key: cord- -rfncgtnf authors: sarukkai, sundar title: self-reliant india: self of a nation or a national self? date: - - journal: j doi: . /s - - -z sha: doc_id: cord_uid: rfncgtnf the pandemic has led to a renewed reflection on what it means to be self-reliant in terms of our everyday practices. nations too follow this logic in their own claims of self-reliance. this paper discusses the implications in these claims of self-reliance in the context of the nation by positioning this claim within the tension between two different formulations of the self: self of the nation as against the idea of national self. although there is an increased push for self-reliance globally these days, the idea of being self-reliant is a long one. the relationship between the independence movement and selfrule is an expression of political self-reliance. the latest invocation of self-reliance by governments in india and elsewhere is primarily about economic self-reliance but like in the indian case it is more specifically about self-reliance in manufacturing. but the nature of self-reliance is such that it is difficult to understand economic self-reliance without other forms of self-reliance, most importantly, a self-reliance of the 'self' as well as of the 'intellect'. it is this range of ideas that are present in self-reliance that needs to be understood, even for the narrow vision of self-reliance in manufacturing or other economic processes. in the context of the self-reliance of the nation, there is a new conceptual challenge that we have to face, namely, the use of the term self in the context of the nation. what work does the term 'self' do in the articulation of self-reliance of a nation? how does the nation get or possess a self, since the self is most commonly seen as the attribute of individuals? does this imply that the nation gets unified as an individual even though the nation is a collection of individuals? and does the association of self to the nation lead to contradictions for a democratic nation? in this essay, i want to explore the notion of self-reliance in the context of the nation in a very limited way. on the one hand, the term 'self-reliance' needs little philosophical reflection since its meanings are seemingly apparent. in fact, in our common usage of this term, the word 'self' plays very little part. it primarily functions in terms of insideoutside: self-reliance means nothing more than not to be reliant on the outside (others) but even this simple meaning has deep assumptions about inside-outside, self-other and so on. while this is a common usage of this term, in this essay i want to argue that there is a hidden function of the many meanings related to the self. these multiple approaches and paradoxes about the self arise in the many different questions about self-reliance. there are many different ways to understand the meaning of 'self', ranging from the ontological to the narratological. i do not want to enter into these different formulations but will focus on one implication of invoking the self in a term that has pragmatic considerations for the functions of a nation. i begin with some reflections on the question of the self during covid. what i say here are some preliminary remarks to motivate the reason for critically focussing on the meaning of self in self-reliance. then i try and attempt to understand why the notion of the self (which is so much related to the individual) is invoked in the context of the nation. what is in the understanding of a nation that allows the possibility of linking the nation to a self? i suggest that there are two primary ways of understanding the meaning of a self in relation to the nation: self of a nation and a national self. the implications of these two formulations are quite distinct and have differing implications on the meaning of self-reliance. the covid- pandemic has created a special problem that has to do with the relationship between the self and the society. the social pre-covid was a field which catered to individual interests-from security, health, infrastructure and travel to shopping. what the pandemic really destroyed was our access to the social world, a world in which others performed their work on behalf of others. labour itself was oriented around this act of distributing the tasks that one had to do for oneself. restaurants took care of the individual's need for cooking one's own food, schools took care of the children (at least for a major part of the day), hospitals took control of health (much of which could have been in the hands of individuals themselves) and so on. pre-covid we were a society that increasingly developed a sense of the social defined through dependency. that was not a social that came together through friendship or kinship or as members working towards a common goal. the society itself was moving more and more towards not just a service economy but a service society, where the very idea of the social was reduced to a system designed to take care of the interests of individuals. shopping malls were a literal exemplification of this social in urban areas. technology plays a major role in this subordination of the individual to the society since the basic functions of the individual were outsourced to technology. right from the beginning, the ideal of technology was to replace manual labour-labour characterized as routine, as a drudgery and not having sufficient value. thus, labour associated with hard physical work was slowly replaced by machines and household labour by women was taken up by technologies such as the washing machine. the aim of this view of technology was that eventually all human actions-particularly those that were repetitive and monotonouscould be completely outsourced to machines. this view of technology has become so much a part of our very understanding of a society that the great chess player, gary kasparov ( ), in his book deep thinking extends the promise of new digital technologies by arguing that now they can take care of 'menial' mental tasks which includes the human capabilities of memory, recall, calculating and so on. technology became an important part of the society in that it made possible the worldview that saw the social world as a world which was there to take care of, protect and more increasingly entertain individuals. in this view of society, not just the government but also other people in a society had become like technology-they were all cogs who took care of one or the other of the jobs to support the interests and desires of the individual. the fact that any social based on this utilitarian end is inherently hierarchical only meant that this form of the social was always geared towards protecting the interests and desires of the more privileged. the pandemic rudely halted this unquestioned function of society. it first squeezed off the subletting of individual action to others. people who did not know the basics of cooking had to learn them. those who saw shopping as a social interaction found that the most taken for granted liberty-the 'right' to shop-was suddenly removed. there were no gyms for exercise and one had to find ways to exercise by oneself in the confines of their house or in the restricted space of their apartment blocks. social distancing literally distanced the social from each other's lives. the claim that this was not really social distancing but only physical distancing misses the point about the impact of the presence of individuals in the creation of the social. the anonymous and virtual social of social media, mediated through digital technology, was just a two-dimensional caricature of the real social that characterizes human relations. this phenomenon is not new and can be seen occurring repeatedly in discussions on the idea of 'presence' in theatre in contrast to films, for example. but just as the social was being distanced, there was a concomitant discovery of the individual and a revival of that worn-out cliche, 'discovering oneself'. it was as much a discovery of what one could do by oneself, tasks which were originally expected to be done by others-whether it was laundry, ironing one's clothes, carrying out garbage and for a lot of people just sweeping and mopping. many of these chores were not easy but at least it became clear why they were not easy. i do not believe that we will learn lessons from this forced reallocation of labour practices, which ideally should make us respect the people who do these jobs for us more than before. once the situation normalizes, we will go back into the surrogate world of the social but at least now we are forced to confront how much of the individual self has been mortgaged to others in the name of labour and service. what does this re-discovery of the self imply for the future ideas of the social? it is quite instructive to see what has happened to the hospital services during this time. hospitals which were full of patients seeking treatment for something or the other suddenly found that many who would have otherwise landed up for consultation preferred to wait or depend on home remedies. although the covid has had some negative impact on those who needed urgent medical intervention, overall the number of people who discovered individual practices to help them fight their problems increased. this was one direct mode of the strengthening of the individual and this included changes in lifestyle practices including exercising, control over food, etc. in other words, the pandemic allowed us a chance to rethink what it means to be self-reliant with respect to our own selves. however, the meaning of being self-reliant depended to a large extent on the modes of the discovery of the self as described above. while it might seem that the examples above point to a 'strengthening' of the self, it is not necessarily the case. i used these examples only to show how a re-organization of our everyday understanding of the self happened through these responses to the covid situation. as i also mentioned above, these new examples of self-reliance came in response to the prior situation of our society functioning largely as a 'service society' as well as the deeply social nature of individual lives in places like india. one could also argue that the covid situation actually created more selfishness and antisocial tendencies in our society leading to important ethical problems. what these tendencies point to is the confusion in the meaning of self-reliance. in the examples discussed above, we can note the processes of strengthening the self and also becoming more selfish. but how do these qualities affect the question of reliance, being reliant upon? what i would argue is that the very notion of reliance implies the social and self-reliance is only about strengthening the self as a social actor whereas being selfish is relying on the self in a world of just that self. in a similar analogy, we can think of self-reliance of a nation as being totally inward looking and acting as if other nations do not exist or we can consider it as acknowledging that the nation is part of a global system and yet is able to be selfsustaining. thus, while the covid period has led to selfish practices there has also been the possibility of expanding one's own awareness of the self in relation to relying on others. what happens to us as individuals happens to nations also. 'make in india' was already a saleable slogan. trump had further legitimized such slogans through his own version of 'make in america'. make in became a new slogan of legitimate nationalism. the pandemic, as much as it shone a spotlight on the social dependency of individuals, also made nations realize how much they depended on other nations. the global was always a lot like the social-it was not really based on notions of friendship, ideas of kinship or a sensitivity to the common humanity but was more utilitarian and driven by dependencies. suddenly we realized that in the great story of indian pharma producing cheap drugs, there was another story of dependence on china for a major part of the raw material for these drugs. the finance sector is anyway so globally wired that the very idea of strengthening the nation like strengthening the individual would be a non-starter. the market economy drives so much of the idea of the global that in spite of market crashes few are worried as they all realize that the world we have created is not possible if the market dependencies are over. however, as i argued earlier, the pandemic also revived more strongly the spirit of individual self-reliance as against individualism as a social practice. this recognition of the possibility of individual strength is also a model for the revival of the strength of a nation. and the most powerful example of the strength of the nation-in the model of the individual-lies in the 'self-reliance' of a country. but what is the meaning of the self here? why invoke the idea of self-reliance of a nation when the very idea of the self of an individual is itself so complicated? what task does the term 'self' perform in these articulations? we can begin with the reasons why the self is invoked in the context of the individual. what role does the 'self' perform in the case of individuals? why do we even invoke this term? i will not enter into a debate on whether we should make an ontological commitment to the self but only discuss the reasons why we tend to invoke the notion of the self. the self helps us make sense of some of the experiences we have such as the feeling that experiences happen to 'me'. the use of the notions of me, mine and myself are indicators of the action of a self. thus, self marks the basic identity that one has of who they are. but there are also other important reasons for our naive invocation of the self: unity of the senses that is presupposed in the belief that different experiences (such as seeing, hearing, touching, etc.,) all happen to the 'same me', that all experiences over time (from the time we are born) happen to the 'same me' and so on (bhatt ) . the self generates a notion of the unity of the experiences that are part of our lives and gives us a sense of identity. it gives us a sense of 'ownership' over our experiences (guru and sarukkai ) . it helps us to understand the nature of human action and human agency, such as the question 'who' is acting. we could go to the extent of saying that the basic notions of the unity presupposed in an object is one that is modelled on the self. an object is nothing more than a collection of different qualities, such as colour, shape, size and taste. so, what is the object other than these qualities? how do these qualities all belong to 'one' object? this cognitive inclination to unify diverse qualities in one is common to our basic recognition of objects (and therefore the world) and the self. we talk about the social in pretty much the same way (guru and sarukkai ). we use terms like 'we' and the 'we-self' just like we talk about i and the i-self. we belong to a social in ways similar to that in which different experiences belong to the same individual. the very idea of a nation with concomitant ideas such as 'belonging to the nation' is based on these beliefs about the self. so, it is not a surprise when the nation repeatedly invokes ideas of self-rule and self-reliance for these are all assertions of the self. there is an important characteristic of the sense of unity which is an essential element of the notion of the self. an individual has a wide variety of experiences. this diversity of experiences, some of which may be pleasant but some undesirable like experiences of sickness or sadness, are all unified, however diverse they are. the unification that is the core of the idea of the self is not a unification based on reducing all the experiences to an idea of sameness. rather, the unity is one that is based on the idea of the self as the substratum of all experiences. all experiences that we have are unified not because these senses have common elements but because they are all 'located in oneself'. this idea of unity is extremely important when we talk about the self of the nation. the nation is most fundamentally defined by a sense of unity and identity. the nation borrows its vocabulary of belongingness from the notions of a self. but this is of a social self and not the individual self. a social self adds an important component to a forgotten aspect of the individual self. this is the aspect of responsibility to others who are part of the social self. for traditions which have engaged deeply with the question of the individual self, there is a sense of self-responsibility which is extremely important. the individual self experiences but also regulates itself. (this can be contrasted to the culture of 'me and mine' that is a particular understanding of the self where there are no questions of selfresponsibility.) in the case of a social self like the nation, the regulatory aspect becomes most problematical since it raises a question of who is going to regulate the actions made on behalf of the nation, the socialized self. the concept of the nation has always had a parasitic dependence on the notion of the self. in the independence movement, it is most prevalent in the debate on self-rule. the idea of self-rule is self-explanatory: in both these terms which use the word self, the meaning of the self is in opposition to the outside(r). self-explanatory means that there are no external requirements to understand an expression and self-rule is about the capacity to rule one selves without the assistance of the outsider. (it is important not to conflate the outsider and the other in this context.) the idea of self-rule is an essential component of any notion of the nation since the nation, by definition, gets defined with respect to the insider-outsider dichotomy. gandhi's understanding of self-rule illustrates the need for invoking the idea of self in the context of the nation. one of his most influential works, hind swaraj, is a handbook for self-rule as indicated in the title itself. the list of terms that work around the idea of the self become defining elements of the independence movement: terms such as swaraj, swadeshi, swabhiman. the reason that self or the prefix swa is so important to these articulations is because within the idea of self there is a notion of both freedom and governance. the self is an excellent example of responsibility with freedom since the self will indulge in what it wants but has a core of survival within it-what we refer to as self-preservation. the fight against the british is not captured merely by the word 'independence'. the indian language connotations for this word include swatantra and swavalamban, both of which have an explicit grounding in the self. this necessary connection with swa locates the principal idea of independence within the self first and thus all invocations of swaraj by gandhi and other leaders have to be understood not just as liberation from the british but as an essential practice related to freedom and responsibility of the self. an important addition to this debate comes through the tension between gandhi and ambedkar. nagaraj ( ) captures this tension through the invocation of two terms derived from the self: self-rule versus self-respect. the distinction between these two terms has a significant impact on the very definition of freedom and its relation to the self. selfreliance (and the expressions of make-in) in the context of the nation has elements both of self-rule and a strong dose of self-respect. much of india's rhetoric on self-reliance (especially the make in india kind) is a call for self-respect within a hierarchy where india is placed low in the order. self-reliance in this context is not self-rule but only about assertions of self-respect. self-reliance is closely related to the ideas of swaraj. it is a reaffirmation of the idea that ruling itself has to be from within and by oneself. one is free and accountable to that freedom at the same time. much depends on what we mean by the self here. for gandhi, ruling oneself meant disciplining the self and that includes the responsibility of the (individual) self. being self-reliant does not mean asociality but only the responsibility of oneself for oneself. but how is it possible to be self-reliant? what are we supposed to be self-reliant about? these questions become important in the context of the self-reliance of a nation. we can glimpse the contours of this question in the philosopher k. c. bhattarcharyya's (kcb) essay 'swaraj in ideas' (bhattacharya ) . this was an essay which has been understood in different ways but the fundamental question that bhattacharya poses is the possibility of thinking about our society in ways that do not draw upon the 'outsider'. he suggests that the foreigner cannot understand the indian society like 'we' do and that drawing upon the resources of the society might offer a better understanding of the society. as raju ( ) points out, kcb should be seen as responding to the crisis of organic thinking and organic solutions to the problems of our society. independence is not limited to political independence but also needs the independence of the mind. the independence of the mind can only be supported by a self that is self-confident, that can feel secure in the foundations of its philosophies and experiences. there can be no swaraj without swaraj in ideas, in worldviews, in projecting the future which we want and not based on the interest of 'outsiders'. it is as much a question of self-articulation of who we are and what our vision of the world will be. while there are many points which may be debated in this view, it is nevertheless an important theme that will arise in any claim of self-reliance. perhaps the most important point in this idea of self-articulation is the problem of articulating on behalf of others who constitute the 'us' and 'we'. who is going to speak on behalf of a group, a community, a society, a nation? what kind of a social self will be allowed by the individuals to speak on their behalf? nation is one of the most powerful illustration of the action of a social self and thus the meaning of a nation becomes as complex as that of the individual and social self. i believe that there are two functions of the term 'self' in the context of the nation: one referring to the 'self of a nation' and the other to 'national self'. the difference between these formulations is quite stark and impacts the way we understand self-reliance in the context of the nation. when references are made to the self of a nation, it is primarily about the qualities of the nation related to the themes of identity, belongingness and the space of experiences for those who live and/or belong to it. in this sense, it is analogous to, and possibly modelled on, how one understands articulations of oneself. on the other hand, the national self does not refer to the nation at all but is more a reference to some quality of the individual selves. it is a quality of the members of that nation and is not really about the self of a nation per se. depending on the meanings we ascribe to self, we can discover different meanings for self-reliance in the context of the nation. why would we even invoke the notion of self in the context of the nation? what can accommodate a meaningful understanding of the self when it is used in the context of the nation? at a pragmatic level, it is easy to see why the invocation of self is 'natural' for a nation: we refer to a nation as 'my' nation and so concepts of my, mine, mineness and related issues of identity arise for the nation in a way similar to that of the experiences of the individual self. but at the same time, the self related to the nation also refers to a we-self, a self of a larger social. it is also an embodied social and this quality makes it different from other social selves. just as the individual self is embodied in the physical body, the self in relation to the nation is embodied in the physical nation, with its geographies and boundaries. but it is also precisely because of these characteristics, that the self in the context of a nation has to accommodate plurality, diversity. this quality again distinguishes the self of the nation from other social selves related to gender, caste and religion, for example. this self which can accommodate plurality and difference is one that functions as a substratum and does not insist on sameness. it is the quality of ashraya-a shelter for the multiple, diverse individuals, practices and traditions. the self of a nation is this true shelter, the foundational substratum where unity is possible only because of a sense of feeling that it is happening to all of us. however, this is not the only notion of a self that is possible in the context of the nation. there is also another possibility, one that is often imposed on individuals. the nationinstead of being seen as a collective social-can be reduced to a quality of the individual. in this case, it is not a self that stands 'outside' the individual. a self which incorporates the nation within itself is a national self and thus is one quality of a self, a quality that is hegemonic and imposed. it arises through the cognitive act of an individual and is most often not directly related to their experiences. but the power of the (internal) national self as against the (external) self of the nation is that it evokes deep emotions within the individual. the self of the nation is a recognition of a more complex, plural self that operates outside the individual but yet one in which the individual is part of. whereas the national self incorporates the nation within the self and thus creates a sense that the nation belongs to 'me'. so, when certain individuals start speaking on behalf of the nation-what the nation should be like, what people living in that nation should do and should not do-they are illustrating the functioning of the national self. nationalism in its most troublesome form arises through the formation of a national self. these are not merely some abstract formulations about the self and the nation. these notions of the self are invoked in the rhetoric of self-reliance and my argument is that the two different meanings of the self in relation to the nation create different meanings for 'self-reliance'. if the meaning of self in the expression 'self-reliance of the nation' is referring to the 'self of the nation', then self-reliance cannot be just about producing what we need for the citizens of this country. it also means a discipline of the self of the people in the country, and this is a civilizational and axiological task. it is about values in a society and not material production. these qualities, taken, for example, from gandhi, tagore and others, would imply a very different meaning of the nation where the nation is not one which is homogenized, is violent, is hierarchical, is non-egalitarian, is consumerist and so on. as parel ( ) points out, gandhi's formulation of self-rule had four components, three related to independence of the nation, economic freedom and political freedom but the essential fourth component was self-rule, here seen as the rule of the individual self by the individual self. this self-rule included the important quality of self-control including control of the body and the desires of the senses, control over thinking and so on (banerjee ) . why should this difference matter? it matters because these two versions of the self/ nation relation have implications for the meaning of self-reliance. what does it mean to be self-reliant? the simplest answer is to be independent of others. but what is the independence from others that we are seeking? the nation can be independent from others in the products it produces, in its economy, in its policies and so on. but this does not really encompass the many meanings of swaraj that we talk about. as kcb points out, it is equally important to have swaraj in ideas, a freedom in the intellectual domain. are we anywhere close to having the freedom in the intellectual domain? we do not even produce knowledge and worldviews which matter to the rest of the world. it does not seem to matter to our own intellectuals and students. what are the ideas that drive the nation? where are the ideas being produced? how democratic is this source of ideas? is it able to include the visions and aspirations of not just the 'intellectual community' but also the everyday experiences of diverse communities in india? this is not a question about geographical origins but about philosophical origins. what kind of views about the nature of society, family, individuals should matter to us today when we imagine the future of the nation? the answer is not in the geographical 'outside' or the cultural 'inside'. it is not going to come from the 'west' or from the 'past' alone. the self-reliance that the government talks about is about factory goods but without the swaraj in ideas none of these are self-sustaining. self-reliance is not in manufacturing alone. it has to be the articulation of the self of a nation about progress and development, about educational goals for the future citizens of the country, about basic well-being of all the citizens particularly the dispossessed and the marginalised. what we need to 'make in india' are civilizational values, our own articulations of the idea of equality in an unequal society, a democracy that functions effectively, and anything else which can lead to a truly free, democratic and egalitarian society. to 'make' all this in a self-reliant manner is the true idea of a nation and the true self of a nation. the easier task is to reduce the self of a nation to one idea of a national self is but this is also the more dangerous. the national self is an individual self which understands the national as one quality of the individual self. but a nation cannot be a quality of a self because it reduces the nation to the interests of individuals. in such a case, the nation as such cannot acquire a unified self just because all the people in the country possess one national self. the self of a nation is one that is self-reliant in the true sense of the term, one that is truly independent. tracing gandhi: satyarthi to satyagrahi. routledge, london bhatt gp ( ) the basic ways of knowing. motilal banarsidass, delhi bhattacharyya kc ( ) svaraj in ideas the cracked mirror: an indian debate on experience and theory deep thinking. where machine intelligence ends and human creativity begins. hatchette india, delhi nagaraj dr ( ) the flaming feet and other essays acknowledgements i thank the two referees for their insightful and critical comments which have helped me clarify some points in this essay. publisher's note springer nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. key: cord- -s lk authors: bairagi, anupam kumar; masud, mehedi; kim, do hyeon; munir, md. shirajum; nahid, abdullah al; abedin, sarder fakhrul; alam, kazi masudul; biswas, sujit; alshamrani, sultan s; han, zhu; hong, choong seon title: controlling the outbreak of covid- : a noncooperative game perspective date: - - journal: nan doi: nan sha: doc_id: cord_uid: s lk covid- is a global epidemic. till now, there is no remedy for this epidemic. however, isolation and social distancing are seemed to be effective preventive measures to control this pandemic. therefore, in this paper, an optimization problem is formulated that accommodates both isolation and social distancing features of the individuals. to promote social distancing, we solve the formulated problem by applying a noncooperative game that can provide an incentive for maintaining social distancing to prevent the spread of covid- . furthermore, the sustainability of the lockdown policy is interpreted with the help of our proposed game-theoretic incentive model for maintaining social distancing where there exists a nash equilibrium. finally, we perform an extensive numerical analysis that shows the effectiveness of the proposed approach in terms of achieving the desired social-distancing to prevent the outbreak of the covid- in a noncooperative environment. numerical results show that the individual incentive increases more than % with an increasing percentage of home isolation from % to % for all considered scenarios. the numerical results also demonstrate that in a particular percentage of home isolation, the individual incentive decreases with an increasing number of individuals. the novel coronavirus ( -ncov or covid- ) is considered to be one of the most dangerous pandemics of this century. covid- has already affected every aspect of individual's life i.e. politics, sovereignty, economy, education, religion, entertainment, sports, tourism, transportation, and manufacturing. it was first identified in wuhan city, china on december , , and within a short span of time, it spread out worldwide [ ] , [ ] . the world health organization (who) has announced the covid- outbreak as a public health emergency of international concern (pheic) and identified it as an epidemic on january , [ ] . till july , , covid- has affected countries and territories throughout the globe and international conveyances [ ] . the recent statistics on covid- also indicate that more than , , persons have been affected in different ways [ ] , [ ] . currently, the ten most infected countries are usa, brazil, india, russia, south africa, peru, mexico, chile, spain, and uk, where affected people of these countries more than % of the worldwide cases. since the outbreak, the total number of human death and recovery to/from covid- are , and , , , respectively [ ] , [ ] (till july , ). the fatality of human life due to covid- is frightening in numerous countries. for instance, among the highest mortality rates countries, % of the mortality belongs to the top countries due to covid- . furthermore, the percentages of affected cases for male and female are around . % and . %, whereas these values are about % and %, respectively in death cases globally [ ] . different countries are undertaking different initiatives to reduce the impact of the covid- epidemic, but there is no clear-cut solution to date. one of the most crucial tasks that countries need to do for understanding and controlling the spread of covid- is testing. testing allows infected bodies to acknowledge that they are already affected. this can be helpful for taking care of them, and also to decrease the possibility of contaminating others. in addition, testing is also essential for a proper response to the pandemic. it allows carrying evidence-based steps to slow down the spread of covid- . however, to date, the testing capability for covid- is quite inadequate in most countries around the world. south korea was the second covid- infectious country after china during february . however, mass testing may be one of the reasons why it succeeded to diminish the number of new infections in the first wave of the outbreak since it facilitates a rapid identification of potential outbreaks [ ] . for detecting covid- , two kinds of tests are clinically carried out: (i) detection of virus particles in swabs collected from the mouth or nose, and (ii) estimating the antibody response to the virus in blood serum. this covid- epidemic is still uncontrolled in most arxiv: . v [cs.cy] jul countries. as a result, day by day, the infected cases and death graph are rising exponentially. however, researchers are also focusing on the learning-based mechanism for detecting covid- infections [ ] - [ ] . this approach can be costeffective and also possibly will take less time to perform the test. meanwhile, other studies [ ] - [ ] focus on analyzing the epidemiological and/or clinical characteristics of covid- . however, the infected cases of the covid- can be reduced by maintaining a certain social distance among the people. in particular, to maintain such social distancing, self-isolation, and community lockdown can be possible approaches. thus, it is imperative to develop a model so that the social community can take a certain decision for self-isolation/lockdown to prevent the spread of covid- . to the best of our knowledge, there is no study that focuses on the mathematical model for monitoring and controlling individual in a community setting to prevent this covid- epidemic. thus, the main contribution of this paper is to develop an effective mathematical model with the help of global positioning system (gps) information to fight against covid- epidemic by monitoring and controlling individual. to this end, we make the following key contributions: • first, we formulate an optimization problem for maximizing the social utility of individual considering both isolation and social distancing. here, the optimization parameters are the positions of individual. • second, we reformulate the objective function which is incorporated with the social distancing feature of an individual as a noncooperative game. here, we show that home isolation is the dominant strategy for all the players of the game. we also prove that the game has a nash equilibrium (ne). • third, we interpret the sustainability of lockdown policy with the help of our model. • finally, we evaluate the effectiveness of the proposed approach with the help of extensive numerical analysis. the remainder of the paper is organized as follows. in section ii, we present the literature review. we explain the system model and present the problem formulation in section iii. the proposed solution approach of the above-mentioned problem is addressed in section iv. we interpret the sustainability of lockdown policy with our model in section v. in section vi, we provide numerical analysis for the proposed approach. finally, we draw some conclusions in section vii. covid- is the seventh coronavirus identified to contaminate humans. individuals were first affected by the -ncov virus from bats and other animals that were sold at the seafood market in wuhan [ ] , [ ] . afterward, it began to spread from human to human mainly through respiratory droplets produced while people sneeze cough or exhaling [ ] . epidemiological and/or clinical characteristics of covid- are analyzed in the studies [ ] - [ ] . in [ ] , the authors investigate the epidemiologic and clinical characteristics based on cases of covid- patients of zhejiang, china. among these samples, . % were laboratory-confirmed covid- tested positive for sars-cov- while . % were clinical-diagnosed covid- cases. the average age of the patients was while females accounted for . %. the typical indications were fever ( . %), cough ( . %) and fatigue ( . %). . %o these patients were affected from local cases, . % went to or were in wuhan/hubei, . % came in contact with peoples from wuhan, and . % were from aircraft transmission. the authors represent a detailed statistical analysis of , individuals collected from january to february , , and covering regions of the henan province, china [ ] . among these cases, % were male and ages of these patients were from to years. among these patients, . % had wuhan's travel history. in [ ] , the authors investigate epidemiological, demographic, clinical, and radiological features and laboratory data for cases of -ncov collected from jinyintan hospital, wuhan, china. they found that % of these patients traveled to the huanan seafood market. the average age of the victims was . years, and most of them ( . %) were men. the main clinical manifestations were fever ( %), cough ( %), shortness of breath ( %). among the sufferers, % exhibited bilateral pneumonia also. the work in [ ] analyzes the clinical characteristics of , patients with laboratory-confirmed -ncov ard from hospitals in provinces/provincial municipalities of wuhan, china. this work concluded that the median age of these patients was years where . % of them were female. the most common symptoms of these patients were fever ( . %) and cough ( . %). most of these cases had a wuhan connection ( . % had been to wuhan, and . % had contacted people from wuhan). epidemiological investigations were conducted in [ ] among all close contacts of covid- patients (or suspected patients) in nanjing, jiangsu province, china. among them, . % recently traveled hubei and the average age of these cases was . years including . % male. . % of these patients showed fever, cough, fatigue symptoms during hospitalization whereas . % cases showed typical ct images of the ground-glass chest and . % presented stripe shadowing in the lungs. the study in [ ] estimates the clinical features of covid- in pregnancy and the intrauterine vertical transmission potential of covid- infection. the age range of the subjects was - years and everybody of them had laboratory-confirmed covid- pneumonia. they showed a similar pattern of clinical characteristics to non-pregnant adult patients. the authors mainly found that no intrauterine fetal infections occurred as a result of covid- infection during a late stage of pregnancy. machine learning can play an important role to detect covid- infected people based on the observatory