important insights and outlining future research agenda. shortage of raw materials in global scs), legal disputes, or strikes (ivanov et al., b) . such risks are characterized by a very strong and immediate impact on the sc network design structure since some factories, suppliers and dcs, and transportation links become temporarily unavailable. adversely, the resulting material shortages and delivery delays propagate downstream the sc, causing the ripple effect and performance degradation in terms of revenue, service level and productivity decreases (ivanov et al., , garvey et al., , dolgui et al., , ivanov et al., b , pavlov et al., b , goldbeck et al., , li and zobel, . once specific case of sc disruptions are the epidemic outbreaks. epidemic outbreaks represent a special case of sc risks which is distinctively characterized by three components. these components are: (i) long-term disruption existence and its unpredictable scaling, (ii) simultaneous disruption propagation in the sc (i.e., the ripple effect) and epidemic outbreak propagation in the population (i.e., pandemic propagation), and (iii) simultaneous disruptions in supply, demand, and logistics infrastructure. unlike other disruption risks, the epidemic outbreaks start small but scale fast and disperse over many geographic regions. recent examples include sars, mers, ebola, swine flu, and most recently, coronavirus (covid- /sars-cov- ). the recent coronavirus (covid- /sars-cov- ) outbreak came from wuhan area, china and immediately impacted chinese exports and drastically reduced the supply availability in global scs. araz et al. ( ) underline that the covid- outbreak represents one of the major disruptions encountered during the last decades which is "breaking many global supply chains". in the period from january th to february th, the number of confirmed cases of coronavirus in china rose from to , cases with a further increase to , cases as on march (worldometers, ) . in the last decade of february and early in march , the number of covid- cases has exponentially increased in asia, europe and usa resulting in border closures and quarantines. on march , , the world health organization (who) announced the pandemic given more than , covid- cases confirmed worldwide. being lean and globalized in structures, the scs of many companies became specifically prone to the epidemic outbreaks. % of the fortune companies have been reported seeing coronavirus-driven sc disruptions (fortune, ) . a report by corporate data analytics firm dun & bradstreet says that , companies around the world have one or more direct suppliers in wuhan and at least million companies around the world have one or more tier-two suppliers in the wuhan region, covid- ′s origin. moreover, of the fortune companies have tier-one or tier-two suppliers in the wuhan region (dun and bradsteet, ) . linton and vakil ( ) show on the example of data obtained through the resilinc system that the world's largest , scs own more than , facilities (i.e., factories, warehouses and other operations) in covid- ′s quarantine areas. more adversely, the coronavirus causes simultaneous disturbances in both supply and demand. our discussion on march , with a company in berlin that operates in the gift industry revealed that they have been suffering from both supply shortages from china and demand disruptions in italy which was badly affected by coronavirus. in such a turbulent environment, the firms facing the epidemic outbreaks have a series of common questions to ask, i.e., how long can an sc sustain a disruption, how long does it take for an sc to recover after an epidemic outbreak, which sc operating policy (e.g., accepting the temporal shortages; using prepared contingency pandemic plans; reacting situationally by changing the operation policies during the epidemic time) is the most efficient to cope with disruptions at different levels of severity of the epidemic dispersal? in this paper, we present the results of a fast but robust simulation study that opens some new research tensions on the impact of covid- outbreak on the global scs. the contribution of this study is twofold. first, we articulate the specific features that frame epidemic outbreaks as a specific sc risk. second, we demonstrate how simulation-based methodology can be used to examine and predict the impacts of epidemic outbreaks on the sc performance using the example of coronavirus covid- and anylogistix simulation and optimization software. more specifically, we offer analysis for predicting both short-term and long-term impacts of epidemic outbreaks on the scs and uncover critical parameters and scenarios of positive and negative sc performance dynamics. this analysis can help to identify the successful and wrong elements of risk mitigation/preparedness and recovery policies in case of epidemic outbreaks. a set of sensitivity experiments for different epidemic scenarios allows to illustrate the model's behavior, its value for decision-makers, and to derive several useful insights. the outcomes of this research can be used by decision-makers to predict the operative and long-term impacts of epidemic outbreaks on the scs and develop pandemic sc plans. the rest of this paper is organized as follows. in section , we analyse literature on sc risks with a focus on epidemic outbreaks and simulation. section presents our case-study and describes the simulation model. the experimental setup and results are shown in section . this section discusses managerial implications as well. the paper is concluded in section by summarizing the most important insights and outlining future research agenda, especially in the areas of data analytics and digital twins. while the research on coping with epidemic outbreaks from the humanitarian logistics point of view provides a mature body of knowledge (lee et al., , koyuncu and erol, , dasaklis et al., , green, , mamani et al., , altay and pal, , altay et al., , anparasan and lejeune, , dubey et al., c , farahani et al., , the literature on analyzing the impacts of epidemic outbreaks on the commercial scs is scarce. we consider this as a research gap and an opportunity to develop substantial contributions. some scarce information on previous epidemic outbreaks can be found in relation to sc operations. johanis ( ) reported on a pandemic response plan developed at toronto pearson international airport following the consequences of sars epidemic outbreak d. ivanov transportation research part e ( ) in - . sars has adversely affected the airline industry, especially in taiwan when around % of international flights have been suspended (chou et al., ) . though, the globalization degree and the role of china in the global scs at the times of sars were different to the current situation, and the impacts of sars on the scs have been relatively low. ebola virus spread has negatively impacted the global logistics (bsi, ) . calnan et al. ( ) and esra büyüktahtakın et al. ( ) describe the lessons learned during the ebola times and point to a need of building a decision-support framework which would help predicting the impacts of epidemic outbreaks on the scs and coordinating the operational and logistics policies during and after the crisis. it is intuitively to expect decreases in operative performance (e.g., ebit), material shortages, and price fluctuations during epidemic outbreaks. this confirms the analysis of coronavirus-related reports. for example, german post declared an ebit reduction in the range between and million euro; retail prices in china raised in february by . % at average (bild, ) . on february , apple announced to expect its quarterly earnings to drop (apple, ). by late february , the covid- outbreak had rendered almost % of container shipping fleets inactive and chinese manufacturing indices hit their lowest point since the great recession as a result of suspending the manufacturing operations to stem the spread of covid- (retaildive, ) . dynamic simulation models are recognized as a suitable tool to observe and predict sc behaviors over time. simulation studies allow adding additional, dynamic features to the optimization techniques which are widely used in sc risk analysis , sadghiani et al., , cui et al., , ivanov et al., along with heuristic approaches (meena and sarmah, , zhang et al., , hasani and khosrojerdi, . most of the existing studies utilize discrete-event simulation approach (schmitt and singh, , ivanov, a , b , schmitt et al., , ivanov and rozhkov, , macdonald et al., , ivanov, , tan et al., while some studies use agent-based (li and chan, , hou et al., and system dynamics (wilson, , aboah et al., methods, too. a very few studies (e.g., hackl and dubernet, ) have incorporated the simulation and transportation disruptions during the epidemic crises. the simulation models are especially useful for analysis when the impacts of disruptions on sc performance need to be computed under conditions of time-dependant changes (klibi and martel, , ivanov, b) . besides, detailed control policies can be analysed subject to a variety of financial, customer, and operational performance indicators (li et al., , pavlov et al., a , ivanov, . the simulation models consider logical and randomness constraints, such as randomness in disruptions, inventory, production, sourcing, and shipment control policies, and gradual capacity degradation and recovery . since simulation studies deal with time-dependent parameters, duration of recovery measures, and capacity degradation and recovery, they have earned an important place in academic research. simulation has the advantage that it can extend the handling of the complex problem settings of optimization through situational behavior changes in the system over time. among software tools to simulate the sc behaviors under risks, anylogistix has been proven to be a very successful tool utilized in sc risk and resilience analysis (ivanov, a , b , b , , aldrighetti et al., . based on discrete-event simulation of anylogic which was also successfully applied to sc risk and resilience analysis rozhkov, , cavalcantea et al., ) , anylogistix provides a combination of simulation, optimization (cplex), and performance visualization of scs constituting a full set of technologies to build a digital sc twin (ivanov et al., c, ivanov and . we model a global sc of a company selling the lightning equipment, in total five different products. this is a multi-stage sc with suppliers, factory, distributions centres (dc), and customers located in different geographic zones (fig. ) . the sc network design contains two producers in china (in xiamen and shenzhen) which are supplied by two local suppliers (which are invisible in the map in fig. since located very close to the producers), in a region affected by an epidemic outbreak in form of quarantine and production stops. the producers deliver the lightning equipment via ship and multi-modal (truck-train) transportation paths to the dcs in the usa, brazil, and germany with an average transportation time of days. from there, goods are shipped to the customers. in the usa, the distribution is organized either directly to customers from main dc in houston, or via four regional dcs. there are customers in total all over the world. they all order at dcs every days with expected lead-time (elt) between and days. in other words, if the order is delivered within a frame between and days, it is considered as on-time delivery; if later -as delayed delivery. the delayed deliveries negatively impact the elt service level which is a fraction of on-time delivered orders to the total number of orders. the demand is deterministic and between and units per order depending on the customer. the assumption of the deterministic demand can be justified as follows. first, the demand volatility for lightning equipment is indeed low. second, our main objective is to uncover the impact of disruption and we therefore would like to omit other variations as the model as much as possible. the facilities operate at some fixed and variable costs including inventory holding costs, overhead costs, and processing costs. we omit the detailed presentation of all input data due to the limited length of the paper and refer the reader to the model "sim global network examination" which is supplied with anylogistix software and can be seen and run in every anylogistix version, even in the ple edition. for analysis we use the timeline of coronavirus dispersal which was found in different internet sources starting from mid of january until march , as follows: we are interested to examine the epidemic outbreak impact on the sc subject to some scenarios which are likely to happen after march assuming mitigation of epidemic outbreak in china (fig. ) . in order to reduce the number of possible "what-if" scenarios, we consider the following three cases: • scenario i: localization of epidemic outbreak in china • scenario ii: propagation of epidemic outbreaks and closure of facilities worldwide • scenario iii: propagation of epidemic outbreaks into the markets and demand disruption by % note that we consider different epidemic durations and include the time delays into the epidemic propagation dynamics. in total, this results in possible scenarios. for some scenarios, all the sc elements would be disrupted. in other scenarios, the closing of some facilities downstream would be accompanied by opening of some facilities upstream. in summary, we design our experimental environment to examine the sc reaction to epidemic outbreaks of different severities in terms of revenue, profit and elt service level impact and subject to answering the following questions: • what is the impact of the epidemic outbreak on the sc performance? • how long does it take for an sc to recover after an epidemic outbreak? • how long can an sc sustain a disruption (i.e., what is a critical disruption time)? • what is the role of the scope and timing of disruption propagations? • what are the most critical scenarios of epidemic propagation? in summary, we consider different scenarios of epidemic outbreaks, e.g., only in china vs. also in europe, north america and south america, simultaneous epidemic crises (stops at facilities and demand disruptions in the markets), and different sequences of opening/closing facilities and markets (cf. fig. ) . transportation research part e ( ) . . simulation model we utilize the discrete-event simulation methodology. our model is created and solved in anylogistix simulation and optimization toolkit. for analysis, we utilized a standard anylogistix model "sim global network examination" which has been validated by the software developer for a large-scale problems in order to test the correctness of the results and the scalability. we adjusted some parameters of this model (e.g., transportation times and disruption events) without any changes in the model structure. that is why we do not perform additional validation tests in this study. in order to validate the output results within the scope of our research, replications have been created for each of the simulation experiments for reducing output randomness. simulation was run for a period of one year with a warm-up period of months. we now justify some assumptions and parameters used for simulation experiments. recent literature , lücker et al., , schmitt et al., gupta and ivanov, ) has recognized the risk mitigation inventory, lead-time and backup suppliers as crucial elements affecting the sc reactions to disruptions. moreover, the ripple effect is usually accompanying the disruptions which are rarely to be localized and usually spread over many sc echelons (ivanov et al., , garvey et al., , dolgui et al., , ivanov et al., b , pavlov et al., b , li and zobel, . anparasan and lejeune ( ) presented a data set of the cholera epidemic that occurred in the aftermath of the earthquake in haiti. they demonstrated that geographic location data, lead-time data, and demand data is primarily needed to run the simulation models and how to use this data for sc response models during epidemic outbreaks. risk mitigation inventory: according to haren and simchi-levi ( ), "as a result of events such as the - sars epidemic, the march iceland's volcano eruption, japan's earthquake and tsunami in march , and the flood in thailand in august , companies increased the amount of inventory they keep on hand. but they still usually carry only to days' worth of inventory." we develop our model based on these assumptions. lead-time: shipping by sea to either the u.s. or europe takes, on average, days. this implies that if chinese plants stopped manufacturing prior to the beginning of the chinese holiday on january , the last of their shipments will be arriving the last week of february (haren and simchi-levi, ) . we use these estimates in our model. ripple effect existence: for example, fiat chrysler automobiles nv reported that "it is temporarily halting production at a car factory in serbia because it can't get parts from china." (foldy, ) similarly, hyundai "decided to suspend its production lines from operating at its plants in korea … due to disruptions in the supply of parts resulting from the coronavirus outbreak in china." (straitstime, ). these two examples show that the coronavirus has caused the ripple effect. moreover, haren and simchi-levi ( ) observe that in the case of short lead times, the disruptions at downstream sc facilities occur earlier, and therefore the ripple effect propagates faster. we build our simulation model according to the above analysis and following the previously developed and validated simulation models for sc risk analysis (ivanov, a (ivanov, , b (ivanov, , a (ivanov, , (ivanov, , . case-study scenarios for simulation. transportation research part e ( ) in this section, we describe the sc operational rules as applied in the model. fig. illustrates the principal scheme of material and information flows in the sc. the following logic (fig. ) has been created in the model in line with the study (ivanov, a) . we assume that dcs and producer are running order-up-to-level, re-order point based (s,s) inventory control policy. for analytical formulations of the orderup-to-level, continuous review inventory control policy, we refer the readers to specialized literature on inventory management. our model follows the procedures described in (ivanov et al., d, chapter ) . the facilities have a risk mitigation inventory for a period between and days. the sc is characterized by partial visibility, i.e., the demand of an upstream echelon is visible for the downstream echelon. the markets generate orders to the dc according to their demand which is normally distributed. the dcs and producers exhibit the s,s inventory control policy and place the orders at the factory. production is controlled by the parameters of inventory control policy. the factories also exhibit the s,s inventory control policy. in the case of a disruption and scarce supply, the shipments as shown in fig. are interrupted, too. in case of some remaining capacity, the deliveries are directed randomly with equal distribution probability to the destinations downstream the sc. we test the impact of an epidemic outbreak in china on sc performance (i.e., revenue, profit, service level). our experiments are designed to address three major features of epidemic outbreaks which distinguish them from other sc risks: • long-term disruption existence and its unpredictable scaling, • simultaneous disruption propagation (i.e., the ripple effect) and epidemic outbreak propagation (i.e., pandemic effect), and • simultaneous disturbances in supply, logistics infrastructure and demand. we examine this impact for different disruption durations and scales of epidemic propagation. organization of the experiments is as follows. first, we compute sc performance subject to such key performance indicators as service levels, sales, lead time, inventory on-hand, and profit for a disruption-free scenario. subsequently, sc dynamics in different disruption scenarios are simulated in order to analyse the estimated magnitude of the disruptions and the ripple effect as caused by an epidemic outbreak. such an analysis will be performed for different combinations of factors. finally, we compare the sc reactions in different cases and draw conclusions on the disruption and ripple effect impacts on the sc performance. for verification, tracking of the simulation runs, analysis of output log files, and testing at deterministic parameters were used. for testing, we use replications in comparison and variation experiments. in fig. , we illustrate the sc behaviour in disruption-free scenario without any epidemic outbreaks. it can be observed in fig. that the sc operates at an elt service level