data. the work in [ ] proposes an algorithm to investigate the readings from the smartphone's sensors to find the covid symptoms of a patient. some commons symptoms of covid- victims like fever, fatigue, headache, nausea, dry cough, lung ct imaging features, and shortness of breath can be captured by using the smartphone. this detection approach for covid- is faster than the clinical diagnosis methods. the authors in [ ] propose an artificial intelligence (ai) framework for obtaining the travel history of people using a phone-based survey to classify them as no-risk, minimal-risk, moderate-risk, and high-risk of being affected with covid- . the model needs to be trained with the covid- infected information of the areas where s/he visited to accurately predict the risk level of covid- . in [ ] , the authors develop a deep learning-based method (covnet) to identify covid - from the volumetric chest ct image. for measuring the accuracy of their system, they utilize community-acquired pneumonia (cap) and other non-pneumonia ct images. the authors in [ ] also use deep learning techniques for distinguishing covid- pneumonia from influenza-a viral pneumonia and healthy cases based on the pulmonary ct images. they use a location-attention classification model to categorize the images into the above three groups. depth cameras and deep learning are applied to recognize unusual respiratory pattern of personnel remotely and accurately in [ ] . they propose a novel and effective respiratory simulation model based on the characteristics of original respiratory signals. this model intends to fill the gap between large training datasets and infrequent real-world data. multiple retrospective experiments were demonstrated to examine the performance of the system in the detection of speculated covid- thoracic ct characteristics in [ ] . a d volume review, namely "corona score" is employed to assess the evolution of the disease in each victim over time. in [ ] , the authors use a pre-trained unet to fragment the lung region for automatic detection of covid- from a chest ct image. afterward, they use a d deep neural network to estimate the probability of covid- infections over the segmented d lung region. their algorithm uses ct volumes as a training dataset and ct volumes as a test dataset and achieves . roc auc and . pr auc. the study in [ ] presents evidence of the diversity of human coronavirus, the rapid evolution of covid- , and their clinical and epidemiological characteristics. the authors also develop a deep learning model for identifying . and trained the model using a small ct image datasets. they find an accuracy of around % using a small ct image dataset. in [ ] , the authors propose a stochastic transmission model for capturing the phenomenon of the covid- outbreak by applying a new model to quantify the effectiveness of association tracing and isolation of cases at controlling a severe acute respiratory syndrome coronavirus (sars-cov- )-like pathogen. in their model, they analyze synopses with a varying number of initial cases, the basic reproduction number, the delay from symptom onset to isolation, the probability that contacts were traced, the proportion of transmission that occurred before symptom start, and the proportion of subclinical infections. they find that contact tracing and case isolation are capable enough to restrain a new outbreak of covid- within months. in [ ] , the authors present a risk-sensitive social distance recommendation system to ensure private safety from covid- . they formulate a social distance recommendation problem by characterizing conditional value-at-risk (cvar) for a personal area network (pan) via bluetooth beacon. they solve the formulated problem by proposing a two phases algorithm based on a linear normal model. in [ ] , the authors mainly dissect the various technological interventions made in the direction of covid- impact management. primarily, they focus on the use of emerging technologies such as internet of things (iot), drones, artificial intelligence (ai), blockchain, and g in mitigating the impact of the covid- pandemic. the works [ ] - [ ] , [ ] - [ ] focused on covid- detection and analyzed the characteristic of its respiratory pattern. hence, the literature has achieved a significant result in terms of post responses. in fact, it is also imperative to control the epidemic of covid- by maintaining social distance. therefore, different from the existing literature, we focus on the design of a model that can measure individual's isolation and social distance to prevent the epidemic of covid- . the model considers both isolation and social distancing features of individuals to control the outbreak of covid- . consider an area in which a set n of n individuals are living under covid- threat and must decide whether to stay at home or go leave their homes to visit a market, shop, train station, or other locations, as shown in figure . everyone has a mobile phone with gps. from analyzing the gps information, we can know their home locations of each individuals, and longitude and latitude of these locations are denoted by x h , and y h , respectively. we consider one time period (e.g., or minutes) for our scenario and this time period is divided into t smaller time steps in a set t . for each of time step t ∈ t , we have the gps coordinates x and y of every individual. now, the deviation from home for any individual i ∈ n in between two time steps can be measured by using euclidean distance as follows: thus, the total deviation from home by each individual i ∈ n in a particular time period can be calculated as follows: on the other hand, at the end of a particular time period, the distance between an individual i ∈ n and any other individuals j ∈ n, j i is as follows: hence, the total distance of individual i ∈ n from other individuals n i ⊆ n , who are in close proximity with i ∈ n , can be expressed as follows: our objective is to keep δ minimum for reducing the spread of covid- from infected individuals, which is an isolation strategy. meanwhile, we want to maximize social distancing which mathematically translates into maximizing d for reducing the chance of infection from others. however, we can use log term to bring fairness [ ] , [ ] in the objective function among all individuals. hence, we can pose the following optimization problem: in ( ), z is a large number for changing the minimization problem to maximization one, and z > δ i , ∀i ∈ n . the optimization variables x and y indicate longitude, and latitude, respectively, of the individuals. moreover, the first term in ( ) encourages individual for isolation whereas the second term in ( ) encourages individual to maintain fair social distancing. in this way, solving ( ) can play a vital role in our understanding on how to control the spread of covid- among vast population in the society. constraint ( a) guarantees small deviation to maintain emergency needs, while constraint ( b) assures a minimum fair distance among all the individuals to reduce the spreading of covid- from one individual to another. constraint ( c) shows that ω can take any value between and which captures the importance between two key factors captured in the objective function of ( ). for example, if covid- is already spreading in a given society, then most of the weight would go to isolation term rather than social distancing. the objective of ( ) is difficult to achieve as it requires the involvement and coordination among all the n individual. moreover, if the individuals are not convinced then it is also difficult for the government to attain the objective forcefully. thus, we need an alternative solution approach that encourage individual separately to achieve the objective and game theory, which is successfully used in [ ] , [ ] , can be one potential solution, which will be elaborated in the next section. to attain the objective for a vast population, governments can introduce incentives for isolation and also for social distancing. then every individual wants to maximize their utilities or payoffs. in this way, government can play its role for achieving social objective. hence, the modified objective function is given as follows: where α = α ω and β = β ( − ω) with α > and β > are incentives per unit of isolation and social distancing. in practice, α and β can be monetary values for per unit of isolation and social distancing, respectively. in ( ), one individual's position affects the social distancing of others, and hence, the individuals have partially conflicting interest on the outcome of u. therefore, the situation can be interpreted with the noncooperative game [ ] , [ ] . a noncooperative game is a game that exhibit a competitive situation where each player needs to make choices independent of the other players, given the possible policies of the other players and their impact on the player's payoffs or utilities. now, a noncooperative game in strategic form or a strategic game g is a triplet g = (n, (s i ) i ∈n , (u i ) i ∈n ) [ ] for any time period where: • n is a finite set of players, i.e., n = { , , · · · , n }, • s i is the set of available strategies for player i ∈ n , • u i : s → r is the payoff function of player i ∈ n , with s = s × s × .. × s n . in our case s i = {s h i , s m i } where s h i and s m i indicate the strategies of staying at home and moving outside for player i ∈ n , respectively. the payoff or incentive function of any player i ∈ n in a time period can be defined as follows: [ ] is the most used solution concept for a noncooperative game. formally, nash equilibrium can be defined as follows [ ] : definition . : a pure strategy nash equilibrium for a non- however, to find the nash equilibrium, the following two definitions can be helpful. thus, if we can show that every player of our game g has a strategy that gives better utility irrespective of other players strategies, then with the help of definition and , we can say that proposition is true. proposition . g has a pure strategy nash equilibrium when α > β. proof. let us consider a -player simple matrix game as shown in table i with the mentioned strategies. for simplicity, we consider a distance laplacian distance ∆ that each player can pass in any timestamp. thus, the utilities of p : where ± indicates the movement of player to other player and opposite direction, respectively. now, as α > β, so the following conditions hold from ( ): hence, rewriting ( ), we get the followings: hence, s h is the dominant strategy of p . moreover, for the player p , the utilities are as follows: now, as α > β, so the following conditions hold from ( ): hence, rewriting ( ), we get the followings: hence, s h is the dominant strategy of player p . when there are n-players (n > ) in the game, incentive of player i ∈ n (takes strategy s h i , without considering others strategy), is given as follows: however, if the player i ∈ n takes the strategy s m i , i.e., the player visits some crowded place like market, shop, train station, school, or other location, then a person may come in close contact with many others. thus, the incentive of player i ∈ n with this strategy is given as follows: where δ i is calculated from ( ) and d i is measured from ( ) for that particular location. moreover, d i <d i as these places are crowded and individuals are in short distance with one another. hence, that means, s h i is the dominant strategy for player i ∈ n irrespective of the strategies of other players in the game g. thus, there is a strategy profile s * = {s h , s h , · · · , s h n } ∈ s where each element s * i is a dominant strategy. hence, by definition , s * is a dominant strategy equilibrium. moreover, a dominant strategy equilibrium is always a nash equilibrium [ ] . hence, the game g has always a pure strategy nash equilibrium. thus, nash equilibrium is the solution of the noncooperative game g. in this equilibrium, no player of n has the benefit of changing their strategy while others remain in their strategies. that means, the utility of each player i ∈ s is maximized in this strategy, and hence ultimately maximize the utility of ( ). in fact, incentivizing the social distancing mechanism is promoting social distancing to each individual. to this end, maximizing u of ( ) ultimately maximize the original objective function of ( ). moreover, the nash equilibrium point has a greater implication on controlling the spread of covid- in the society. at the ne point, every individual stays at home. so, if someone gets affected by covid- , the individual will not go in contact with others. similarly, an unaffected individual has no probability to come in contact with an affected individuals. unfortunately, the family members have the chance to be affected if they don't follow fair distance and health norms. the sustainability of the lockdown policy can be interpreted by using the outcome of the nash equilibrium point that is achieved in the noncooperative game in section iv. the total amount of incentive a particular time period is presented in ( ) . in a particular day, we have t s = × t time period where t is the length of a time period in minutes. thus, we can denote the incentive of a time stamp t s in a particular day p as follows: hence, the amount of resources/money that is necessary to incentivize peoples in a particular day, p can be expressed as follows: now, if we are interested to find the sustainability of lockdown policy for a particular country till a certain number of days, denoted by p, we have to satisfy the following inequality: where r is the amount of resource/money of a particular country at the starting of lockdown policy that can be used as incentive and r p is the collected resources in a particular day, p, of the lockdown period. here, r p includes governmental revenue and donation from different individuals, organizations and even countries. moreover, the unit of α, β, r and r p are same. if we assume for simplicity that u p and r p are same for every day and they are denoted byŨ andr, respectively, then we can rewrite ( ) as follows: hence, if we are interested to find the upper limit of sustainable days for a particular country using lockdown policy, then we have the following equality: thus, by simplifying ( ), we have the following: here, the sustainable days p depends on r ,Ũ, andr. however, we cannot change r but government can predictr. moreover, depending on r andr, government can formulate its policy to set α and β so that individuals are encouraged to follow the lockdown policy. alongside, we cannot continue lockdown policy infinitely based upon the limited total resources. hence, the governments should formulate and update its lockdown policy based on the predicted sustainable capability to handle covid- , otherwise resource crisis will be a further bigger worldwide pandemic. in this section, we assess the proposed approach using numerical analyses. we consider an area of , m × , m for our analysis where individuals' position are randomly distributed. the value of the principal simulation parameters are shown in the table ii . figure illustrates a comparison between home isolation (stay at home) and random location in the considered area for a varying value of ω. in this figure, we consider two cases of n = and n = , . in both the cases, home isolation (quarantine) is beneficial over staying in random location and the differences between two approaches are increased with the increasing value of ω. moreover, the difference of payoffs between two approaches are increased with the increasing value of ω as the more importance are given in home isolation. figure a exhibits that the incentives are below , , and , for %, and % sure, respectively, for % and % home quarantine cases whereas the incentives are % sure in between , and , for % home isolation case. further, the same values are at least , for % sure in case of full home isolation. figure b depicts that the incentive of being below , is % sure for % home isolation case, however, the same values of being above , , and , are %, and %, sure, respective, for %, and % cases. moreover, for % home isolation case, the values are in between , to , for sure. the incentives for %, %, %, and % home isolation cases are above , , , , , , and , , respectively, with probability . , . , . , and . , respectively, as shown in figure c . additionally, the same values are at least , , , , , , and , with . , . , . , and . probabilities, respectively, which is presented in figure d . the total incentive (averaging of runs) for varying percentage of home isolation individuals with different sample size are shown in figure . from this figure, we observe that the total payoff increases with increasing number of home isolation individuals for all considered cases. the incentives are %, %, %, and % better from home quarantine of % to % for n = , n = , , n = , , and n = , , respectively. moreover, for a particular percentage of home isolation, the total incentive is related with the sample size. in case of % individuals in the home isolation, the incentive for n = , is . %, . %, and . % more than that of n = , n = , , and n = , , respectively. figure shows the average individual payoff for varying parentage of home isolation individuals for different scenarios. the figure exhibits that the average individual incentive increases with an increasing percentage of home isolation as the deviation δ decreases and hence, the value of home isolation incentive increases. for n = , the incentive of % home isolation is . % more than that of % home isolation. moreover, in a particular percentage of home isolation, the incentive decreases with an increasing number of considered individuals as the social distancing decreases due to the more number of individuals. in case of % home isolation, the individual incentive for n = is . % more than that of n = , . figure shows the maximum possible lockdown period for a varying number of individuals within a fixed amount of resource r . the figure reveals that with the increasing percentage of home isolation individuals, the maximum lockdown period significantly decreases for all considered cases. the reason behind this is that the more individuals are in home isolation, the more it is necessary to pay the incentives. with a fixed amount of resources, a country with less individuals can survive a longer lockdown period. with more percentages of home isolation individuals, the number of loackdown period is less, and possible of spreading of covid- is also less. therefore, the governments can consider a trade-off between increasing expenditure as a incentive and lockdown period. for , individuals, the maximum possible lockdown period for varying amount of r andr is presented in figure . the figure also illustrates that with the increasing percentages of home isolation individuals, the continuity of the lockdown period reduces for every scenarios. however, for a particular percentage of home isolation individuals where total number of individuals are fixed, a country can continue higher lockdown period who has more am amount of resources, r . additionally,r also play an important role to continue the lockdown period. in this paper, we have introduced a mathematical model for controlling the outbreak of covid- by augmenting isolation and social distancing features of individuals. we have solved the utility maximization problem by using a noncooperative game. here, we have proved that staying home (home isolation) is the best strategy of every individual and there is a nash equilibrium of the game. by applying the proposed model, we have also analyzed the sustainability period of a country with a lockdown policy. finally, we have performed a detailed numerical analysis of the proposed model to control the outbreak of the covid- . in future, we will further study and compare with extended cases such as centralized and different game-theoretic models. in particular, an extensive analysis between the government-controlled spread or people controlled spread under more diverse epidemic models. 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wireless and communication networks: theory, models, and applications 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- - ddb de authors: meslin, eric m.; garba, ibrahim title: biobanking and public health: is a human rights approach the tie that binds? date: - - journal: hum genet doi: . /s - - - sha: doc_id: cord_uid: ddb de ethical principles guiding public health and genomic medicine are often at odds: whereas public health practice adopts collectivist principles that emphasize population-based benefits, recent advances in genomic and personalized medicine are grounded in an individualist ethic that privileges informed consent, and the balancing of individual risk and benefit. indeed, the attraction of personalized medicine is the promise it holds out to help individuals get the “right medicine for the right problem at the right time.” research biobanks are an effective tool in the genomic medicine toolbox. biobanking in public health presents a unique case study to unpack some of these issues in more detail. for example, there is a long history of using banked tissue obtained under clinical diagnostic conditions for later public health uses. but despite the collectivist approach of public health, the principles applied to the ethical challenges of biobanking (e.g. informed consent, autonomy, privacy) remain individualist. we demonstrate the value of using human rights as a public health ethics framework to address this tension in biobanking by applying it to two illustrative cases. at first blush, the ethical foundations guiding public health and genomic medicine are at odds: whereas public health practice adopts collectivist principles that emphasize utilitarian and population-based benefits, genomic (and especially personalized) medicine is squarely grounded in an individualist ethic that emphasizes autonomous decisionmaking for personal benefits. one definition of public health illustrates its breadth and focus: the promotion of health and the prevention of disease and disability; the collection and use of epidemiological data, population surveillance, and other forms of empirical quantitative assessment; a recognition of the multidimensional nature of the determinants of health; and a focus on the complex interactions of many factors -biological, behavioral, social, and environmental -in developing effective interventions (childress et al. ) . lawrence o. gostin ( ) further highlights the critical role of collective entities like communities and governments in ensuring the public's health because although individuals, given the means, can do many things to protect their own health, there are health benefits such as a healthy environment, safe roads, potable water and clean air that require ''organized and sustained community activities''. in short, public health programs deliver to populations health benefits that cannot be effectively secured on an individual or small group basis (childress et al. ) . in contrast, genomic medicine-sometimes conflated with personalized medicine-has been described as an endeavor that ''will provide a link between an individual's molecular and clinical profiles, allowing physicians to make the right patient-care decisions and allowing patients the opportunity to make informed and directed lifestyle decisions for their future well-being'' (ginsburg and mccarthy ) . it envisions medical care in which ''drugs and drug doses are made safer and more effective because they are chosen according to an individual's genetic makeup'' (lesko ) . others, such as the ickworth group (burke et al. ) , characterize personalized medicine as any medical ''care that is tailored to the individual or stratified by the population subgroup''. common to all of these definitions is the emphasis on customizing therapy to the individual patient. indeed, for as long as clinicians have been caring for patients, medicine has been personalized (ramsey ) , but it is the accelerant of genetic technology that has led some to think that today's medicine has the potential to be even more ''personalized'' than its historical predecessors. of course, with the benefit of further reflection, the contrast between personalized medicine and public health is not so stark. for instance, the collectivist approach of public health does not preclude a role for clinical interventions and choices at the individual level. moreover, the claim that the treatment of a sick individual improves the health of the population of which she is a member is all but tautologous. vaccination is an example that fits both conditions. seen this way, personalized medicine and public health are not mutually exclusive, but rather incompletely overlapping. the goals of public health practice certainly include the impact on the health of individuals, and included in the potential value of a genomic approach to medical care is its generalizability to the public's health, for example through better screening and prevention programs (burke et al. ). recognition of this potential for demonstrating the relationship between public health and genomics is evident in a new area of study complete with its own journal, public health genomics that hopes to address some of these very issues. it has been noted, for instance, that a better understanding of what lies between the genes that make up the genome, the role of the environment on gene expression and the role of the interaction between genes will help us to know why some individuals remain healthy while others are more susceptible to genetic diseases. this understanding will also benefit the public health sector where the prevention and expression of communicable and infectious diseases, for example, is related in part to understanding genetic susceptibility… ). the ickworth group recently examined the potential for genomics and personalized medicine to inform public health practice and concluded that much still needs to be done before the promise can be realized (burke et al. ) . in particular, they made six recommendations: . efforts to integrate genomics into public health and practice should continue. . an appropriate research infrastructure for generating an evidence base for genomic medicine needs to be established and maintained. . model public health genomics programs and clinical services need to be developed, implemented and evaluated. . international collaborations should be promoted. . appropriate genetic services and genome-based research should be fostered within low and middle income countries. . programs, research and strategies in public health genomics should be informed by accepted ethical principles and practices. such qualified support for the potential for genomic impact on public health is not surprising, as others have commented on the status of promises made and kept (evans et al. ; hall et al. ) . biobanking is a useful case study to unpack issues at the intersection of genomics and public health. the storied history of the many uses of biological materials that help to improve the understanding, clinical diagnosis and treatment of human disease is long and impressive with detailed reports of the clinical value of banked specimens dating to the early eighteenth century (ackerknecht ; korn ) . without access to stored specimens of blood, urine, tumors, body tissues, dna and other human biological materials, important advances in cancer, infectious disease, cardiovascular care and mental disorders would not have been possible (nat'l bioethics adv. comm. ) . for example, the pap smear would not have been developed (younge et al. ) and the nonsteroidal estrogen hormone, diethylstilbestrol (des), would not have been found to be carcinogenic (herbst ) . without the knowledge gained from autopsies of korean war veterans, science would have known less about the age of onset for atherosclerosis (enos et al. ) . moreover, the cdc would not have been able to isolate and understand the hantavirus (wrobel ) and researchers would not have been able to make progress on certain brain tumors . no doubt researchers hoping to understand the impact of radiation leaks on residents near the fukushima nuclear plant in japan will make use of the chernobyl tissue bank established in to study the effects from (until this point) the world's foremost nuclear plant disaster (http://www. chernobyltissuebank.com). the completion of the human genome sequence (and other genomes) greatly expanded the capacity of science to use and obtain greater value from both previously collected biological specimens and those still to be collected (meslin and quaid ) . for example, the international community, led by canadian researchers, was able to rapidly sequence the sars virus from obtained specimens (marra et al. ) . others used similar technology for the h n virus (graham et al. ; zhang and chen ), dramatically shortening the time it took to understand the nature of the threat and prepare a public health response. moreover, the prospect of using genome technology on already stored specimens for enhanced genetic diagnostics, drug development, and even domestic and international security threat analysis (meslin ; bugl et al. ; atlas ) offers a glimpse into the future of a genetically-informed public health capacity for nation-states. indeed, it is the fortuitous combination of genomics and pharmacology that gives rise to the most promising example of personalized medicine-the field of pharmacogenomics (evans ; evans et al. ; desta and flockhart ) . just as the past benefits to human health from using banked human biological materials stand on their own merit, any future benefits will need to be assessed over time. for us, the important challenge is whether the ethical and legal basis for using banked materials is sufficient to support its expanded use in more areas of public health practice and research. in other words, while we acknowledge that the boundary between the two domains is by no means a stark one; the failure to appreciate what makes them different may prevent productive engagement between these two domains of health care to serve the health interests of society. several explanations have been offered for why public health approaches to health and disease differ from clinical medical approaches, each of which have ethical valence. one theory credits medicine's increasing focus early in the twentieth century on treating the biological causes of disease, and public health's contrasting occupation with the social and environmental causes of illness, resulting in efforts geared toward health promotion and prevention (khoury et al. ). the vectors of medicine and public health diverged further when schools of medicine and public health in the united states were officially separated in (khoury et al. ), in part due to the conflicting goals of professionals in the fields (porter ) . additional ideas include ''the rise of medical authority with the expansion of hospital-based specialist practices'' (porter ) as well as a corresponding split between individualist and collectivist modes of analysis in the social sciences (arah ). this disciplinary, professional and institutional dissociation between the two fields has been blamed for the current gap between personal medical care and public health (arah ). the public health approach presupposes that an exclusive focus on the treatment of individuals is not sufficient to protect, promote and sustain effectively the health of a population. this is evident in the work and writings of public health practitioners such as the sanitarians (susser and susser a) , thomas mckeown (szreter ) , geoffrey rose (marmot ) , dan e. beauchamp (kass ) , marc lappe (kass ) , marvin susser (susser and susser b) , ezra susser (march and susser ) , norman daniels (kass ) , paula braveman (braveman et al. ) and the world health organization (who) commission on the social determinants of health among numerous others (marmot ) . whatever the historical source of the ''schism'' between clinical medicine and public health (khoury et al. ), the gap between them translates directly into the ethical plane. the individuating drive of personalized medicine could make the breach felt all the more keenly, especially when values of individual and population health conflict. for instance, genomics research has focused on ''individually rare single gene disorders,'' prompting warnings that such investments redirect limited resources from ''efforts to address the social and environmental causes of ill health'' (khoury et al. ) . moreover, the challenge of ethical analysis is exacerbated by a disparity in the maturity of ethical frameworks governing medicine and public health. whereas early bioethics scholarship often focused on the individual patient receiving care and to ethical principles supporting this relationship, a similar comprehensive and widelyaccepted ethical framework for public health is yet to be established (nixon and forman ; mann ; callahan and jennings ) . tellingly, nancy e. kass ( ) observes that the language of public health was conspicuously absent among the early bioethicists, despite some achievements with implications for public health ethics. daniel callahan and bruce jennings ( ) likewise point out the focus in bioethics on novel medical technologies in clinical settings at the expense of social and economic inequities. another reason an individualist outlook has prevailed in bioethics is that some public health interventions are conducted on the individual rather than the population level. for instance, postwar antismoking campaigns in great britain set a trend that involved educating and influencing individual behavior and lifestyles (porter ) . the approach, later adopted to combat heart disease, obesity and cancer, helped solidify the individualist and behavioral model already prevalent in clinical medicine (beauchamp ; porter ) . hence, the population perspective implicit in public health ethics was at times at odds with the individualist methods employed to serve the public's health. a further rationale for the individualist bias of hum genet ( ) : - bioethics is the backlash against the misuse of populationbased policies in the field of eugenics, resulting in an understandable suspicion of collectivist bioethical analysis (pernick ; kirkman ; lombardo ). these factors have combined to generate a rich framework for ethical analysis, but one that has remained individualist in orientation. the inadequacy of the framework was noted by bioethicists such as dan e. beauchamp who argued, against the prevailing political valorization of individual autonomy, that a framework that privileged ''individual interests'' and ''market justice'' was detrimental to public health (kass ). beauchamp suggested that public health might require its own ''ethic,'' a proposal taken up by marc lappé ( ) who differentiated medical ethics from public health ethics. as the new millennium unfolded, several efforts were undertaken to establish frameworks for public health ethics. among these was the american public health association's (apha) adoption of the public health code of ethics in early . the apha was the first national organization to adopt the code (thomas et al. ) , which is based on the public health leadership society's principles of the ethical practice of public health. the code is relatively narrow in scope, catering primarily to an audience in traditional public health institutions such as public health departments and schools of public health (thomas et al. ) . moreover, it focuses on public health practice rather than research, and has in view the united states' public health system. meanwhile, efforts were underway to mainstream another and more comprehensive ethical framework for public health ethics in the form of human rights. the appeal and promise of human rights as an ethics framework for public health was articulated by the late jonathan mann: given that the major determinants of health status are societal in nature, it seems evident that only a framework that expresses fundamental values in societal terms, and a vocabulary of values that links directly with societal structure and function, can be useful to the work of public health. for this reason, modern human rights, arising entirely outside the health domain, and seeking to articulate the societal level preconditions for human well-being, seems a more useful framework, vocabulary, and template for public health efforts to analyze and respond directly to the societal determinants of health than any framework inherited from the past biomedical or public health tradition. (mann ) apart from the capacity of human rights to speak in ''societal terms,'' a crucial part of mann's argument was his identification of the goals of human rights as virtually inseparable from those of health, i.e., human well-being (mann ) . although a human rights perspective has the practical advantage over other frameworks of being realized in (mostly international) law, it also benefits from being rooted in an established and fertile ethical vision. human rights can be traced back to the ancient world, but we describe here the prevailing view, which has origins in the writings of such philosophers as hugo grotius, thomas hobbes, jean jacques-rousseau and john locke. modern human rights assume that all persons possess inherent dignity and certain inalienable rights by the simple fact of their being human. the words ''inherent'' and ''inalienable'' mean these things belong to them naturally and are not granted to them by any political authority. to advance their individual and common well-being, however, people give up certain rights to set up a government that serves their needs. a functioning human rights framework is based on the proposition that a government should not take more rights from people than people give to the government in the first place. on this view, the government exists to ensure the well-being of the individuals who give up certain rights in exchange for certain protections and benefits from the government. the same applies to the community they jointly establish. from this analysis, the traditional roles of government include such things as collective security, the administration of justice, the protection of property and, relevant for our purposes, the promotion of the public's health. seen in this way, a human rights perspective provides an ethical framework for describing the conditions under which the government can protect and promote both individual and community well-being. with the onset of the cold war, however, rights that were part of a single ethical vision in the universal declaration of human rights ( ) were gradually split into two categories. the two classes of rights reflected the ideological priorities of the contending sides and were enshrined in two separate treaties in the s. the international covenant on civil and political rights ( ) (iccpr) reflected the capitalist and liberal emphasis on such rights as free speech, freedom of movement, freedom of religion, the right to vote and the right to privacy. these civil and political rights required governments to refrain from interfering with the liberties of their individual citizens. on the other hand, the international covenant on economic, social and cultural rights ( ) (icescr), spearheaded by the communist eastern bloc, focused on such priorities as the right to work, the right to housing, the right to education and the right to health-rights that require governments to take some kind of action for the benefit of the whole society. in part due to their being costlier than civil and political rights and also because of their questionable justiciability (i.e., their enforcement in courts of law) (tarantola ) , social and economic rights were not given the same priority as civil and political rights by governments. the main result of this focus on individualist civil and political rights is that many governments have not invested as heavily in addressing issues at societal or population level-issues such as housing, education and health. hence, human rights norms in the twentieth century have developed along broadly individualist rather than collectivist lines. roberto adorno ( ) describes the potential for human rights as a framework for biomedicine and public health in the global context. he notes that ''[a]s our world becomes increasingly interconnected and threats to the global public health continue to proliferate, it is hard to see how the global governance of health could be managed without assigning an integral role to human rights''. the reasons he provides in support of a human rights framework include the fact that much biomedical activity has clear human rights implications (e.g., the rights to life and physical integrity); human rights have developed into a transcultural ethical discourse with the potential for setting common standards; and there are few if any other viable mechanisms that can serve as a ''global normative foundation''. considering the then incipient unesco universal declaration on bioethics and human rights, t. a. faunce ( ) noted the increasing application of human rights to address challenges traditionally considered within the sole purview of bioethics and medical ethics. in the narrower context of genomics, knoppers ( ) has argued that benefit-sharing in the context of genetic research ''is an aspect of fundamental human rights and serves to counterbalance the effects of commercialization and patenting''. she has also proposed human rights as a compelling model for policy governing new genetic technologies (knoppers ) . these developments notwithstanding, commentators have been quick to point out the limitations of adopting human rights approach for public health and genome-based medicine. meier and mori ( ) criticize the ''limited, atomized right to health'' contained in the icescr, a provision that establishes neither a robust individual right to health nor an effective means of ensuring public health. similarly, adorno ( ) acknowledges the criticism ''that human rights are conceived as excessively individualist for non-western mentalities and lack a significant concern for personal duties and for the common interest of society''. with particular reference to the field of genomics, iles ( ) points to two specific shortcomings of human rights as an ethical framework, both of which are traceable to the individualist orientation of the current system. his first criticism is that such a framework pays inadequate attention to the structural and social effects of genetic information. he argues that because economic, racial, ethnic and power disparities already exist between groups in societies, genetic information used without ethical oversight can exacerbate these differences and result in discrimination and exclusion. iles infers that human rights may adequately protect individuals facing genetic profiling in employment or insurance contexts, but it is questionable whether the framework's individualist lens can monitor the effects of genetic information on relations between and among groups. iles' second criticism of the applicability of human rights as a foundation for ethical uses of genomics is that individual freedom of choice regarding the use of genetic information can have an aggregate population-wide effect. for example, the choice parents make to have a ''normal'' child rather than one with a ''comparatively inert and tolerable'' disorder is not only heavily influenced by society's values but also determines eventually the society's constitution (iles ) . a narrow focus on individual choice, therefore, may obscure the effects of the uses of genetic information on a society. the preceding discussion demonstrates that even human rights as a framework for public health ethics are not immune from the individualist approach that characterized early bioethics. toward the end of the cold war, however, there were renewed efforts to reintegrate the individualist civil and political rights with the community-oriented economic and social rights (meier and fox ) . we outline three of these developments below. the first development is the increasing recognition of a category of rights known as ''solidarity'' or third-generation rights (wellman ) . the phrase ''third-generation'' distinguishes solidarity rights from the more individualist civil and political rights (''first-generation'' rights) and the more collectivist social, economic and cultural rights (''second-generation'' rights). like the other two generations of rights, solidarity rights were a response to a particular set of problems facing the international community. these included ''securing peace after the first and second world wars, achieving freedom for colonial peoples, reducing the gross economic inequalities between developed and underdeveloped countries, and preserving a healthy environment when the technologies in one nation seriously damage an environment shared by all nations'' (wellman ) . solidarity rights, in other words, are aimed at conditions that can be addressed only by global efforts rather than the laws of any single country. the classic examples of solidarity rights are the rights to peace, development, a healthy environment, self-determination, humanitarian intervention, communication and ownership of the common heritage of humankind (wellman ; monshipouri et al. ) . apart from requiring the concerted efforts of all countries, solidarity rights have two other criteria: first, that the rights belong to peoples (i.e., groups), not just individuals; second, that obligations apply to all actors on the international scene, not just governments. more recently, solidarity has been described as a key ethical foundation for biobanks (chadwick and berg ) . from an ethical perspective, solidarity rights complement first-and second-generation rights. whereas firstgeneration rights protect individuals from the abuses of their governments (e.g., no torture or arbitrary arrests), and second-generation rights enable individuals to claim benefits from their governments (e.g., education, housing), solidarity rights recognize that individuals cannot reach their full potential without ''cooperative participation in the social life of the various communities to which they belong'' (wellman ) . hence, solidarity rights further establish in human rights the ethical principle that human well-being has a communal dimension that goes beyond an individual citizen's relationship with her government. the second development emphasizing a collectivist approach in human rights is growth in the area of indigenous peoples' rights. the united nations general assembly adopted the declaration on the rights of indigenous peoples in . what makes this declaration unique is that it explicitly recognizes a category of ''collective'' rights. until the declaration's adoption, human rights were concerned primarily with ''the rights of the individual against the state, without much attention to the collective and associational dimensions of human existence beyond the state'' (anaya ) . in an historic shift, the declaration recognizes rights to indigenous peoples as groups rather than merely as individual members of their communities. it is a particular instance of the ethical principle underlying solidarity rights, which proposes that community is not an elective component of human well-being. this development, moreover, has significant ethical implications for the involvement of indigenous peoples in research and in access to health benefits, and exemplifies the relevance of indigenous perspectives on genomics research generally (dodson and williamson ) . the third and final development pertains to regional human rights instruments. the major global regions are encouraged to adopt their own treaties, thereby customizing global human rights norms to their particular situations for more effective implementation. of particular relevance is the african charter on human and peoples' rights (also known as the banjul charter), which was adopted by the organization of african unity (now the african union) in , and which includes ''a mixture of all three generations of rights'' (shepherd ) . as its official title suggests, the banjul charter includes the concept of peoples' rights, which, like the collective rights of indigenous peoples, is a version of group rights. the banjul charter deliberately omits a definition of the term ''people,'' thereby leaving the term open to several interpretations, e.g., persons struggling to gain political independence, persons living in a territory and sharing certain characteristics, or simply all people living in a country (kiwanuka ) . whatever their precise legal definition, peoples' rights in the banjul charter are based on the african philosophical belief that a human being is not ''an isolated and abstract individual, but an integral member of a group animated by a spirit of solidarity'' (kiwanuka ) . the kinship between this african principle and the ethical norms undergirding solidarity rights and the rights of indigenous peoples discussed above is evident. they all recognize the importance of community to human wellbeing and reject an approach to human rights that focuses exclusively on the individual. these three developments demonstrate how human rights have been finding ways to complement the protection of individual rights with approaches that recognize the ethical importance of community. these attempts to expand the vision of human rights beyond the individual are analogous to the efforts of public health ethicists to develop a population perspective that transcends the clinical encounter between a single patient and her caregiver. this similarity makes the human rights framework a compelling candidate for analyzing the ethics of biobanking and public health. as with early debates in medical ethics and bioethics generally, much of the ethical and legal attention in biobanking has been individualistic, focusing on informed consent (beskow and dean ; brekke and sirnes ) , privacy protections (chen et al. ; evans ) , and risks of exploitation, especially in vulnerable populations (lo ; bernhardt et al. ; dodson and williamson ) . important as these topics are, some now believe the time has come to update the ethical/legal dialog about biobanks to accommodate broader social and political perspectives (meslin and cho ; kaye ; caulfield et al. ) . it is against this backdrop that our analysis is set. a human rights approach may offer two advantages over other potential public health ethics frameworks. first, it may avoid having to resolve the seemingly interminable debate about the proper approach to obtaining individual informed consent for research using human biological materials. in situations in which groups may be consulted, approached and from which permission to participate in biobanks may be sought, informed consent may be necessary but not a sufficient mechanism for engaging a community. second, it recognizes the institutionalization and application of human rights discourse at international forums by providing tools for discussing the values of public health across national borders. this is important in light of observations by recent commentators of a linguistic shift with both practical and ethical implications: the gradual transition of the term ''international health'' to ''global health.'' ''international health'' was used to describe a technical endeavor conducted jointly by developing countries and their partners in the industrialized world through such large institutions as the world health organization (who) and care international (elmendorf ) . it was useful in this context to distinguish between ''international'' and ''domestic'' health. in contrast, the term ''global health'' reflects an acknowledgment that intensifying interaction between countries through trade and travel renders national borders increasingly immaterial for health challenges (elmendorf ) . the shift in terms represents the change from health conceived as an issue for diplomacy and knowledge transfer between countries to health conceived as a common asset and concern of the international community. importantly, the terminological shift from ''international'' to ''global health'' is also reflected in the bioethics literature (chadwick et al. ) . a specific example of the application of ''global'' rather than ''international'' health is the ''one world, one health'' initiative, a framework that builds on efforts to contain the avian influenza outbreak (fao et al. ) . the initiative is built on the premise that infectious diseases have potentially national, regional and international effects, thus requiring approaches that are not only ''interdisciplinary'' and ''cross-sectoral'' but indeed global. the changes signified by the term ''global health'' have implications for biobanking in many ways (burke et al. ) . public health genomics research is becoming ''increasingly international and collaborative'' resulting from the need for larger and more diverse datasets to evaluate genetic differences within groups (ickworth ). aided by more robust bioinformatics, genotypic and phenotypic data will be employed with greater frequency to study the significance of genetic variation (mendoza ). this will involve the use of larger databases and the consolidation of samples from sites around the globe (meslin and goodman ; ickworth ) . this raises the obvious challenge of harmonizing norms concerning privacy and confidentiality across jurisdictions and, beyond that, consideration of the varied cultural norms guiding data sharing particularly when information moves between developed and lower and middle income countries (lmic) (chalmers ; holman et al. ; asslaber and zatloukal ) . biobanking in the global public health arena is also faced with the challenge of determining research priorities given the different health problems facing populations in developed and lmic. although both regions face the complex diseases of urbanization (e.g., cancer, heart disease, diabetes), environmental factors like climate change and resource scarcity are likely to affect lmic more profoundly than their developed country counterparts. this is especially troubling given that a research imbalance exists between the regions: although african populations are ''the 'root and branch of genetic variability''' the bulk of genomic research is conducted by developed countries and among european populations (ickworth ). fortunately, new initiatives such as h africa may begin to redress this historic injustice (nordling ) . these challenges confirm the need for an ethical framework that can be understood and implemented at global forums. s. h. e. harmon ( ) echoes the need for global frameworks ''given the rise of predictive medicine (involving genetic research and clinical genetics), which is driven by private global operators, thereby suggesting a need for regulatory responses which are similarly global''. although a who report on genetic databases concludes that biobanks are based more on ''communal value'' than on ''individual gain,'' the reality is that the ethics of biobanking has been analyzed predominantly in the traditional individualist bioethical categories of confidentiality, autonomy and informed consent (knoppers and chadwick ) . the fact has not been lost on some commentators. garrath williams, for instance, discusses the daunting task of developing ethical principles for large-scale biobanks. he attributes the difficulty in part to an excessive focus on the individual research subject's right to informed consent, an emphasis he finds inconsistent with the inevitably collective nature of large-scale biobanking (williams ) . williams maintains that this conceptual incongruity obscures important ethical questions about how research priorities are set and how to accommodate the diverse motives of actors in health care systems. he warns that ignoring analyses that transcend individualist frameworks may, paradoxically, end up harming the interests of individuals (williams ) . human rights can make no original contributions to the ethics of biobanking if they are incapable of transcending their individualist biases. the second challenge of a human rights framework for biobanking involves developments in global politics. the observation by knoppers and chadwick ( ) that genetic research has compelled ''a public and therefore a political examination of personal and social values'' illustrates the close connection between politics and ethics in biobanking. therefore, ethical analyses of international biobanking and public health that omit the global political context will likely remain deficient. the developments in global politics that pose the greatest challenge to human rights as an ethical framework for biobanking are efforts, in the context of globalization, to entrench policies that entail an increasing delegation of governmental responsibilities to private actors. in a publication on health and human rights, who ( ) notes that [w]ithin the human rights community, certain trends associated with globalization have raised concern with respect to their effect on states' capacity to ensure the protection of human rights, especially for the most vulnerable members of society. located primarily in the economic-political realm of globalization, these trends include: an increasing reliance upon the free market; a significant growth in the influence of international financial markets and institutions in determining national policies; cutbacks in public sector spending; the privatization of functions previously considered to be the exclusive domain of the state; and the deregulation of a range of activities with a view to facilitating investment and rewarding entrepreneurial initiative. these trends serve to reduce the role of the state in economic affairs, and at the same time increase the role and responsibilities of private (non-state) actors, especially those in corporate business, but also those in civil society. this transfer of responsibilities from governments to private actors is critical because the operation of international law depends both on governments assuming legal obligations by signing agreements and on these governments being held accountable for fulfilling the responsibilities they undertake. generally speaking and despite recent changes in international criminal law, private actors are not accountable under public international law, the branch of international law to which human rights belong (jessberger ) . hence, the transfer of governmental responsibilities such as health provision to private actors removes a growing number of issues from the direct supervision of human rights. governments retain the duty to ensure that private actors such as transnational corporations do not violate human rights, but monitoring and enforcing the norms remains a major challenge (gruskin et al. ; tarantola ) . we conclude this discussion with two examples of key ethical issues raised by the prospect of expanding international biobanking: the first addressing differences in national laws governing biobanks, and the second addressing ethical obligations of transnational corporations operating in lmic. various commentators have discussed the problem for international biobanking arising from the absence of common regulations applying across country borders. the regulatory terrain has been depicted as ''a patchwork of national laws, regulations and ethics advisory body guidelines'' (maschke ) , and comparisons have proven ''laborious and defy generalizations'' (helgesson et al. ). the discrepancies in ethical rules governing such issues as consent and secondary uses raise obvious barriers to the principled collection of tissue samples and the development of personalized medicine. adopting human rights as a public health ethic is not an ideal guide for drafting specific rules governing individual focused biobanking issues such as consent, privacy and secondary uses. however, such an ethic can inform efforts to determine the general principles that should govern the activity of biobanking as a broader societal undertaking. human rights can do this by integrating three concepts: ( ) collective rights (from international human rights); ( ) global public goods (from economics); and ( ) the common heritage of humanity (from international environmental law). we have discussed above the welcome and increasing recognition of community-oriented socio-economic rights as well as solidarity rights in international human rights toward the end of the cold war. we noted also how the change was reflected in the explicit recognition of ''collective'' rights in the united nations declaration on the rights of indigenous peoples. these rights ''operate at an international level to assure public goods that can only be enjoyed in common with similarly-situated individuals and thus cannot be realized through individual rights claims against the state'' (meier and fox ) . the premise grounding the recognition of collective rights is that the realization of some human rights is simply not reducible to their exercise by an aggregate of individuals. harmon ( ) writes that social solidarity has been incorporated, even if implicitly, into unesco's major instruments on genomic research, namely the universal declaration on the human genome and human rights ( ) and the universal declaration on bioethics and human rights ( ) . he maintains that the emergent notion of social solidarity mitigates the excesses of modern individualism and is ''grounded in the recognition that individuals are socially embedded''. his analysis of the unesco documents describes a solidarity based on the fundamental unity of all humans, a focus on ''the collective, the observance of duties and the creation and preservation, through personal and collective action, of a just and decent society''. the notion that the human genome is the ''common heritage of humanity'' has been eloquently defended (knoppers a ), but has not avoided the disquiet among some commentators, some of whom suggest that the human genome be classified as a common resource rather than the common heritage of humanity (spectar ; resnik ) . developed in the context of international law governing the management of resources in outer space and the high seas, this concept is founded on three basic principles: ''( ) absence of private property rights i.e. the right [usually of governments] to use resources but not to own them; ( ) international management of all uses of the common heritage; and ( ) sharing of benefits derived from such use'' (white ) . also included in the concept is an obligation to use the resource in a peaceful and responsible way, keeping the resource accessible to all and considering the interests of future generations (knoppers a) . in economic terms, a global public good is a good ''for which the cost of extending the service to an additional person is zero and for which it is impossible or expensive to exclude individuals from enjoying'' (nordhaus ) . a global public good is marked by two criteria: that the good be non-excludable and non-rivalrous. stated differently, ''[a] good is non-excludable if persons cannot be excluded from accessing it, and non-rivalrous if one person's use of the good does not diminish the supply of that good'' (chadwick and wilson ) . a classic example is a lighthouse that lights the sea and which is not diminished in its use by multiple sailors (chadwick and wilson ) . other examples include a global positioning system (gps) whose value is not compromised by multiple users, or the eradication of an infectious disease, the benefits of which cannot be diverted from any susceptible persons (nordhaus ) . it has been argued that both genetic information (knoppers and fecteau ; chadwick and wilson ) and public health (meier and fox ) should be classified as global public goods in this same way. these three concepts have been integrated by several commentators in efforts to develop ethics frameworks for public health and biobanking. meier and fox ( ) consider public health a public good and make a case for its recognition in international law as a collective right. knoppers ( a) notes growing support in international normative documents for the human genome to be classified as the common heritage of humanity, and argues, as do chadwick and wilson ( ) , that genetic databases should be considered a global public good (knoppers and fecteau ; knoppers b; chadwick and wilson ) . the combination of features from all three concepts can provide the basic constituents of a human rights public health ethic for international biobanking. first, collective rights, premised conceptually on the fact that certain rights can be protected only in groups, is virtually analogous to the population perspective of public health, which presumes that certain health challenges require society-wide, rather than individual, interventions. the kinship of the two perspectives is highlighted in the argument made by meier and fox ( ) that public health be recognized as a collective right. second, the classification of genetic databases as the common heritage of humanity, which precludes private ownership while requiring shared uses and benefits, buttresses the view that biobanks should be managed under principles that consider the whole of humanity rather than narrower interests, no matter how seemingly benign. again, these principles would share an affinity with the principles of public health that target the health of the whole population. third, the arguments for the status of genetic information as a non-rivalrous and non-excludable global public good also support an approach to managing biobanks that recognizes the public character of the resource. together, these features ground the management of international biobanking in a framework that keeps foremost the population perspective of public health. biobanking and developments in personalized medicine entail the involvement of private investors. commentators have pointed out the costs associated with this infusion of private funding. they raise concerns that such involvement may influence the type of research, distort the process by restricting the direction of research, prevent collaboration, and restrict the sharing of the raw data generated by the research. it also might prevent the results of the research being disseminated effectively or cause publication bias. most importantly, it may serve to reduce public trust in the research process. some evidence suggests that potential participants may be less willing to engage in research if this is privately funded (as they perceive themselves to be more exposed to potential exploitation) (ickworth ). the risks expand significantly when, as projected, biobanking expands globally. most lmics have vulnerable populations and lax to minimal research regulation. but even where lmic governments have the ability to regulate research activity, we have noted above the growing trend under globalization for governments to delegate traditional responsibilities to private actors. this constitutes a major administrative and ethical challenge in the regulation of biobanks because, as a rule, governments rather than private actors assume international obligations (ratner ). the situation requires an ethical framework for protecting vulnerable populations living under governments either unwilling or incapable of protecting their interests. in , john ruggie was appointed the united nations special representative of the secretary general (srsg) on business and human rights for an initial term of years. ruggie's primary charge was to clarify the human rights obligations of companies operating internationally and the responsibilities of host governments to regulate such businesses (u.n. comm. on human rights ). in extending the srsg's mandate another years in , the human rights council observed that weak national legislation and implementation cannot effectively mitigate the negative impact of globalization on vulnerable economies, fully realize the benefits of globalization or derive maximally the benefits of activities of transnational corporations and other business enterprises and that therefore efforts to bridge governance gaps at the national, regional and international levels are necessary… (u.n. human rights council ) the appointment of the srsg underscores the ethical implications of international trade and politics. it also testifies to the potential of human rights as a framework for addressing global governance challenges. the srsg fulfills his mandate through research, consultations and workshops that lead to recommendations, standards and tools for the use of businesses and other stakeholders. in the course of his mandate, the srsg has developed a human rights framework for business in the global economy. the framework (known as the ''un framework'') has three pillars: the duty of governments to protect their citizens from human rights violations by third parties (particularly international businesses); the responsibility of businesses to respect human rights (typically contained in corporate codes of conduct); and the establishment of remedies for people whose human rights have been violated (u.n. spec. rep. of the sec. gen. ). the un framework provides a useful tool for helping mitigate the regulatory hazards associated with privatelyfunded biobanking enterprises in lmics. by further clarifying the responsibilities of both host governments and foreign investors, the un framework increases the chances that clear laws regulating biobanking will be passed by lmic governments. effective biobanking governance models (kaye and stranger ) are necessary if biobanking is to benefit public health as governments remain the primary actors in public heath practice. moreover, by ensuring the availability of remedies for violations, the un framework reduces the incentive of foreign investors to take advantage of weak and/or corrupt governments unwilling to implement existing biobanking regulations. the un framework was endorsed by the human rights council in june , thereby enhancing its credibility as a global ethical standard for regulating international business activity. this endorsement ensures that the un framework will help guarantee that the projected extension of especially privately financed biobanking to lmics will take into account the public health interests of lmic populations. we have taken the view that one of the ethical challenges raised by genomic medicine reflects an enduring problem in public health: the appropriate balancing of individual and collective values, rights and interests. biobanking in the context of public health genomics reflects a unique case study in this classical problem because it must accommodate both individual and community interests (including multiple types of affected communities). while no single ethical-legal framework has been accepted to bridge this gap, we believe that a renewed attention to a human rights perspective in the context of global health may offer a way forward. medicine at the paris hospital human dignity and human rights as a common ground for a global 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-w copp z authors: fresnadillo, maría j.; garcía, enrique; garcía, josé e.; martín, Ángel; rodríguez, gerardo title: a sis epidemiological model based on cellular automata on graphs date: journal: distributed computing, artificial intelligence, bioinformatics, soft computing, and ambient assisted living doi: . / - - - - _ sha: doc_id: cord_uid: w copp z the main goal of this work is to introduce a new sis epidemic model based on a particular type of finite state machines called cellular automata on graphs. the state of each cell stands for the fraction of the susceptible and infected individuals of the cell at a particular time step and the evolution of these classes is given in terms of a local transition function. the public health issues have a lot of importance in our society, particularly viral spread through populated areas. epidemics refer to a disease that spreads rapidly and extensively by infection and affecting many individuals in an area at the same time. in this way, the most recent worrying epidemic was the severe acute respiratoy syndrome (sars) outbreak in asia. infectious disease accounts for of major causes of human morbidity and mortality listed by the world health organization and the world bank, and % of global deaths (over million deaths annually). consequently, since the publication of the first modern mathematical epidemic models in the first years of xx century (see [ , ] ), several mathematical models to study the dynamics of epidemics have been appeared in the literature. traditionally, mathematical models are based on differential equations. nevertheless, this approach has some drawbacks since they do not take into account spatial factors such as population density, they neglect the local character of the spreading process, they do not include variable susceptibility of individuals, etc. as a consequence, this can lead to very unrealistic results, such as, for example, endemic patterns relaying on very small densities of individuals, which are called "atto-foxes" or "nano-hawks" (see [ ] ). other mathematical models are based on a particular type of discrete dynamical systems called cellular automata (see, for example [ , , , , ] ). these simple models of computation eliminate the last mentioned shortcomings, and are specially suitable for computer simulations. roughly speaking, cellular automata (ca for short) are a special type of finite state machines capable to simulate physical, biological or environmental complex phenomena. consequently, several models based on such mathematical objects have been proposed to simulate growth processes, reaction-diffusion systems, selfreproduction models, epidemic models, forest fire spreading, image processing algorithms, cryptographic protocols, etc. (see, for example, [ , ] ). specifically, a two-dimensional ca is formed by a two-dimensional array of identical objects called cells which can be disposed in a rectangular, triangular or an hexagonal lattice (called cellular space). these cells are endowed with a state that changes in discrete steps of time according to a specific rule. as the ca evolves, the updated function (whose variables are the states of the neighbor cells) determines how local interactions can influence the global behaviour of the system. usually, mathematical models to study epidemic spreading are divided into three types: sis models, sir models and seir models, depending on the classes in which the population can be classified. the model introduced in this paper deals with sis epidemic diseases (for example the group of those responsible for the common cold), that is, the population is divided into susceptible individuals (s) and infected individuals (i). the susceptible individuals are those capable to contracting the disease whereas the infected individuals are those capable of spreading the disease. for a sis model, infected individuals return to the susceptible class on recovery because the disease confers no immunity against reinfection. moreover, some assumptions will be common to all models: ( ) the disease is transmitted by contact between an infected individual and a susceptible individual; ( ) there is no latent period for the disease, hence the disease is transmitted instantaneously upon contact; ( ) all susceptible individuals are equally susceptible and all infected individuals are equally infectious; ( ) the population under consideration is fixed in size. this means that no births or migration occurs, and no deaths are taken into account. the main goal of this work is to introduce a new sis model to simulate the spread of a general epidemic based on cellular automata on graph. specifically, in the proposed model, the state of each cell stands for the fraction of the susceptible and infected individuals of the cell at a particular time step. the local transition function is a function involving the states of the neighbor cells and other parameters such as the virulence of the epidemic, the rate of recovered infected individuals, etc. moreover, as is mentioned above, the standard paradigm for cellular automata states that the topology of the cellular space is given in terms of a regular rectangular or hexagonal lattices. nevertheless, in this paper we will consider a more efficient topology to model an epidemic disease, which is given by an undirected graph where its nodes stand for the cells of the cellular automata. there are several ca-based algorithms to simulate a sis epidemic model (see, for example [ , , ] ). the standard paradigm of these models states that each cell stands for an only one individual. unfortunately, there are few models considering more than one invidual in each cell (see for example [ ] ). we think that this new paradigm is more accurate than the other one in order to obtain more realistic simulations. the main advantage of the model presented in this paper over the model introduced in [ ] is the use of graph tology and a more realistic transition function involving new parameters as the portion of susceptible individuals that moves from one cell to another one. the rest of the paper is organized as follows: in section the basic theory about cellular automata on graphs is provided; the proposed model is introduced in section ; the analysis of the model is shown in section ; and, finally, the conclusions and the future work are presented in section . . . , v n } is a ordered non-empty finite set of elements called nodes (or vertices), and e is a finite family of pairs of elements of v called edges. two nodes of the graph, v i , v j ∈ v , are said to be adjacent (or neighbors) if there exists an edge in e of the form (v i , v j ). we consider undirected graphs, that is, is not two edges of g with the same ends and no loops exist, i.e. edges whose start and end is located at the same node. the neighborhood of a node v ∈ v , n v , is the set of all nodes of g which are adjacent to v, that is: the degree of a node v, d v , is the number of its neighbors. a cellular automaton on an undirected graph g = (v, e) is a -uple a = (v, s, n, f ) where: the set v defines the cellular space of the ca such that each node stands for a cell the cellular automaton. s is the finite set of states that can be assumed by the nodes at each step of time. the state of the node v at time step t is denoted by s t v ∈ s. these states change accordingly to the local transition function f . n is the neighborhood function which assigns to each node its neighborhood, that is: note that the neighborhoods of the nodes are, in general, different from others. the local transition function f calculates the state of every node at a particular time step t + from the states of the its neighbors at the previous time step t, that is, in the mathematical epidemiological model introduced in this paper, the population is divided into two classes: those who are susceptible to the disease and those who are infected to the disease. moreover, the population is located at city centres which stand for the nodes of a graph g. if there is some type of transport connection (by car, train, airplane, etc.) between two of these cities, the associated nodes are connected by an edge. the following assumptions are also made: . the population of each node remains constant over time, that is, no births or deaths are taking into account (it is a sis model without vital dynamics). moreover, the population distribution is inhomogeneous: let p u be the number of individuals of the node u ∈ v , and set p = max {p u , u ∈ v }. . the transmission of the disease (that is, the passing of the disease from an infected individual to a susceptible individual) is through direct physical contact: touching an infected person, including sexual contact. . the population (susceptible and infected people) are able to move from its node to another one and return to the origin node at every step of time. since the model introduced in this work is a sis model, then the state of the node u ∈ v at time step t is: s t u = (s t u , i t u ) ∈ q × q = s, where s t u ∈ [ , ] stands for the fraction of susceptible individuals of the node u at time t, and i t u ∈ [ , ] stands for the fraction of infected individuals of the node u at time t. consequently, the transition function of the ca is as follows: where d is a suitable discretization function. the ground where the epidemic is spreading is modeled as a weighted graph where each node stands for a city or a town, and the arc between two nodes represents the connection between the corresponding cities. in this sense, the connection factor between the nodes u and v is the weight associated to the arc (u, v) ∈ e and it is denoted by w uv . it depends on the transportation capacity of the public and non-public transport. consequently where h uv is the total amount of population wich move from u to v during a time step. the evolution of the number of infected individuals of the node u ∈ v is as follows: the infected individuals of u at time step t is given by the sum of: . the infected individuals at the previous time step which have not been recovered from the disease. . the susceptible individuals which have been infected during the time step. in this case we have to take into account the recovery rate r ∈ [ , ]. these new sick individuals of u can be infected both by the infected individuals of u or by the infected individuals of the neighbor nodes of u which have moved to u during the time step. in the first case, only the rate of transmission, p ∈ [ , ], is involved, whereas in the second case we have to consider the connection factors between the nodes, and the population and movement factor of each node. moreover we also consider the susceptible individuals of u moved to a neightbor node during the step of time and infected in this neighbor node by its corresponding infected individuals; in this case η u ∈ [ , ] yields the portion of moved susceptible individuals from u to its neighbor