of about - % achieving a profit of $ , million, with quite a stable lead-time and balanced inventory dynamics. now we simulate the different cases according to scenarios i-iii (cf. transportation research part e ( ) fig. ) and observe the gaps in sc performance as compared to the disruption-free mode (fig. ) . a summary of the results of the most interesting simulation runs is presented in table . table provides a summary of simulation runs for different scenarios. some of the most interesting results which we will discuss in this section are highlighted yellow in table . table shows the absolute values of some key performance indicators (kpi) and their changes as compared to the ideal (no disruption) situation ( fig. ; recall that the kpi values in the non-disruptive scenario have been as follows: elt service level %, profit $ , , revenue $ , , and total lead time from all dcs to all customers days). in addition, we measure the total sc disruption time as the duration of elt service level degradation (alternatively, one can use the duration of profit degradation). these kpis are used to assess the sc reaction to the epidemic outbreak. for the scenario i, the results confirm the intuitive sentiments that a longer disruption duration upstream the sc results in a) production-inventory dynamics b) customer (elt service level) performance c) financial performance d) lead-time performance ivanov transportation research part e ( ) performance decrease. all the kpis decrease whereas the increase of disruption duration to days results in profit drop by almost % and lead-time has grown times. insight : if the epidemic outbreak is localized upstream the sc, the sc performance reaction is proportional to the duration of the disruption. analysing the results in the scenario ii, we encounter several interesting observations. for short disruption duration in china ( days), the further propagation of the epidemic outbreak in the usa, south america and europe accompanied by closing the dc facilities in there regions results in performance decreases for all kpis. with that said, a difference in sc reaction can be observed when comparing the speed of the epidemic propagation and the duration of epidemic cases downstream the sc. more specifically, the longer delays in epidemic propagation (i.e., days vs. days) and shorter disruption duration downstream the sc (i.e., the scenario with days disruption in china, days in epidemic outbreak delay, and days disruption duration downstream the sc) result in the lowest performance degradation. however, in case of longer disruptions in china, the longer epidemic propagation downstream the sc does not bring any positive effect (cf. scenarios with days of disruption durations in the scenario ii). at the same time, we can again observe a positive effect of slowing down the epidemic propagation in the case of very long disruption in china of days. moreover, the sc performs better for all kpis in the case of a days disruption in china and the longer epidemic propagation downstream the sc as compared to the case of the scenario i without any epidemic propagation. these observations lead to us to another useful insight: insight : in the case of an epidemic outbreak propagation, the sc performance reaction depends on the timing and scale of disruption propagation (i.e., the ripple effect) as well as the sequence of facility closing and opening at different sc echelons rather than on the disruption duration upstream the sc. in the most complex scenario iii, we can observe synergetic effects of several negative events. interestingly, the aggregation of two negative events frequently results in a positive effect on sc performance. if the facility disruptions downstream are accompanied by demand disruptions, the overall sc performance increases due to a decrease in backlogs. however, this synergetic effect disappears in cases with very long (e.g., days) facility and demand disruption durations downstream the sc. another observation from simulation runs with the scenario iii is that, differently to the cases in the scenario ii, the longer epidemic propagation delays rather decrease the sc performance. the longer lasting demand disruptions also contribute to further performance decreases. moreover, we can observe that longer delays in disruption propagation and longer lasting disruptions downstream the sc are more dangerous as the disruption duration upstream the sc (e.g., cf. in scenario iii the case with days disruption in china, days delay in epidemic propagation, days of disruption at downstream facilities and days of demand disruption with the case of days disruption in china, days delay in epidemic propagation, days of disruption at downstream facilities and days of demand disruption). a positive effect can be observed when the timing of facility recovery at different echelons in the sc is synchronized. for example, in the case with days disruption in china, days delay in epidemic propagation, days of disruption at downstream facilities and days of demand disruption, we have a situation when the chinese production stops on january , the dcs downstream close on february , the production in china is resumed on march , and the dc operations are resumed on april . this results in high profits, service level, and short lead times along with quite low total sc disruption time. the corresponding sc performance dynamics for this case is depicted in fig. . the experiments with cases in the scenario iii allow for the following insights: insight : simultaneous disruptions in demand and supply may have positive effects on the sc performance as a reaction to an epidemic outbreak. the lowest decrease in the sc performance can be observed in cases when the facility recovery at different echelons in the sc is synchronized in time. the most negative impact on the sc performance is observed in the cases with very long facility and demand disruption durations downstream the sc regardless of the disruption period in the upstream part. one explanation of the insight is that if the facilities at different sc echelons are closed simultaneously, the variable costs and a part of fixed costs decrease. on the contrary, if the upstream facilities (e.g., the producers in china) are working but the downstream facilities (e.g., dcs in usa and europe) are closed, the inventory, manufacturing and transportation costs increase but the revenue is not generated. of course, these observations need to be detailed in each particular case considering additional specifics of lead-time, ordering policies, and available logistics infrastructure. table provides a summary of the managerial insights obtained through this study. in this paper, we presented the results of a fast but robust simulation study that opens some new research tensions on the impact of covid- on the global scs. the objectives of this study were twofold. first, we aimed at articulating the specific features that frame epidemic outbreaks as a unique type of sc risks. second, our goal was to demonstrate how simulation-based methodology can be used to examine and predict the impacts of epidemic outbreaks on the sc performance using the example of coronavirus covid- and anylogistix simulation and optimization software. regarding our first objective, the results of our study show that epidemic outbreaks represent one specific case of sc disruptions. this type of sc risks is distinctively characterized by long-term disruption existence and its unpredictable scaling, simultaneous disruption propagation (i.e., the ripple effect) and epidemic outbreak propagation (i.e., pandemic effect), and simultaneous disruptions in supply, demand, and logistics infrastructure. unlike other disruption risks, the epidemic outbreaks start small but scale fast and disperse over many geographic regions creating a lot of unknowns which makes it difficult to fully determine the impact of the epidemic outbreak on the sc and the right measures to react. overall, the epidemic outbreaks create a lot of uncertainty and companies need a guided framework in developing their pandemic plans for their sc. regarding our second objective, we undertook an attempt to observe and predict the impacts of epidemic outbreaks on the sc using simulation-based methodology and the example of coronavirus covid- . an sc simulation model along with experimental results have been presented using a case-study constructed on the basis of primary and secondary data and using anylogistix simulation and optimization software. our analysis offers possibility of predicting both short-term and long-term impacts of epidemic outbreaks on the scs and uncovers the most critical epidemic outbreak scenarios in terms of sc performance decrease. this analysis allows identifying the successful and wrong elements of risk mitigation/preparedness and recovery policies in case of epidemic outbreaks. a set of sensitivity experiments allows to illustrate the model's behavior, its value for decision-makers, and to derive useful managerial insights. more specifically, the outcomes of this research can be used by decision-makers to predict the operative and long-term impacts of epidemic outbreaks on the scs and develop pandemic sc plans. a) production-inventory dynamics b) customer (elt service level) performance c) financial performance d) lead-time performance ivanov transportation research part e ( ) the major observation from the simulation experiments is that the timing of the closing and opening of the facilities at different echelons might become a major factor that determines the epidemic outbreak impact on the sc performance rather than an upstream disruption duration upstream or the speed of epidemic propagation. other important factors are lead-time, speed of epidemic propagation, and the upstream and downstream and disruption durations in the sc. in particular, our analysis revealed that in the case of an epidemic outbreak propagation, the sc performance reaction depends on the timing and scale of disruption propagation (i.e., the ripple effect) as well as the sequence of facility closing and opening at different sc echelons rather than on the disruption duration upstream the sc. the lowest decrease in sc performance can be observed in cases when the facility recovery at different echelons in the sc is synchronized in time. the most negative impact on the sc performance is observed in the cases with very long facility and demand disruption durations downstream the sc regardless the disruption period in the upstream part. as such it is not only important to consider where the epidemical outbreak starts, and even not so important what percentage of supply base is located in the origin region but it is the scale of the ripple effect that should be particularly taken into account. we have also observed that the simultaneous disruptions in demand and supply may have positive effects on the sc performance as a reaction to an epidemic outbreak. these insights are partially in line and partially extending the existing body of knowledge on correlated disruptions in the sc (lu et al., , zhao and freeman, ) . in the generalized terms, this paper contributes to the existing literature on the sc risk management and resilience by positioning the epidemic outbreaks as a specific type of sc risks and offering an approach that supports the decision-makers at the times of epidemic outbreaks. our approach allows simulating the scs with a specific consideration of epidemic outbreaks and answer such questions as: • what is the impact of the epidemic outbreak on the sc performance? • how long does it take for an sc to recover after an epidemic outbreak? • how long can an sc sustain a disruption so what is the critical disruption time? • what is the role of the scope and timing of disruption propagations? • which sc operating policy (e.g., accepting the temporal shortages; using prepared contingency pandemic plans; reacting situationally by changing the operation policies during the epidemic time) is the most efficient one to cope with disruptions at different levels of severity of the epidemic dispersal? • what are the most critical scenarios of epidemic propagation? as for limitations of this study, we concisely reduced the technical complexity to make the managerial insights more depictive. another limitation is the design of the case-study which lacks some details due to missing detailed information at the time of writing this paper. in future research, we are going to test the sc reactions subject to different pandemic plans. for example, we can consider in this case, there is no disruption propagation the performance reaction depends on the timing and scale of disruption propagation (i.e., the ripple effect) as well as the sequence of facility closing and opening at different sc echelons rather than on the disruption duration upstream the sc. simultaneous disruptions in demand and supply may have positive, synergetic effects on sc performance as a reaction to an epidemic outbreak, especially for short-term disruptions and a synchronized recovery timing d. ivanov transportation research part e ( ) different risk mitigation inventory levels as elements of pandemic plans. the complexity can be easily increased by including other elements such as reserved capacities, back-up suppliers, lead-time reservations, regional subcontracting; though we omit this complexity in the particular experimental setting in this paper to present the results in a depictive way. currently, we consider upstream disruptions as the trigger of epidemic-based disruption propagations. one interesting research topic could be to examine a disruption outbreak in the downstream sc echelons or even in the markets, and how these events would affect the forward and backward propagations of the ripple effect. on another note, the epidemic outbreak impacts on the scs highly depend on the type of a product that is globally supplied to the customers across different continents. indeed, the impact of epidemic outbreaks on the scs for items with urgent demand during the outbreak such as hand sanitizer, medical mask, and medical alcohol is a special research topic and a promising research avenue. regarding further future directions, we point to the new digital technologies that have a potential to improve the ripple effect control in cases of epidemic outbreaks. making innovations and data work for the sc resilience in crisis times is a promising future research avenue with a particular focus on data analytics, artificial intelligence, and machine learning. the understanding and progressing the research of how all these technologies can be used to operate the scs in a resilient way in cases of epidemic outbreaks is an important future research area (choi et al., (choi et al., , choi and lambert, b , dubey et al., a , ganasegeran and abdulrahman, , queiroz and wamba, , yoon et al., . in particular, digital sc twins ) -i.e., the computerized sc models that represent the network state for any given moment in real time -can be used to support the decision-making during the epidemic outbreaks. in the pre-disruption mode, digital twins allow for a visualization of sc risks, assessment of supplier disruption risks, prediction of possible supply interruptions, and computation of alternative supply network topologies and back-up routes with assessment of estimated times of arrival. in the dynamic, reactive mode, i.e., in the case of a real epidemic outbreak the digital twins can be applied using real-time data to simulate disruption impacts on the sc and alternative sc designs that contain non-disrupted network nodes and arcs depending on real-time inventory, demand, and capacity data. identifying the precursors of vulnerability in agricultural value chains: a system dynamics approach healthcare supply chain simulation with disruption considerations: a case study from northern italy information diffusion among agents: implications for humanitarian operations agility and resilience as antecedents of supply chain performance under moderating effects of organizational culture within humanitarian setting: a dynamic capability view data laboratory for supply chain response models during epidemic outbreaks data analytics for operational risk management 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conditions of structural dynamics integrated detection of disruption scenarios, the ripple effect dispersal and recovery paths in supply chains blockchain adoption challenges in supply chain: an empirical investigation of the main drivers in india and the usa retail supply chain network design under operational and disruption risks selection of supply portfolio under disruption risks mitigating disruptions in a multi-echelon supply chain using adaptive ordering a quantitative analysis of disruption risk in a multi-echelon supply chain coronavirus exposes cracks in carmakers' chinese supply chains structural-aware simulation analysis of supply chain resili-ence perspectives in supply chain risk management on the value of mitigation and contingency strategies for managing supply chain disruption risks resilient supplier selection and order allocation under operational and disruption risks the impact of transportation disruptions on supply chain performance disruption risks in supply chain management: a literature review based on bibliometric analysis the value of blockchain technology implementation in international trades under demand volatility risk a metaheuristic approach to the reliable location routing problem under disruption modelling supply chain adaptation for disruptions: an empirically grounded complex adaptive systems approach robust sourcing from suppliers under ambiguously correlated major disruption risks we thank professor tsan-ming (jason) choi for inviting us to prepare this article. we thank three anonymous reviewers for their invaluable suggestions which helped us to improve the manuscript immensely. key: cord- - txtk b authors: feng, liang; zhao, qianchuan; zhou, cangqi title: epidemic in networked population with recurrent mobility pattern date: - - journal: chaos solitons fractals doi: . /j.chaos. . sha: doc_id: cord_uid: txtk b the novel coronavirus (covid- ) has caused a global crisis and many governments have taken social measures, such as home quarantine and maintaining social distance. many recent studies show that network structure and human mobility greatly influence the dynamics of epidemic spreading. in this paper, we utilize a discrete-time markov chain approach and propose an epidemic model to describe virus propagation in the heterogeneous graph, which is used to represent individuals with intra social connections and mobility between individuals and common locations. there are two types of nodes, individuals and public places, and disease can spread by social contacts among individuals and people gathering in common areas. we give theoretical results about epidemic threshold and influence of isolation factor. several numerical simulations are performed and experimental results further demonstrate the correctness of proposed model. non-monotonic relationship between mobility possibility and epidemic threshold and differences between erdös-rényi and power-law social connections are revealed. in summary, our proposed approach and findings are helpful to analyse and prevent the epidemic spreading in networked population with recurrent mobility pattern. recently, the novel coronavirus (covid- ) has caused a global crisis and more than million people of more than countries have been infected up to now ( th may, ) [ ] . the primary measures taken by many governments are home quarantine and maintaining social distance, with the aim to break transmission of this infective virus and halt the spread of pandemic. although most public places are locked down, supermarkets and drugstores which are essential for daily life remain open. different from commonly used homogeneous mixing approaches [ , ] , we give an analysis of epidemic spreading in population following a structured network with recurrent mobility pattern in this work. the influences of network structure and human mobility on epidemic spreading have received lots of attention in recent years. on one hand, homogeneous mixing assumption among individuals is often invalid and variations of social interaction network bring large differences in the propagation process of virus [ ] [ ] [ ] [ ] [ ] [ ] [ ] . on the other hand, human mobility also greatly affects the peak and duration of epidemic outbreak [ ] [ ] [ ] [ ] [ ] , and recurrent patterns between people and their familiar locations (e.g. workplace, supermarket) often dominate the behaviour of human mobility [ , ] . however, the interactions of individuals in public places provide another route of virus transmission, which makes the analyse of epidemic spreading much more difficult. one widely used approach to analyse epidemic spreading in complex networks is metapopulation model, which divides the whole population into several geographical structured parts [ , ] , and contacts among individuals in the same subpopulation are assumed to be well-mixed. though some challenges remain [ ] , a useful strategy of analysing the impact of human mobility behaviour on epidemic spreading is to integrate metapopulation model with reaction-diffusion process [ , ] . each subpopulation can be formulated as a node and edges between different metapopulations indicate the mobility probabilities of individuals. reaction-diffusion process has been widely studied in physics, for epidemic spreading, diffusion often refers to individual movements between different places and reaction indicates the contagion process within each place after human behaviour. in addition to the way of using a unipartite network to model metapopulations for analysis of epidemic spreading with recurrent mobility pattern, heterogeneous networks are adopted recently [ , ] . all these methods take the assumption individuals in the same subhttps://doi.org/ . /j.chaos. . - /© elsevier ltd. all rights reserved. population will contact with each other in a well-mixed fashion, however, each individual only interacts with his neighbors in real social networks. in this paper, we utilize a heterogeneous network to represent the social connections among individuals and recurrent human mobility pattern between population and locations. there are two types of connections: one is the edge between any two individuals, and the other is connection between individual and common areas. the social network may follow different network structures, such as erdös-rényi or power-law networks. in order to model the dynamics of virus spreading, we apply the discrete-time markov chain method in the context of susceptible-infected-susceptible (sis) infection process like [ , , , ] . with a mobility possibility, each agent will choose to get into public places which he connects to or stay in social network. since there are no fixed individuals and connections among them, we assume people gathering in a public area will have contacts with all other individuals. the agent who chooses to stay in social network will have contacts with his remaining neighbors, and he may get infected if and only if he has some contagious neighbors who do not go outside at that time step. in this paper, detailed formulation of epidemic model in this kind of networked population with recurrent mobility pattern is introduced, and we also give theoretical results of the epidemic threshold. besides, the decay of epidemic infection below threshold and impact of isolation factor are presented. as far as we know, this is the first attempt to analyse epidemic spreading in networked population with human recurrent mobility by using social contacts network among individuals. the remaining of this paper is organized as follows. in section , we give the formulation of epidemic model for virus spreading in networked population with recurrent mobility pattern, along with theoretical results of epidemic threshold. the analyse of epidemic threshold from the view of non-linear dynamical system (nlds) and its decay property are introduced in section . experimental results on two types of social networks, erdös-rényi and power-law networks are showed in section , and we conclude this work with a summary in section . the heterogeneous graph of networked population in our paper consists of two different parts. one is composed of m individuals with specific social network structure, and the other is n public places. different from previous works [ , , ] which only consider connections between metapopulations and common areas, we discard the well-mixed assumption in metapopulation and suppose there is a contact network among individuals. we formulate an epidemic model of virus propagating in networked population with recurrent mobility pattern between individuals and public areas. the social connections are defined by a m × m matrix a , where a ij is if individual i has a contact with agent j . the edges between individuals and locations are dependent on a m × n matrix b , where b ij is if agent i will visit place j if he goes out, and otherwise. here, we assume edges are unweighted, and undirected, hence a is a symmetric matrix. in order to simulate the recurrent mobility pattern between individuals and public places, at each time step, individuals will go to all public places which they connect to with a possibility of p . after movements of individuals, virus propagates in both remaining networked population and common areas independently. we also force individuals in common places to return back to social network at the end of step, for the purpose of ensuring recurrent mobility patterns of individuals. fig. gives an example of epidemic spreading at time t when some individuals get into public places with possibility p . it should be noted that, the edges of both a and b for a specific heterogeneous network remain unchanged during the whole simulation. however, at each time step, since some individuals will go outside, the remaining a and resulting infection process based on b in common areas might be different. for dynamics of epidemic spreading among individuals, we adopt the popular sis model. there are two states, susceptible and infective, for each individual. we assume the homogeneous spreading of virus where the infection rate is β and recovery rate is μ. a susceptible individual will become infected by a possibility of β when contacting with a contagious agent, and individuals who got infected at previous time steps will recover with possibility μ and become susceptible again at each time step. the states of population at t + are only dependent on those at t , thus a discretetime markov chain can be taken to model the dynamics of epidemic spreading. the possibility individual i is infective at the beginning of time t is denoted as p i,i,t , and susceptible p i,s,t where p i,s,t = − p i,i,t for sis model. the evolution of p i,i,t can be formulated as where the left part is possibility when i has already got infected and remains infective, and right is possibility that susceptible individual i becomes infective at time t where i ( t ) is the infection possibility. different from formulation in traditional networked populations [ , , , , ] , i ( t ) consists of two different components where p is the mobility possibility, d i ( t ), c i ( t ) are infection possibilities when agent i stays in social contact network or gets into public places. in this paper, we define the possibility of a susceptible individual getting infected when interacting with k contagious people as where we use a i j = for neighbors of i only in the contact network a and assume probabilities p j,i,t are independent of each other. for individuals in common areas, we take the assumption of well-mixed fashion used in [ , , , , ] , which means every one will have a contact with each other in the same place. therefore, we can get where j refers to a public place and b ij takes the value of for places j which individual i connects to. combining eq. and eq. into i ( t ), eq. can be reformulated as when whole population is near the critical onset of epidemic outbreak, the infective possibility for each individual and corresponding infection probability are negligible which means p i,i,t+ = p i,i,t = p i,i and β . by using approximations ( − β ) n ≈ − nβ, and neglecting high-order terms o ( β ), we can reduce eq. into if we use p i = [ p ,i , p ,i , · · · , p m,i ] t to indicate infected possibilities of all m individuals, eq. can be easily rewritten as hence, the infection threshold of epidemic spreading can be obtained [ , ] where λ max ( q ) is the largest eigenvalue of matrix q . similar to [ ] , we consider the impact of isolation factor γ where ≤ γ ≤ which constrains infected individuals from going into common places and they can only have contacts with social neighbors who do not go outside. therefore, we can get i,t and the epidemic threshold with isolation factor is in the last section, we derive the epidemic threshold for networked population with recurrent mobility pattern of individuals. on one hand, when p equals , no individual goes out and virus spreads only through contact network a , eq. turns into situations in [ , , , ] . on the other hand, when all individuals get into corresponding common areas which means p = , eq. becomes dynamics of epidemic spreading in bipartite networks as discussed in [ , ] . here we give some theoretical analysis of epidemic threshold from the view of non-linear dynamical system ( nlds ) and introduce the exponential decay property of infective individuals when β is below epidemic threshold. for sis model, the transitions of individual i can be described by ( ) when no one gets infected in system, the equilibrium point is p i = [ , , · · · , ] t and p s = [ , , · · · , ] t where the numbers of and are both m . according to [ ] where we can easily get j | p where i is the identity matrix and q = β( − p) a + β p bb t . therefore, the system is asymptotically stable at equilibrium point p if all the eigenvalues are less than in absolute value. assume the eigenvector is [ v , v ] t , and corresponding eigenvalue is λ j , we can get following equations although when v = , λ j = , it is related to ∂p s,t+ ∂p s,t which does not cause instability when system is at equilibrium point p . then we just need λ max (( − μ) i + q ) < which means ( ) hence the obtained epidemic threshold is consistent with result of eq. . by using the same strategy, we can also easily prove that epidemic threshold of sir model is the same as sis model. recall that we use approximations ( − β ) n ≈ − nβ, if we take the high-order terms o ( β ) into account, the following results can be obtained by combining above results with eq. , dynamic of infection possibility for individual i becomes and transitions for all people satisfy which indicates λ i,w < for every i , therefore where c is a constant. hence, the values of p i will exponentially decrease over time if β is less than the epidemic threshold. in order to validate the correctness of proposed model, we evaluate results from monte carlo simulations with theoretical predictions of eq. . two different types of network structures are used in the following experiments: erdös-rényi network and power-law network. we keep the edges between individuals and locations fixed, which means b is unchanged while changing structure of social connections a among individuals. in order to better analyse the impact of mobility possibility p on different networks, total number of edges among individuals remains almost the same for erdös-rényi and power-law network. a comparison between simulation and theoretical results is showed in fig. . the average infected ratio for the whole population is defined as η = m j p j,i /m. we run times for each mobility possibility p . for each simulation, we run time steps and use average value of η in the last steps as the steady infection ratio. as we can see, numerical solutions of proposed model have good correspondences with results of monte carlo simulations. for small mobility possibility p = . , the epidemic threshold of powerlaw network is significantly smaller than that of erdös-rényi net-work. as explicated in [ ] , the heterogeneity of degree distribution in power-law network makes the largest eigenvalue larger than erdös-rényi network, and this makes virus more easily break out among individuals. when p increases, the differences between erdös-rényi and power-law network both in epidemic threshold and steady infection ratio become less obvious. this can be explained by the fact that, when more individuals go outside, more and more spreads of epidemic take place in common areas while the connections b between individuals and common locations are the same for both social contact networks. in the next, we analyse the impact of recurrent mobility possibility p on epidemic threshold β min with different numbers of contact edges. from fig. , all curves show non-monotonic behaviours where epidemic threshold achieves its largest value β min for a specific value of p . similar non-monotonic phenomena are also founded in [ , ] . also, the largest epidemic thresholds in power-law network are smaller than those in erdös-rényi network. besides, when total edges of social contacts ( e ) increase, β min decreases and p increases for the synthetic networks. after that, we investigate how isolation factor γ influence epidemic spreading and the results are plotted in fig. . when γ is , there are no isolations for infected individuals, and the curve behaves consistently with fig. . for small isolation factors ( γ < . in fig. ) , the restriction of infected individuals makes β min monotonically increase with mobility possibility. interestingly, in erdös-rényi network, all curves nearly intersect at one point and similar phenomenon is also founded in [ ] which can be explained by the effective contact number of infected neighbors as discussed in [ , ] , while curves in power-law network show more obvious dispersion due to the heterogeneity of degree distribution. at last, we demonstrate the total number of infected individuals for different infection rates β at different time steps in fig. . as we can see, when β < β min , the spread dies out exponentially, and becomes an epidemic otherwise. the experimental results have good agreements with outcomes of eq. . we can also find that, for the same scale of threshold, such as β min and β min , the number of steady infected individuals in power-law network is relatively smaller than erdös-rényi network. this indicates that although epidemic threshold in power-law network is usually smaller, there will be more infected population in erdös-rényi network due to the homogeneity of individual's social contacts with their neighbors when infection rate increases by the same scale. in this paper, we propose an epidemic model for networked population with recurrent mobility pattern. a heterogeneous network is used to represent the structure containing different connections. there are two types of edges, social connections among individuals and mobility connections between individuals and common areas. a detailed formulation by discrete-time markov chain method to describe the dynamics of epidemic spreading is given, and we derive theoretical results about epidemic threshold. several simulations on both erdös-rényi and power-law social networks are conducted and experimental results verify the correctness of our model and analysis. the non-monotonic relationship between epidemic threshold and mobility possibility indicates there is an optimal value which will make virus hard to spread. the influences of different values of isolation factor which restricts infected individuals from getting into common areas are analysed, and more obvious dispersion appears in power-law network because of heterogeneity of degree distribution. in addition, we demonstrate and prove the exponential decay of infection when epidemic rate is less than threshold. in summary, this pa-per not only provides an approach to model epidemic spreading in networked population with recurrent mobility pattern, but offers a tool to analyse different network structures and social measures, such as restricting infected individuals. the authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. mathematical tools for understanding infectious disease dynamics epidemic processes in complex networks mean field theory of epidemic spreading with effective contacts on networks epidemic thresholds in real networks epidemic spreading in real networks: an eigenvalue viewpoint mean-field modeling approach for understanding epidemic dynamics in interconnected networks discrete-time markov chain approach to contact-based disease spreading in complex networks dynamics and control of diseases in networks with community structure sir dynamics in random networks with communities human mobility patterns predict divergent epidemic dynamics among cities multiscale mobility networks and the spatial spreading of infectious diseases reaction-diffusion processes and metapopulation models in heterogeneous networks interaction between epidemic spread and collective behavior in scale-free networks with community structure optimal control and stability analysis of an epidemic model with population dispersal memory in network flows and its effects on spreading dynamics and community detection recurrent host mobility in spatial epidemics: beyond reactiondiffusion intervention threshold for epidemic control in susceptible-infected-recovered metapopulation models seven challenges for metapopulation models of epidemics, including households models critical regimes driven by recurrent mobility patterns of reaction-diffusion processes in networks the spreading of infectious diseases with recurrent mobility of community population vaccination and epidemics in networked populations-an introduction epidemic spreading in localized environments with recurrent mobility patterns analysis, estimation, and validation of discrete-time epidemic processes got the flu (or mumps)? check the eigenvalue! differential equations, dynamical systems, and linear algebra spectra of random graphs with given expected degrees this work is supported in part by national natural science key: cord- -fz nfdf authors: weiner, joseph a.; swiatek, peter r.; johnson, daniel j.; louie, philip k.; harada, garrett k.; mccarthy, michael h.; germscheid, niccole; cheung, jason p. y.; neva, marko h.; el-sharkawi, mohammad; valacco, marcelo; sciubba, daniel m.; chutken, norman b.; an, howard s.; samartzis, dino title: learning from the past: did experience with previous epidemics help mitigate the impact of covid- among spine surgeons worldwide? date: - - journal: eur spine j doi: . /s - - - sha: doc_id: cord_uid: fz nfdf purpose: spine surgeons around the world have been universally impacted by covid- . the current study addressed whether prior experience with disease epidemics among the spine surgeon community had an impact on preparedness and response toward covid- . methods: a -item survey was distributed to spine surgeons worldwide via ao spine. questions focused on: demographics, covid- preparedness, response, and impact. respondents with and without prior epidemic experience (e.g., sars, h ni, mers) were assessed on preparedness and response via univariate and multivariate modeling. results of the survey were compared against the global health security index. results: totally, surgeons from global regions completed the survey. . % of respondents had prior experience with global health crises. only . % reported adequate access to personal protective equipment. there were no differences in preparedness reported by respondents with prior epidemic exposure. government and hospital responses were fairly consistent around the world. prior epidemic experience did not impact the presence of preparedness guidelines. there were subtle differences in sources of stress, coping strategies, performance of elective surgeries, and impact on income driven by prior epidemic exposure. . % expressed a need for formal, international guidelines to help mitigate the impact of the current and future pandemics. conclusions: this is the first study to note that prior experience with infectious disease crises did not appear to help spine surgeons prepare for the current covid- pandemic. based on survey results, the ghsi was not an effective measure of covid- preparedness. formal international guidelines for crisis preparedness are needed to mitigate future pandemics. the covid- pandemic has rapidly become one of the most catastrophic global health crises of our time [ ] [ ] [ ] . patients infected with covid- have placed an enormous strain on healthcare systems across the world in both the ambulatory and inpatient settings [ ] . many initial epidemiologic models predicted tremendous demands on existing hospital resources and staff across the globe [ ] [ ] [ ] [ ] . unfortunately, the ability to meet these demands has been variable around the world [ ] . some conjecture exists that this is due, in part, to different degrees of preparedness to treat and prevent spread of the virus [ ] . for example, many countries have dealt with prior serious public health outbreaks, such as severe acute respiratory syndrome (sars), middle east respiratory syndrome (mers), h n swine flu, or ebola [ ] [ ] [ ] [ ] . the world health organization (who) and the