nodes. then, the mean-field equation for infected individuals is the following: on the other hand, the susceptible individuals of each node is given by the difference of the susceptible individuals of the node at the previous time step and the susceptible individuals which have been infected as is mentioned above. note that, as a simple calculus shows: then a discretization function d : [ , ] → q must be used in order to get a finite state set. in our case, the discretization function used is the following: where [m] stands for the nearest integer to m. as a consequence, q ={ , . , . . . , }. then, the system of equations governing the evolution of the two classes of population is: one of the most important question in a mathematical epidemiological model is the study of the possibility of the eradication of disease. in relation with every mathematical epidemiological model, it is very important to determine under what circumstances the epidemic occurs. taking into account the intrinsic characteristics of our model, we will demand two conditions: ( ) the epidemic disease must spread among the nodes of the graph; and ( ) the infected population grows. the initial conditions in the study are the following: at time step t = , we will consider only one node, for example u ∈ v , with infected individuals: first of all we will show the necessary condition for epidemic spreading from the node u to its neighbor v ∈ n u , at the next step of time t = . thus, it as the unique node with infected population at time t = is u, then taking into account ( ), it yields: as a consequence: . this equation must hold for every neighbor nodes of u, then the following result holds: theorem. the epidemic disease spreads from node u to its neighbor nodes if the following condition holds: now we will study what conditions that must be held to get a growth of the infected population in a node u. we have to distinguish two cases: ( ) there not exist infected individuals from neighbor nodes to u; ( ) there exist such infected individuals. . in the first case it is i t+ u > i t u , that is: as a consequence the growth occurs if: . in the second case, the inequality i t+ u > i t u gives: in this example, for the sake of simplicity we will suppose that the epidemic is spreading over n = cities, v , . . . , v , forming a complete graph k . in this example, we will consider the following initial configuration: that is, there is only one node at time t = with infected population. moreover, the parameters used are p = . , r = . , η ui = . , ≤ i ≤ . moreover, let us suppose that the population of each node is the same: p ui = with ≤ i ≤ , and also the transport capacity between two nodes is the same: w uiuj = for ≤ i, j ≤ . note that this example deals with an homogeneous-symmetric case. in figure the evolution of the total number of infected and susceptible individuals is shown. if we set p = . instead of p = . , the number of infected and susceptible individuals also remains constant with time, but in this case the number of susceptible is greater than the number of infected individuals. in this work a new mathematical model to simulate the spreading of an epidemic is introduced. it is based on the use of cellular automata on graphs endowed with fig. . evolution of the total number of infected and susceptible individuals a suitable local transition function. the state of each cell is considered to be the portion of its population which is infected at each time step. the analysis of the model proposed in this paper seems to be in agreement with the results obtained for other mathematical models not based on discrete event systems, such as odes or pdes. future work aimed at designing a more complete ca-based epidemic model involving additional effects such as the population movement, virus mutation, etc. furthermore, it is also interesting to consider non-constant connections factors and also the effect of migration between the cells must be considered. on some applications of cellular automata a simple cellular automaton model for influenza a viral infections critical behaviour of a probablistic automata network sis model for the spread of an infectious disease in a population of moving individuals cellular automata and epidemiological models with spatial dependence a model based on cellular automata to simulate epidemic diseases contributions to the mathematical theory of epidemics, part i a cellular automata model for citrus variegated chlorosis the dependence of epidemic and population velocities on basic parameters the prevention of malaria extending the sir epidemic model a cellular automaton model for the effects of population movement and vaccination on epidemic propagation cellular automata machines: a new environment for modeling a new kind of science acknowledgments. this work has been partially supported by consejería de sanidad, junta de castilla y león (spain). key: cord- -k wcibdk authors: pacheco, jorge m.; van segbroeck, sven; santos, francisco c. title: disease spreading in time-evolving networked communities date: - - journal: temporal network epidemiology doi: . / - - - - _ sha: doc_id: cord_uid: k wcibdk human communities are organized in complex webs of contacts that may be represented by a graph or network. in this graph, vertices identify individuals and edges establish the existence of some type of relations between them. in real communities, the possible edges may be active or not for variable periods of time. these so-called temporal networks typically result from an endogenous social dynamics, usually coupled to the process under study taking place in the community. for instance, disease spreading may be affected by local information that makes individuals aware of the health status of their social contacts, allowing them to reconsider maintaining or not their social contacts. here we investigate the impact of such a dynamical network structure on disease dynamics, where infection occurs along the edges of the network. to this end, we define an endogenous network dynamics coupled with disease spreading. we show that the effective infectiousness of a disease taking place along the edges of this temporal network depends on the population size, the number of infected individuals in the population and the capacity of healthy individuals to sever contacts with the infected, ultimately dictated by availability of information regarding each individual’s health status. importantly, we also show how dynamical networks strongly decrease the average time required to eradicate a disease. understanding disease spreading and evolution involves overcoming a multitude of complex, multi-scale challenges of mathematical and biological nature [ , ] . traditionally, the contact process between an infected individual and the susceptible ones was assumed to affect equally any susceptible in a population (mean-field approximation, well-mixed population approximation) or, alternatively, all those susceptible living in the physical neighborhood of the infected individual (spatial transmission). during recent years, however, it has become clear that disease spreading [ ] [ ] [ ] [ ] transcends geography: the contact process is no longer restricted to the immediate geographical neighbors, but exhibits the stereotypical small-world phenomenon [ ] [ ] [ ] [ ] , as testified by recent global pandemics (together with the impressive amount of research that has been carried out to investigate them) or, equally revealing, the dynamics associated with the spreading of computer viruses [ , [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] . recent advances in the science of networks [ , , , , ] also provided compelling evidence of the role that the networks of contacts between individuals or computers play in the dynamics of infectious diseases [ , ] . in the majority of cases in which complex networks of disease spreading have been considered [ ] , they were taken to be a single, static entity. however, contact networks are intrinsically temporal entities and, in general, one expects the contact process to proceed along the lines of several networks simultaneously [ , - , , , , - ] . in fact, modern societies have developed rapid means of information dissemination, both at local and at centralized levels, which one naturally expects to alter individuals' response to vaccination policies, their behavior with respect to other individuals and their perception of likelihood and risk of infection [ ] . in some cases one may even witness the adoption of centralized measures, such as travel restrictions [ , ] or the imposition of quarantine spanning parts of the population [ ] , which may induce abrupt dynamical features onto the structure of the contact networks. in other cases, social media can play a determinant role in defining the contact network, providing crucial information on the dynamical patterns of disease spreading [ ] . furthermore, the knowledge an individual has (based on local and/or social media information) about the health status of acquaintances, partners, relatives, etc., combined with individual preventive strategies [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] (such as condoms, vaccination, the use of face masks or prophylactic drugs, avoidance of visiting specific web-pages, staying away from public places, etc.), also leads to changes in the structure and shape of the contact networks that naturally acquire a temporal dimension that one should not overlook. naturally, the temporal dimension and multitude of contact networks involved in the process of disease spreading render this problem intractable from an analytic standpoint. recently, sophisticated computational platforms have been developed to deal with disease prevention and forecast [ , , , , , [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] . the computational complexity of these models reflects the intrinsic complexity of the problem at stake, and their success relies on careful calibration and validation procedures requiring biological and socio-geographic knowledge of the process at stake. our goal here, instead, will be to answer the following question: what is the impact of a temporal contact network structure in the overall dynamics of disease progression? does one expect that it will lead to a rigid shift of the critical parameters driving disease evolution, as one witnesses whenever one includes spatial transmission patterns? or even to an evanescence of their values whenever one models the contact network as a (static and infinite) scale-free network, such that the variance of the network degree distribution becomes arbitrarily large? or will the temporal nature of the contact network lead to new dynamical features? and, if so, which features will emerge from the inclusion of this temporal dimension? to answer this question computationally constitutes, in general, a formidable challenge. we shall attempt to address the problem analytically, and to this end some simplifications will be required. however, the simplifications we shall introduce become plausible taking into consideration recent results (i) in the evolutionary dynamics of social dilemmas of cooperation, (ii) in the dynamics of peer-influence, and even (iii) in the investigation of how individual behavior determines and is determined by the global, population wide behavior. all these recent studies point out to the fact that the impact of temporal networks in the population dynamics stems mostly from the temporal part itself, and not so much from the detailed shape and structure of the network [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] . indeed, we now know that (i) different models of adaptive network dynamics lead to similar qualitative features regarding their impact in what concerns the evolution of cooperation [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] , (ii) the degree of peer-influence is robust to the structural patterns associated with the underlying social networks [ ] , and (iii) the impact of temporal networks in connecting individual to collective behavior in the evolution of cooperation is very robust and related to a problem of n-body coordination [ , ] . altogether, these features justify that we model the temporal nature of the contact network in terms of a simple, adaptive network, the dynamics of which can be approximately described in terms a coupled system of odes. this "adaptive-linking" dynamics, as it was coined [ , [ ] [ ] [ ] , leads to network snapshot structures that do not replicate what one observes in real-life, in the same sense that the small-world model of watts and strogatz does not lead to the heterogeneous and diverse patterns observed in data snapshots of social networks. notwithstanding, the active-linking dynamics allows us to include, analytically, the temporal dimension into the problem of disease dynamics. the results [ ] , as we elaborate in sects. and , prove rewarding, showing that the temporal dimension of a contact network leads to a shift of the critical parameters (defined below) which is no longer rigid but, instead, becomes dependent on the frequency of infected individuals in the population. this, we believe, constitutes a very strong message with a profound impact whenever one tries to incorporate the temporal dimension into computational models of disease forecast. this chapter is organized as follows. in the following sect. , we introduce the standard disease models we shall employ, as well as the details of the temporal contact network model. section is devoted to present and discuss the results, and sect. contains a summary of the main conclusions of this work. in this section, we introduce the disease models we shall employ which, although well-known and widely studied already, are here introduced in the context of stochastic dynamics in finite populations, a formulation that has received less attention than the standard continuous model formulation in terms of coupled ordinary differential equations (odes). furthermore, we introduce and discuss in detail the temporal contact network model. here we introduce three standard models of disease transmission that we shall employ throughout the manuscript, using this section at profit to introduce also the appropriate notation associated with stochastic dynamics of finite populations and the markov chain techniques that we shall also employ in the remainder of this chapter. we shall start by discussing the models in the context of well-mixed populations, which will serve as a reference scenario for the disease dynamics, leaving for the next section the coupling of these disease models with the temporal network model described below. we investigate the popular susceptible-infected-susceptible (sis) model [ , ] , the susceptible-infected (si) model [ ] used to study, e.g., aids [ , ] , and the susceptible-infected-recovered (sir) model [ , ] , more appropriate to model, for instance, single season flu outbreaks [ ] or computer virus spreading [ ] . it is also worth pointing out that variations of these models have been used to successfully model virus dynamics and the interplay between virus dynamics and the response of the immune system [ ] . in the sis model individuals can be in one of two epidemiological states: infected (i) or susceptible (s). each disease is characterized by a recovery rate (•) and an infection rate (oe). in an infinite, well-mixed population, the fraction of infected individuals (x) changes in time according to the following differential equation where y d x is the fraction of susceptible individuals and hki the average number of contacts of each individual [ ] . there are two possible equilibria (p x d ): x d and x d r , where r d hki/ı denotes the basic reproductive ratio. the value of r determines the stability of these two equilibria: x d r is stable when r > and unstable when r < . let us now move to finite populations, and consider the well-mixed case where the population size is fixed and equal to n. we define a discrete stochastic markov process describing the disease dynamics associated with the sis model. each configuration of the population, which is defined by the number of infected individuals i, corresponds to one state of the markov chain. time evolves in discrete steps and two types of events may occur which change the composition of the population: infection events and recovery events. this means that, similar to computer simulations of the sis model on networked populations, at most one infection or recovery event will take place in each (discrete) time step. thus, the dynamics can be represented as a markov chain m with nc states [ , ] -as many as the number of possible configurations -illustrated in the following fig. . . in a finite, well-mixed population, the number i of infected will decrease at a rate given by where denotes the recovery time scale, i n the probability that a randomly selected individual is infected and ı the probability that this individual recovers. adopting as a reference, we assume that the higher the average number of contacts hki, the smaller the time scale inf at which infection update events occur ( inf d /hki) [ ] . consequently, the number of infected will also increase at a rate given by equations ( . ) and ( . ) define the transitions between different states. this way, we obtain the following transition matrix for m: where each element p kj of p represents the probability of moving from state k to state j during one time step. the state without any infected individual (id ) is an absorbing state of m. in other words, the disease always dies out and will never re-appear, once this happens. at this level of approximation, it is possible to derive an analytical expression for the average time t i it takes to reach the single absorbing state of the sis markov chain (i.e., the average time to absorption) starting from a configuration in which there are i infected individuals. denoting by p i (t) the probability that the disease disappears at time t when starting with i infected individuals at time , we may write [ ] using the properties of p i (t) we obtain the following recurrence relation for t i whereas for t n we may write defining the auxiliary variables i d l , a little algebra allows us to write, for t such that t i can be written as a function of t as follows the intrinsic stochasticity of the model, resulting from the finiteness of the population, makes the disease disappear from the population after a certain amount of time. as such, the population size plays an important role in the average time to absorption associated with a certain disease, a feature we shall return to below. equations ( . ) and ( . ) define the markov chain m just characterized. the fraction of time the population spends in each state is given by the stationary distribution of m, which is defined as the eigenvector associated with eigenvalue of the transition matrix of m [ , ] . the fact that in the sis model the state without infected (id ) is an absorbing state of the markov chain, implies that the standard stationary distribution will be completely dominated by this absorbing state, which precludes one to gather information on the relative importance of other configurations. this makes the so-called quasi-stationary distribution of m [ ] the quantity of interest. this quantity allows us to estimate the relative prevalence of the population in configurations other than the absorbing state, by computing the stationary distribution of the markov chain obtained from m by excluding the absorbing state id [ ] . it provides information on the fraction of time the population spends in each state, assuming the disease does not go extinct. the markov process m defined before provides a finite population analogue of the well-known mean-field equations written at the beginning of sect. . . . indeed, in the limit of large populations, g.i/ d t c .i/ t .i/ provides the rate of change of infected individuals. for large n, replacing i n by x and n i n by y, the gradients of infection which characterize the rate at which the number of infected are changing in the population, are given by again, we obtain two roots: g(i) d for i d and i r d n .n / ı hki . moreover, i r becomes the finite population equivalent of an interior equilibrium for r Á ı hki n n > (note that, for large n we have that n n ). the disease will most likely expand whenever i < i r , the opposite happening otherwise. the si model is mathematically equivalent to the sis model with ı d , and has been employed to study for instance the dynamics of aids. the markov chain representing the disease dynamics is therefore defined by transition matrix eq. ( . ), with t i d for all i. the remaining transition probabilities t c i ( < i < n) are exactly the same as for the sis model. since all t i equal zero, the markov chain has two absorbing states: the canonical one without any infected (id ) and the one without any susceptible (idn). the disease will expand monotonically as soon as one individual in the population gets infected, ultimately leading to a fully infected population. the average amount of time after which this happens, which we refer to as the average infection time, constitutes the main quantity of interest. this quantity can be calculated analytically [ ] : the average number of time steps needed to reach % infection, starting from i infected individuals is given by ( . ) with sir one models diseases in which individuals acquire immunity after recovering from infection. we distinguish three epidemiological states to model the dynamics of such diseases: susceptible (s), infected (i) and recovered (r), indicating those who have become immune to further infection. the sir model in infinite, well-mixed populations is defined by a recovery rate ı and an infection rate . the fraction of infected individuals x changes in time according to the following differential equation where y denotes the fraction of susceptible individuals, which in turn changes according to p y d hki xy: ( . ) finally, the fraction of individuals z in the recovered class changes according to p z d ı x: ( . ) to address the sir model in finite, well-mixed populations, we proceed in a way similar to what we have done so far with sis and si models. the markov chain describing the disease dynamics becomes slightly more complicated and has states (i, r), where i is the number of infected individuals in the population and r the number of recovered (and immune) individuals (i c r Ä n). a schematic representation of the markov chain is given in fig. . . note that the states ( , r), with Ä r Ä n, are absorbing states. each of these states corresponds to the number of individuals that are (or have become) immune at the time the disease goes extinct. consider a population of size n with average degree hki. the number of infected will increase with a rate where denotes the recovery time scale. as before, the gradient of infection g(i), such that g.i/ d t c .i/ t .i/, measures the likelihood for the disease to either expand or shrink in a given state, and is given by note that we recover eq. ( . ) in the limit n ! . for a fixed number of recovered individuals r , we have that g(i, r ) d for i d and for i r d n becomes the finite population analogue of an interior equilibrium. furthermore, one can show that the partial derivative @g.i;r/ @i has at most one single root in ( , ), possibly located at i r d i r Ä i r . hence, g(i, r ) reaches a local maximum at i r (given that at that point @ g.i;r/ @i ˇi r d hki n.n / < ). the number of infected will therefore most likely increase for i < i r (assuming r immune individuals), and most likely decrease otherwise. the gradient of infection also determines the probability to end up in each of the different absorbing states of the markov chain. these probabilities can be calculated analytically [ ] . to this end, let us use y a i;r to denote the probability that the population ends up in the absorbing state with a recovered individuals, starting from a state with i infected and r recovered. we obtain the following recurrence relationship for y a i;r y a i;r d t .i; r/ y a i ;rc c t c .i; r/ y a ic ;r c t .i; r/ t c .i; r/ y a i;r ; ( . ) which reduces to the following boundary conditions ( . ) allow us to compute y a i;r for every a, i and r. our network model explicitly considers a finite and constant population of n individuals. its temporal contact structure allows, however, for a variable number of overall links between individuals, which in turn will depend on the incidence of disease in the population. this way, infection proceeds along the links of a contact network whose structure may change based on each individual's health status and the availability of information regarding the health status of others. we shall assume the existence of some form of local information about the health status of social contacts. information is local, in the sense that individual behavior will rely on the nature of their links in the contact network. moreover, this will influence the way in which individuals may be more or less effective in avoiding contact with those infected while remaining in touch with the healthy. suppose all individuals seek to establish links at the same rate c. for simplicity, we assume that new links are established and removed randomly, a feature which usually does not always apply in real cases, where the limited social horizon of individuals or the nature of their social ties may constrain part of their neighborhood structure (see below). let us further assume that links may be broken off at different rates, based on the nature of the links and the information available about the individuals they connect: let us denote these rates by b pq for links of type pq (p , q fs, i, rg. we assume that links are bidirectional, which means that we have links of pq types si, sr, and ir. let l pq denote the number of links of type pq and l m pq the maximum possible number of links of that type, given the number of individuals of type s, i and r in the population. this allows us to write down (at a mean-field level) a system of odes [ , ] for the time evolution of the number of links of pq-type (l pq ) [ , ] which depends on the number of individuals in states p and q (l m pp d p .p / = and l m pq d pq for p ¤ q) and thereby couples the network dynamics to the disease dynamics. in the steady state of the linking dynamics ( p l pq d ), the number of links of each type is given by l pq d ' pq l m pq , with ' pq d c/(c c b pq ) the fractions of active pq-links, compared to the maximum possible number of links l m pq , for a given number of s, i and r. in the absence of disease only ss links exist, and hence ss determines the average connectivity of the network under disease free conditions, which one can use to characterize the type of the population under study. in the presence of i individuals, to the extent that s individuals manage to avoid contact with i, they succeed in escaping infection. thus, to the extent that individuals are capable of reshaping the contact network based on available information of the health status of other individuals, disease progression will be inhibited. in the extreme limit of perfect information and individual capacity to immediately break up contacts with infected, we are isolating all infected, and as such containing disease progression. our goal here, however, is to understand how and in which way local information, leading to a temporal reshaping of the network structure, affects overall disease dynamics. we investigate the validity of the approximations made to derive analytical results as well as their robustness by means of computer simulations. all individual-based simulations start from a complete network of size nd . disease spreading and network evolution proceed together under asynchronous updating. disease update events take place with probability ( c ) , where d net / dis . we define dis as the time-scale of disease progression, whereas net is the time scale of network change. the parameter d net / dis provides the relative time scale in terms of which we may interpolate between the limits when network adaptation is much slower than disease progression ( ! ) and the opposite limit when network adaptation is much faster than disease progression ( ! ). since d net / dis is the only relevant parameter, we can make, without loss of generality, dis d . for network update events, we randomly draw two nodes from the population. if connected, then the link disappears with probability given by the respective b pq . otherwise, a new link appears with probability c. when a disease update event occurs, a recovery event takes place with probability ( c hki) , an infection event otherwise. in both cases, an individual j is drawn randomly from the population. if j is infected and a recovery event has been selected then j will become susceptible (or recovered, model dependent) with probability •. if j is susceptible and an infection event occurs, then j will get infected with probability oe if a randomly chosen neighbor of j is infected. the quasi-stationary distributions are computed (in the case of the sis model) as the fraction of time the population spends in each configuration (i.e., number of infected individuals) during disease event updates ( generations; under asynchronous updating, one generation corresponds to n update events, where n is the population size; this means that in one generation, every individual has one chance, on average, to update her epidemic state). the average number of infected hii and the mean average degree of the network hki observed during these generations are kept for further plotting. we have checked that the results reported are independent of the initial number of infected in the network. finally, for the sir and si models, the disease progression in time, shown in the following sections, is calculated from independent simulations, each simulation starting with infected individual. the reported results correspond to the average amount of time at which i individuals become infected. in this section we start by (i) showing that a quickly adapting community induces profound changes in the dynamics of disease spreading, irrespective of the underlying epidemic model; then, (ii) we resort to computer simulations to study the robustness of these results for intermediate time-scales of network adaptation; finally, (iii) we profit from the framework introduced above to analyze the impact of information on average time for absorption and disease progression in adaptive networks. empirically, it is well-known that often individuals prevent infection by avoiding contact with infected once they know the state of their contacts or are aware of the potential risks of such infection [ , , [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] : such is the case of many sexually transmitted diseases [ , [ ] [ ] [ ] , for example, and, more recently, the voluntary use of face masks and the associated campaigns adopted by local authorities in response to the sars outbreak [ , [ ] [ ] [ ] or even the choice of contacting or not other individuals based on information on their health status gathered from social media [ , , ] . in the present study, individual decision is based on available local information about the health state of one's contacts. thus, we can study analytically the limit in which the network dynamics -resulting from adaptation to the flow of local information -is much faster than disease dynamics, as in this case, one may separate the time scales between network adaptation and contact (disease) dynamics: the network has time to reach a steady state before the next contact takes place. consequently, the probability of having an infected neighbor is modified by a neighborhood structure which will change in time depending on the impact of the disease in the population and the overall rates of severing links with infected. let us start with the sir model. the amount of information available translates into differences mostly between the break-up rates of links that may involve a potential risk for further infection (b si , b ir , b ii ), and those that do not (b ss , b sr , b rr ). therefore, we consider one particular rate b i for links involving infected individuals (b i Á b si d b ir d b ii ), and another one, b h , for links connecting healthy . in general, one expects b i to be maximal when each individual has perfect information about the state of her neighbors and to be (minimal and) equal to b h when no information is available, turning the ratio between these two rates into a quantitative measure of the efficiency with which links to infected are severed compared to other links. note that we reduce the model to two break-up rates in order to facilitate the discussion of the results. numerical simulations show that the general principles and conclusions remain valid when all break-up rates are incorporated explicitly. it is worth noticing that three out of these six rates are of particular importance for the overall disease dynamics: b ss , b sr and b si . these three rates, combined with the rate c of creating new links, define the fraction of active ss, sr and si links, and subsequent correlations between individuals [ ] , and therefore determine the probability for a susceptible to become infected (see models and methods). this probability will increase when considering higher values of c (assuming b i > b h ). in other words, when individuals create new links more often, therefore increasing the likelihood of establishing connections to infected individuals (when present), they need to be better informed about the health state of their contacts in order to escape infection. in the fast linking limit, the other three break-up rates (b ii , b ir and b rr ) will also influence disease progression since they contribute to changing the average degree of the network. when the time scale for network update ( net ) is much smaller than the one for disease spreading ( dis ), we can proceed analytically using at profit the separation of times scales. in practice, this means that the network has time to reach a steady state before the next disease event takes place. consequently, the probability of having an infected neighbor is modified by a neighborhood structure which will change in time depending on the impact of the disease in the population and the overall rates of severing links with infected individuals. for a given configuration (i,r) of the population, the stationary state of the network is characterized by the parameters ' ss , ' si and ' sr . consequently, the number of infected increases at a rate [ ] where we made d . the effect of the network dynamics becomes apparent in the third factor, which represents the probability that a randomly selected neighbor of a susceptible is infected. in addition, eq. ( . ) remains valid, as the linking dynamics does not affect the rate at which the number of infected decreases. it is noteworthy that we can write eq. ( . ) in the form which is formally equivalent to eq. ( . ) and shows that disease spreading in a temporal adaptive network is equivalent to that in a well-mixed population with (i) a frequency dependent average degree hki and (ii) a transmission probability that is rescaled compared to the original according to note that this expression remains valid for both sir, sis (r d ) and si (ı d , r d ) models. since the lifetime of a link depends on its type, the average degree hki of the network depends on the number of infected in the population, and hence becomes frequency (and time) dependent, as hki depends on the number of infected (through l m pq ) and changes in time. note that Á scales linearly with the frequency of infected in the population, decreasing as the number of infected increases (assuming ss ı si > ); moreover, it depends implicitly (via the ratio ss ı si ) on the amount of information available. it is important to stress the distinction between the description of the disease dynamics at the local level (in the vicinity of an infected individual) and that at the population wide level. strictly speaking, a dynamical network does not change the disease dynamics at the local level, meaning that infected individuals pass the disease to their neighbors with probability intrinsic to the disease itself. at the population level, on the other hand, disease progression proceeds as if the infectiousness of the disease effectively changes, as a result of the network dynamics. consequently, analyzing a temporal network scenario at a population level can be achieved via a renormalization of the transmission probability, keeping the (mathematically more attractive) well-mixed scenario. in this sense, from a well-mixed perspective, dynamical networks contribute to changing the effective infectiousness of the disease, which becomes frequency and information dependent. note further that this information dependence is a consequence of using a single temporal network for spreading the disease and information. interestingly, adaptive networks have been shown to have a similar impact in social dilemmas [ ] . from a global, population-wide perspective, it is as if the social dilemma at stake differs from the one every individual actually plays. as in sect. , one can define a gradient of infection g, which measures the tendency of the disease to either expand or shrink in a population with given configuration (defined by the number of individuals in each of the states s, i and r). to do so, we study the partial derivative @g.i;r/ @i at i d this quantity exceeds zero whenever note that taking r d yields the basic reproductive ratio r a for both sir and sis: on the other hand, whenever r a < , eradication of the disease is favored in the sis model (g(i)< ), irrespective of the fraction of infected, indicating how the presence of information (b h < b i ) changes the basic reproductive ratio. in fig. . we illustrate the role of information in the sis model by plotting g for different values of b i (assuming b h < b i ) and a fixed transmission probability . the corresponding quasi-stationary distributions are shown in the right panel and clearly reflect the sign of g. whenever g(i) is positive (negative), the dynamics will act to increase (decrease), on average, the number of infected. figure population and, once again, allows us to identify when disease expansion will be favored or not. figure . gives a complete picture of the gradient of infection, using the appropriate simplex structure in which all points satisfy the relation icrcsdn. the dashed line indicates the boundary g(i, r) d in case individuals do not have any information about the health status of their contacts, i.e., links that involve infected individuals disappear at the same rate as those that do not (b i d b h ). disease expansion is more likely than disease contraction (g(i, r) > ) when the population is in a configuration above the line, and less likely otherwise. similarly, the solid line indicates the boundary g(i, r) d when individuals share information about their health status, and use it to avoid contact with infected. once again, the availability of information modifies the disease dynamics, inhibiting disease progression for a broad range of configurations. up to now we have assumed that the network dynamics proceeds much faster than disease spreading (the limit ! ). this may not always be the case, and hence it is important to assess the domain of validity of this limit. in the following, we use computer simulations to verify to which extent these results, obtained analytically via time scale separation, remain valid for intermediate values of the relative timescale for the linking dynamics. we start with a complete network of size n, in which initially one individual is infected, the rest being susceptible. as stated before, disease spreading and network evolution proceed simultaneously under asynchronous updating. network update events take place with probability ( c ) , whereas a disease model (si, sis or sir) state update event occurs otherwise. for each value of , we run simulations. for the si model, the quantity of interest to calculate is the average number of generations after which the population becomes completely infected. these values are depicted in fig. . . the lower dashed line indicates the analytical prediction of the infection time in the limit ! (the limit when networks remain static), which we already recover in the simulations for > . when is smaller than , the average infection time significantly increases, and already reaches the analytical prediction for the limit ! (indicated by the upper dashed line) when < . hence, the validity of the time scale separation does again extend well beyond the limits one might expect. for the sir model, we let the simulations run until the disease goes extinct, and computed the average final fraction of individuals that have been affected by is given by eqs. ( . ) and ( . ) . one observes that linking dynamics does not affect disease dynamics for > . once drops below ten, a significantly smaller fraction of