global health community have made pandemic preparedness one of their main missions [ , ] , and research on pandemic preparedness is plentiful [ , [ ] [ ] [ ] . in , the nuclear threat initiative (nti) and the johns hopkins center for health security (jhu) developed the global health security index (ghsi) [ ] . it was the first comprehensive assessment of health security and pandemic preparedness across the countries that make up the states parties to the international health regulations (ihr ) [ ]. the ghsi provided a ranking by overall pandemic preparedness, early detection capabilities, ability to mitigate a health disaster, along with numerous other variables. the goal of the ghsi project was to use data obtained from prior pandemics, along with information on international health systems, to spur measurable changes in global health security and improve the international capability to address infectious disease outbreaks [ ] . while global pandemics are catastrophic events for the entire population, they are particularly impactful on healthcare systems. resource limitations, healthcare worker illness, and severe economic repercussions have impacted providers and hospitals across the world. previous studies have focused on the effect of covid- on emergency room, critical care, and internal medicine specialties [ , ] . however, the impact of preparedness on subspecialty surgical care, such as spine surgery, in the context of the covid- pandemic is unknown [ ] [ ] [ ] [ ] . with low back pain ranking as the most disabling condition worldwide and neck-related issues ranked as the fourth leading cause globally, there is a major demand for spine providers [ , ] . many spine surgeons have shifted away from their normal clinical duties to assist large multidisciplinary teams in caring for covid patients [ ] . a recent study by louie et al. [ ] highlighted, in over spine surgeons worldwide, that covid- had a substantial impact upon their patient care, practice, and personal lives; however, such impact varied. as such, it remains unknown whether previous experience with outbreaks/ pandemics played a role in their preparedness, response, and perceptions. the current study addresses the role of prior infectious disease outbreaks on the preparedness, response, and impact of covid- on spine surgeons across the world. this study also assessed the ability of the ghsi to predict preparedness and response to covid- . the ao spine covid- and spine surgeon global impact survey was developed by a working group of board-certified spine surgeons, epidemiologists, and statisticians who are experts in spinal disorders and represented different global regions. question selection was based on a delphi methodology [ , ] to achieve consensus through several rounds of expert review before finalization. overall scope of the survey included surgeon demographics, country and region of practice, covid- perceptions, institutional preparedness and response, personal and practice impact, and future perceptions. demographics obtained included country of practice, region of practice, population of city of practice, specialty, fellowship experience, year in practice, and practice type. previous experience with sars, mers, h n , or ebola was queried to ascertain experience with prior infectious disease outbreaks. additional details of the survey can be found in the louie et al. [ ] report. the -item survey was presented in english and distributed via email to the ao spine membership who agreed to receive surveys for academic purposes (n = ). ao spine represents the largest society composed of spine surgeons worldwide (www.aospi ne.org). each recipient was instructed that they had nine days to complete the survey (march , , to april , ) . for all survey respondents, participation was voluntary, that they could end their participation at any time point, their involvement would be anonymous, and all data would be kept confidential. participants were also informed that study findings would be disseminated in peer-reviewed journals, web sites, and on social media platforms. all statistical analyses were performed with sas (sas institute, cary, nc). graphical representation of survey responses was performed using rstudio v . . (rstudio inc, boston, ma) and excel (microsoft inc, redmond, wa). percentages and means were made for count data and rankorder questions, respectively. all means were presented with standard deviations (mean ± standard deviation). statistical analyses were performed to assess significant differences in count data using a combination of fisher's exact and chisquared tests, where applicable. differences in continuous variables between groups were assessed using analysis of variance (anova). a nominal multivariate logistic regression was performed, controlling for baseline demographic differences between respondents with and without prior epidemic exposure, adjusting for covariates (e.g., home city population, geographic region, fellowship training, practice breakdown). outcome variables with p < . on univariate analysis were assessed in the multivariate model. variables with dichotomous categorical outcomes presented as odds ratios (or) and % confidence intervals (ci) were also noted. an or > indicated increased occurrence of outcome with prior epidemic exposure. an or < indicated decreased occurrence of outcome (protective exposure). variables with numerous categorical outcomes were presented as likelihood ratios. linear regression analysis was performed to assess the relationship between ghsi and survey responses. r regression coefficients less than . were considered poor correlation [ ] [ ] [ ] [ ] . the threshold for statistical significance for all tests was p < . . in total, spine surgeons responded to the survey, representing distinct countries and global regions (africa, asia, australia, europe, the middle east, north america, and south america/latin america respondents overall reported a moderate to high level of concern regarding the covid- outbreak, with a mean score of . ± . on a scale of one to five. recent epidemic experience did not impact mean worry ( . ± . vs. . ± . , p = . ), but did increase the proportion of those reporting personal health as a main source of stress ( . % vs . %, p = . ). the three most common stressors identified for respondents with previous epidemic experience groups were family health ( . %), personal health ( . %), and economic issues ( . %). the three most common stressors identified for respondents without previous epidemic experience groups were family health ( . %), community health ( . %), and timeline to resume work ( %) ( table ) . coping strategies were fairly consistent between those with and without previous epidemic experience. however, respondents with previous epidemic exposure reported using music as a coping strategy more frequently ( . % vs. . %, p = . ). media coverage and sources of media did not differ by epidemic experience (p = . and p = . ). media coverage was reported as "accurate" among . % of all respondents and "overblown" by . % of respondents (table ) . overall, . % of respondents reported having access to covid- testing. there was no difference in access to testing between surgeons with prior epidemic experience and those without epidemic experience ( . % vs . %, p = . ) (fig. a) . a total of . % of surgeons reported being tested for covid- , without notable difference based on prior epidemic exposure ( . % vs. . %, p = . ). formal hospital guidelines for epidemic/pandemic response were in place in . % of respondents' hospitals; prior epidemic experience did not impact on the presence of guidelines ( . % vs. %, p = . ) ( table ) . surgeons reported having adequate ppe at a rate of . %; prior epidemic experience did not impact ppe availability rates ( . % vs. . %, p = . ) (fig. b ). n masks were provided to % of respondents, surgical masks to . %, face shields to %, gowns to . %, and full-face respirators to . %. there were no significant differences in the type of available ppe based on previous epidemic experience (p > . ). surgeons reported that % of their hospitals had adequate ventilators for the volume of patients they expected (table ) . of the respondents who underwent viral testing, nine ( . %) reported testing positive for covid- . in areas of prior epidemics, surgeons reported being placed into quarantine at a greater rate compared to those from areas without prior epidemics ( . % vs. . %, p = . ) ( table ) . respondents reported consistency among hospital restrictions; there were no differences in rates of quarantine after travel, domestic travel bans, cancellations of academic activities, work-from-home orders, or cancellation of hospital meetings (p > . ) (fig. a) . surgeons from areas of prior epidemics reported a lower rate of hospital-mandated elective surgery cancellation compared to those from areas without prior epidemics ( . % vs. . %, p = . ). respondents reported significant differences among government restrictions; governments with prior epidemic experience had fewer shelter-in-place orders ( % vs. . %, p = . ), less restrictive bans on gathering with those outside their household ( . % vs. . %, p = . ), but more mandatory restaurant closures ( . % vs. . %, p = . ). there was no difference in government-mandated cancellation of elective surgeries ( . % vs. . %, p = . ) or stay-athome orders ( . % vs . %, p = . ) ( table , fig. b ). with regard to the impact of covid- on the personal practice of surgeons, there were several significant differences between those with and without prior epidemic experience (table ) . respondents from areas with prior epidemics reported still performing elective spine surgery at a higher rate compared to those from areas without prior epidemics ( . % vs. . %, p < . ). however, there was no difference in the rate of essential spine surgeries or reduction in case volume (p > . ). there were significant differences in income lost (p = . ) and percent personal revenue lost (p = . ), with those from areas without epidemic experience reporting a larger financial impact from covid- . there were no significant differences in hospital revenue lost (p = . ), furloughs (p = . ), hospital layoffs (p = . ), personal layoffs (p = . ), or time frame to resume elective surgeries (p = . ) between surgeons with and without prior epidemic experience (table ) . multivariate regression analysis, controlling for statistically significant demographic differences (geographic region, population, fellowship training, and practice breakdown), revealed that prior epidemic exposure was independently associated with an increase in respondents reporting personal health as a source of stress (or . ; % ci . - . ; p = . ), music as a coping strategy (or . ; % ci . - . ; p < . , and still performing elective spine surgery (or . ; % ci . - . ; p = . ). the differences in hospital cancellations of elective surgeries (p = . ), government-mandated shelter-in-place orders (p = . ), bans on gathering with those outside their household (p = . ), and mandatory restaurant closures (p = . ) on univariate analysis were not significant after multivariate analysis. prior epidemic exposure was also independently associated with respondents reporting impact on income (lr . , p = . ) and personal revenue lost (lr . , p = . ) ( table ) . global health security index scores for countries with significant burdens of covid- were reported (fig. ) . the usa received a ghsi score of . and was ranked first, as the most prepared country for a global pandemic. there was poor correlation between ghsi score and access to adequate ppe (r = . , p = . ), access to n masks (r = . , p = . ), and access to adequate ventilators (r = . , p = . ). there was no correlation between ghsi score and formal hospital guidelines (r = . , p = . ) (fig. ) . the impact of covid- and government responses varied greatly among countries, regardless of ghsi score (fig. ) . overall, % of surgeons felt that future formal guidelines are needed to mitigate future pandemics (fig. ) . covid- is a defining global health crisis. understanding how spine surgeons around the world prepared for, and responded to, covid- will help guide response to future pandemics. louie et al. [ ] highlighted, in over spine surgeons worldwide, that covid- had a substantial impact upon their patient care, practice, and personal lives; however, such impact varied. as such, our goal was to outline whether previous experience with outbreaks/pandemics played a role in surgeons' preparedness, response, and perceptions. interestingly, based on survey results, surgeons felt generally underprepared for a pandemic of this magnitude. the who and other global health experts have prioritized learning from previous health crises, yet our study noted that regions with previous infectious disease outbreaks were no more prepared to respond to covid- . our study further outlines that previous measures of global health security were not predictive of preparedness or minimized impact. the covid- pandemic is neither novel nor unexpected. during the twentieth century, there were three major pandemics that ravaged the globe: the h n spanish flu of , the h n asian flu of , and the h n hong kong flu of [ ] . since , only the hiv/aids outbreak spread across the globe and has had widespread impact on healthcare workers [ ] . the more recent epidemic level outbreaks of sars in , h n swine flu in , mers in , and ebola in provided certain regions around the world with an early opportunity to prepare for deadly infectious disease outbreaks [ , , , , [ ] [ ] [ ] . our survey indicates that respondents who indicated prior experience with the sars, mers, h n , and ebola outbreaks were no better prepared to take on the covid- pandemic. this likely indicates that countries around the world have struggled to change government and hospital policy based upon prior experiences. limitations in access and availability of testing have been cited as a major shortcoming in the media [ , ] . our results indicate that access to testing is no longer a major limitation for surgeons, with over % of surgeons reporting access to a covid- test. however, only . % of surgeons around the world reported actually being tested. surprisingly, . % of respondents with prior epidemic experience reported being tested compared to . % of those without prior epidemic experience. this gap between testing availability and completed testing indicates that universal testing of healthcare workers is not occurring. numerous health departments across the world have outlined that formal local and institutional guidelines are critical for pandemic preparedness [ ] [ ] [ ] . in , the who reported that many countries around the world were in the process of forming a pandemic plan, but no standard pattern in content or timing was in place, and many countries were waiting for who to lead with their own plan. the who warned that without regional or global leadership on formal pandemic plans, preparedness could diverge even further across the world [ ] . in our study, a surprisingly low . % of respondents reported that formal hospital guidelines for pandemic response were in place. this number only marginally increased to . % among respondents with prior epidemic exposure but did not reach statistical significance. clearly, formal institutional guidelines should have been a priority among all hospitals prior to the outbreak reaching pandemic proportions. another preparedness deficiency was access to personal protective equipment and other critical hospital resources. the media in the usa and across the world highlighted the critical lack of ppe that frontline healthcare workers faced in the early days of the covid- outbreak [ , , [ ] [ ] [ ] . while many respondents felt the media was sensationalizing the outbreak, our study indicates that the critical shortage of ppe is real with only . % of respondents reporting access to adequate ppe. even in regions with prior health crises, the availability of ppe was not significantly improved. another key resource limitation facing health systems during this pandemic is the ventilator shortage. not only are physicians facing the possibility of difficult decisions surrounding allocation of ventilators [ , ] , but operating room anesthesia machines are being reallocated to intensive care units (icus) closing operating rooms (ors) for surgeon use [ ] . an alarmingly low % of respondents reported adequate ventilator supplies, and access to ventilators was not improved by experience with prior epidemics. clearly, a need exists for larger stockpiles of these critical resources that can be mobilized during global pandemics. overall, respondents from countries with previous infectious disease outbreaks did not report improved government or hospital-level preparedness. this indicates that health systems and governments likely failed to learn from prior health crises or did not dedicate the time, resources, or manpower to strategic planning. regardless of these prior oversights, there is now a major need to come together and prepare for future pandemics. ing on a vertex of the innermost pentagon correspond to a cumulative total of % of survey responses received. each subsequent pentagon corresponds to a % increase in responses for a given category. *indicates difference significant at the % confidence level (p < . ) in the early days of covid- , there were a variety of responses to the growing threat spreading across the world. china instituted a swift government-mandated lockdown of wuhan in the hubei province in an attempt to slow the spread [ ] [ ] [ ] . south korea quickly implemented a widespread testing initiative that helped to isolate cases and prevent a prolonged nationwide lockdown [ , ] . both of these nations had previous experience with sars, mers, and other infectious disease outbreaks and had instituted national policies allowing for rapid approval of testing in the face of new disease outbreaks [ ] . prior experiences likely guided the response to, and impact of, covid- . surprisingly, the government and hospital restrictions instituted around the world were fairly consistent. respondents reported high rates of government-mandated cancellation of elective surgeries, mandatory stay-at-home orders, limitations on group gatherings, and closure of businesses and schools. a few subtle differences were noted. respondents who indicated prior experience with infectious disease epidemics reported being placed into quarantine at a higher rate after exposure to covid- . this may be because these governments had prior experience with quarantines and were willing to swiftly institute mandatory isolation. hospital-based restrictions were also remarkably conserved across the world. there were high rates of travel bans, cancellations of academic activities, cancellations of hospital meetings, and work-from-home orders. interestingly, prior epidemic experience was an independent predictor of still performing elective spine surgeries. the significance of fig. impact of covid- by ghsi score. bar graph comparing the impact of covid- stratified by country/ghsi score. all countries with > respondents were included in the analysis (n = ). a total of countries were included fig. assessing the need for formal international guidelines. pie chart reporting the overwhelming support for international formal guidelines to mitigate the impact of future pandemics. % of respondents from all regions of the world were in favor of formal guidelines this finding is unclear, given that epidemic experience was not predictive of preparedness. overall, surgeons appear to be somewhat dissatisfied with their governmental and hospital responses. a total of . % of respondents reported their government's response as "acceptable," while . % rate their government's action as "not enough." satisfaction rates with hospital responses are similar with . % of respondents rating their hospital's response as "acceptable," while . % rate their hospital's action as "not enough." respondents with prior infectious disease epidemic experience did not rate their government or hospital response any better. a moral and ethical obligation exists to improve our ability to respond to future crises. government and hospital policies in response to covid- are impacting spine practices across the world. over % of respondents reported a greater than % decrease in their weekly case volume. this reduction in volume has led to significant economic concerns among surgeons [ ] . nearly % of surgeons reported a reduction in income from the current covid- crisis. however, having prior experience with epidemics did lead to a significant decrease in rates of reported income loss. this may be confounded by the fact that most countries with prior epidemics utilize government run health systems. apart from economically impacting surgeons, the covid- pandemic has financial implications for all healthcare staff. in this study, . % of respondents reported having staff furlough at their institutions, with . % reporting layoffs. unfortunately, having prior experience with infectious disease epidemics did not protect against these financial effects. this point highlights the need for comprehensive government policies that prevent these economic impacts, rather than reacting to them. the ghsi is the first comprehensive assessment of health security and pandemic preparedness across countries [ ] . the ghsi provides a ranking by overall pandemic preparedness, early detection capabilities, and ability to mitigate a health disaster. the goal of the ghsi project was to use data obtained from prior disease outbreaks to improve the international capability to address pandemics [ ] . our survey results indicate that the ghsi was poorly correlated with covid- preparedness and surgeons' perceptions on response. countries such as the usa were rated as "most prepared" by the ghsi yet were not adequately prepared based on our survey. china, a country rated as "more prepared" with a low ghsi of . , had similar access to ppe and critical resources as the usa. the poor performance of the ghsi may indicate that traditional methods for assessing pandemic preparedness are faulty, or covid- did not follow the patterns established by previous infectious disease outbreaks. either way, we have an ethical and moral obligation to learn from the current situation to revamp the ways in which we prepare for pandemics and the way we assess pandemic preparedness. improvements in global coordination and cooperation have the potential to lessen the impact of infectious disease outbreaks, not only on surgeons, but on all of humanity. as with many questionnaire-based studies, there are limitations to this study. the survey distribution was limited to the current ao spine surgeon members network. the survey was sent out to spine surgeons worldwide; however, only surgeons responded ( . %). this may introduce a response bias because individuals with strong opinions may be more likely to respond. previous studies have described that low response rate is a risk factor for low validity, but does not necessitate low validity [ ] . response rates are important to consider, but, independently, should not be considered a proxy for study validity. our study lacked the power to break down responses by individual country. therefore, certain countries may have adequately learned from previous epidemics, but their response is diluted by the many others who did not. we attempted to control for this by using geographic region in our multivariate analysis. however, there may be questionable generalizability in regions in which there were few or no respondents. the timing of the survey may have also impacted our results as countries around the world were at different stages of the pandemic when they received the questionnaire. given the limit of survey length due to fatigue, we were not able to explore all of the possible domains related to covid- . finally, our targeted demographic was ao spine surgeons. this is one group of subspecialty surgeons, and the results may not represent the view and concerns of other medical specialties. however, given that covid- is impacting all healthcare providers around the world, we feel spine surgeons are reasonably representative of other surgical providers. we are unable to comment on covid- preparedness or impact for the general public. despite these limitations, this survey remains the largest, international effort to assess multiple domains of the impact of covid- on spine surgeons. this is the first, international study to assess the impact of covid- on spine surgeons in an effort to explore the effect of previous epidemics on preparedness and response. this study outlines that previous infectious disease outbreaks had only subtle influence on the impact of covid- and no substantial bearing on preparation for the current pandemic. furthermore, current methods for assessing preparedness, such as ghsi, were poorly correlated with preparedness for the current outbreak. findings from our study indicate that covid- substantially impacted spine surgeons globally; 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fda emergency use authorization china's aggressive measures have slowed the coronavirus. they may not work in other countries china shows covid- responses must be tailored to the local context what china's coronavirus response can teach the rest of the world coronavirus without shutting everything down : goats and soda : npr covid- in south korea-challenges of subclinical manifestations containing coronavirus: lessons from asia | financial times covid- and its impact on physician compensation how low should you go? low response rates and the validity of inference in is questionnaire research acknowledgements the authors would like to extend their sincere gratitude to kaija kurki-suonio and fernando kijel from ao spine (davos, switzerland) for their assistance with circulating the survey to ao spine members. conflict of interest the authors have no financial or competing interests to disclose in relation to this work.open access this article is licensed under a creative commons attribution . international license, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the creative commons licence, and indicate if changes were made. the images or other third party material in this article are included in the article's creative commons licence, unless indicated otherwise in a credit line to the material. if material is not included in the article's creative commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. to view a copy of this licence, visit http://creat iveco mmons .org/licen ses/by/ . /. key: cord- - njgmdd authors: leecaster, molly; gesteland, per; greene, tom; walton, nephi; gundlapalli, adi; rolfs, robert; byington, carrie; samore, matthew title: modeling the variations in pediatric respiratory syncytial virus seasonal epidemics date: - - journal: bmc infect dis doi: . / - - - sha: doc_id: cord_uid: njgmdd background: seasonal respiratory syncytial virus (rsv) epidemics occur annually in temperate climates and result in significant pediatric morbidity and increased health care costs. although rsv epidemics generally occur between october and april, the size and timing vary across epidemic seasons and are difficult to predict accurately. prediction of epidemic characteristics would support management of resources and treatment. methods: the goals of this research were to examine the empirical relationships among early exponential growth rate, total epidemic size, and timing, and the utility of specific parameters in compartmental models of transmission in accounting for variation among seasonal rsv epidemic curves. rsv testing data from primary children's medical center were collected on children under two years of age (july -june ). simple linear regression was used explore the relationship between three epidemic characteristics (final epidemic size, days to peak, and epidemic length) and exponential growth calculated from four weeks of daily case data. a compartmental model of transmission was fit to the data and parameter estimated used to help describe the variation among seasonal rsv epidemic curves. results: the regression results indicated that exponential growth was correlated to epidemic characteristics. the transmission modeling results indicated that start time for the epidemic and the transmission parameter co-varied with the epidemic season. conclusions: the conclusions were that exponential growth was somewhat empirically related to seasonal epidemic characteristics and that variation in epidemic start date as well as the transmission parameter over epidemic years could explain variation in seasonal epidemic size. these relationships are useful for public health, health care providers, and infectious disease researchers. respiratory syncytial virus (rsv) has long been recognized as a substantial public health threat [ ] with annual epidemics exacting an enormous toll on vulnerable populations and health care delivery systems. rsv is associated with substantial morbidity in children in both the hospitalized and outpatient setting [ ] [ ] [ ] [ ] . in addition to the toll on the health of the population, this disease imposes a large burden on the health care system in terms of human and material resources. although no rsv vaccine exists, infants and children with risk factors for severe rsv infection (eg, lung disease or prematurity) can receive monthly doses of palivizumab, a humanized murine anti-rsv monoclonal antibody, during the rsv season. palivizumab treatment is extremely costly; the cost-effectiveness of this therapy could be improved if treatment is given only during times of high rsv activity. treatment of vulnerable individuals also improves overall health in the population. prediction of seasonal epidemic characteristics including times of high activity and total size would support efficient management of resources and delivery of palivizumab. health care facilities could forecast requirements for beds, staffing, testing, treatment, and other resources needed to care for sick children. for greatest effectiveness, these predictions should be made early in the rsv season; the authors, including public health practitioners and physicians, hold the expert opinion that these predictions would be useful within the first month of the observed start of the rsv seasonal epidemic. in some regions, total epidemic size generally follows a biennial cycle from year to year with smaller epidemic seasons followed by larger epidemic seasons [ ] . this cycle is currently used to gauge upcoming rsv seasonal epidemic size based on total size of the previous epidemic season. the centers for disease control and prevention (cdc) researchers using the national respiratory and enteric virus surveillance system found that the prior epidemic season's data were a relatively imprecise predictor of the epidemic season onset in a given community and that timing of the rsv epidemic season may vary substantially in the same year among communities in close proximity [ ] . one goal of this research was to explore year-to-year variation in epidemic seasons using local data. the biennial variation in our seasonal epidemic data was seen in the early exponential growth rates (slope of the cumulative case curves, figure ) as well as total epidemic size. we explored the relationship between exponential growth of rsv epidemics and the seasonal epidemic characteristics of total epidemic size, days to peak, and epidemic length to assess predictions made early in the epidemic season. knowledge about viral transmission characteristics and the data derived from surveillance systems can be used to inform novel approaches for estimating characteristics of rsv epidemics through the application of methods rooted in epidemiological models of infectious disease transmission [ , ] . these methods are being increasingly applied to emerging threats like sars [ ] [ ] [ ] and pandemic influenza, but their application to routine epidemics of common respiratory viruses like seasonal influenza and rsv has only begun to be explored. weber et al. [ ] model rsv transmission to examine how climate and social factors influence transmission in a population. they consider compartmental models using susceptible-infected-recovered-susceptible (sirs) with additions to include latency and stages of susceptibility. they find no single best model for rsv epidemics; many "competing" models fit the observed data well. we further explored the variation in seasonal epidemics using compartmental models. the variation in exponential growth could potentially be related to variation in transmission rates, epidemic start dates, or proportions susceptible as well as a host of other factors. the second goal of this research was to evaluate the ability of a compartmental model based on epidemiologic principles to fit observed data from a series of epidemics and examine the extent to which seasonal variations in epidemics can be accounted for by variation in specific model parameters. for these analyses, we used daily laboratory data from the major pediatric health care facility in utah where routine viral testing is a fixture of standard clinical care for children presenting to regional emergency departments. the utility of the data from these surveillance systems for relating final epidemic size and modeling the epidemic curve has not been fully evaluated. we investigated the estimation of seasonal epidemic characteristics using regression of exponential growth across seven epidemic seasons. we also modified the model of weber et al. to explore the model fits and estimates of epidemic size using variation of parameters within a susceptible-exposed-infected-infected/detected-recovered (seidr) model. primary children's medical center (pcmc) is a -bed children's hospital that serves both as a community pediatric hospital for salt lake county, utah ( population million [ ] ), and as a tertiary referral center for five states in the intermountain west (utah, idaho, wyoming, nevada, and montana, total population . million [ ] ). eighty percent of pediatric hospital admissions occurring in salt lake county and % occurring in the state of utah are at pcmc. during the study period, july through june , direct respiratory sampling (mainly saline-assisted nasopharyngeal aspiration) for respiratory viral testing was performed for about % of children evaluated in the pcmc emergency department for respiratory complaints (unpublished data) and was required for all hospitalized children with respiratory symptoms (eg, upper or lower respiratory tract infection, bronchiolitis, asthma, or bacterial or viral pneumonia). in addition, respiratory viral testing was recommended for all febrile infants one to days of age. test results were used to inform patient cohorting and isolation procedures and to assist with medical management. all samples were initially tested by direct fluorescent antibody staining (dfa). dfa testing was performed three to five times daily depending on the season, with a mean turnaround time of four hours. for all dfa negative specimens, multiplex polymerase chain reaction (pcr) or viral culture was performed. the data included in our analyses were all positive test results from the above sampling protocols from any of the testing methods during the study period. the practice of testing and test methods did not change appreciably during the study period (unpublished data on percentage of children tested and methods used). the data were used as daily counts by age group, under two and over two years old. the rsv epidemic year was defined to be from july of one year through june of the following year. this time period was chosen to place the beginning date close to the middle of the inter-epidemic period, approximately six months from the average historical peak of the seasonal epidemic. this study was reviewed by the institutional review boards of intermountain healthcare and the university of utah and determined by both organizations to be exempt. regression analysis was used to explore the relationship between the initial exponential growth rate and the epidemic season characteristics of size, days to peak, and length using the seven epidemic seasons of rsv data from pcmc. the exponential growth rate, λ t , t , for time interval t to t was calculated as , where x t i denotes the cumulative number of cases at time t i , i = , . the exponential growth rate was calculated at four weeks to assess regression predictions made early in the season. for comparison, exponential growth rate was also calculated at weeks one through six. the total epidemic size was the sum of cases over the epidemic year, including sporadic interepidemic cases. an observable seasonal epidemic start date of t was defined as the start of the first week of the epidemic year with at least five confirmed rsv cases. this was the definition used by the hospital epidemiologists at pcmc to declare the start of rsv outbreaks during the study period. the term seasonal epidemic refers to the period from the epidemic start date until the epidemic end date, defined as the end of the last week of the epidemic year with at least five confirmed rsv cases. the number of days until the peak for the epidemic seasons was calculated as the midpoint day of the largest seven-day moving average window minus the epidemic season start day. the length of the epidemic season was calculated as the epidemic season end day minus the epidemic season start day. relationships between the initial exponential growth rate and seasonal epidemic characteristics were described using the pearson correlation coefficient and assessed using standard regression statistics. the fits of the regression models were assessed using the percent error of the model fits from the observed values. to combine across seasons, the absolute values of the percent errors were averaged providing the mean absolute percent error for the model. we modeled the observed rsv cases using an extension of the sir model that included individuals (c for children and a for adults) that were susceptible (s c and s a ), exposed (e c and e a ), infectious(i c and i a ), infectious and subsequently detected children (d), and recovered combined across children and adults (r). this seidr model was applied to a series of seven epidemic years. the population was split into children less than two years old (children) and those older than two (adults). it has been shown that the initial rsv infection is the most severe and occurs in almost every child in their first two years of life. transmission is modeled as a function of time using a cosine function to mirror the cyclic nature of epidemics [ ] . there is an offset to this cycle (α), which we estimate along with transmission parameter (β). births and deaths (μ) are accounted for in the susceptible class only. achievement of age two is accounted for in all age-separated classes (η). assumptions of simple compartmental models that we made were as presented in koopman [ ] . our seidr transmission model ( figure ) was defined using the following system of non-linear differential here β was the transmission parameter, l the latency period, f the under-two detection fraction, and γ the recovery parameter. all parameters are presented in the next subsection with descriptions, ranges, and reference values from the literature. solution to the set of differential equations is addressed below. to fit the seidr model to the empiric epidemic data, three parameters-latency period, birth and death rate, and recovery period-were specified based on the literature. three parameters associated with variation across epidemic years were estimated: ) the temporal offset of the epidemic cycle (α), ) detection fraction (f), and ) transmission parameter (β). different models were specified to explore the effect of these three parameters. all combinations of these were considered: models with one parameter allowed to vary across seasons, models with two parameters allowed to vary across seasons, and a model with all parameters allowed to vary across seasons. each parameter is described below. birth and death rate (μ) the number of daily births and deaths were entered in the model based on census data for salt lake county. it was assumed that / th of the children in each ageseparated compartment reached the age of two each day. detection fraction (f) the detection fraction parameter reflected the fraction of the rsv epidemic in children under two years old that was captured in our data set. the detection fraction parameter was estimated as a constant parameter across years and also allowed to vary by epidemic year. the latency period is the time between exposure resulting in transmission and time of infectiousness. the latency period was specified using the median value from crowcroft [ ] , five days. the transmission parameter determined the rate of transmission from contacts between infectious and susceptible individuals. we assumed a homogeneous, uniformly mixing population. the transmission parameter was estimated as a constant parameter across years and also allowed to vary by epidemic year. the recovery parameter specifies the time from infectiousness to recovery. this was specified as . , which translates to a ten-day recovery period, following the work by weber [ ] and in the range of one to reported by hall [ ] . the final model parameter was the offset of the annual