individuals is affected by the disease. this fraction reaches the analytical prediction for ! as soon as < . . hence, and again, results obtained via separation of time scales remain valid for a wide range of intermediate time scales. we finally investigate the role of intermediate time scales in the sis model. we performed computer simulations in the conditions discussed already, and computed several quantities that we plot in fig. . . figure . shows the average hii of the quasi-stationary distributions obtained via computer simulations (circles) as a function of the relative time scale of network update. whenever ! , we can characterize the disease dynamics analytically, assuming a well-mixed population (complete graph), whereas for ! we recover the analytical results obtained in the fast linking limit. at intermediate time scales, fig. . shows that as long as is smaller than ten, network dynamics contributes to inhibit disease spreading by effectively increasing the critical infection rate. overall, the validity of the time scale separation extends well beyond the limits one might anticipate based solely on the time separation ansatz. as long as the time scale for network update is smaller than the one for disease spreading ( < ), the analytical prediction for the limit ! , indicated by the lower dashed line in fig. . , remains valid. the analytical result in the extreme opposite limit ( ! ), indicated by the upper dashed line in fig. . , holds as long as > . moreover, it is noteworthy that the network dynamics influences the disease dynamics both by reducing the frequency of interactions between susceptible and infected, and by reducing the average degree of the network. these complementary effects are disentangled in intermediate regimes, in which the network dynamics is too slow to warrant sustained protection of susceptible individuals from contacts with infected, despite managing to reduce the average degree (not shown). in fact, for > the disease dynamics is mostly controlled by the average degree, as shown by the solid lines in fig. . . here, the average stationary distribution was determined by replacing, in the analytic expression for static networks, hki by the time-dependent average connectivity hki computed numerically. this, in turn, results from the frequency dependence of hki. when b i > b h , the network will reshape into a configuration with smaller hki as soon as the disease expansion occurs. for < , hki reflects the lifetime of ss links, as there are hardly any infected in the population. for < < , the network dynamics proceeds fast enough to reduce hki, but too slowly to reach its full potential in hindering disease progression. given the higher fraction of infected, and the fact that si and ii links have a shorter lifetime than ss links, the average degree drops when increasing from to . any further increase in leads to a higher average degree, as the network approaches its static limit. contrary to the deterministic sis model, the stochastic nature of disease spreading in finite populations ensures that the disease disappears after some time. however, this result is of little relevance given the times required to reach the absorbing state (except, possibly, in very small communities). indeed, the characteristic time scale of the dynamics plays a determinant role in the overall epidemiological process and constitutes a central issue in disease spreading. figure . shows the average time to absorption t in adaptive networks for different levels of information, illustrating the spectacular effect brought about by the network dynamics on t . while on networks without information (b i d b h ) t rapidly increases with the rate of infection oe, adding information moves the fraction of infected individuals rapidly to the absorbing state, and, therefore, to the disappearance of the disease. moreover, the size of the population can have a profound effect on t . with increasing population size, the population spends most of the time in the vicinity of the state associated with the interior root of g(i). for large populations, this acts to reduce the intrinsic stochasticity of the dynamics, dictating a very slow extinction of the disease, as shown in fig. . . when recovery from the disease is impossible, a situation captured by the si model, the population will never become disease-free again once it acquires at least one infected individual. the time to reach absorbing state in which all individuals are infected, again depends on the presence of information. when information prevails, susceptible individuals manage to resist infection for a long time, thereby delaying the rapid progression of the disease, as shown in the inset of fig. . . naturally, the average number of generations needed to reach a fully infected population increases with the availability of information, as illustrated in the main panel of fig. . . making use of three standard models of epidemics involving a finite population in which infection takes place along the links of a temporal graph, the nodes of which are occupied by individuals, we have shown analytically that the bias introduced into the graph dynamics resulting from the availability of information about the health status of others in the population induces fundamental changes in the overall dynamics of disease progression. the network dynamics employed here differs from those used in most other studies [ , [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] . we argue, however, that the differences obtained stem mostly from the temporal aspect of the network, and not so much from the detailed dynamics that is implemented. importantly, temporal network dynamics leads to additional changes in r compared to those already obtained when moving from the well-mixed assumption to static networks [ ] . an important ingredient of our model, however, is that the average degree of the network results from the selforganization of the network structure, and co-evolves with the disease dynamics. a population suffering from high disease prevalence where individuals avoid contact in order to escape infection will therefore exhibit a lower average degree than a population with hardly any infected individuals. such a frequency-dependent average degree further prevents that containment of infected individuals would result in the formation of cliques of susceptible individuals, which are extremely vulnerable to future infection, as reported before [ , , ] . the description of disease spreading as a stochastic contact process embedded in a markov chain constitutes a second important ingredient of the present model. this approach allows for a direct comparison between analytical predictions and individual-based computer simulations, and for a detailed analysis of finite-size effects and convergence times, whose exponential growth will signal possible bistable disease scenarios. in such a framework, we were able to show that temporal adaptive networks in which individuals may be informed about the health status of others lead to a disease whose effective infectiousness depends on the overall number of infected in the population. in other words, disease propagation on temporal adaptive networks can be seen as mathematically equivalent to disease spreading on a well-mixed population, but with a rescaled effective infectiousness. in accord with the intuition advanced in the introduction, as long as individuals react promptly and consistently to accurate available information on whether their acquaintances are infected or not, network dynamics effectively weakens the disease burden the population suffers. last but not least, if recovery from the disease is possible, the time for disease eradication drastically reduces whenever individuals have access to accurate information about the health state of their acquaintances and use it to avoid contact with those infected. if recovery or immunity is impossible, the average time needed for a disease to spread increases significantly when such information is being used. in both cases, our model clearly shows how availability of information hinders disease progression (by means of quick action on infected, e.g., their containment via link removal), which constitutes a crucial factor to control the development of global pandemics. finally, it is also worth mentioning that knowledge about the health state of others may not always be accurate or available in time. this is for instance the case for diseases where recently infected individuals remain asymptomatic for a substantial period. the longer the incubation period associated with the disease, the less successful individuals will be in escaping infection, which in our model translates into a lower effective rate of breaking si links, with the above mentioned consequences. moreover, different (social) networks through which awareness of the health status of others proceeds may lead to different rates of information spread. one may take these features into account by modeling explicitly the spread of information through a coupled dynamics between disease expansion and individuals' awareness of the disease [ , ] . creation and destruction of links may for instance not always occur randomly, as we assumed here, but in a way that is biased by a variety of factors such as social and genetic distance, geographical proximity, family ties, etc. the resulting contact network may therefore become organized in a specific way, promoting the formation of particular structures, such as networks characterized by long-tailed degree distributions or with strong topological correlations among nodes [ , [ ] [ ] [ ] which, in turn, may influence the disease dynamics. the impact of combining such effects, resulting from specific disease scenarios, with those reported here will depend on the prevalence of such additional effects when compared to linkrewiring dynamics. a small fraction of non-random links, or of ties which cannot be broken, will likely induce small modifications on the average connectivity of the contact network, which can be incorporated in our analytic expressions without compromising their validity regarding population wide dynamics. on the other hand, when the contact network is highly heterogeneous (e.g., exhibiting pervasive long-tail degree distributions), non-random events may have very distinct effects, from being almost irrelevant (and hence can be ignored) to inducing hierarchical cascades of infection [ ] , in which case our results will not apply. modeling infectious diseases in humans and animals infectious diseases in humans evolution of networks: from biological nets to the internet and www dynamical processes in complex networks epidemic processes in complex networks small worlds: the dynamics of 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vaccination sentiments with online social media: implications for infectious disease dynamics and control social and news media enable estimation of epidemiological patterns early in the haitian cholera outbreak the effects of local spatial structure on epidemiological invasions epidemic processes over adaptive state-dependent networks classes of small-world networks statistical mechanics of complex networks the structure and function of complex networks velocity and hierarchical spread of epidemic outbreaks in scale-free networks key: cord- - qld authors: agrawal, prashant; singh, anubhutie; raghavan, malavika; sharma, subodh; banerjee, subhashis title: an operational architecture for privacy-by-design in public service applications date: - - journal: nan doi: nan sha: doc_id: cord_uid: qld governments around the world are trying to build large data registries for effective delivery of a variety of public services. however, these efforts are often undermined due to serious concerns over privacy risks associated with collection and processing of personally identifiable information. while a rich set of special-purpose privacy-preserving techniques exist in computer science, they are unable to provide end-to-end protection in alignment with legal principles in the absence of an overarching operational architecture to ensure purpose limitation and protection against insider attacks. this either leads to weak privacy protection in large designs, or adoption of overly defensive strategies to protect privacy by compromising on utility. in this paper, we present an operational architecture for privacy-by-design based on independent regulatory oversight stipulated by most data protection regimes, regulated access control, purpose limitation and data minimisation. we briefly discuss the feasibility of implementing our architecture based on existing techniques. we also present some sample case studies of privacy-preserving design sketches of challenging public service applications. a welfare state may have legitimate interests in building large data registries with personally identifiable information (pii) for efficiency of service delivery. a state may also legitimately need to put its residents under purpose-specific surveillance. in fact, several commentators have alluded to the possibility of pervasive underthe-skin surveillance in a post-covid world [ ] . however, mandatory recordings of pii require enacting reasonable and fair laws to ensure that the processing of pii is proportionate to the stated objective, and safeguard the basic operative principles of privacy and fairness. citizens' basic rights need to be protected even when there is a legitimate state interest in digitisation with pii [ ] . the need to ensure that the information collected is not used adversely against citizens to harm them takes us into one of the hard problems of modern public policy: creating rules and technologies around information privacy to help strike this critical balance for online collection of pii at national scale. in this paper we address the problem of operationalising the broad privacy-by-design principles outlined in [ , ] , in the context of large public service databases. we present an architecture for implementing the data protection principles after the utility and proportionality of an application have been established through an appropriate regulatory analysis [ , , ] . the general principles of fair and reasonable processing, purpose, collection and storage limitation, notice and consent, data quality etc. have evolved since the s, both through sector specific standards in the us such as the social security number protection act [ ] and health insurance portability and accountability act (hipaa) [ ] , or through omnibus laws in general data protection standards such as the gdpr in the european union [ ] and the draft data protection bill of india [ ] . however, they have largely failed to prevent both direct harms that can occur as a result of data breaches or through unauthorised access of personal datasuch as identity thefts, unethical profiling and unlawful surveillance, or secondary harms that could arise due to the use of the data to adversely affect a person -such as through discrimination or exclusion, predatory targeting for unsuitable products, loss of employment, inaccurate credit rating etc. dictums such as personal data shall be processed in a fair and reasonable manner are non-specific, and they do not adequately define the contours of the required regulatory actions. as episodes like cambridge analytica [ ] demonstrate, harm is often not immediately obvious, and causal links of harm are not always easy to determine. this is compounded by the fact that data collection and use are becoming ubiquitous making it hard to trace misuse; the effects of misuse of personal data may not immediately manifest, and when they do they may not be easily quantifiable in monetary terms despite causing grave distress. hence, ex-post accountability and punitive measures are largely ineffective, and it is imperative to operationalise ex-ante preventive principles. as a consequence of the weak protection standards, most attempts at building large public services like national identity systems [ , ] , health registries [ , , ] , national population and voter registries [ , , ] , public credit registries [ , ] , income [ ] and tax registries [ ] etc. have often been questioned on privacy and fairness grounds and have been difficult to operationalise. the concerns have invariably been related to the need for protective safeguards when large national data integration projects are contemplated by governments and acknowledgment of the unprecedented surveillance power that this could create. in some situations they have even had to be abandoned altogether as they were unable to deal with these risks [ , , ] . in india too, the recent momentum and concerns around informational privacy guarantees have occurred in the context of the creation of new government databases and digital infrastructures for welfare delivery [ , ] . recording transactions with pii projects an individual into a data space, and any subsequent loss of privacy can happen only through the data pathway. hence data protection is central to privacy protection insofar as databases are concerned. the critical challenge in design of a data protection framework is that the main uses of digitisation -long term record keeping and data analysis -are seemingly contradictory to the privacy protection requirements. the legal principles around "fair information practice" attempt to reconcile these tensions, but there are four broad areas that require careful attention for effective data protection. first, a data protection framework is incomplete without an investigation of the nuances of digital identity, and guidelines for the various use cases of authentication, authorisation and accounting. it is also incomplete without an analysis of the extent to which personal information needs to be revealed for each use case, for example during know-your-citizen or -customer (kyc) processes. in addition, effective protection requires an understanding of the possible pathways of information leaks; of the limits of anonymisation with provable guarantees against re-identification attacks [ ] ; and of the various possibilities with virtual identities [ , ] . second, there have to be clear-cut guidelines for defining the requirements and standards of access control, and protection against both external and insider attacks in large data establishments, technically as well as legally. in particular, insider attacks are the biggest threat to privacy in public databases [ ] . these include possible unauthorised and surreptitious examination of data, transaction records, logs and audit trails by personnel with access, leading to profiling and surveillance of targeted groups and individuals, perhaps at the behest of interested and influential parties in the state machinery itself [ ] . thus, there must be guidelines on how the data may be accessed, under what authorisation and for what purpose. in addition, post data access purpose limitation -ensuring that there is no illegal use after the data crosses the access boundaries -is also crucial for privacy protection. third, a data protection framework is incomplete without guidelines for safe use of ai and data analytics. most theories for improving state efficiency in delivery of welfare and health services using personal data will have to consider improved data processing methods for targeting, epidemiology, econometrics, tax compliance, corruption control, analytics, topic discovery, etc. this, in turn, will require digitisation, surveillance and processing of large-scale personal transactional data. this requires detailed analyses of how purpose limitation of such surveillance -targeted towards improving efficiency of the state's service delivery -may be achieved without enabling undesirable mass surveillance that may threaten civil liberty and democracy. there must also be effective guidelines to prevent discriminatory and biased data processing [ ] . finally, it is well recognised in data protection frameworks [ , , ] that regulatory oversight is a necessary requirement for ensuring the above. while there is a rich set of tools and techniques in computer science arising out of decades of innovative privacy research, there is no overarching general framework for a privacy preserving architecture which, in particular, allows regulatory supervision and helps deal with the above issues in effective designs. in this paper we propose such an operational architecture for implementing the data protection principles. our immediate objective here is design space exploration and not specific implementations to evaluate performance and scalability. we illustrate the effectiveness of our proposal through design sketches of some challenging large public service applications. in particular, we illustrate through some real world case studies how some state-of-the-art designs either fail in their data protection goals, or tend to be overly defensive at the cost of utility in the absence of such an architecture. the rest of the paper is organized as follows. section briefly reviews the basic legal principles for data protection. section reviews concepts, tools and techniques from computer science for privacy protection. section presents our operational architecture. section discusses the feasibility and section discusses some illustrative case studies of large government applications. in what follows we briefly discuss the context of digitisation and privacy in india and the basic legal principles around privacy. we situate this analysis within the context of india's evolving regulatory and technical systems. however, many of these principles are relevant for any country seeking to align legal and technical guarantees of privacy for citizens. building public digital infrastructures has received an impetus in india in recent times [ ] and privacy has been an obvious concern. india has a long-standing legal discourse on privacy as a right rooted in the country's constitution. however, informational privacy and data protection issues have gained renewed visibility due to the recent national debate around the country's aadhaar system [ ] . aadhaar is a unique, biometric-based identity system launched in , with the ambitious aim of enrolling all indian residents, and recording their personal information, biometric fingerprints and iris scans against a unique identity number. aadhaar was designed as a solution for preventing leakages in government welfare delivery and targeting public services through this identity system. in addition, the "india stack" was envisioned as a set of apis that could be used -by public and private sector entities contract -to query the aadhaar database to provide a variety of services [ ] . however, as the project was unrolled across the country, its constitutionality was challenged in the courts on many grounds including the main substantive charge that it was violative of the citizens' right to privacy. over petitions challenging the system were eventually raised to the supreme court of india for its final determination. in the course of the matter, a more foundational question arose, i.e., whether the indian constitution contemplated a fundamental right of privacy? the question was referred to a separate -judge bench of the indian supreme court to conclusively determine the answer to this question. the answer to this question is important both for law and computer science, since the response creates deep implications for the design of technical systems in india. the supreme court's unanimous response to this question in justice k.s.puttaswamy (retd.) vs union of india (puttaswamy i) [ ] was to hold that privacy is a fundamental right in india guaranteed by part iii (fundamental rights) of the indian constitution. informational privacy was noted to be an important aspect of privacy for each individual, that required protection and security. in doing so, the court recognised the interest of an individual in controlling or limiting the access to their personal information, especially as ubiquitous data generation and collection, combined with data processing techniques, can derive information about individuals that we may not intend to disclose. in addition to cementing privacy as a constitutional right for indians, the supreme court in puttaswamy i [ ] also played an important role in clarifying certain definitional aspects of the concept. first, when defining privacy, the lead judgement noted that every person's reasonable expectation of privacy has both subjective and objective elements (see page of puttaswamy i), i.e., . the subjective element which is to the expectation and desire of an individual to be left alone, and . the objective element, which refers to objective criteria and rules (flowing from constitutional values) that create the widely agreed content of "the protected zone", where a person ought to be left alone in our society. second, informational privacy was also recognised (see page of puttaswamy i, from a seminal work which set out a typology of privacy) to be: ". . . an interest in preventing information about the self from being disseminated and controlling the extent of access to information." it would be the role of a future indian data protection law to create some objective standards for informational privacy to give all actors in society an understanding of the "ground rules" for accessing an individuals' personal information. these principles are already fairly well-developed through several decades of international experience. india is one of the few remaining countries in the world that is yet to adopt a comprehensive data protection framework. this section provides a brief overview of some of these established concepts. one of the early and most influential global frameworks on privacy protection are the oecd guidelines on the protection of privacy and transborder flows of personal data [ ] . these were formulated as a response to the advancements in technology that enabled faster processing of large amounts of data as well as their transmission across different countries. these guidelines were updated in , reflecting the multilateral consensus of the changes in the use and processing of personal data in that year period. therefore, it is a good starting point for the fundamental principles of privacy and data protection. the key principles of the oecd privacy framework are: collection limitation: personal data should be collected in a fair and lawful manner and there should be limits to its collection. use limitation: collected personal data be used or disclosed for any purposes other than those stated. if personal data must be used for purposes other that those stated, it should with the consent of the data subject or with the authority of the law. purpose specification: the purpose for collection of personal data should be stated no later than the point of collection. all subsequent uses of such data must be limited to the stated purposes. data quality: collected personal data should be relevant for the stated purposes and its accuracy for such a purpose must be maintained. security safeguards: reasonable safeguards must be adopted by the data controller to protect it from risks such as unauthorised access, destruction, use, modification or disclosure of the data. accountability: any entity processing personal data must be responsible and held accountable for giving effect to the principles of data protection and privacy. openness: any entity processing personal data must be transparent about the developments and practices with respect to the personal data collected. individual participation: individuals should have the rights to confirm from the data controller whether they have any personal data relating to them and be able to obtain the same within a reasonable time, at a reasonable charge and in a reasonable manner. if these requests are denied, individuals must be given the reasons for such denial and have the right to challenge such denials. individuals must also retain the right to be able to challenge personal data relating to them and able to erase, rectify, complete or amended. these principles, and many international instruments and national laws that draw from them, set some of the basic ground rules around the need for clear and legitimate purposes to be identified prior to accessing personal information. they also stress on the need for accountable data practices including strict access controls. many of these principles are reflected to varying degrees in india's personal data protection bill in [ ] which was introduced in the lower house of the indian parliament in december . the bill is currently under consideration by a joint select committee of parliamentarians following which it will enter parliament for final passage. the oecd privacy framework [ ] in article (g) also recognised the need for the promotion of technical measures to protect privacy in practice. there is also a growing recognition that if technical systems are not built with an appreciation of data protection and privacy principles, they can create deficits of trust and other dysfunctions. these are particularly problematic in government-led infrastructures. the failure of privacy self-management and the need for accountability-based data protection the need for data processing entities to adhere to objective and enforceable standards of data protection is heightened because of vulnerability of the individuals whose data they process. although research shows that individuals value their privacy and seek to control how information about them is shared, cognitive limitations operate at the level of the individuals' decision-making about their personal data [ ] . this "privacy paradox" signals the behavioural biases and information asymmetries that operate on people making decisions about sharing their personal information. especially in contexts where awareness that personal data is even being collected in digital interactions is low, such as with first-time users of digital services in india, it is often unfair and meaningless to delegate the self-management of privacy to users entirely through the ineffective mechanism of "consent". the inadequacy of consent alone as a privacy protection instrument has been well established, especially given that failing to consent to data collection could result in a denial of the service being sought by the user [ ] . in the context of these findings, it is crucial that digital ecosystems be designed in a manner that protects the privacy of individuals, does not erode their trust in the data collecting institution and does not make them vulnerable to different natures of harm. therefore, mere dependence on compliance with legal frameworks by data controllers is not sufficient. technical guarantees that the collected data will only be used for the stated purposes and in furtherance of data protection principles must become a reality, if these legal guarantees are to be meaningful. the need for early alignment of legal and technical design principles of data systems, such as access controls, purpose limitation and clear liability frameworks under appropriate regulatory jurisdictions are essential to create secure and trustworthy public data infrastructures [ , , ] . before we present our architectural framework, we briefly review some privacy preserving tools from computer science. cryptographic encryption [ ] , for protecting data either in storage or transit, have often been advocated for privacy protection. the following types are of particular importance: symmetric encryption symmetric encryption allows two parties to encrypt and decrypt messages using a shared secret key. diffie-hellman key exchange protocol [ ] is commonly used by the parties to jointly establish a shared key over an insecure channel. asymmetric encryption asymmetric or public key encryption [ ] allows two parties to communicate without the need to exchange any keys beforehand. each party holds a pair of public and private keys such that messages encrypted using the receiver's public key cannot be decrypted without the knowledge of the corresponding private key. id-based encryption id-based encryption [ ] allows the sender to encrypt the message against a textual id instead of a public key. a trusted third party provisions decryption keys corresponding to the ids of potential receivers after authenticating them through an out-of-band mechanism. id-based encryption considerably simplifies the public key infrastructure: a sender can encrypt messages using the semantic identifier of the intended recipient without explicitly knowing the public keys of the particular receivers. encryption with strong keys is a powerful method for privacy protection provided there are no unauthorised accesses to the keys. insider attacks, however, pose serious risks if the keys also reside with the same authority. even when the keys are stored securely, they have to be brought into the memory for decryption during run-time, and can be leaked by a compromised privileged software, for example an operating system or a hypervisor. digital signature a digital signature [ ] σ pk (m) on a message m allows a verifier to verify using the public key pk that m was indeed signed with the corresponding the private key. any alteration of m invalidates the signature. signatures also provide non-repudiation. blind signatures blind signatures [ ] are useful to obtain a signature on a message without exposing the contents of the message to the signer. a signature σ pk (b(m)) by a signer holding public key pk allows the signer to sign a blinded message b(m) that does not reveal anything about m. the author of the message can now use the σ pk (b(m)) to create an unblinded digital signature σ pk (m). chfs are functions that are a) 'one-way', i.e., given hash value h, it is difficult to find an x such that h = hash(x), and b) 'collision-resistant', i.e., finding any x and x such that hash(x ) = hash(x ) is difficult. chfs form the basis of many privacy preserving cryptographic primitives. there are several techniques from computer science that are particularly useful for data minimisation -at different levels of collection, authentication, kyc, storage and dissemination. some of these are: zkps [ ] are proofs that allow a party to prove to another that a statement is true, without leaking any information other than the statement itself. of particular relevance are zkps of knowledge [ ] , which convince a verifier that the prover knows a secret without revealing it. zkps also enable selective disclosure [ ] , i.e., individuals can prove only purpose-specific attributes about their identity without revealing additional details; for example, that one is of legal drinking age without revealing the age itself. "anonymity refers to the state of being not identifiable within a set of individuals, the anonymity set" [ ] . in the context of individuals making transactions with an organisation, the following notions of anonymity can be defined: unlinkable anonymity transactions provide unlinkable anonymity (or simply unlinkability) if a) they do not reveal the true identities of the individuals to organisations, and b) organisations cannot identify how different transactions map to the individuals. linkable anonymity transactions provide linkable anonymity if an organisation can identify whether or not two of its transactions involve the same individual, but individuals' true identities remain hidden. linkable anonymity is useful because it allows individuals to maintain their privacy while allowing the organisation to aggregate multiple transactions from the same individual. linkable anonymity is typically achieved by making individuals use pseudonyms. anonymous credentials authenticating individuals online may require them to provide credentials from a credential-granting organisation a to a credential-verifying organisation b. privacy protection using anonymous credentials [ , , ] can ensure that transactions with a are unlinkable to transactions with b. anonymous credentials allow an individual to obtain a credential from an organisation a against their pseudonym with a and transform it to an identical credential against their pseudonym with organisation b. an identity authority provisions a master identity to each individual from which all pseudonyms belonging to an individual, also known as virtual identities, are cryptographically derived. anonymous credentials are typically implemented by obtaining blind signatures (see section . . ) from the issuer and using zkps of knowledge (see section . . ) of these signatures to authenticate with the verifier. the credential mechanism guarantees: • unlinkable anonymity across organisations. this property ensures that a cannot track the uses of the issued credentials and b cannot obtain the individual's information shared only with a even when a and b collude. • unforgeability. a credential against an individual's pseudonym cannot be generated without obtaining an identical credential against another pseudonym belonging to the same individual. • linkable anonymity within an organisation. depending on the use case requirements, individuals may or may not use more than one pseudonym per organisation. in the latter case the transactions within an organisation also become unlinkable. if an organisation a requires to link multiple transactions from the same individual, it can indicate this requirement to the identity authority that checks if pseudonyms used by individuals with a are unique. if a does not require linking, the identity authority merely checks if the pseudonyms are correctly derived from the individual's master identity. if the checks pass, an anonymous credential certifying this fact is issued by the identity authority. all checks by the identity authority preserve individuals' anonymity. accountable anonymous credentials anonymity comes with a price in terms of accountability: individuals can misuse their credentials if they can never be identified and held responsible for their actions. trusted third parties can revoke the anonymity of misbehaving users to initiate punitive measures against them [ , , ] . one-time credentials and k-times anonymous authentication schemes [ , , ] also prevent overspending of limited-use credentials by revoking individuals' anonymity if they overspend. blacklisting misbehaving users for future access without revoking their anonymity is also feasible [ ] . linkability by a trusted authority linking across organisations may also be required for legitimate purposes, for example for legitimate data mining. also see examples in section . such linkability also seems to be an inevitable requirement to deter sharing of anonymous credentials among individuals [ ] . linkability by a trusted authority can be trivially achieved by individuals attaching a randomised encryption of a unique identifier against the trusted authority's public key for transactions requiring cross-linking. of course, appropriate mechanisms must exist to ensure that the trusted authority does not violate the legitimate purpose of linking. note that the anonymity of credentials is preserved only under the assumption that individuals interact with organisations through anonymous channels (e.g., in [ ] ). in particular, neither the communication network nor the data that individuals share with organisations should be usable to link their transactions (see section . . and . . ). anonymous networks, originally conceptualised as mix networks by chaum [ ] , are routing protocols that make messages hard-to-trace. mix networks consist of a series of proxy servers where each of them receives messages from multiple senders, shuffles them, and sends to the next proxy server. an onion-like encryption scheme allows each proxy server to only see an encrypted copy of the message (and the next hop in plaintext), thus providing untraceability to the sender even if only one proxy server honestly shuffles its incoming messages. anonymisation is the process of transforming a database such that individuals' data cannot be traced back to them. however, research in de-anonymisation has shown that anonymisation does not work in practice, as small number of data points about individuals coming from various sources, none uniquely identifying, can completely identify them when combined together [ ] . this is backed by theoretical results [ , ] which show that for high-dimensional data, anonymisation is not possible unless the amount of noise introduced is so large that it renders the database useless. there are several reports in literature of de-anonymisation attacks on anonymised social-network data [ , ] , location data [ ] , writing style [ ] , web browsing data [ ] , etc. in this setting, analysts interact with a remote server only through a restricted set of queries and the server responds with possibly noisy answers to them. dinur and nissim [ ] show that given a database with n rows, an adversary having no prior knowledge could make o(n polylog(n)) random subset-sum queries to reconstruct almost the entire database, unless the server perturbs its answers too much (by at