epidemic cycle. a regular annual cycle is thought to vary due to weather and climate conditions. the seidr model captures the entire epidemic, detected and not detected. prior to observing rsv cases, the epidemic cycle started within the undetected population. this offset parameter was estimated as a constant parameter across years and also allowed to vary by epidemic year. the nonlinear equations were solved using the lsoda function from the odesolve library [ ] in r statistical software [ ] . the parameters were estimated using a grid search. two fitting statistics were used. the estimates were the values that minimized the square root of the sum of standardized squared errors (rse) and/or the square root of the sum of squared standardized errors (rmse the denominator from these measures adjusted for the magnitude of the epidemic curve to avoid fitting the model mainly to the peak, where differences could over-inflate the fitting statistic and under-value differences during the early and late stages of the epidemic. the rmse reduces the effect of fit to the peak more than does the rse. a grid search was used starting with an initial wide range of values for f, β, and α. the search grid was repeated with successively narrowing ranges to minimize the rse. the grid started with the range of reasonable values, - for β and f and one to days for α. the range was reduced and resolution increased iteratively around minimal rse and rmse values. the minimum grid resolution was . for β, . for f, and one day for α. the rses and rmses from the grid search results were used to select the best parameter estimates within each model type (eg, one model type had only transmission rates that varied by epidemic year). the model with all three parameters allowed to vary by epidemic year was fit as a saturated model to provide a benchmark for rse and rmse, along with the schwarz criteria described below, and percent error in estimating epidemic size when evaluating more parsimonious models in which only one of the parameters was allowed to vary by epidemic year. multiple measures were used to compare the models, in part because the schwarz criteria assumed the residuals were independent and identically distributed, which was not the case; they are, in fact, autocorrelated. the schwarz information criterion [ ] were calculated based on the weighted least squares method used for parameter estimation. there were n = data points, days of case data for each of seven years, and k, the number of parameters estimated was in the full model (four parameters for seven years) and in each other model (two parameters for seven years and two parameters overall). the schwarz criteria were calculated as: bic = × ln j= m j + k ln( ) where m represents either the rse or rmse fit statistic [ ] . the absolute values of the percent error in estimating total epidemic size were summed across seasons for comparison of models. the number of children with test-positive rsv infection ranged from cases in - to cases in - ( table ). the median size of the annual epidemic was cases. overall, % of cases were detected between the months of october and april. larger epidemics alternated with smaller epidemics. the amplitude of this biennial cycle was approximately cases. the total number of children (under years of age) tested per epidemic year ranged from approximately to , with numbers of tests increasing over time. overall, % percent of these were positive for rsv, varying according to the biennial cycle. of children tested, % were less than three years old and % were less than years old. of children with positive tests, % were less than three years old and % were less than years old. of the children tested, % were from salt lake county and % of children with positive tests were from salt lake county. exponential growth rates calculated from cases accumulated for four weeks from the observed epidemic season start ranged from . to . (table ) across the epidemic seasons. the effective reproductive numbers ranged from . to . using a serial interval of seven days [ ] . in regression analyses (table ) , the fourweek exponential growth rate exhibited a substantial positive correlation with epidemic size (r = . , p = . ), and was negatively correlated with start day (r = - . , p-value = . ), days to peak (r = - . , p-value = . ), and length of the epidemic (r = - . , p-value = . ). the regression models provided estimates of epidemic season characteristics that were on average within % of observed epidemic season size, % of observed days to peak, and % of observed epidemic length. using exponential growth rates calculated from weeks one through six provided, in general, increasing correlation (table ) . the saturated seidr model was fit to seven epidemic years of observed rsv data with epidemic year-specific rse values that ranged from to , rmse values that ranged from . to . and percent error of total cases that ranged from % to %. the fit statistics for the models with either transmission parameter or table observed rsv epidemic size, start date, days to peak, duration, and -week exponential growth detection fraction estimated as a constant across epidemic year did not differ substantially from those from the saturated model (table ) . the minimum rse model with detection fraction held constant across epidemic years had the smallest % error, smallest schwarz rse criterion, and had other fit statistics nearly equal to the saturated model. the minimum rmse models were, in general, fitting to the tails of the epidemic and resulted in large errors in estimating epidemic size. the pattern of variation in estimates of offset from all models matched the biennial cycle variation in total epidemic size across epidemic years (figure ) . the variation in estimates of the transmission parameter and detection fraction did not necessarily match this cycle for all epidemic years. the parameter estimates for the transmission parameter were negatively correlated with total epidemic size. the seidr model we presented made assumptions that simplified the reality of rsv transmission. we have identified three limitations to the seidr modeling effort. first, the population age separation does not take full advantage of differences in interaction among a non-homogenous population. second, related to this, the parameter values were not allowed to vary within the population. transmission, for instance, could be age-dependent (due, eg, to hand-washing habits). third, the grid search method of parameter estimation did not provide estimated standard errors for parameter estimates, which limited the ability to compare models and seasons. despite these limitations, this seidr model was useful; it modeled the observed rsv cases from pcmc as part of larger unobserved epidemic seasons and provided a framework for investigating the model parameters. the parameters offset and transmission may not be completely identifiable within this framework but more likely represent combined other forces unmeasured here. our future work includes addressing these limitations and expanding the complexity of the models. rsv is carried by all age groups but is, in general, only a concern for infants. thus, an age-stratified model, possibly with different mixing mechanisms, would more closely resemble the true transmission. the biennial cycle of large, early, and short seasonal epidemics followed by smaller, later, and longer seasonal epidemics the next year observed in utah is similar to other published studies of seasonal rsv epidemics in temperate climates. the theories for this phenomenon include the existence and switching of two rsv disease strains, climate patterns, and waning immunity after infection [ , , , [ ] [ ] [ ] . these and other theories could be investigated in more complex models. it is understood that immunity after infection of rsv is partial, at best. this incomplete immunity and severity of re-infections could be incorporated into more complex models [ , ] . finally, future modeling efforts will involve approaches that include measures of uncertainty in parameter estimates, including bayesian methods [ , ] and likelihood and other methods [ , ] . the first main conclusion of this work was that exponential growth was somewhat empirically related to seasonal epidemic characteristics. the variations in epidemic seasons from data collected at pcmc during the seven years of the study can be partially explained by the variation in exponential growth, especially characteristics of epidemic size, peak day, and length of the epidemic. the seven years of data were not sufficient to make conclusive statements on the nature of the relationships. these early findings based on just seven data points can be built upon to explore early prediction of table results of regression analysis using exponential growth to predict epidemic size, days to peak, and length the upcoming rsv epidemic season. these early predictions could be used by hospitals to budget and allocate resources and to coordinate the timing of palivizumab treatment. they can be used by public health to advise clinicians and the public and also to help identify nonstandard epidemics earlier in the season. for example, health departments might take specific actions if the number of observed cases during the season greatly exceeds early predictions. the second main conclusion of this work was that variation of the transmission parameter and the start of the epidemic (offset) over epidemic years could explain the variation in seasonal epidemic size. the three model parameters allowed to vary by epidemic year (detection fraction, transmission parameter, and offset) provided possible rationale for the variation in seasonal epidemic size. the model with detection fraction held constant across epidemic year fits the observed data well with the fewest parameters. the parameter estimates from this model also match the expected biennial pattern of the epidemic years. from the models considered in this study, this one performs best overall (figure ). write the introduction and discussion sections of the text, providing public health perspective to the study. cb helped conduct the literature review and write the introduction and discussion sections of the text. ms conceived the study and directed its implementation, including contributions to all sections of the text. all authors read and approved the final manuscript. respiratory syncytial virus epidemics: the ups and downs of a seasonal virus prospective population-based study of viral lower respiratory tract infections in children under years of age (the pride study) recent trends in severe respiratory syncytial virus (rsv) among us infants economic impact of respiratory syncytial virus-related illness in the us: an analysis of national databases bronchiolitisassociated hospitalizations among us children defining the timing of respiratory syncytial virus (rsv) outbreaks: an epidemiological study variation in timing of respiratory syncytial virus outbreaks: lessons from national surveillance modeling epidemics caused by respiratory syncytial virus (rsv) understanding the transmission dynamics of respiratory syncytial virus using multiple time series and nested models transmission dynamics and control of severe acute respiratory syndrome invited commentary: real-time tracking of control measures for emerging infections different epidemic curves for severe acute respiratory syndrome reveal similar impacts of control measures census bureau population division-counties census bureau population division-states modeling infection transmission respiratory syncytial virus infection in infants admitted to paediatric intensive care units in london, and in their families respiratory syncytial virus infections in infants: quantitation and duration of shedding solvers for ordinary differential equations. r package version . - edn vienna, austria: r foundation for statistical computing development core team: a language and environment for statistical computing generalizing the derivation of the schwarz information criterion multiexponential, multicompartmental and noncompartmental modeling, ii: data analysis and statistical considerations pattern of respiratory syncytial virus epidemics in finland: twoyear cycles with alternating prevalence of groups a and b occurrence of groups a and b of respiratory syncytial virus over years: associated epidemiologic and clinical characteristics in hospitalized and ambulatory children the incidence of infectious diseases under the influence of seasonal fluctuation a stochastic method for solving inverse problems in epidemic modeling bayesian inference for partially observed stochastic epidemics predicting case numbers during infectious disease outbreaks when some cases are undiagnosed inference for nonlinear dynamical systems statistical challenges of epidemic data partial support for this work was provided by the public health services research grant ul -rr from the national center for research resources, nih/niaid u ai and u -a , us cdc # po cd , and the nih/eunice kennedy shriver nichd k -hd . author details division of epidemiology, university of utah school of medicine, salt lake city, usa. department of pediatrics, university of utah school of medicine, salt lake city, usa. division of disease control and prevention, utah department of health, salt lake city, usa.authors' contributions ml performed the analysis and wrote the bulk of the manuscript. pg helped to conceive the study and prepare the data and also wrote a large part of the introduction, methods, and discussion sections of the text. tg advised on the design of the study's analysis and helped prepare the methods and results sections of the text. nw acquired and managed the data. ag provided clinical insight and helped conduct the literature review. rr helped the authors declare that they have no competing interests. key: cord- -qzgxe c authors: shang, yilun title: modeling epidemic spread with awareness and heterogeneous transmission rates in networks date: - - journal: journal of biological physics doi: . /s - - - sha: doc_id: cord_uid: qzgxe c during an epidemic outbreak in a human population, susceptibility to infection can be reduced by raising awareness of the disease. in this paper, we investigate the effects of three forms of awareness (i.e., contact, local, and global) on the spread of a disease in a random network. connectivity-correlated transmission rates are assumed. by using the mean-field theory and numerical simulation, we show that both local and contact awareness can raise the epidemic thresholds while the global awareness cannot, which mirrors the recent results of wu et al. the obtained results point out that individual behaviors in the presence of an infectious disease has a great influence on the epidemic dynamics. our method enriches mean-field analysis in epidemic models. the effect of individual awareness (or risk perception) in the context of an infectious disease outbreak in a human population has been under investigation for a few years [ , ] . human responses to disease outbreaks are sometimes decisive factors. for example, when aware of a disease in their vicinity, people can take precautionary measures such as wearing masks, frequent hand washing, and evading contact with infected individuals to reduce the risk of infection and lower the possibility of disease transmission [ ] [ ] [ ] . the behavioral change triggered in a population corresponds to the information obtained from the circumstances [ ] . the information taken from a social or spatial neighborhood is called local information, while information that comes from the news media and public health authorities is called y. shang (b) institute for cyber security, university of texas at san antonio, san antonio, tx , usa e-mail: shylmath@hotmail.com global information. both sources of information have strong impacts on epidemic dynamics. we refer the readers to [ , ] for comprehensive surveys of related results. to investigate the effect of behavioral response, two kinds of awareness, global awareness, which increases with the overall disease prevalence, and local awareness, which increases with the fraction of infected contacts, were studied in [ , ] . global and local awareness were described by exponential functions of respective global and local information. by using a mean-field approximation, it was shown that the network topology, homogeneous random network or scale-free network, has an intrinsic impact on the existence of a critical value (in terms of global and local awareness) that stops the epidemics. in [ ] , a third kind of awareness, called contact awareness, which increases with the individual contact number, was proposed. by using a linear formulation of awareness, the authors showed that both the local and contact awareness can raise the epidemic threshold (hence, inhibit the epidemic from spreading), while the global awareness cannot. the precise functioning of awareness, nevertheless, is still not well understood. one of the goals in this paper is to understand the role of the aforementioned three forms of awareness by providing a more flexible yet analytically tractable framework. in most of the existing relevant literature (including the work mentioned above), it is assumed that the transmission rate is constant for all individuals. to describe the vast spectrum of disease propagation strategies, the degree-correlated transmission rates were examined in [ ] . it was shown that the connectivity-dependent infection scheme can yield threshold effects even in scale-free networks where they would otherwise be unexpected (see e.g., [ , ] ). therefore, for a more realistic epidemic model, the degree-correlated transmission rates should be taken into account. in view of the above considerations, in this paper we investigate the impact of global, local, and contact awareness on epidemic spreading with degree-correlated transmission rates. our model is based on an sis epidemiological process where, at a given time, each individual can be susceptible (s) or infected (i). the contact network of the population is modeled by a configuration model (described below) where nodes represent individuals and edges indicate potential contacts between individuals. building on a continuous meanfield approach and the lyapunov stability theory, we establish the epidemic dynamics and derive the epidemic threshold. the function of awareness is expressed by a non-linear function (the linear function used in [ , ] can be viewed as a special case) that provides additional flexibility in applications. through numerical simulation on scale-free networks, we confirm that both local and contact awareness can raise the epidemic threshold while global awareness can only decrease the final epidemic size. however, the influence degree of the awareness is shown to be closely related to the heterogeneous transmission rates. the rest of the paper is organized as follows. we describe the model and establish the epidemic dynamics by mean-field analysis in section . we determine the epidemic threshold in section and present numerical simulations in section . finally, we conclude the paper in section . we use a modified sis (susceptible-infected-susceptible) model to study the epidemic dynamics on a network consisting in n individuals. the contact network is defined as a configuration model [ , ] , where only the network's degree distribution (that is, the distribution, p k , which governs the probability that a node will have degree k) is specified and the edges are made by random pairing. configuration model networks are increasingly used for infectious diseases in complex networks, which yield to analytical treatment and allow for heterogeneous contact levels [ ] . data-driven studies reveal that the accuracy of such models is mostly high; see, for example, [ , ] . in the simplest sis model, each individual is either in a susceptible state or an infected state. a susceptible individual, say node i, becomes infected upon contact with a single infected individual, say node j, at some infection rate. the infection rate along the edge from j to i can be expressed as a i t j , where a i is the admission rate of node i describing the rate that susceptible node i would actually admit an infection through an edge connected to an infected node and t j is the transmission rate of node j meaning the rate that infected node j would actually transmit an infection through an edge connected to a susceptible node [ , ] . once infected, a node recovers (i.e., returns to the susceptible state) at rate γ . in case of no awareness, the admission rate a i is usually assumed to be and the transmission rate t i = β for all nodes i. as mentioned above, we will consider the degreecorrelated transmission rate β k [ ] , which is defined as the transmission rate of a node with degree k. in addition, we modulate the admission rate a i by some multiplicative factors. first, let ≤ ψ k ≤ be a decreasing function, which represents the contact awareness of a node with degree k. naturally, an individual having a larger contact number has a higher risk of being infected [ ] . this factor of contact awareness reflects an individual's risk perception based on the contact information. second, let ≤ φ k ≤ with φ = being a decreasing function accommodating the local and global epidemic information. specifically, for a node, say i, with degree k, let k inf be the number of its infected neighbors. the local awareness of node i is given by φ l k = − α(k inf /k) α for some precaution level, ≤ a ≤ and α is a positive integer reflecting the use of special prophylaxis [ ] . the quantity ρ is taken to be representative of the global infection density, that is, the fraction of infected individuals over the whole population. the global awareness of a node with degree k is supposed to be φ g k = − bρ α with ≤ b ≤ and α similarly being a k positive integer. the parameters α and α embody the impact strength of the local and global epidemic information on the admission rate. the role of them will be clear in the following. for a susceptible node i with degree k and one of its infected neighbor j, the modified infection rate along the edge from j to i can be written as where β k is the transmission rate of node i, and k inf is the number of node i's infected neighbors. note that both the infection density ρ and the number of infected neighbors k inf evolve with respect to time t. we mention that the functions φ l x and φ g x can be viewed x as an approximation of the exponential function φ x = e −ax α analyzed in [ , ] . setting α = α = , we readily reproduce the linear functions used in the work [ ] . at time t, let θ(t) be the probability that a randomly chosen edge points to an infected individual. let ρ k (t) be the infection density among nodes having degree k. as in [ ] , we obtain and where k is the average degree of the network. denote by x k a random variable counting the number of infected neighbors of a node with degree k. thus, x k follows a binomial distribution bin(k, θ(t)) with [ ] for ≤ s ≤ k. given a susceptible individual with degree k, who has s infected neighbors, the probability of infection is by using ( ). thus, the probability that a susceptible node with degree k becomes infected is shown to be given by hence, the discrete-time epidemic dynamics can be described as considering an infinitesimal interval (t, t + h], similarly as in [ , ] , we can transform ( ) and ( ) into where the probability p(x k = s) is given by ( ) . by employing l'hôpital's rule, we obtain the moment-generating function of x k is defined for all ∈ (−∞, ∞) by m ( ) = e e xk = θ e + − θ k . it is well known that by differentiation at = , and for any positive integer α . dividing both sides of ( ) by h and letting h → , we obtain employing ( ), ( ) and ( ), where ρ and θ are given by ( ) and ( ), respectively. for α = α = and β k ≡ β, ( ) reduces to ( ) obtained in [ ] . the consistency confirms that ( ) is valid. notice that the above system ( ) (k = , · · · , n) is highly involved. however, we will see in the next section that a neat formulation of the epidemic threshold can be derived. without loss of generality, we will set the recovery rate γ = in the following. in this section, we determine the epidemic threshold in terms of the connectivity-correlated (i.e., k-dependent) transmission rates β k . in the simplest networked sis model, the epidemic threshold corresponds to a critical value of infection rate β c (or the reproductive ratio r ), above which the disease in question spreads, while below it the disease dies out [ ] . the critical value has been shown to rely on the infection and recovery rates of a disease, as well as the topology of the host population through which it spreads [ ] [ ] [ ] [ ] [ ] . by studying the local stability of the infection-free equilibrium, we will present the dependency of awareness on the epidemic threshold. our results also have implications for the dissemination of a computer virus/worm across the internet as well as opinions/rumors/news in social networks. to start with, we establish a linearization system of ( ). on omitting higher powers of ρ k and noting that γ = , we obtain notice that where * represents an unspecified or unknown quantity. therefore, we have linear differential equations for k = , · · · , n d dt which implies that the jacobian matrix of ( ) can be calculated as where f k = β k (k − a/k α − ) ψ k and g k = kp k / k for k = , · · · , n. by basic determinant transformations (see e.g., [ , lemma ]), we obtain the n eigenvalues of j from the characteristic equation det (j − λi) = as λ = · · · = λ n− = − and λ n = − + n k= f k g k . the trivial solution ρ k ≡ of system ( ) (which is the infection-free equilibrium) is locally stable if and only if λ n < , which yields hence, if ( ) holds, the disease dies out; otherwise, the disease spreads. this expression shows that local and contact awareness play a pivotal role in determining whether an epidemic spreads in a population, while the global awareness is independent of the epidemic threshold. the same result was observed in [ ] . in what follows, we study the epidemic threshold by instantiating the above general correlated transmission rates in two special examples. in the first example, we set β k ≡ β. this infection scheme implies that an infected individual can transmit the infection from all of its edges with the same rate. this example has been addressed in [ ] and it has relevance for many of the respiratory infectious diseases such as the severe acute respiratory syndrome (sars) [ ] and the influenza a (h n ) [ ] . introducing β k = β into ( ), we obtain the threshold for containing the disease as if we set α = , the above threshold reduces to that deduced in [ , eq. ( ) ]. next, we consider a reciprocal infection scheme where β k = β /k. here, the transmission rate is connectivity correlated. this scheme reflects the infection dynamics of some macroparasite diseases where infected agents have a limited pathogen reservoir and the more the agent contacts the less would be the chance of transmission per contact (or per capita) [ ] . substituting β k = β /k into ( ) yields we mention that this infection scheme also has implications in cyber security. in peer-topeer (p p) file-sharing networks (e.g., napster and kazaa), every node has a limited upload capacity. the larger the connectivity, the slower each one of its neighbors can download. the probability of successful downloading would thus be inversely proportional to the connectivity. another plausible scenario is the denial of service (dos) attacks, which flood a target computer system with bogus requests, making it unable to provide normal services to legitimate users. the variance σ = k − k of the degree in a network is an indicator of the degree of asymmetry [ ] . compared with regular graphs or classical random graphs, scale-free networks have much larger σ and their degree distributions are asymmetric. to take a look at the effect of σ on the epidemic threshold, for simplicity, we set ψ k = and α = . from ( ) and ( ) we obtain and it is clear that the threshold β c decreases with respect to σ while β c remains unchanged. this suggests that, in our first infection scheme where β k = β, an epidemic is more inclined to occur for asymmetric networks, and that in a reciprocal infection scheme the asymmetry has no influence on the epidemic threshold. for scale-free networks, a similar result was observed in [ ] without considering awareness. to complement the theoretical analysis carried out in the previous section, we now investigate the impact of awareness on the epidemic thresholds ( ) and ( ) by numerical simulations. simulations are performed on a scale-free network of n = , nodes with degree distribution p k∼ k − . (see fig. ). the graph is generated by using the configuration_ model in networkx [ ] . this degree exponent is a typical value for networks seen in the real world [ ] . initially % of the nodes are infected. we iterate the sis process until convergence to a steady/equilibrium state. following [ ] , we choose the contact awareness as a power-law function ψ k = k −μ , where μ ≥ . hence, it follows from ( ) and ( ) that we obtain the thresholds and first, we examine the dependence of β c and β c on local and global awareness, namely the parameters a, b, α and α . we fix μ = . . the epidemic threshold β c is measured by calculating the final infected portion ρ for each β from to in steps of . and the epidemic threshold β c is measured by calculating ρ for each β starting from in steps of . . if ρ > . , we accept the corresponding value of β (or β ) as the threshold value. to reduce the fluctuation, for each β (or β ), we calculate the average of ρ over simulation runs with different initial infected nodes. in fig. we show the results of calculations of the epidemic thresholds β c and β c from the exact formulas ( ) and ( ), compared with explicit simulations of the model with α = α = . we find that both β c and β c are almost unchanged for different b, while they increase with a. an intuitive interpretation is that a higher level of precaution measures adopted by individuals (i.e., larger a) can decrease the likelihood of an epidemic outbreak (i.e., larger β c and β c ). the simulated values are slightly larger than the theoretical predictions, which is likely due to a finite-size effect [ , ] . we illustrate the epidemic ( ) and ( ) thresholds for α = , α = in fig. and those for α = , α = in fig. . we find similar behaviors as observed in fig. . by comparing fig. with fig. and comparing fig. with fig. , we see that the epidemic thresholds β c and β c decrease with α , while they are almost unchanged for different α . (the dependency between β c (β c ) and α is re-plotted in fig. for the sake of comparison). these observations agree well with our analytical solutions. the decrease of epidemic thresholds with respect to α has an important epidemiological implication. nodes with exposure to many infectious contacts (corresponding to a high value of k inf /k) in a network may fail to be infected due to their increased perception of the risk or safety measures (here, smaller α ) and thus stopping the epidemic spreading. in the real world, medical doctors and care/sex workers should adopt strong safety measures, which may efficiently contain the disease transmission. a similar phenomenon was observed in bagnoli et al. [ ] for a network with a power-law in-degree distribution and an exponential out-degree distribution using degree-independent transmission rates (corresponding to our fig. a ). the ineffectiveness of factor α as well as b, nevertheless, indicates the incapability of altering an epidemic threshold for a global influence over the population. next, we examine the dependence of β c and β c on contact awareness, namely the parameter μ. we show the changes of β c and β c with respect to μ in fig. . simulated solutions are slightly increased from the expected values, again due to a finite-size effect. in fig. a , the value of β c is absent when μ is close to . this is because β c = k /( k − . ) > exceeding the range of β. this paper has addressed the impact of awareness on epidemic outbreaks by proposing a mean-field approach accommodating heterogeneous transmission rates. our analysis is based on an sis epidemiological process in random networks modeled by a configuration model. theoretical and numerical results show that both the contact and local awareness can raise the epidemic threshold, while the global awareness cannot. our results confirm and further extend the previous observations in [ , , ] to more general forms of awareness as well as degree correlated transmission rates. we found that the non-linear effect encoded in parameter α of local awareness implies that individuals who are exposed to many infectious contacts can effectively contribute to disease control by increasing their awareness of risk. in the present work, we implicitly assumed that the disease is visible at the same moment it becomes infective. however, from a practical point of view, the information reaction may experience time delay or retardation for an individual. oscillatory behavior may be displayed if we take delayed/periodic updating mechanisms into account [ ] . applications of the techniques described here are also possible for other network structures, for example, the dynamic contact networks [ ] , etc. finally, we mention that a relevant issue we have not addressed is the risk estimation. the form of risk functions in ( ) might have implications for disease control [ ] . risk perception in epidemic modeling capturing human behaviour the public's response to severe acute respiratory syndrome in toronto and the united states adaptive human behavior in epidemiological models the impact of information transmission on epidemic outbreaks modelling the influence of human behaviour on the spread of infectious diseases: a review towards a characterization of behavior-disease models risk perception and disease spread on social networks the impact of awareness on epidemic spreading in networks unexpected epidemic thresholds in heterogeneous networks: the role of disease transmission infection dynamics on scale-free networks networks: an introduction discrete-time epidemic dynamics with awareness in random networks a critical point for random graphs with a given degree sequence spread of epidemic disease on networks modeling human mobility responses to the large-scale spreading of infectious diseases network theory and sars: predicting outbreak diversity epidemic spreading in scale-free networks mean-field theory of a recurrent epidemiological model a stochastic model for the spread of a sexually transmitted disease which results in a scalefree network mathematical epidemiology of infectious diseases disease spread in small-size directed networks: epidemic threshold, correlation between links to and from nodes, and clustering epidemic dynamics and endemic states in complex networks percolation and epidemic thresholds in clustered networks epidemic threshold and control in a dynamic network mixed si(r) epidemic dynamics in random graphs with general degree distributions responding to global infectious disease outbreaks: lessons from sars on the role of risk perception, communication and management pandemic novel h n influenza: what have we learned? semin. respir exploring network structure, dynamics, and function using networkx scale-free networks: a decade and beyond time-delayed information can induce the periodic outbreaks of infectious diseases the dynamic nature of contact networks in infectious disease epidemiology risk estimation of infectious diseases determines the effectiveness of the control strategy key: cord- -m d ntg authors: tomie, toshihisa title: relations of parameters for describing the epidemic of covid― by the kermack―mckendrick model date: - - journal: nan doi: . / . . . sha: doc_id: cord_uid: m d ntg in order to quantitatively characterize the epidemic of covid― , useful relations among parameters describing an epidemic in general are derived based on the kermack-mckendrick model. the first relation is /τgrow= /τtrans− /τinf, where τgrow is the time constant of the exponential growth of an epidemic, τtrans is the time for a pathogen to be transmitted from one patient to uninfected person, and the infectious time τinf is the time during which the pathogen keeps its power of transmission. the second relation p(∞) ≈ −exp(−(r − )/ . ) is the relation between p(∞), the final size of the disaster defined by the ratio of the total infected people to the population of the society,and the basic reproduction number, r , which is the number of persons infected by the transmission of the pathogen from one infected person during the infectious time. the third relation /τend= /τinf−( −p(∞))/τtrans gives the decay time constant τend at the ending stage of the epidemic. derived relations are applied to influenza in japan in for characterizing the epidemic. we reported the understanding of the present status and forecasting of pneumonia by in china which is supposed to have originated in wuhan by analyzing the data up to february (ref. ). in ref. , we clarified that the behavior of the epidemic was different in different regions and that the outbreak was well described by a gaussian as was for influenza in japan. we reported the following; . the epidemic in china passed the peak in the beginning of february, . the date of the epidemic peak was different by region and was the latest in wuhan. for more than days after our forecast, the epidemic closely followed our forecast. the new patients outside wuhan decreased to less than % of that at the peak around february . although the epidemic in china is near the end, patients by covid- are found in many other countries, and covid- is still a big fear of the people over the world. in order to forecast the epidemic of covid- in other countries, we need to theoretically characterize the covid- epidemic by fitting a model calculation to the data observed in china. we choose the kermack- ) for our analysis. the kermack-mckendrick model was proposed as early as , but still, it is the basis of many modified models for describing epidemics. we want to analyze the epidemic of covid- in detail by applying a model. as a preparation of the analysis, useful relations of parameters describing an epidemic are derived in the present paper. useful relations of parameters of an epidemic are eqs. ( ) to ( ) in the following, which are derived from the kermack-mckendrick model (ref. ). the number of susceptible people in the group is set as s , the number of infected persons is i(t), the number of persons who have been infected and recovered to obtain immunity or have died is r(t), the number of persons who is susceptible but not yet infected is s(t). s = s(t) + i(t) + r(t). when the transmission power of the disease is set as β and the recovery rate from the infection is γ, the epidemic of the disease is given by the following three differential equations. the author/funder, who has granted medrxiv a license to display the preprint in perpetuity. the copyright holder for this preprint (which was not peer-reviewed) is . https://doi.org/ . / . . . doi: medrxiv preprint we define the initial transmission time constant, τ trans , after which a pathogen is transmitted to one susceptible host in the early stage of the epidemic and the infectious time of a pathogen, τ inf , after which the pathogen loses the power of transmission as follows, the basic reproduction number, r , which is the number of persons infected by the transmission of a pathogen from one infected person during the infectious time, is given by in the following, we see that an epidemic starts with exponential growth with a time constant τ grow given by and decays exponentially with a time constant τ end given by here, p(∞) is the final size of the disaster which is defined by the ratio of the total number of the infected people, r(∞), to the population of the society, s . as shown later, p(∞) is approximated as, by using r , eq. ( ) is rewritten as r , τ inf, and p(∞) are parameters describing an epidemic. the above relations, eqs. ( ) to ( ), are derived as follows. in the beginning of the epidemic, i(t) and r(t) are negligible compared to s , and eq. the author/funder, who has granted medrxiv a license to display the preprint in perpetuity. the copyright holder for this preprint (which was not peer-reviewed) is which gives exponential decay of the patients. the time constant of the decay τ end is given by thus, eq. ( ) is derived. the final size equation was numerically solved and the result is shown by the solid curve in fig. . as r increases from , p (∞) increases from zero and saturates at a large r . when r is larger than . , more than % of people in the group are we apply the above model to the epidemic of influenza in japan as cited in ref. as a reference for the general epidemic. figure shows the influenza epidemic in japan over the past decade (ref. the author/funder, who has granted medrxiv a license to display the preprint in perpetuity. the copyright holder for this preprint (which was not peer-reviewed) is from . weeks, the time constant of the rising of the epidemic can be increased to . weeks in the model calculation, but the width of the epidemic in the model calculation was too wider than the real one as shown in fig. . in all the cases