least o( √ n)). this means that preventing inference attacks is impossible if the adversary is allowed to make arbitrary (small) number of queries. determining whether a given set of queries preserves privacy against such attacks is in general intractable (np-hard) [ ] . inferential privacy [ , ] is the notion that no information about an individual should be learnable with access to a database that could not be learnt without any such access. in a series of important results [ , , ] , it was established that such an absolute privacy goal is impossible to achieve if the adversary has access to arbitrary auxiliary information. more importantly, it was observed that individuals' inferential privacy is violated even when they do not participate in the database, because information about them could be leaked by correlated information of other participating individuals. in the wake of the above results, the notion of differential privacy was developed [ ] to allow analysts extract meaningful distributional information from statistical databases while minimising the additional privacy risk that each individual incurs by participating in the database. note that differential privacy is a considerably weaker notion than inferential privacy as reconstruction attacks described in section . . or other correlation attacks can infer a lot of non-identifying information from differentially private databases too. mechanisms for differential privacy add noise to the answers depending on the sensitivity of the query. in this sense, there is an inherent utility versus privacy tradeoff. differentially private mechanisms possess composability properties. thus, privacy degrades gracefully when multiple queries are made to differentially private databases. however, this alone may not protect against an attacker making an arbitrary number of queries. for example, the reconstruction attacks mentioned in section . . prevent many differentially private algorithms from answering a linear (in the number of rows) number of queries [ ] . for specific types of queries though, e.g., predicate queries, sophisticated noise-addition techniques [ ] can be used to maintain differential privacy while allowing for an exponential number of queries [ , ] . differentially private mechanisms also degrade gracefully with respect to group privacy as the group size increases. these guarantees may not be enough for policymakers who must protect the profile of specific communities constituting a sizable proportion of the population. the ability of an adversary to manipulate and influence a community even without explicitly identifying its members is deeply problematic, as demonstrated by episodes like cambridge analytica [ ] . therefore, the goal of modern private data analysis should not be limited to protecting only individual privacy, but also extend to protecting sensitive aggregate information. due to the inherently noisy nature of differentially private mechanisms, they are not suitable for any nonstatistical uses, e.g., financial transactions, electronic health records, and password management. privacy mechanisms for such use-cases must prevent misuse of data for malicious purposes such as illegal surveillance or manipulation, without hampering the legitimate workflows. the difficulties with differential privacy, and the impossibility of protection against inferential privacy violations, suggest that privacy protection demands that there should be no illegal access or processing in the first place. these check whether a given code-base uses personal data in accordance with a given privacy policy [ , , ] . privacy policies are expressed in known formal languages [ , ] . a compiler verifies, using standard information flow analysis [ ] and model-checking techniques [ ] , if a candidate program satisfies the intended privacy policy. in order to enforce various information flow constraints these techniques rely on manual and often tedious tagging of variables, functions and users with security classes and verify if information does not flow from items with high security classes to items with low security classes. these techniques define purpose hierarchies and specify purpose-based access-control mechanisms [ , , ] . however, they typically identify purpose with the role of the data requester and therefore offer weak protection from individuals claiming wrong purposes for their queries. jafari et al. [ ] formalise purpose as a relationship between actions in an action graph. hayati et al. [ ] express purpose as a security class (termed by them as a "principal") and verify that data collected for a given purpose does not flow to functions tagged with a different purpose. tschantz et al. [ ] state that purpose violation happens if an action is redundant in a plan that maximises the expected satisfaction of the allowed purpose. however, enforcement of these models still relies on fine-grained tagging of code blocks, making them tedious, and either a compiler-based verification or post-facto auditing, making them susceptible to insider attacks that bypass the checks. secure remote execution refers to the set of techniques wherein a client can outsource a computation to a remote party such that the remote party does not learn anything about the client's inputs or intermediate results. homomorphic encryption (he) schemes compute in the ciphertext space of encrypted data by relying on the additive or multiplicative homomorphism of the underlying encryption scheme [ , , ] . designing an encryption scheme that is both -which is required for universality -is challenging. gentry [ ] gave the first theoretical fully homomorphic encryption (fhe) scheme. even though state-of-the-art fhe schemes and implementations have considerably improved upon gentry's original scheme, the performance of these schemes is still far from any practical deployment [ ] . functional encryption (fe) [ ] schemes have similar objectives, with the crucial difference that fe schemes let the remote party learn the output of the computation, whereas fhe schemes compute encrypted output, which is decrypted by the client. secure multiparty computation (smc) -originally pioneered by yao through his garbled circuits technique [ ] -allows multiple parties to compute a function of their private inputs such that no party learns about others' private inputs, other than what the function's output reveals. smc requires clients to express the function to be computed as an encrypted circuit and send it to the server alongwith encrypted inputs; the server needs to evaluate the circuit by performing repeated decryptions of the encrypted gates. as a result, smc poses many challenges in its widespread adoption -ranging from the inefficiencies introduced by the circuit model itself to the decryption overhead for each gate evaluation, even as optimisations over the last two decades have considerably improved the performance and usability of smc [ ] . however, he, fe and smc based schemes involve significant application re-engineering and may offer reduced functionality in practice. in recent times, secure remote execution is increasingly being realised not through advances in cryptography but through advances in hardware-based security. this approach commoditises privacy-preserving computation, albeit at the expense of a weakened trust model, i.e., the increased trust on the hardware manufacturer. intel software guard extensions (sgx) [ ] implements access control in the cpu to provide confidentiality and integrity to the executing program. at the heart of the sgx architecture lies the notion of an isolated execution environment, called an enclave. an enclave resides in the memory space of an untrusted application process but access to the enclave memory and leakage from it are protected by the hardware. the following are the main properties of sgx: confidentiality information about an enclave execution can not leak outside the enclave memory except through explicit exit points. integrity information can not leak into the enclave to tamper with its execution except through explicit entry points. remote attestation for an enclave's execution to be trusted by a remote party, it needs to be convinced that a) the contents of the enclave memory at initialisation are as per its expectations, and b) that confidentiality and integrity guarantees will be enforced by the hardware throughout its execution. for this the hardware computes a measurement, essentially a hash of the contents of the enclave memory and possibly additional user data, signs it and sends it over to the remote party [ ] . the remote party verifies the signature and matches the enclave measurement with the measurement of a golden enclave it considers secure. if these checks pass, the remote party trusts the enclave and sends sensitive inputs to it. secure provisioning of keys and data sgx enclaves have secure access to hardware random number generators. therefore, they can generate a diffie-hellman public/private key pair and keep the private key secured within enclave memory. additionally, the generated public key can be included as part of additional user data in the hardware measurement sent to a remote verifier during remote attestation. these properties allow the remote verifier to establish a secure tls communication channel with the enclave over which any decryption keys or sensitive data can be sent. the receiving enclave can also seal the secrets once obtained for long-term use such that it can access them even across reboots, but other programs or enclaves cannot. sgx has been preceded by the trusted platform module (tpm) [ ] . tpm defines a hardware-based root of trust, which measures and attests the entire software stack, including the bios, the os and the applications, resulting in a huge trusted computing base (tcb) as compared to sgx whose tcb includes only the enclave code. arm trustzone [ ] partitions the system into a secure and an insecure world and controls interactions between the two. in this way, trustzone provides a single enclave, whereas sgx supports multiple enclaves. trustzone has penetrated the mobile world through arm-based android devices, whereas sgx is available for laptops, desktops and servers. sgx is known to be susceptible to serious side-channel attacks [ , , , ] . sanctum [ ] has been proposed as a simpler alternative that provides provable protection against memory access-pattern based software side-channel attacks. for a detailed review on hardware-based security, we refer the reader to [ ] . stateful secure remote execution requires a secure database and mechanisms that protect clients' privacy when they perform queries on them. the aim of these schemes is to let clients host their data encrypted in an untrusted server and still be able to execute queries on it with minimal privacy loss and maximal query expressiveness. one approach for enabling this is searchable encryption schemes, i.e., encryption schemes that allow searching over ciphertexts [ , ] . another approach is to add searchable indexes along with encrypted data, or to use special property-preserving encryptions to help with searching [ [ , ] is a useful primitive that provides read/write access to encrypted memory while hiding all access patterns, but these schemes require polylogarithmic number of rounds (in the size of the database) per read/write request. enclavedb [ ] has been recently proposed as a solution based on intel sgx. it hosts the entire database within secure enclave memory, with a secure checkpoint-based logging and recovery mechanism for durability, thus providing complete confidentiality and integrity from the untrusted server without any loss in query expressiveness. private information retrieval (pir) is concerned with hiding which database rows a given user query touches -thus protecting user intent -rather than encrypting the database itself. kushilevitz and ostrovsky [ ] demonstrated a pir scheme with communication complexity o(n ), for any > , using the hardness of the quadratic residuosity problem. since then, the field has grown considerably and modern pir schemes boast of o( ) communication complexity [ ] . symmetric pir (also known as oblivious transfer), i.e., the set of schemes where additionally users cannot learn anything beyond the row they requested, is also an active area of research. as is evident from the discussion in the previous section, none of the techniques by themselves are adequate for privacy protection. in particular, none are effective against determined insider attacks without regulatory oversight. hence we need an overarching architectural framework based on regulatory control over data minimisation, authorisation, access control and purpose limitation. in addition, since the privacy and fairness impacts of modern ai techniques [ ] are impossible to determine automatically, the regulatory scrutiny of data processing programs must have a best effort manual component. once approved, the architecture must prevent any alteration or purpose extension without regulatory checks. in what follows we present an operational architecture for privacy-by-design. we assume that all databases and the associated computing environments are under physical control of the data controllers, and the online regulator has no direct physical access to it. we also assume that the data controllers and the regulators do not collude. we illustrate our conceptual design through an example of a privacy-preserving electronic health record (ehr) system. ehrs can improve quality of healthcare significantly by providing improved access to patient records to doctors, epidemiologists and policymakers. however, the privacy concerns with them are many, ranging from the social and psychological harms caused by unwanted exposure of individuals' sensitive medical information, to direct and indirect economic harms caused by the linkage of their medical data with data figure : an illustration of the architecture of trusted executables using an example involving an ehr database, a patient, an mri imaging station, a doctor and a data analysis station. tes marked "approved by r" are preaudited and pre-approved by the regulator r. er(·) represents a regulator-controlled encryption function and acr represents online access control by regulator r. dti(x) represent various data types parametrised by the patient x (as explained in the right-hand side table). in particular, v irtualhospitalid(x) represents the hospital-specific virtual identity of the patient. the regulator checks the consents, approvals and other static rules regarding data transfer at each stage of online access control. presented to their employers, insurance companies or social security agencies. building effective ehrs while minimising privacy risks is a long standing design challenge. we propose trusted executables (te) as the fundamental building blocks for privacy-by-design. we introduce them in the abstract, and discuss some possibilities for their actual realisation in section . tes are dataprocessing programs, with explicit input and output channels, that are designed by the data controllers but are examined, audited, and approved by appropriate regulators. tes execute in controlled environments on predetermined data types with prior privacy risk assessment, under online regulatory access control. the environment ensures that only approved tes can operate on data items. in particular, all data accesses from the databases, and all data/digest outputs for human consumption, can only happen through the tes. we prescribe the following main properties of the tes: . runtime environment: tes are approved by regulators. they execute in the physical infrastructure of the data controllers but cannot be modified by them. . authentication: a regulator can authenticate related tes during runtime, and verify that indeed the approved versions are running. integrity: there is no way for a malicious human or machine agent, or even for the data controller, to tamper with the execution of a te other than by sending data through the te's explicit input channels. there is no way for any entity to learn anything about the execution of a te other than by reading data written at the te's explicit output channels. all data accesses and output can only happen through tes. besides, all tes should be publicly available for scrutiny. the above properties allow a regulator to ensure that a te is untampered and will conform to the limited purpose identified at the approval stage. as depicted in figure , a data agent -for example, a hospital -interacts with databases or users only through pre-approved tes, and direct accesses are prevented. all data stores and communication messages are encrypted using a regulator-controlled encryption scheme to prevent any information leakage in transit or storage. the data can be decrypted only inside the tes under regulated access control. the regulator provisions decryption keys securely to the te to enable decryption after access is granted. the regulator allows or denies of the patient and the doctor, respectively. σx (·) represents digital signature by patient x . autht e (·) represents authentication information of the te and authdt (·) represents authentication information of the supplied data's type. individuals are authenticated by verifying their virtual identities. access, online, based on the authentication of the te and the incoming data type, consent and approval checks as required, and the credential authentication of any human consumers of output data (e.g., the doctor(s) and data analysts). all sink tes -i.e., those that output data directly for consumption by a human agent -are pre-audited to employ appropriate data minimisation before sending data to their output channels. note that extending the te architecture to the doctors' terminals and the imaging stations ensures that the data never crosses the regulated boundary and thus enables purpose limitation. in the above example an independent identity authority issues credentials and engages in a three-way communication to authenticate individuals who present their virtual identities to the regulator. an individual can use a master health id to generate hospital-specific or doctor-specific unlinkable anonymous credentials. only a health authority may be allowed to link identities across hospitals and doctors in a purpose-limited way under regulated access control. we depict the regulatory architecture in figure . the first obligation of the regulator is to audit and approve the tes designed by the data controllers. during this process, the regulator must assess the legality of the data access and processing requirements of each te, along with the privacy risk assessment of its input and output data types. in case a te is an ai based data analytics program, it is also an obligation of the regulator to assess its fairness and the potential risks of discrimination [ ] . before approving a te, the regulator also needs to verify that the te invokes a callback to the regulator's online interface before accessing a data item and supplies appropriate authentication information, and that it employs appropriate encryption and data minimisation mechanisms at its output channels. finally, the regulator needs to put in place a mechanism to be able to authenticate the te in the data controller's runtime environment. the second obligation of the regulator is to play an online role in authorising data accesses by the tes. the authorisation architecture has both a static and a dynamic component. the static authorisation rules typically capture the relatively stable regulatory requirements, and the dynamic component typically captures the fast-changing online context, mainly due to consents and approvals. specifically, each static authorisation rule takes the form of a set of pre-conditions necessary to grant access to a te the data of a given type; and, in case of sink tes, to output it to a requester. the design of these rules is governed by regulatory requirements and the privacy risk assessment of tes and data types. the rules are typically parametric in nature, allowing specification of constraints that provide access to a requester only if the requester can demonstrate some specific relationship with the data individual (e.g., to express that only a doctor consulted by a patient can access her data). the pre-conditions of the authorisation rules may be based on consent of data individuals, approvals by authorities or even other dynamic constraints (e.g., time-bound permissions). the consent architecture must be responsible for verifying signatures on standardised consent apis from consent givers and recording them as logical consent predicates. the regulator, when designing its authorisation rules, may use a simple consentfor example, that a patient has wilfully consulted a doctor -to invoke a set of rules to protect the individual's privacy under a legal framework, rather than requiring individuals to self-manage their privacy. similar to the consent architecture, the approval architecture for data access must record standardised approvals from authorities as logical approval predicates. an approval from an authority may also be provided to an individual instead of directly to the regulator, as a blind signature against a virtual identity of the individual known to the approver, which should be transformed by the individual to a signature against the virtual identity known to the data controller and the regulator. this, for example, may enable a patient to present a self generated virtual identity to a doctor or a hospital instead of her universal health id. the regulator also requires an authentication architecture. first, it needs to authenticate individuals, i.e., consent givers, approvers and data requesters, by engaging in a three-way communication with an identity authority which may be external to both the data controller and the regulator. second, it needs to authenticate tes in order to be able identify the access requests as originating from one of the pre-approved tes. third, it needs to authenticate data types, i.e., identify the underlying type of the te's encrypted input data. the consent/approval predicates and the authentication information flow to the dynamic authorisation module, which can instantiate the static authorisation rules with the obtained contextual information to determine, in an online fashion, if access should be allowed to the requesting te. if yes, then it must also provision decryption keys to the te securely such that only the te can decrypt. the keys can be securely provisioned to the te because of the authentication, integrity and confidentiality properties, and by the fact that approved tes must never output the obtained decryption keys. an example control-flow diagram depicting the regulatory access control in a scenario where a doctor is trying to access the data of a patient who consulted them is shown in figure . several existing techniques can be useful for the proposed architecture, though some techniques may need strengthening. trusted executables can be implemented most directly on top of trusted hardware primitives such as intel sgx or arm trustzone where authentication of tes is carried out by remote attestation. secure provisioning of keys and data to tes can be done in case of intel sgx as per section . . . however, since sgx includes only the cpu in its tcb, it presents challenges in porting ai applications that run on gpus for efficiency. graviton [ ] has been recently proposed as an efficient hardware architecture for trusted execution environments on gpus. in our architecture, tes fetch or update information from encrypted databases. this may be implemented using special indexing data structures, or may involve search over encrypted data, where the tes act as clients and the database storage acts as the server. accordingly, techniques from section . can be used. since the tes never output data to agents unless deemed legitimate by the regulator, the inferential attacks identified with these schemes in section . have minimal impact. for added security, enclavedb [ ] , which keeps the entire database in secure enclave memory, can be used. enclavedb has been evaluated on standard database benchmarks tpc-c [ ] and tatp [ ] with promising results. for authentication of data types messages may be encrypted using an id-based encryption scheme, where the concrete runtime type of the message acts as the textual id and the regulator acts as the trusted third party (see section . . ). the receiver te can send the expected plaintext type to the regulator as part of its access request. the regulator should provision the decryption key for the id representing the requested type only if the receiver te is authorised to receive it as per the dynamic authorisation check. note that authentication of the received data type is implicit here, as a te sending a different data type in its access request can still not decrypt the incoming data. data minimisation for consents and approvals based on virtual identities is well-established from chaum's original works [ , ] . individuals should use their purpose-specific virtual identities with organisations, as opposed to a unique master identity. to prevent cross-linking of identities, anonymous credentials may be used. in some cases, individuals' different virtual identities may need to be linked by a central authority to facilitate data analytics or inter-organisation transactions. this should be done under strict regulatory access control and purpose limitation. modern type systems can conveniently express the complex parametric constraints in the rules in the authorisation architecture. efficient type-checkers and logic engines exist that could perform the dynamic authorisation checks. approval of tes needs to be largely manual as the regulator needs to evaluate the legitimacy and privacy risks associated with the proposed data collection and processing activity. however, techniques from program analysis may help with specific algorithmic tasks, such as checking if the submitted programs adhere to the structural requirement of encrypting data items with the right type at their outgoing channels. we require the regulatory boundary to be extended even to agent machines, which must also run tes so that data they obtain is not repurposed for something else. however, when a te at an authorised agent's machine outputs data, it could be intercepted by malicious programs on the agent's machine leading to purpose violation. solutions from the drm literature may be used to prevent this. in particular, approaches that directly encrypt data for display devices may be useful [ ] . we note that this still does not protect the receiving agent from using more sophisticated mechanisms to copy data (e.g., by recording the display using an external device). however, violations of this kind are largely manual in nature and ill-suited for large-scale automated attacks. finally, we need internal processes at the regulatory authority itself to ensure that its actual operational code protects the various decryption keys and provides access to tes as per the approved policies. to this end, the regulator code may itself be put under a te and authenticated by the regulatory authority using remote attestation. once authenticated, a master secret key may be provisioned to it using which the rest of the cryptosystem may bootstrap. in this section, we present two additional case studies to showcase the applicability of our architecture in diverse real-world scenarios. direct benefit transfer (dbt) [ ] is a government of india scheme to transfer subsidies to citizens' bank accounts under various welfare schemes. its primary objective is to bring transparency and reduce leakages in public fund disbursal. the scheme design is based on india's online national digital identity system aadhaar [ ] . all dbt recipients have their aadhaar ids linked to their bank accounts to receive benefits. figure shows a simplified schematic of the scheme that exists today [ ] . a ministry official initiates payment by generating a payment file detailing the aadhaar ids of the dbt recipients, the welfare schemes under which payments are being made and the amounts to be transferred. the payment file is then signed and sent to a centralised platform called the public financial management system (pfms). pfms hosts the details of various dbt schemes and is thus able to initiate an inter-bank fund transfer from the bank account of the sponsoring scheme to the bank account of the beneficiary, via the centralised payments facilitator npci (national payments corporation of india). npci maintains a mapping of citizen's aadhaar ids to the banks hosting their dbt accounts. this mapping allows npci to route the payment request for a given aadhaar id to the right beneficiary bank. the beneficiary bank internally maintains a mapping of its customers' aadhaar ids to their bank account details, and is thus able to transfer money to the right account. as dbt payments are primarily directed towards people who need benefits, precisely because they are structurally disadvantaged, their dbt status must be protected from future employers, law enforcement, financial providers etc., to mitigate discrimination and other socio-economic harms coming their way. further, since dbt relies on the recipients' national aadhaar ids, which are typically linked with various other databases, any leakage of this information makes them directly vulnerable. indeed, there are reports that bank and address details of millions of dbt recipients were leaked online [ ] ; in some cases this information was misused to even redirect dbt payments to unauthorised bank accounts [ ] . we illustrate our approach for a privacy-preserving dbt in figure . in our proposal, dbt recipients use a virtual identity for dbt that is completely unlinkable to the virtual identity they use for their bank account. they may generate these virtual identities -using suitably designed simple and intuitive interfaces -by an anonymous credential scheme where the credentials are issued by a centralised identity authority. additionally, they provide the mapping of the two virtual identities, along with the bank name, to the ncpi mapper. this information is provided encrypted under the control of the financial regulator r such that only the npci mapper te can access it under r 's online access control. this mechanism allows the npci mapper to convert payment requests against dbt-specific identities to the target bank-specific identities, while maintaining the mapping private from all agents. regulator-controlled encryption of data in transit and storage and the properties of tes allow for an overall privacy-preserving dbt pipeline. note that data flow is controlled by different regulators along the dbt pipeline, providing a distributed approach to privacy protection. pfms is controlled by a dbt regulator; npci mapper is controlled by a financial regulator, and the sponsor and beneficiary banks are controlled by their respective internal regulators. there have been a plethora of attempts recently from all over the world towards electronic app-based contact tracing for covid- using a combination of gps and bluetooth [ , , , , , , , , ] . (a) collecting spatiotemporal information. a and b come in contact via ble, as denoted by the dotted arrows. c does not come in contact with a or b via ble but is spatially close within a time window, as per gps data. vidx represents the virtual identity of agent x; locx i represents x's i-th recorded location; timex i represents its i-th recorded time. tx i represents i-th token generated by x; rx i represents i-th receipt obtained by x; σx () represents signing by x. dashed arrows represent one-time registration steps (illustrated only for c). (b) tracing the contacts of infected individuals. a gets infected, as certified by the doctor's signature σ doc on a's virtual identity vida and medical report reporta. ds and dt respectively represent chosen spatial and temporal distance functions and and δ the corresponding thresholds, as per the disease characteristics. ∆ represents the infection window, the time during which a might have remained infectious. timenow represents the time when the query was executed. even keeping aside the issue of their effectiveness, some serious privacy concerns have been raised about such apps. in most of these apps the smartphones exchange anonymous tokens when they are in proximity, and each phone keeps a record of the sent and received tokens. when an individual is infected -signalled either through a self declaration or a testing process -the tokens are uploaded to a central service. there are broadly two approaches to contact tracing: . those involving a trusted central authority that can decrypt the tokens and, in turn, alert individuals and other authorities about potential infection risks [ , , , ] . some of these apps take special care to not upload any information about individuals who are not infected. . those that assume that the central authority is untrusted and use privacy preserving computations on user phones to alert individuals about their potential risks of infection [ , , , , ] . the central service just facilitates access to anonymised sent tokens of infected individuals and cannot itself determine the infection status of anybody. the following are the main privacy attacks on contact tracing apps: ) individuals learning about other individuals as high-risk spreaders, ) insiders at the central service learning about individuals classified as high risk, ) exposure of social graphs of individuals, and ) malicious claims by individuals forcing quarantine on others. see [ ] for a vulnerability analysis of some popular approaches. the centralised approaches clearly suffer from many of the above privacy risks. while alerting local authorities about infection risks is clearly more effective from a public health perspective, to enable them to identify hotspots and make crucial policy decisions, it is mainly the privacy concerns that sometimes motivate the second approach. also, it is well known that location data of individuals can be used to orchestrate de-anonymisation attacks [ ] , and hence many of the above approaches adopt the policy of not using geolocation data for contact tracing despite their obvious usefulness at least in identifying hotspots. in addition, bluetooth based proximity sensing -which are isolated communication events over narrow temporal windows between two smartphonesis ineffective for risk assessment of indirect transmission through contaminated surfaces, where the virus can survive for long hours or even days. such risk assessment will require computation of intersection of space-time volumes of trajectories which will be difficult in a decentralised approach. it appears that the privacy considerations have forced many of these approaches to adopt overly defensive decentralised designs at the cost of effectiveness. in contrast, we propose an architecture where governments can collect fine-grained location and proximity data of citizens, but under regulated access control and purpose limitation. such a design can support both shortrange peer-to-peer communication technologies such as ble and gps based location tracking. additionally, centralised computing can support space-time intersections. in figure , we show the design of a state-mandated contact-tracing app that, in addition to protecting against the privacy attacks outlined earlier, can also protect against attacks by individuals who may maliciously try to pose as low-risk on the app, for example to get around restrictions (attack ). as before, we require all storage and transit data to be encrypted under a regulator-controlled encryption scheme, and that they be accessible only to pre-approved tes. we also require the app to be running as a te on the users' phones (e.g., within a trusted zone on the phone). we assume that everyone registers with the app using a phone number and a virtual identity unlinkable to their other identities. periodically, say after every few minutes, each device records its current gps location and time. the tuple made up of the registered virtual identity and the recorded location and time is signed by the device and encrypted controlled by the regulator, thus creating an ephemeral "token" to be shared with other nearby devices over ble. when a token is received from another device, a tuple containing the virtual identity of self and the incoming token is created, signed and stored in a regulator-controlled encrypted form, thus creating a "receipt". periodically, once every few hours, all locally stored tokens and receipts are uploaded to a centralised server te, which stores them under regulated access control as a mapping between registered virtual identities and all their spatiotemporal coordinates. for all the receipts, the centralised server te stores the same location and time for the receiving virtual identity as in the token it received, thus modelling the close proximity of ble contacts. when a person tests positive, they present their virtual identity to a medical personnel who uploads a signed report certifying the person's infection status to the centralised server te. this event allows the centralised server te to fetch all the virtual identities whose recorded spatiotemporal coordinates intersects within a certain threshold, as determined by the disease parameters, with the infected person's coordinates. as the recorded (location, time) tuples of any two individuals who come in contact via ble necessarily collide in our approach, the virtual identities of all ble contacts can be identified with high precision. moreover, virtual identities of individuals who did not come under contact via ble but were spatially nearby in a time window as per gps data are also identified. a notifier te securely obtains the registered phone numbers corresponding to these virtual identities from the centralised server te and sends suitably minimised notifications to them, and also perhaps to the local administration according to local regulations. the collected location data can also be used independently by epidemiologists and policy makers in aggregate form to help them understand the infection pathways and identify areas which need more resources. note that attack is protected by the encryption of all sent tokens; attacks and are protected by the properties of tes and regulatory access control; attack is protected by devices signing their correct spatiotemporal coordinates against their virtual identity before sending tokens or receipts. attack is mitigated by requiring the app to run within a trusted zone on users' devices, to prevent individuals from not sending tokens and receipts periodically or sending junk data. we have presented the design sketch of an operational architecture for privacy-by-design [ ] based on regulatory oversight, regulated access control, purpose limitation and data minimisation. we have established the need for such an architecture by highlighting limitations in existing approaches and some public service application designs. we have demonstrated its usefulness with some case studies. while we have explored the feasibility of our architecture based on existing techniques in computer science, some of them will definitely require further strengthening. there also needs to be detailed performance and usability evaluations, especially in the context of large-scale database and ai applications. techniques to help a regulator assess the privacy risks of tes also need to be investigated. these are interesting open problems that need to be solved to create practical systems for the future with built-in end-to-end 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operating procedure (sop) modules for direct benefit transfer (dbt) information security practices of aadhaar (or lack thereof): a documentation of public availability of aadhaar numbers with sensitive personal financial information aadhaar mess: how airtel pulled off its rs crore magic trick china's high-tech battle against covid- coronavirus: south koreas success in controlling disease is due to its acceptance of surveillance tracetogether app government of india apps gone rogue: maintaining personal privacy in an epidemic anonymous collocation discovery: harnessing privacy to tame the coronavirus epione: lightweight contact tracing with strong privacy privacy-preserving contact tracing the pact protocol specification key: cord- -us llnva authors: gonçalves, judite; martins, pedro s. title: effects of self-employment on hospitalizations: instrumental variables analysis of social security data date: - - journal: small bus econ doi: . /s - - -w sha: doc_id: cord_uid: us llnva the importance of self-employment and small businesses raises questions about their health effects and public policy implications, which can only be addressed with suitable data. we explore the relationship between self-employment and health by drawing on comprehensive longitudinal administrative data to explore variation in individual work status and by applying novel instrumental variables. we focus on an objective outcome—hospital admissions—that is not subject to recall or other biases that may affect previous studies. our main findings, based on a sample of about , individuals followed monthly from to and who switch between self-employment and wage work along that period, suggest that self-employment has a positive effect on health as it reduces the likelihood of hospital admission by at least half. the self-employed represent nearly % of employment in the european union (eurostat ) . moreover, as much as % of the adult population of the eu has used online platforms for the provision of labor services at some point in their lives (pesole et al. ) . the ongoing growth of the "platform" economy contributes to the expansion of the proportion of self-employed, especially among younger workers, and raises a number of public policy questions regarding, for example, occupational health and safety risks, social protection, and representation (european commission ; garben ; ilo ) . indeed, platform economy jobs-and self-employment more generally as well as some types of small businessesare characterized by more flexible work formats, distinct from formal employer-employee relationships framed by employment law, and typically have more limited access to social protection. in the current context of such novel forms of selfemployment, one important issue concerns the impact of self-employment on workers' health-the subject of this study. occupational characteristics, namely job control and job demand, vary significantly between self-employment and wage work. job control stands for decision authority, e.g., the freedom to decide what work to do, when and at what pace, which reduces work-related stress. job demand, on the other hand, represents sources of stress at work, such as being assigned a considerable amount of work and/or having little time to carry out specific tasks. this job demand-job control framework, proposed by karasek ( ) , karasek and theorell ( ) , and theorell and karasek ( ) , suggests that compared with wage work, self-employment is associated with both higher job control and higher job demand, an interaction termed 'job strain' in the literature (prottas and thompson ; stephan and roesler ). in fact, self-employed individuals are not subject to orders from other workers higher up the organizational hierarchy, so they have more decision authority and potentially lower work-related stress. research also shows that the self-employed are more satisfied with their jobs than wage workers because they can be creative and have more autonomy. in other words, the self-employed may often be able to derive utility from the way outcomes are achieved, a process sometimes referred to as 'procedural utility' (benz and frey ; schneck ) . however, when self-employed, labor income and assets directly hinge on one's ability to work and work effort in each period. in addition, greater exposure to unanticipated demand shocks leaves selfemployed individuals subject to more volatile workload and income flows. social support at work may note that the covid- crisis and its aftermath may contribute to the growth of self-employment, as wage employment opportunities in the labor market will decrease. additionally, the covid- crisis may lead to a larger share of wage employment conducted under remote work formats given their social/physical distancing properties. such remote work formats are typically more common among the self-employed, which may lead to some blurring of the differentiation between wage work and self-employment. see, e.g., ingre ( ) for a discussion of the job strain model with respect to the appropriateness of the interaction between the job demand and job control dimensions in karasek's model. also be more limited given the smaller number of co-workers around (blanch ( ) , discusses the demand-control-support model). all these variables represent sources of stress. given these two opposite mechanisms-higher job demand and higher job control-it is unclear whether we should expect selfemployed individuals to suffer from more or less work-related stress, compared with wage workers. the medical literature identifies stress as an important cause of disease, e.g., cardiovascular problems and digestive disorders (mayer ; steptoe and kivimäki ) . overall, stress impacts negatively on health and well-being, and in addition to increasing incidence of disease, it may increase absence from work due to sickness and use of health care services (e.g., browning and heinesen ; halpern ; holmgren et al. ). bloemen et al. ( ) also find that the probable mechanism driving the effect of job loss on mortality is stress, through acute diseases of the circulatory system. stress is also associated with unhealthy behavior, such as smoking and drinking. the typical occupations of self-employed and wage workers may differ in terms of risk of workplace accidents and other occupational hazards. at the same time, in many countries self-employment is subject to little or no social protection, in terms of coverage by occupational safety regulation, social security, employment law, or collective bargaining, potentially representing additional negative implications for health. on the other hand, the greater flexibility regarding regulation may also represent additional work opportunities compared with wage work. overall, whether self-employment has a positive or detrimental effect on health is a public policy question that can only be answered with empirical evidence of a causal nature. there are two main empirical challenges to the identification of a causal effect of self-employment on health: reverse causality and individual unobserved heterogeneity (torrès and thurik ) . reverse causality has to do with the possibility that individuals become self-employed or wage workers at least partly for health-related reasons. on the one hand, self-employment may attract individuals that are healthier on average because healthier individuals tend to be more able to focus on business opportunities or may have easier access to financing (e.g., gielnik et al. ). additionally, income when self-employed tends to be more closely linked to one's ability to work than when a wage worker, and access to sickness benefits is harder for the self-employed. all these factors suggest a positive (self-)selection of the healthy into self-employment. on the other hand, health problems may constitute a barrier to finding a wage job, particularly if they are visible to the employer, and push individuals who are less healthy into self-employment (e.g., zissimopoulos and karoly ) . furthermore, several individual traits that are difficult to measure may be related to both health and selfemployment decisions (bujacz et al. ) . examples include optimism, perseverance, resilience, risk aversion, as well as genetics. some individuals who are attracted to and persist in self-employment may also have higher capacity to tolerate and manage stress, and may therefore experience lower stress (baron et al. ) . this capacity to deal with stressful factors is another example of an individual characteristic related to both health and type of employment. earlier life circumstances such as childhood health also influence adult health and type of employment (case et al. ; case and paxson ) . taken together, these traits and earlier circumstances mean that self-employed individuals and wage workers may have different health profiles along dimensions not observable in the data. the empirical literature on self-employment and health is growing but still scarce. most of it is plagued by the endogeneity issues mentioned above, which are difficult to tackle without longitudinal data. a recent study finds significantly lower work-related stress among self-employed individuals without employees compared with wage workers, using longitudinal data from australia and controlling for individual fixed effects (hessels et al. ) . previous studies on selfemployment and stress provide contradictory findings, but most of them are based on cross-sectional data and use descriptive methods (see hessels et al. ( ) , table , for a review). in the study by rietveld et al. ( ) , selfemployed individuals appear healthier than wage workers. however, while the positive association between self-employment and health holds when the authors control for reverse causality, it vanishes when they control for individual unobserved heterogeneity. this finding suggests a positive selection of the healthy into self-employment. that study considers subjective health measures, including self-reported number of conditions, overall health, and mental health. it uses longitudinal survey data representative of the population + in the usa. the results may therefore not be generalizable to a broader workingage population. another study by yoon and bernell ( ) relies on cross-sectional survey data representative of the adult population in the usa and adopts an instrumental variable approach. the authors find that selfemployment has a positive impact on several health indicators, namely the absence of chronic conditions such as hypertension and diabetes. they find no effects on other health outcomes, including perceived physical health and mental health. nikolova ( ) , using german longitudinal survey data and a difference-in-differences strategy, finds that switching from wage work to self-employment leads to both physical and mental health gains. considering more objective indicators and administrative data, a five-year follow-up study of the total working population in sweden finds that selfemployed individuals who own limited liability companies (but not sole proprietors) have lower average risk of mortality than wage workers (toivanen et al. ) . similarly, toivanen et al. ( ) find that limited liability company owners have lower rates of hospitalization for myocardial infarction than wage workers, and no different hospitalization rates for stroke. the authors unveil relevant heterogeneous effects not only by enterprise legal type of self-employed individuals but also by industry. overall, there is little robust evidence on the causal effect of self-employment on health. most of the literature does not take endogeneity into account, as longitudinal data or instrumental variables are seldom available. furthermore, it is important to distinguish the effect that is due to differences in the intrinsic characteristics of self-employment and wage work, namely job control and job demand, from institutional factors such as different access to social security benefits. this may be difficult with survey data and selfreported health indicators. separating-out the effect that is due to differences in the typical occupations of self-employed and wage workers, which are associated with different exposure to occupational hazards, would also be of interest. the main research question in this study is "what is the impact of self-employment on the likelihood of hospital admission?" we answer this question based on a large sample of administrative social security records representative of the working-age population in portugal, that includes almost , self-employed and wage workers followed between january and december . we focus on a subsample of about , individuals who switch between self-employment and wage work along that -month period. we contribute to the literature in several ways. first, we tackle explicitly the endogeneity of the decision to become self-employed by controlling for individual fixed effects and employing instrumental variables. second, looking at hospitalizations allows us to separate-out institutional factors, because access to hospital care and social security benefits when hospitalized are unrelated with type of employment, and most hospitalizations correspond to unplanned or unavoidable acute events. administrative records of hospital admissions are also comparable across individuals and time periods and not subject to recall bias, an advantage over self-reported indicators in survey data. third, to explore to which extent the effect may be due to differences in the typical occupations of self-employed and wage workers, we look at diagnoses underlying hospitalizations. fourth, we consider the whole working population regardless of age, and explore potentially heterogeneous effects across demographic subgroups. lastly, we also investigate the effects of self-employment on the length of hospitalization and mortality. hospital admissions are also a relevant outcome for policy. they represent roughly % of health expenditure in portugal. a significant % of sickness leave episodes correspond to hospital admissions (own calculations for the years - ). in , sickness leave episodes cost social security million euros; % of that represents almost million euros. this adds to the costs for the health system and other societal costs more difficult to quantify, including productivity and well-being losses. the remaining of this paper is as follows: the next section lays down the background for the study, section presents our data and empirical strategy, section presents the results, and in section we discuss our findings. in , about % of employment in portugal corresponded to self-employment or own-account workers. more than one-fourth of those had employees. the proportion of own-account workers differs across groups. it is lower in the capital region than in other regions, among women, among younger age groups, and among more educated groups. by industry, we find the largest proportions of own-account workers in agriculture and other primary sector activities ( . %), real estate ( %), consulting, scientific, and technical activities ( . %), construction ( . %), retail ( . %), hospitality services ( . %), and artistic and sports activities ( . %). from the "self-employment" module of the labor force survey (lfs), conducted in the second quarter of , we also know that more than % of own-account workers decide their work schedule. they also report much higher autonomy over their tasks than wage workers. this is in line with the hypothesis of higher job control. while only less than % of own-account workers report no difficulties with their work over the previous months, % report periods without work, and % claim that clients do not pay or pay late. this may suggest that the self-employed are subject to higher job demand. own-account workers report lower levels of satisfaction at work than wage workers, although this is driven by the low satisfaction levels of those who have employees. virtually no ownaccount workers report that they would prefer to be wage workers (torres and raposo ) . in this study, we adopt the portuguese social security definition of self-employment or "independent workers" (trabalhadores independentes), which does not include own-account workers with employees. family and informal workers, which are captured in the lfs, do not appear in our data, as they do not pay social security contributions. this explains the lower proportion of self-employment in our data, described below, compared with the proportion of own-account workers in the lfs. for example, agriculture and other primary sector activities, which have by far the largest proportion of own-account workers in the lfs, will have limited expression in our data for those reasons. in portugal, statutory sick leave covers both the self-employed and wage workers. as in many european countries, to deter moral hazard, wage workers face a three-day gap from the onset of a sickness episode until a sickness benefit starts to be paid (i.e., waiting or "elimination" period). however, for the self-employed, this waiting period is much longer, at thirty days (ten days from onwards). due to the different waiting periods, social security records include sickness episodes that last four days or more in the case of wage workers, but at least thirtyone days in the case of the self-employed. the first three/thirty days are not eligible for sickness benefits. thus, all other things equal, the sickness spells of the self-employed that are administratively recorded are, on average, much more selected and severe. these different waiting periods can entail different incentives for wage workers and self-employed individuals. wage workers face much lower opportunity costs from reporting sick to work, i.e., fewer days without income. in some cases, collective bargaining provisions, determined by unions and firms or employer associations, may even lead to the payment (by the firms) of the first three days of absence as well. as these provisions apply to wage workers but not to the self-employed, the former may engage more often in moral hazard: "cheat" by going on sick leave when they are not really sick. in stark contrast, there is no waiting period for either self-employed or wage workers in the case of hospitalization. furthermore, benefits are the same for both types of workers. besides, due to the specific, acute nature of hospitalizations, these are less likely to be timed deliberately by individuals and therefore less likely to be artificial episodes of sickness. in sum, compared with standard-i.e., non-hospitalizationsickness episodes, hospitalizations are a significantly more objective outcome and hospital admissions should be strictly comparable between wage workers and self-employed individuals. as to the amount of the support, for nearly the entire period under analysis here (sep -dec ), the replacement rate of the portuguese sickness benefit was equal to % of forgone wages for the first days of sick leave, % from the st to the th day, and % from the th day onwards. during the first eight months of , the replacement rate was % of forgone wages for the first days of sick leave, and % from the st to the th day. sickness benefits are granted for a maximum of days for wage workers and days for self-employed individuals (law-decrees / (law-decrees / , / (law-decrees / and / . the portuguese national health service, financed through taxes, provides general and universal coverage and is almost free at the point of use. in portugal, secondary and tertiary care (both acute and post-acute care) is mainly provided in hospitals. general practitioners act as gatekeepers in access to hospital care in the public sector; otherwise, people can be admitted through the emergency department. private voluntary health insurance may speed up access to elective hospital treatment and ambulatory consultations, but it has very limited expression in portugal (< %) and is not associated with type of work (i.e., self-employment or wage work). some public and private subsystems provide care to specific groups not relevant for this study (public servants, military, banking sector workers). in general, access to hospital care in portugal should be identical for both self-employed and wage workers. the only concern is that self-employed individuals may delay care in order not to lose business, as their income is closely tied to them actually working. (wage workers could also delay care in order to maintain a good reputation with their employer.) because we are looking at hospitalizations, which are generally acute, untimed events, this concern is limited. nonemergency acute interventions are scheduled by the hospital, and because waiting lists are usually long, it is unlikely that individuals pass on the opportunity to receive the care they need when hospitals schedule them, as it may be a long time before a new opportunity arises. we use data from the portuguese social security information system, made available by the instituto de informática public agency. the dataset is a random sample such that included individuals represent both a) at least % of all individuals who pay social security contributions and b) at least % of all individuals who receive sickness, maternity, or other benefits from social security, stratified by region and gender. we observe individuals on a monthly basis, from january to december . we use information on whether they are wage workers or self-employed, as well as whether they receive sickness benefits in a specific month due to hospitalization. the data allow us to distinguish sickness benefits due to hospitalization from sickness benefits due to standard (nonacute) sickness spells, as the two cases are treated differently by social security (see section ). the dataset also includes information on the individuals' gender, age, nationality, place of residence, and income from work, but not their industry or occupation. we drop individuals below and above years old (mandatory schooling age and statutory retirement age). after deleting also observations with missing information on the key variables, we are left with almost , individuals, of which about , are self-employed at some point over the period - . in our main analyses, we focus on more than , individuals who switch at least once between self-employment and wage work over that period (which we refer to as 'switchers'). over the -monthlong period, there are more than , individualmonth observations when considering only switchers (almost million individual-month observations in the full sample). to determine the effect of self-employment on the likelihood of hospitalization, we estimate four different specifications of a linear probability model like the following: the binary dependent variable, hosp i,t , indicates whether individual i is hospitalized in month t or not. the variable of main interest is the one-month lag of the self-employment indicator, self-employed i,t− , which takes value one if individual i is self-employed in month t − . we opt for the linear probability model given the computational difficulties associated with applying instrumental variables methods to nonlinear panel data models, especially when various large vectors of fixed effects are included. to investigate if the chosen functional form is appropriate, we estimated the logit/panel logit versions of models and (i.e., with or without individual fixed effects), which provided marginal effects similar to the ones obtained with the linear versions. some individuals who receive income from both selfemployment and wage work in some months are counted as self-employed. excluding these observations provides almost identical results. using the one-month lag of the self-employment indicator, or all lags up to the third or the twelfth, for example, gives estimated total effects of selfemployment with the same sign and level of statistical significance, differing only slightly in magnitude. this shows the stability of the self-employment indicator, as individuals rarely change type of work more than once over the seven-year period considered. we are interested in the overall effect of self-employment and not in the time dynamics. that overall effect can be captured by any single lag, given the high correlation between adjacent lags. furthermore, using more than one lag would result in many more observations being lost. in conclusion, β gives the effect of being self-employed, as opposed to being a wage worker, on the likelihood of being hospitalized in the following month. the four specifications that we consider are the following: model controls for the individual's gender, age group ( - , - , - , - , or - ) , nationality (portuguese or foreign), and place of residence (one of the districts in the mainland or one of the islands), included in x i,t . we also include fixed effects for each month in the sample, denoted by τ t ( months minus jan , due to the lag, and feb , which is the reference month). model takes advantage of the longitudinal nature of the dataset and includes also individual fixed effects, denoted by μ i , to control for time-invariant individual unobserved heterogeneity. still, it is possible that endogeneity due to unobserved individual characteristics that vary over time remains, as discussed in the introduction. to tackle this potential threat, in addition to the individual fixed effects, we employ an instrumental variable strategy. thus, model applies instrumental variables without controlling for individual fixed effects (i.e., instrumental variable estimation of model ), and model applies instrumental variables controlling for individual fixed effects (i.e., instrumental variable estimation of model ). in sum, models and treat the data as pooled cross-sections, whereas models and are fixed effects panel data models; models and apply an instrumental variable strategy. we use two instruments. instrument one is the proportion of self-employed workers in individual i's district, excluding her municipality of residence, in the same month (see online resource for the division of the portuguese territory into districts and municipalities). instrument two is the proportion of selfemployed workers of the same gender and age group of individual i in the whole country, also excluding her municipality of residence, in the same month. the proportion of workers in a given district or gender-age group who are self-employed captures the structure of the labor market in that area or demographic group. for example, there may be a predominant industry in a given district that relies on wage workers, or there may be a new service expanding where young self-employed women abound. in general, we expect that the larger that proportion, the higher the likelihood that any individual i residing in district j or belonging to gender-age group m is self-employed. however, in some cases, low self-employment in the district/demographic group may signal opportunities or conversely, high selfemployment may signal a saturated market. that is, some individuals may be defiers, responding in the opposite way to a higher proportion of self-employed workers in the district/demographic group (i.e., violation of the monotonicity assumption). when there are defiers, the two-stage least squares estimator gives a weighted difference between the effect of the treatment among compliers and defiers, which could be misleading. nevertheless, de chaisemartin ( ) derives a weaker condition under which the two-stage least squares estimator still provides a local average treatment effect (late) for "surviving compliers." with binary outcomes, like is our case, that condition holds if defiers' late and the two-stage least squares coefficient are both of the same sign, or if defiers' and compliers' lates are both of the same sign and the ratio of these two lates is lower than the ratio of the shares of compliers and defiers in the population. in this context, it is difficult to assess if that condition is likely to hold, because the effect of self-employment on the likelihood of hospitalization can be positive or negative. still, we see no reason for the lates of compliers and defiers to differ significantly, especially since fixed effects capture individuals' intrinsic characteristics that may explain why they respond differently to the instruments. so, we argue that the condition holds as the ratio of compliers to defiers should exceed the ratio of the two lates. the proportion of self-employed workers in an individual's geographical area has previously been used to instrument self-employment decisions (e.g., noseleit ) . the novelty here is that instead of considering the proportion of self-employed workers in the individual's municipality, we consider only neighboring municipalities excluding the individual's own. this approach to devise instrumental variables has been employed, e.g., in autor et al. ( ) and nevo ( ) . in both our instruments, the exclusion of the individual's own municipality contributes to eliminate concerns regarding instrument exogeneity. overall, we believe our instruments are validly excluded from the main equation conditional on the remaining explanatory variables (i.e., they impact hospitalizations solely through their impact on the likelihood of self-employment). for instance in the case of the proportion of self-employed workers in the district (instrument one), the crucial explanatory variables are the district fixed effects. district fixed effects take into account any district characteristics that correlate with both the instrument and the outcome, hospitalizations, as long as those characteristics are constant over time. to explore this issue further, we look at the evolution over time of some district characteristics: a general income index, a general health index, and a firm dimension index, which are composite indices produced by a portuguese polling firm, marktest (online resource ). what we observe is that all of those indices are fairly constant over time; therefore such characteristics should be appropriately captured by the district fixed effects. note also that by comparison, the proportion of self-employed workers in the district exhibits some within-district variation, so the instrument is relevant even when controlling for district fixed effects (online resource ). with two instruments and one potentially endogenous variable, we are able to test statistically the validity of the overidentifying restriction. given that the endogeneous variable, self-employed i,t− , is lagged, we also use the lags of the instruments. as mentioned previously, our main analyses focus on the subsample that includes only individuals who switch between wage work and self-employment at least once over the sample period ("switchers"). after all, those are the individuals that are used for identification in the models with individual fixed effects. moreover, in the instrumental variables model with individual fixed effects, non-switchers are by definition non-compliers, and non-compliers reduce the instruments' statistical power (de chaisemartin ). we also present results for all model specifications for the entire sample, for comparison. lastly, standard errors are robust to heteroscedasticity and to clustering at the individual level in models and , and at the district level in models and (because that is the level of observation of instrument one). the main time-varying unobserved individual characteristic that may affect both self-employment and the likelihood of hospitalization is health. unfortunately, we do not have information on health status; only hospitalizations. we construct an indicator variable that takes value one if the individual had any hospitalization in the previous three months, to try to capture any recent (serious) changes in health status. this variable is potentially not enough to fully rule out endogeneity, which is why we resorted to instrumental variables models. still, as a sensitivity check, we add this variable to model as a control. we also compare the effect of self-employment on the likelihood of hospitalization for women versus men, individuals up to versus and more years old, and nationals versus foreigners. to do this, we include interaction terms between the lagged selfemployment indicator and the respective demographic dummies. since we have two instruments, we are able to instrument both the lagged self-employment indicator and the interaction term. we repeat the main analyses using quarterly rather than monthly data and compare the magnitudes of the estimates. aggregating the data in this way reduces total sample size to about one third. to shed further light on the types of hospitalizations of self-employed and wage workers, we obtained information on hospitalizations from the national diagnosis-related groups dataset. this allowed us to learn the main diagnosis underlying each hospitalization as well as if it was planned or not, but only for about half of the hospitalizations in the social security dataset that we could match indirectly, as there is not an individual identifier to fully merge the two datasets. these complementary analyses are detailed in the online resource . we also apply the model specifications described in the previous section to study the impact of selfemployment on the length of hospitalization. first, in a two-part model type of approach, we restrict the sample to individual-month observations with a hospitalization. we use the natural logarithm of hospitalization days as the dependent variable to account for the skewness in the distribution of hospitalization days. this approach drastically reduces the sample size. we compare the results, qualitatively, to those obtained for the full sample, using the natural logarithm of hospitalization days plus one in order to keep the zeroes. our data also allow us to investigate mortality. to explore the effect of self-employment on mortality, we aggregate the data to the person-year level, as we know the year but not the month in which the individual passes away. we create a binary dependent variable that takes value one if individual i passes away in year t + and zero otherwise, while excluding observations for the year in which the person passes away. we compare results obtained when the self-employment indicator takes value one if the individual is selfemployed during at least one, six, or all twelve months of year t. we estimate the same model specifications as described in the previous section, adjusted for the annual frequency considered here. control variables are measured in year t. we discuss results for the subsample of individuals who switch at least once between self-employment and wage work over time ("switchers"). results for the full sample are also presented for comparison, in the bottom half of the tables (panel b). descriptive statistics by type of employment in the previous month are shown in table . looking at the switchers, the self-employed account for . % of the person-month observations (panel a). the average monthly rates of hospitalization of self-employed and wage workers are . % and . % respectively. note that these seemingly very low numbers correspond to monthly, not annual, hospitalization rates. the average number of days of hospitalization, conditional on there being any, is slightly larger among the self-employed: . compared with . days for wage workers. the differences in the rates and lengths of hospitalization over time in both samples are shown in the online resource . the proportion of women is slightly lower among the self-employed than among wage workers ( % versus %), the self-employed are on average slightly older (about versus years old), and the proportion of foreigners is also slightly lower among the self-employed ( % versus %). the proportion of self-employed workers in the district (instrument one) is on average . % and varies between and . %. the proportion of self-employed workers in the same gender-age group in the country (instrument two) is on average . % and varies between . and . %. table shows the results of models - . starting with the first-stage results, we conclude that when the proportion of self-employment in the district or demographic group increases, the individual likelihood of self-employment also increases, as expected. specifically, when the proportion of self-employed workers in a given district (/demographic group) is one percentage point higher, the likelihood of any individual in that district (/demographic group) becoming selfemployed is about (/ . ) percentage points higher, on average (panel a, model ). returning to why we focus on the subsample of switchers, as noted, e.g., by de chaisemartin ( ), non-compliers reduce the instruments' statistical power. in the instrumental variables model with individual fixed effects, non-switchers are by definition non-compliers. judging from the large fand t-statistics, the instruments appear strong when considering the full sample (panel b, model ). however, looking at the second stage, we can see that the coefficient on the self-employment indicator is implausibly large in absolute terms, and has a huge standard error as well. this suggests that the instruments may actually not be strong enough even though the f-and t-statistics are above conventional thresholds. therefore, we focus our discussion on the results for the sample of switchers. note that even in model , which includes individual fixed effects but not instrumental variables, identification of the effect of self-employment also comes from switchers. as for the instrument validity test, the null hypothesis is not rejected in any case. there is also no evidence of endogeneity. in fact, the coefficients on the self-employment indicator in the instrumental variables models (models and ) are very similar to the coefficients in models and , except they are less precisely estimated and not statistically significant (panel a). in light of this result, unobserved individual characteristics, in particular those that vary over time (e.g., health status), and reversed causality don't seem to pose an issue in our analyses. this is possibly because hospitalization is a fairly objective and a rare/extreme outcome, which doesn't capture health in general but serious (unexpected) manifestations of illness. furthermore, the estimated coefficient on the self-employment indicator is about the same whether or not individual fixed effects are included (model versus model ), suggesting that self-selection of the healthy into self-employment has no impact on don't respond to changes in the labor market as captured by the instruments. recall that in the full sample, only . % of the observations are self-employed; in the subsample of switchers, this proportion increases to . % (table ) . the difference in effect size of the instruments when looking at the full sample versus the subsample of switchers can be interpreted in relation to these proportions of self-employment in each sample. in the model without individual fixed effects, instrument one actually has a small t-statistic and the f-statistic is also small (panel b, model ). instrumental variables estimation using only instrument one or instrument two produces identical results. the negative association between self-employment and likelihood of hospitalization. lastly, controlling for any hospitalization in the previous three months, which is another (partial) way to address endogeneity, does not change the estimated coefficients from model . standard errors in parentheses, robust to heteroscedasticity and to clustering at the individual level in models and and at the district level in models and . *p < . , **p < . , ***p < . the coefficient of the self-employment indicator was multiplied by to facilitate reading we find that self-employed individuals are about . percentage points less likely than wage workers to be hospitalized in any given month. this is the same as the unadjusted difference in hospitalization rates of self-employed and wage workers observed in table . compared with the average monthly hospitalization rate of . % among wage workers, this means that self-employed individuals are less than half as likely to be hospitalized. overall, our findings indicate a large negative impact of self-employment on the likelihood of hospitalization that is consistent across models. results also indicate that female, older, and native workers have higher rates of hospitalization (results available upon request). looking at potentially heterogeneous effects of selfemployment for different subgroups, we find that the negative impact of self-employment on the likelihood of hospitalization is stronger for women than for men. there are no differences between individuals less than or + years old or between nationals and foreigners (table ) . using quarterly data gives negative and strongly significant coefficients, which are roughly three times as large as the coefficients in the main analysis, as expected (not shown). results from our exploration of the types of hospitalizations of self-employed and wage workers, detailed in the online resource , indicate that selfemployment is associated with lower likelihood of hospitalization for any underlying health problem, as well as whether hospitalizations are urgent or planned. looking at the natural logarithm of hospitalization days, conditional on there being a hospitalization, we find no significant effects of self-employment. however, this analysis is limited because only observations with a hospitalization are used and many individuals have only one hospitalization over the entire period of analysis. when including the zeroes, by looking standard errors in parentheses, robust to heteroscedasticity and to clustering at the individual level *p < . , **p < . , ***p < . the coefficient of the self-employment indicator was multiplied by to facilitate reading at the logarithm of hospitalization days plus one, the estimated coefficients are negative and strongly significant, indicating that self-employment reduces the length of hospitalization by almost . %. however, this analysis is also limited because the choice of adding one to the number of days, in order to keep the zeroes, may influence results. in sum, we find no evidence that a lower likelihood of hospitalization among self-employed individuals comes at the expense of longer lengths of hospital stays, which would suggest that self-employed individuals delay going to the hospital until