of the epidemic, there should be a difference between the reported number of patients and the real number of infected people. not all infected people will go to a hospital and not all patients are not inspected by medical institutes. in analyzing statistics, we assume the ratio of the reported number to the real number is constant during the epidemic, but often the assumption can be wrong. we expect the ratio is smaller in the beginning and at the ending of an epidemic. then, the time constant of the "apparent rise" and "apparent ending" will be shorter than the real ones. however, this expectation was the opposite in fig. . the slower increase and the slower decrease at the skirt of the epidemic could suggest the transmission power β of the virus may change in time, which, we think, is not plausible. at present, we do not know the reason why the simple kermack-mckendrick cannot reproduce the whole epidemic including the skirt parts. thus, from the analysis of jpninf by the model described above, we learn that it is important to remember that the time constant of the "apparent" increase of the epidemic in the early stage does not re-produce the whole epidemic. the above information helps greatly to understand the to-be-planned analysis of covid- . useful by applying the model, we found that the epidemic of influenza in japan in was re-produced by the parameters;τ trans = . week and τ inf = week and that τ grow observed in the early stage can be different from τ grow for re-producing the overall epidemic. understanding the present status and forecasting of covid- in wuhan a contribution to the mathematical theory of epidemics national health commission of the people's republic of china, prevention of epidemics health commission of hubei province, anti-prevention new coronary disease infection, information number of reports at fixed disease points-comparison with the past years national institute of infectious diseases and ministry of health, labor and welfare tuberculosis infectious disease division key: cord- -jqesw e authors: yu, xinhua title: modeling return of the epidemic: impact of population structure, asymptomatic infection, case importation and personal contacts date: - - journal: travel med infect dis doi: . /j.tmaid. . sha: doc_id: cord_uid: jqesw e background: proactive interventions have halted the pandemic of coronavirus infected disease in some regions. however, without reaching herd immunity, the return of epidemic is possible. we investigate the impact of population structure, case importation, asymptomatic cases, and the number of contacts on a possible second wave of epidemic through mathematical modelling. methods: we built a modified susceptible-exposed-infectious-removed (seir) model with parameters mirroring those of the covid- pandemic and reported simulated characteristics of epidemics for incidence, hospitalizations and deaths under different scenarios. results: a larger percent of elderly people leads to higher number of hospitalizations, while a large percent of prior infection will effectively curb the epidemic. the number of imported cases and the speed of importation have small impact on the epidemic progression. however, a higher percent of asymptomatic cases slows the epidemic down and reduces the number of hospitalizations and deaths at the epidemic peak. finally, reducing the number of contacts among young people alone has moderate effects on themselves, but little effects on the elderly population. however, reducing the number of contacts among elderly people alone can mitigate the epidemic significantly in both age groups, even though young people remain active within themselves. conclusion: reducing the number of contacts among high risk populations alone can mitigate the burden of epidemic in the whole society. interventions targeting high risk groups may be more effective in containing or mitigating the epidemic. : flowchart of the epidemic model the above flowchart is applied to both young (age < ) and old populations (age>= ). we assume there is cross infection between younger and older age groups. the combined flowcharts can be modeled in differential equations (with index t suppressed and subscript y for young people, s for old people) as follows: table : detailed parameter estimates and ranges. all rates are set as daily rates in a region with population size of , , . range and references f importing rate for susceptible population, proportional to the size of population people per day, only for young people arbitrary, net travel inflow of - people per day for a city of a million. f y , f s importing rate for exposed and infectious persons, proportional to the size of population note: ) the infecting rate per contact per day is based on the basic reproductive number and serial interval between case generations. early reports suggested a r of . (range . - ), and a serial interval range of - days. however, several recent studies found the r was greater than , one reported as high as . . in this study, we took a conservative estimate of . and a moderate serial interval: days for young people, days for old people. based on simple sir model, the reproductive number is k*b*t, where k is contact rate, b is infecting probability per contact, and t is serial interval. assuming k= contacts per person per day for young people, and the infecting probability is b = . for a symptomatic young people. for mild or asymptomatic cases, we assume % less infectious than symptomatic cases, thus b = . for young undiagnosed people. for older people, the parameters are set to higher than young people, with fewer contact and shorter serial interval. ) the base rate per day is based on disease duration such as incubation period, diagnosis delay, hospitalization delay, hospitalization stay and recovery duration. we assumed an exponential distribution of duration, i.e., daily rate is -exp(- /duration). j o u r n a l p r e -p r o o f we investigate the impact of population structure, case importation, asymptomatic cases, and the number of contacts on a possible second wave of epidemic through mathematical modelling. methods: we built a modified susceptible-exposed-infectious-removed (seir) model with parameters mirroring those of the covid- pandemic and reported simulated characteristics of epidemics for incidence, hospitalizations and deaths under different scenarios. have detected virus shedding in nasopharyngeal swap samples among asymptomatic cases [ ] . a few case reports have shown some cluster of cases initiated by asymptomatic cases [ , , ] . researchers have postulated that asymptomatic and pre-symptomatic cases may play a significant role in sustaining the community transmission [ ] . second, government leaders have been pressed to allow people to return to normal work and life to avoid economic recession. after social activities are restored, both international and domestic j o u r n a l p r e -p r o o f travel ban will be lifted. social and work-related gatherings are restored. imported symptomatic and asymptomatic cases may kindle a second wave of epidemic in the community [ ] . the us, the mortality rate for age or younger is below %, while the mortality rate increases to more than % among people aged or above [ ] . finally, as demonstrated in the h n flu pandemic [ ] , a pandemic with lower hospitalization and mortality rates has less impact on the society than those with higher hospitalization and mortality rates, though it may still have heavier impact on the economy. epidemic model simulation has been used extensively to estimate essential epidemic parameters, in this study, we will build a modified susceptible-exposed-infectious-removed (seir) model [ ] to simulate the covid- pandemic and investigate the impact of population structure, asymptomatic cases, case importation, and the number of contacts on the epidemic progression. we will explicitly evaluate the changes of hospitalizations and mortality under various scenarios for young and elderly people. our analysis will provide theoretical evidence for possible strategies to prepare for a second wave of epidemic. the covid- , like many other respiratory infectious diseases such as influenza, often has an incubation period during which the exposed persons cannot transmit the virus to others. after the incubation period, there is an infection period during which cases may or may not have symptoms but are able to infect other people. the infectivity may also vary at different time points of the infection period. as in the covid- pandemic, the highest infectious points are - days around the symptom onset [ ] . after the infection period, the patients are recovered or removed from the infectious pool. in addition, various controlling measures may be implemented j o u r n a l p r e -p r o o f during the epidemic, notably the case isolation, quarantine of high risk people through contact tracing, and also social distancing. all these measures will change the transmissibility of virus during a contact between an infectious person and a susceptible person. therefore, the modified seir model as shown in figure is appropriate (also see the modeling framework section in supplemental documents for details). the seir model and its variants have been used in many previous studies for modeling the covid- pandemic [ , ] . briefly, we divide the population into the susceptible population (s), self-quarantined susceptible people (q), exposed we also assume a dynamic population in which the numbers of imported susceptible persons and assumptions that will be discussed later and also in the supplemental document. to account for population heterogeneity, we also apply the basic framework (figure ) to both young (age < ) and elderly (age >= ) populations. the two flowcharts are connected through cross-infection due to mutual contacts. the combined flowcharts can be translated into a set of ordinary differential equations (see supplemental document). the key equations relevant to the drive of pandemic and cross-infection between two age groups are for the change of exposed people at time t (subscript y for young, and s for elderly people, with time indicator t suppressed): specifically, the first equation models the exposure dynamics among young people. it includes imported exposed people (f y n y ), newly exposed people through contacting within the young people ( + ) and contacting between young susceptible and infected elderly people ( + ). then some percent of exposed young people become symptomatic cases ( ), and some become asymptomatic cases ( ). a fixed percent of exposed people will die of other diseases ( ). the second equation for the exposure dynamics among elderly people can be interpreted similarly. the model involves many parameters. their definitions, default values, and ranges are listed in the supplemental document (supp. the default model is set on a region with million residents, consisting of % elderly people and % of total population with past infection (or immunized). there is no existing symptomatic or asymptomatic case, and no person in self-quarantine in the region. we assume only one imported young exposed case every two days for days (i.e., imported cases). analyses are performed based on the ranges of parameter estimates. we vary one parameter at a the r package epimodel is used for simulating the deterministic epidemic models [ ] . the r codes for simulating the modified seir epidemic models are available (http://github.com/xinhuayu/returnepidemic/). this study is deemed exempt from ethics approval as the research involves no human subjects and we use publicly available data. no informed consent is needed. under the default model setting, all epidemic measures reflect the model parameters satisfactorily (table , also refer to supplemental table ). that is, the resulting epidemic j o u r n a l p r e -p r o o f measures from the default model such as the disease incidence, epidemic peak, and duration of the epidemic are reasonable and mirror those reported in the literature. for example, starting with ten imported infectious persons and assuming % asymptomatic cases at the peak of epidemic, the epidemic reaches peak quickly within days and lasts days. it is ten days quicker among elderly people than among young people ( table ). the epidemic curves for incident cases (symptomatic and asymptomatic), hospitalizations and deaths by age groups are typical (supplemental figure ). the modeling results in an overall hospitalization rate of . %. the in-hospital mortality rate is . % for young and . % for elderly people, with an overall mortality rate of . %, similar to those empirical measures in the covid- pandemic in the early epidemic of the us. therefore, the default model represents the current covid- pandemic sufficiently well. as summarized in table , the size of region and a small percent change of self-quarantined susceptible people do not change the epidemic progression significantly except for the total number of cases. a smaller percent of elderly slows down the epidemic, while a much higher percent of elderly does not change the epidemic curve significantly. as expected, when over % people have prior infections, the epidemic takes very long to reach the peak and results in substantial fewer cases. the effects are similar in both young and elderly people (supplemental both the percent and infectivity of asymptomatic cases were investigated (table ). an increase of the percent of asymptomatic cases from % to % postpones the epidemic peak by days j o u r n a l p r e -p r o o f due to less infectivity of asymptomatic cases, and results in significantly fewer hospitalizations and deaths. on the other hand, a higher infectivity of asymptomatic cases (e.g., % of symptomatic cases) results in a fast developing and narrow epidemic curve which reaches the peak within days. there are more hospitalizations and deaths at the epidemic peak compared with the default model, both assumed % asymptomatic cases. in addition, a change of the percent of asymptomatic cases among elderly people leads to larger changes in hospitalizations and deaths than that of young people (supplemental table a & b) . for example, comparing % with % asymptomatic cases, the total hospitalizations are reduced only by half among elderly people, while it is a two third decrease among young people. furthermore, when the effects of the percent and infectivity of asymptomatic cases are combined, for example, in a low risk epidemic with % asymptomatic cases but with a lower ( %) infectivity, the epidemic reaches its peak slower for both young and elderly people with peak hospitalizations almost half of the default model (assuming % asymptomatic cases and % infectivity) (supplemental figure ) . this epidemic model is initiated by imported infectious persons (may be asymptomatic or presymptomatic cases). the number of imported cases is in absolute sense, regardless of the size of population. a daily arrival of two infectious people speeds up the epidemic by days compared with one case every two days in the default model ( table ). the magnitudes of epidemic are similar between different importation scenarios. in addition, a longer importing duration shifts the epidemic only slightly. finally, if we assume all the imported cases are asymptomatic cases, the epidemic curves are not significantly different from that of default model (supplemental figure ) . respectively, all significantly lower than those of default model ( table ). the times to the epidemic peaks are also postponed in both curves. when both young and elderly people reduce contacts to per day, such as under the stay-at-home rule, the epidemic curves on hospitalizations are significantly mitigated in both age groups (figure d ). finally, we consider two extreme scenarios: ) high risk scenario: assuming one imported case per day continuously throughout the epidemic, % asymptomatic cases at the epidemic peak, and the same infectivity between symptomatic and asymptomatic cases; ) low risk scenario: assuming one imported case every two days for twenty days, % asymptomatic cases, and asymptomatic cases have only % infectivity of symptomatic cases. in both scenarios, limiting contacts among elderly people alone still has significant impact on hospitalizations in both age j o u r n a l p r e -p r o o f groups, and a larger relative difference in the low risk scenario than high risk scenario ( figure and supplemental figure ). we with growing availability of detection kits during the covid- pandemic, more asymptomatic or mild symptomatic cases are identified. ultimately, an optimal view is asymptomatic cases may account for % of infections. however, recent research and case reports have confirmed that asymptomatic or pre-symptomatic cases can shed enough quantify of virus to be infectious [ ] [ ] [ ] [ ] ] . furthermore, if the infectivity of asymptomatic cases is similar to that of symptomatic cases, a faster epidemic will occur. despite more asymptomatic cases at the peak of epidemic, there are also significantly more hospitalizations and deaths, which may overwhelm the health care system. with a lower infectivity ( % infectivity) among asymptomatic cases, the epidemic reaches its peak later and results in half of hospitalizations at the peak compared with the default model (supplemental figure ) . in addition, a closely related issue is case importation [ ] . imported cases are often pre-symptomatic, asymptomatic or with mild symptoms. they seed of a second outbreak, even with just a few cases. therefore, proactively identifying asymptomatic j o u r n a l p r e -p r o o f cases, isolating them and tracing their contacts thereafter will prevent the occurrence of an epidemic [ ] . our study has some strengths. we have devised a modified seir model to incorporate both symptomatic and asymptomatic cases. we emphasize population heterogeneity such as age structure in the model. we include a self-quarantined group who will not infect other people if they are infected with the virus. naturally, these settings can be extended to represent other high risk or special groups with revised parameters. in addition, we separate hospitalization and death from other removed compartments to explicitly estimate the impact of an epidemic on hospitalizations and deaths. from the health impact point of view, severe cases that lead to hospitalizations and deaths are more important than mild cases, as demonstrated in the h n pandemic [ ] . furthermore, we explored a few key determinants of epidemic explicitly, leading to many insights on epidemic prevention strategies. there are a few limitations in our study. as inherent in all modeling studies, simulation interpretations are heavily dependent on model assumptions and parameter estimations. our epidemic model is a population model. although we take account of population heterogeneity such as age in the current model, our age group is overly broad. a more detailed age grouping scheme, including children, young adults, middle age group, and elderly, may reflect the agespecific epidemic more realistically. other factors may also be included, and additional compartments such as pre-symptomatic stage may be modeled. however, more sophisticated models require more assumptions and may not necessarily provide more insights about the epidemic process. instead, in this study, in addition to ensuring the mathematical correctness of the models, we prioritize the epidemiological concepts and clinical relevance in setting up the models rather than model complexity. nevertheless, our findings do not intend to provide j o u r n a l p r e -p r o o f definitive advice to design a new policy but rather gain insights of the epidemic process and provide theoretical support for a possibly more effective prevention strategy based on approaches targeting high risk populations. in addition, we assume random mixing within and between age groups. as a population model, we cannot assess the impact of individual behaviors such as the way of reducing contacts, social distancing and travelling. furthermore, it ignores clustering within the population such as senior group living, community gatherings (e.g., churches, community centers), worksites and schools. these clusters are hotbeds for superspreading events which may lead to a sudden increase of new cases and overwhelm the healthcare system unexpectedly. furthermore, the quarantine compartment in the model is not contact tracing based. modeling contact tracing based quarantine is more relevant to public health interventions [ ] . therefore, the goal of our future research is to exploring the effect of these factors with stochastic simulations of individual behavior [ , ] and network analysis [ ] . 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