they are more severely sick (results available upon request). table presents the effect of self-employment on the likelihood of mortality in the following year. the self-employment indicator takes value one if the individual is self-employed for more than six months in the current year. similar results are obtained when standard errors in parentheses, robust to heteroscedasticity and to clustering at the individual level in models and and at the district level in models and . *p < . , **p < . , ***p < . the coefficient of the self-employment indicator was multiplied by to facilitate reading one month as a self-employed worker is enough to classify an individual as self-employed in year t or when we require individuals to be self-employed during the whole year. the models that (partly) address endogeneity provide negative coefficients for the selfemployment indicator (models - ). although not statistically different from zero, the estimated coefficient from model indicates that self-employed individuals are about . percentage points less likely to die in the following year than wage workers. compared with the average mortality rate of wage workers, this represents a lower likelihood of mortality by about one third. this analysis has limitations, as data are aggregated to a yearly frequency and mortality is such a rare and extreme outcome that there is little variation to identify precisely an effect of self-employment. yet, results are in line with our main findings for hospitalizations, suggesting a protective effect of selfemployment when it comes to acute events such as hospital admission and death. it is probably as challenging as it is important to determine whether self-employment is good or detrimental for health. the potential self-selection of the healthy into or out of self-employment (and their typically small businesses) is difficult to rule out empirically. however, separating the effect of self-employment on health from that selection effect is crucial to inform policy decisions. moreover, informing policy is increasingly pressing these days, as new forms of self-employment emerge and the small businesses that they create can have a significant impact on sustainable economic growth. the ongoing covid- crisis may also represent a significant push towards selfemployment (and wage employment with increased job flexibility, through greater use of remote work) which may have its own additional consequences in terms of health. given the motivation above, we seek to provide causal evidence on the impact of self-employment on hospitalizations in this study. we take advantage of the longitudinal nature of our rich data, where we track roughly , individuals that switch between forms of employment over a period of up to months. on top of that, we also employ an instrumental variable strategy to deal with any remaining endogeneity. we find that self-employed individuals are . percentage points (or about half) less likely to be hospitalized in a given month when compared with wage workers. qualitatively, this result is in line with most available evidence, which tends to find that self-employment is good for health. this includes toivanen et al. ( toivanen et al. ( , , who like us look at hospitalizations and mortality. we do not seem to find evidence of endogeneity, contrary to rietveld et al. ( ) , who find a negative association between selfemployment and health that is fully explained by a selection effect. the different results between the two studies may be due to the type of outcomes considered and samples used. while we focus on administrative records of hospitalizations and consider the whole working population, rietveld et al. ( ) draw on survey-based subjective health measures and focus on the + population. hospitalization is a specific, acute outcome and not a measure of health status per se. the same can be said of mortality. the job demand-job control theory is closely linked to work-related stress, yet the most obvious manifestations of stress do not always lead to hospitalization or death (e.g., anxiety, depression). in this regard, we may miss important impacts of self-employment on health, which can be positive or negative. we believe more research is needed on this important topic, looking at different, complementary health outcomes. nevertheless, as mentioned in the introduction, stress is an important cause of many health problems, ranging from cardiovascular to respiratory, digestive, and other troubles, which frequently lead to hospitalization (or death). in our analyses of the health problems underlying hospital admissions, we find that self-employed individuals are particularly less likely than wage workers to be hospitalized for troubles of the cardiovascular, respiratory, and digestive systems. despite the limitations of those analyses, our results do not contradict the interpretation that self-employed individuals seem to suffer from lower stress than wage workers or, in other words, that the beneficial effects of higher job control when selfemployed exceed the detrimental effects of higher job demands. our results are also consistent with the research on "procedural utility" that finds higher levels of well-being among self-employed individuals, something that may be linked with lower stress/better health. our results may also reflect changes in the occupations when individuals switch to/from selfemployment and small businesses, which may have different exposures to occupational hazards. for instance, manufacturing workers-typically wage workers-may be more prone to injuries at work. we do find that self-employed individuals are significantly less likely than wage workers to be hospitalized for troubles of the musculoskeletal system, which include many work-related episodes. still, we find equally large or larger differences in hospitalization rates for other types of troubles. unfortunately, with the available data we cannot explore this issue precisely, as we do not know the industry/occupation of self-employed individuals. the potentially different effects of self-employment by industry remains a topic that deserves to be explored in future research. toivanen et al. ( ) and toivanen et al. ( ) already showed promising results in this regard. we believe that the premiss that self-employed individuals may delay care in order not to lose business is of limited concern here. hospitalizations are generally acute, untimed events. furthermore, non-emergency acute interventions are scheduled by the hospital and long waiting lists deter individuals from passing on a scheduled intervention they need. we find identical relative risk ratios for urgent and planned hospital admissions. also, if self-employed individuals, having more limited access to sickness benefits, delayed appropriate care until they are seriously sick and have to be hospitalized, we would find that self-employment leads to higher rates of hospitalization, which is the opposite of what we find. as we do not know the diagnoses of all hospital admissions in the data, we cannot exclude admissions related to pregnancy and childbirth, which are unrelated to health status and capture instead fertility decisions. however, while this may partly explain the larger effect of self-employment found for women, it does not explain our findings for men, for whom we also find negative hospitalization effects. with our approach, we were able to at least partly rule out endogeneity, thanks largely to the rich longitudinal dimension of the data we use. further research may want to explore additional individual information to investigate potential heterogeneous effects, e.g., by industry or occupation. further research may also want to consider the case of self-employed individuals with employees, even if this type of self-employment and their small businesses is less common among platform economy jobs. in conclusion, this study provides evidence of a positive impact of self-employment on health and does so by focusing on an objective outcome-hospital admissions-that is not subject to recall or other biases that may affect previous studies. the positive health effect we document may be at least partly explained by greater control by the individual over different aspects of the working life associated with this form of small businesses. one important dimension of the ongoing debate about the "future of work" is precisely how to increase protection for workers under flexible contracts, such as those that increasingly emerge in the platform economy (e.g., garben , european commission . this dimension is now even more significant in the context of the covid- crisis. this may also involve multiple policy aspects such as social security, employment law and collective bargaining. our results indicate that, despite the existing concerns, at least as far as significant health events are concerned, there are important social gains from more flexible work formats. furthermore, as the platform economy grows around the world, leading to increasing shares of the workforce in self-employment, causal evidence about the health implications of that type of work becomes more pressing. the china syndrome: local labor market effects of import competition in the united states why entrepreneurs often experience low, not high, levels of stress: the joint effects of selection and psychological capital being independent is a great thing: subjective evaluations of selfemployment and hierarchy social support as a mediator between job control and psychological strain job loss, firm-level heterogeneity and mortality: evidence from administrative data effect of job loss due to plant closure on mortality and hospitalization not all are equal: a latent profile analysis of well-being among the self-employed causes and consequences of early-life health the lasting impact of childhood health and circumstance tolerating defiance? local average treatment effects without monotonicity proposal for a directive of the european parliament and of the council on transparent and predictable working conditions in the european union employment by sex, age and professional status protecting workers in the online platform economy: an overview of regulatory and policy developments in the eu. luxemburg: european agency for safety and health at work focus on opportunities as a mediator of the relationship between business owners' age and venture growth how time-flexible work policies can reduce stress, improve health, and save money selfemployment and work-related stress: the mediating role of job control and job demand the prevalence of work-related stress, and its association with self-perceived health and sick-leave, in a population of employed swedish women non-standard employment around the world: understanding challenges, shaping prospects. geneva: international labour office p-hacking in academic research. a critical review of the job strain model and of the association between night work and breast cancer in women job demands, job decision latitude, and mental strain: implications for job redesign healthy work: stress, productivity, and the reconstruction of working life the neurobiology of stress and gastrointestinal disease measuring market power in the ready-to-eat cereal industry self-employment can be good for your health female self-employment and children platform workers in europe. evidence from the colleem survey. luxembourg: publications office of the european union stress, satisfaction, and the work-family interface: a comparison of selfemployed business owners, independents, and organizational employees selfemployment and health: barriers or benefits? why the self-employed are happier: evidence from european countries health of entrepreneurs versus employees in a national representative sample stress and cardiovascular disease current issues relating to psychosocial job strain and cardiovascular disease research mortality differences between selfemployed and paid employees: a -year follow-up study of the working population in sweden s eloranta. hospitalization due to stroke and myocardial infarction in self-employed individuals and small business owners compared with paid employees in sweden -a -year study small business owners and health o trabalho por conta própria em portugal. instituto nacional de estatística the effect of self-employment on health, access to care, and health behavior transitions to selfemployment at older ages: the role of wealth, health, health insurance and other factors publisher's note springer nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations key: cord- -uy dykhg authors: albanese, federico; lombardi, leandro; feuerstein, esteban; balenzuela, pablo title: predicting shifting individuals using text mining and graph machine learning on twitter date: - - journal: nan doi: nan sha: doc_id: cord_uid: uy dykhg the formation of majorities in public discussions often depends on individuals who shift their opinion over time. the detection and characterization of these type of individuals is therefore extremely important for political analysis of social networks. in this paper, we study changes in individual's affiliations on twitter using natural language processing techniques and graph machine learning algorithms. in particular, we collected million twitter messages from . million users and constructed the retweet networks. we identified communities with explicit political orientation and topics of discussion associated to them which provide the topological representation of the political map on twitter in the analyzed periods. with that data, we present a machine learning framework for social media users classification which efficiently detects"shifting users"(i.e. users that may change their affiliation over time). moreover, this machine learning framework allows us to identify not only which topics are more persuasive (using low dimensional topic embedding), but also which individuals are more likely to change their affiliation given their topological properties in a twitter graph. technologically mediated social networks flourished as a social phenomenon at the beginning of this century with exponents such as friendster ( ) or myspace ( ) [ ] but other popular websites soon took their place. twitter is an online platform where news or data can reach millions of users in a matter of minutes [ ] . twitter is also of great academic interest, since individuals voluntarily express openly their opinions and they can interact with other users by retweeting the others' tweets. in particular, in the last decade there has been an increase in interest from computational social scientists and numerous political studies have been published using information from this platform [ ] [ ] [ ] [ ] [ ] [ ] . previous works applied different machine learning models to these datasets. xu et al. collected tweets using the streaming api and implemented an unsupervised machine learning framework for detecting online wildlife trafficking using topic modeling [ ] . kurnaz et al. proposed a methodology which first extracts features of a tweet text and then applies deep sparse autoencoders in order to classify the sentiment of tweets [ ] . pinto et al. detected and analyzed the topics of discussion in the text of tweets and news articles, using non negative matrix factorization [ ] , in order to understand the role of mass media in the formation of public opinion [ ] . on the other hand, kannangara implemented a probabilistic method so as to identify the topic, sentiment and political orientation of tweets [ ] . some other works are focused in political analysis and the interaction between users, as for instance the one of aruguete et al., which described how twitter users frame political events by sharing content exclusively with likeminded users forming two well-defined communities [ ] . dang-xuan et al. downloaded tweets during the parliament elections in germany and characterize the role of influencers utilizing the retweet network [ ] . stewart et al. used community detection algorithms over a network of retweets to understand the behavior of trolls in the context of the #blacklivesmatter movement [ ] . conver et al. [ ] also used similar techniques over a retweets network and showed the segregated partisan structure with extremely limited connection between clusters of users with different political ideologies during the u.s. congressional midterm elections. the same polarization on the twitter network can be found in other contexts and countries (canada [ ] , egypt [ ] , venezuela [ ] ). opinion shifts in group discussions have been studied from different points of view. in particular, it was stated that opinion shifts can be produced by arguments interchange, according to the persuasive arguments theory (pat) [ , , ] . primario et al. applied this theory to measure the evolution of the political polarization on twitter during the us presidential election [ ] . in the same line, holthoefer et al analyzed the egyptian polarization dynamics on twitter [ ] . they classified the tweets in two groups (pro/anti military intervention) based on their text and estimated the overall proportion of users that change their position. these works analyzed the macro dynamics of polarization, rather than focus on the individuals. in contrast, we found it interesting not only to characterize the twitter users who change their political opinion, but also predict these "shifting voters". therefore, the focus of this paper is centered on the individuals rather than the aggregated dynamic, using machine learning algorithms. moreover, once we were able to correctly determine these users, we seek to distinguish between persuasive and non persuasive topics . in this paper, we examined three twitter networks datasets constructed with tweets from: argentina parliamentary elections, argentina presidential elections and tweets of donald trump. three datasets were constructed and used in order to show that the methodology can be easily generalized to different scenarios. for each dataset, we analyzed two different time periods and identify the larger communities corresponding to the main political forces. using graph topological information and detecting topics of discussion of the first network, we built and trained a model that effectively predicts when an individual will change his/her community over time, identifying persuasive topics and relevant features of the shifting users. our main contributions are the following: . we described a generalized machine learning framework for social media users classification, in particular, for detecting their affiliation at a given time and whether the user will change it in the future. this framework includes natural language processing techniques and graph machine learning algorithms in order to describe the features of an individual. . we observed that the proposed machine learning model has a good performance for the task of predicting changes of the user's affiliation over time. . we experimentally analyzed the machine learning framework by performing a feature importance analysis. while previous works used text, twitter profiles and some twitting behavior characteristics to automatically classify users with machine learning [ ] [ ] [ ] [ ] , here we showed the value of adding graph features in order to identify the label of a user. in particular, the importance of the "pagerank" for this specific task. . we also identified the topics that are considerably more relevant and persuasive to the shifting users. identifying this key topics has a valuable impact for social science and politics. the paper is organized as follows. in the data collection section, we describe the data used in the study. in the methods section, we describe the graph unsupervised learning algorithms and other graph metrics that were used, the natural language processing tools applied to the tweets and the machine learning model. in the results section, we analyze the performance of the model for the task of detecting shifting individuals. finally, we interpret these results in the conclusions section. the code is in github (omitted for anonymity reasons). twitter has several apis available to developers. among them is the streaming api that allows the developer to download in real time a sample of tweets that are uploaded to the social network filtering it by language, terms, hashtags, etc. [ , ] . the data is composed of the tweet id, the text, the date and time of the tweet, the user id and username, among other features. in case of a retweet, it has also the information of the original tweet's user account. persuasive) for the topics relevant (resp. non relevant) to those individuals for this research, we collected datasets: argentina parliamentary elections ( arg), argentina presidential elections ( arg) and united states tweets of donald trump ( us). for the argentinan datasets, the streaming api was used during the week before the primary elections and the week before the general elections took place. keywords were chosen according the four main political parties present in the elections. details and context can be found in the appendix. for the us dataset, "realdonaldtrump" (the official account of president donald trump) was used as keyword. twitter messages are in the public domain and only public tweets filtered by the twitter api were collected for this work. for the purpose of this research, we have analyzed more than million tweets and more than . million individuals in total. the specific start and end collection date, the total number of tweets and users can be seen in table . in this section, we will introduce the methodology used to characterize the twitter users. first the retweet networks (section . ) and the algorithm to find communities (section . ). then, the different metrics which describe the interaction networks among them (section . ). after that, the features obtained by analyzing the text of the tweets (section . ). finally, we describe the supervised learning model which uses the individual's characteristics as instances and predicts the shifting users. we represent the interaction among individuals in terms of a graph, where users are nodes and retweets between them (one or more) are edges (undirected and unweighted). isolated nodes (never retweeting nor retweeted) were not taken into account for this analysis. in figure , we can visualize the retweet network for each time period and dataset. in the case of the us dataset, most of the users are concentrated in two groups, which allows to visualize the political polarization. on the other hand, in the argentinean datasets we can identify two large groups and also some smaller ones. the graph visualizations are produced with force atlas layout using gephi software [ ]. in a given graph, a community is a set of nodes largely connected among them and with little or no connection with nodes of other communities [ ] . we implement an algorithm to detect communities in large networks which allows us to characterize the users by their relationship with other users. in this context, the modularity is defined as the fraction of the edges that fall within a given community minus the expected fraction if edges were distributed at random [ ] . the louvain method for community detection [ ] seeks to maximize modularity by using a greedy optimization algorithm. this method was chosen to perform the analysis due to the characteristics of the database. while other algorithms such as label propagation are good for large data networks, their performance decreases if clusters are not well defined [ ] . in contrast, in these cases the louvain or infomap methods obtain better results. however, given that the number of nodes is in the order of hundreds of thousands and edges in the order of one million, the louvain method has a better performance [ ] than other ones. despite having found several communities, we just considered the largest for each case. for the arg and arg dataset we used the four biggest communities because, when examining the text of the tweets and the users with the highest degree, each one had a clear political orientation corresponding to the four biggest political parties in the election. these communities are labeled as "cambiemos", "unidad ciudadana", "partido justicialista" and " pais" for arg and "frente de todos", "juntos por el cambio", "consenso federal" and "frente de izquierda-unidad" for arg (electoral context is provided in the appendix). regarding the us dataset, we used the biggest communities because of the bipartisan political system of the united states (republicans and democrats) and the clear structure present in the retweet networks, where only two big clusters concentrate almost all of the users and interactions (see figure ). in contrast, the argentinean election datasets have two principal communities and some minor communities as well. considering the the fact that our dataset has more than million tweets and more than . million users, it was not feasible to determine true labels of political identification of the users for this task. neither it was viable to manually assign them. therefore, we decided to use the communities labels of the retweet network as a proxy of political membership, and interpret changes in their label as changes in affiliation over time. this decision is supported by previous literature, where it is shown that communities identify a user's ideology and political membership [ , , , , , ] . moreover, taking into account the stochasticity of the louvain method and following [ ] , we decided to use for the machine learning task only the nodes that were always assigned to the same community, in order to minimize the possibility of an incorrect labeling. additionally, we did not used individuals with less than retweets, since we might have insufficient data to correctly classify them. finally we also manually sampled and checked users from different communities to verify their political identification. with the intention of characterizing topologically the users of the primary election network, we computed the following metrics: degree of each user in the network (i.e., the number of users that have retweeted a given one), pagerank [ ], betweenness centrality [ ], clustering coefficient [ ] and cluster affiliation (the community detected by the louvain method). we used all these metrics as features in the machine learning classification task. in order to determine the topics of discussion during the primary election, we analyzed the text of the tweets using natural language processing analysis and we calculated a low dimensional embedding for each user. the tweets were described as vectors through the term frequency -inverse document frequency (tf-idf) representation [ ] . each value in the vector corresponded to the frequency of a word in the tweet (the term frequency, tf ) weighted by a factor which measures the degree of specificity (inverse document frequency, idf ). we used -grams and a modified stop-words dictionary that not only contained articles, prepositions, pronouns and some verbs but also the names of the candidates, parties and words like "election". then, we constructed a matrix m concatenating the tf-idf vectors, with dimensions the number of tweets times the number of terms. we performed topic decomposition using non-negative matrix factorization (nmf) [ ] on the matrix m . nmf is an unsupervised topic model which factorizes the matrix m into two matrices h and w with the property that all three matrices have no negative elements. we selected the nmf algorithm because this non-negativity makes the resulting matrices easier to inspect and to understand their meaning. the matrix h has a representation of the tweets in the topic space, in which the columns are the degree of membership of each tweet to a given topic. on the other hand, the matrix w provides the combination of terms which describes each topic [ ] . the obtained results, analyzing just the tweets corresponding to the first time period, are detailed in the appendix. the decomposition dimension was swept between and , and for each dataset we chose a number of topics in the corpus so as to have a clear interpretation of each one. the same methodology was used and described in [ , ] . once we collected all this information, twitter users were also characterized by a vector of features where each cell corresponds to one of the topics and its value to the percentage of tweets the user tweeted with that topic. given that our objective was to identify shifting individuals and persuasive arguments, we implemented a predictive model whose instances are the twitter users who were active during both time periods [ ] and belonged to one of the biggest communities in both time periods networks. consequently, the number of users used at this stage was reduced. individuals were characterized by a feature vector with components corresponding to the mentioned topological metrics depicted in section . and others corresponding to the percentage of tweets in each one of the topics extracted in section . . the information used to construct these embedding was gathered from the whole first time period retweet network. the target was a binary vector that takes the value if the user changed communities between the first and the second time periods and otherwise. the summary of the datasets is shown in table . considering the percentage of positive targets, this is clearly a class imbalance scenario. specially in us, which is reasonable given the bipartisan retweet network with big and opposed communities [ ] . the gradient boosting technique uses an ensemble of predictive models to perform the task of supervised classification and regression [ ] . these predictive models are then optimized iteration by iteration using the gradient of the cost function of the previous iteration. in this scenario, xgboost, a particular implementation of this technique, has proven to be efficient in a wide variety of supervised scenarios outperforming previous models [ ] . we used a / random split between train and test. in order to do hyperparameter tuning, we used the randomized search method [ ] over the training dataset with -fold cross-validation, which consists of trying different random combinations of parameters and then staying with the optimum. with the objective of measuring the efficiency and performance of our machine learning model, two other models, namely random and polar, were taken as baselines for comparison. in the former one, the selected user will change of community with a probability of %. in the latter, for a user that belongs to one of the two biggest communities in the network, we predict that he/she will stay in that community, while a user that belongs to a smaller community will change to one of the two main communities with same probability. this polar model is inspired by idea that in a polarized election, members of the smallest communities shift and are attracted to the biggest communities, and was used in the argentinean datasets. we trained three different gradient boosting models for each dataset: the first one was trained only with the features obtained via text mining (how many tweets of the selected topics the user talks about); a second one was trained just with features obtained through complex network analysis (degree, pagerank, betweeness centrality, clustering coefficient and cluster affiliation); and the last one was trained with all the data. in this way, we could compare the importance natural language processing and complex network analysis for this task. in figure we can see the roc [ ] of the different models for each dataset. the best performance is obtained in all cases by the machine learning model built with all the characteristics of the users, which is able to efficiently predict which users are shifting individuals. this result is expected, since an assembly of models manages to have sufficient depth and robustness to understand the network information, the topics of the tweets and the graph characteristics of the users. we performed random permutation of the features values among users in order to understand which of them are the most important in the performance of our model (the so-called permutation feature importance algorithm [ ] ). in figure , we observe that the most important feature in all cases corresponds to the node's connectivity: pagerank, meaning that shifting individuals are the peripheral and least important nodes of big communities. the result is verifiable when comparing the pagerank averages in users who changed their affiliation ( arg pr = . e − , arg pr = . e − and us pr = . e − ) with those who did not ( arg pr = . e − , arg pr = . e − and us pr = . e − ), the latter being at least % higher. this is also consistent with the fact that the model trained with network features gets a better au c than the model trained with the texts of user tweets in all datasets. previous works have used text, twitter profile and some twitting behavior characteristics to automatically classify users with machine learning, but none of them have incorporated the use of these graph metrics [ ] [ ] [ ] [ ] ] . our work shows the importance of also including these graph features in order to identify shifting individuals. this result has a relevant sociological meaning: the unpopular individuals are more prone to change their opinion. besides the importance of the mentioned topological properties, some discussed topics are also relevant to the classifier model. a simple analysis of the most spoken topics in the network does not differentiate between topics discussed by a shifting individual and other users. considering that most users do not change their affiliation, it is interesting to analyze those that do change. the persuasive arguments theory affirms that changes in opinion occurs when people exchange strong (or persuasive) arguments [ , , ] . consequently, we defined a "persuasive topic" as a topic used primarily by shifting individuals and not used by non shifting individuals. with the intention of doing a deeper analysis of the topic embedding for the arg dataset, we first enumerate the main topics in that corpus: equivalent analysis can be done with the other two corpora and the topic decomposition for each can be found in the appendix. in figure , the most important topics for the classifier are "venezuela", "economy" and "santiago maldonado". we can contextualize these results by looking which are the main topics discussed in each community as well the ones discussed among the users that change between them, as it is shown in figure . we can see that "venezuela" is one of the most discussed topics in the people remaining in four communities and "santiago maldonado" is a relevant topic in the communities "unidad ciudadana" and " pais". when we look at the main topics discussed by users that change their communities between elections, we can observe that "venezuela" identifies those that go from "partido justicialista (pj)" to " pais" and "cambiemos" meanwhile "santiago maldonado" is a key topic among those who arrive to "unidad ciudadana" from "partido justicialista (pj)" and " pais". considering that these topics are considerably more used by the shifting twitter users than by the other users, it can be affirmed that these are "persuadable topics". in contrast, other topics such as "economy" or "santa cruz" were also commonly used by most of the users but not by the shifting individuals. in this paper we presented a machine learning framework approach in order to identify shifting individuals and persuasive topics that, unlike previous works, focused on the persuadable users rather than studying the political polarization on social media as a whole. the framework includes natural language processing techniques and graph machine learning algorithms in order to describe the features of an individual. also, three datasets were used for the experimentation: arg, arg and us. these dataset were constructed with tweets from countries, during different political contexts (during a parliamentary election, during a presidential election and during a non-election period) and in a multi-party system and a two-party system. the machine learning framework was applied to these different datasets with similar results, showing that the methodology can be easily generalized. the implemented predictive models effectively detected whether the user will change his/her political affiliation. we showed that the better performance can be achieved when representing the individuals with their community and other graph features rather than topic embedding. therefore, our results indicate that these proposed features do a reasonable job at identifying user characteristics that determine if a user changes opinion, features that were neglected in previous works of user classification on twitter [ ] [ ] [ ] [ ] ] . in particular, the pagerank was the most relevant according to the permutation feature importance analysis in all datasets, showing that popular people have lower tendencies to change their opinion. finally, the proposed framework also identifies which of the topics are the persuasive topics and good predictors of individuals changing their political affiliation. consequently, this methodology could be useful for a political party to see which issues should be prioritized in their agenda with the intention of maximizing the number of individuals that migrate to their community. understanding the characteristics and the topics of interest of politically shifting individuals in a polarized environment can provide an enormous benefit for social scientists and political parties. the implications of this research supplement them with tools to improve their understanding of shifting individuals and their behavior. the percentage on the arrows are the percentage of users that changed from one community to the other (when the percentage was less than %, the corresponding arrow is not drawn). the topics on the arrows show the most important topics among the users that change between those communities. • the president of argentina and the governor of the province of buenos aires at the time of elections (i.e., "mauriciomacri", "macri" and "mariuvidal"). these last two were added, despite not being actively present in the lists, due to their political importance, their relevance and participation during the campaign. in addition, the tweets were restricted to be in spanish. the electoral context is the following: former president and opposition leader cristina fernández de kirchner (former "unidad ciudadana") and sergio massa (former " pais") create a new party "frente de todos" with alberto fernández as candidate for president. on the other hand mauricio macri (former "cambiemos") run for reelection as candidate of "juntos por el cambio". the socialist nicolas del cao of "frente de izquierda-unidad" and roberto lavagna of "consenso federal" were also candidates for president, among others. considering the previous subsection and the candidates for the senate, for deputy and for governor, the following terms were chosen as keywords for tweeter: "elisacarrio", "ofefernandez ", "patobullrich", "macri", "macrismo", "mauriciomacri", "pichetto", "miguelpichetto", "juntosporelcambio", "alferdez", "cfkargentina", "cfk", "kirchner", "kirchnerismo", "frentetodos", "frentedetodos", "lavagna", "rlavagna", "urtubey", "urtubeyjm", "consensofederal", " consensofederal", "delcao", "nicolasdelcano", "delpla", "rominadelpla", "fitunidad", "fdeizquierda", "fte izquierda", "castaeira", "manuelac ", "mulhall", "nuevomas", "espert", "jlespert", "frentedespertar", "centurion", "juanjomalvinas", "hotton", "cynthiahotton", "biondini", "venturino", "frentepatriota", "romeroferis", "partidoautonomistanacional", "vidal", "mariuvidal", "kicillof", "kicillofok", "bucca", "buccabali", "chipicastillo", "larreta", "horaciorlarreta", "lammens", "matiaslammens", "tombolini", "matiastombolini", "solano", "solanopo", "lousteau", "gugalusto", "recalde", "marianorecalde", "ramiromarra", "maxiferraro", "fernandosolanas", "marcolavagna", "myriambregman", "cristianritondo", "massa", "sergiomassa", "gracielacamano", "nestorpitrola". in addition, the tweets were restricted to be in spanish. also, the topic embedding obtained with non-negative matrix factorization: c tweets of donald trump the following term was used as keyword for the tweeter api: "realdonaldtrump". in addition, the tweets were restricted to be in english. lon from friendster to myspace to facebook: the evolution and deaths of social networks longislandpress garcí emotions in health tweets: analysis of american government what the hashtag? a content analysis of canadian politics on twitter information, communication & society linh political communication and influence through microblogging-an empirical analysis of sentiment in analyzing the digital traces of political manipulation: the russian interference twitter campaign politics, sentiments, and misinformation: an analysis of the twitter discussion on the mauricio interest communities and flow roles in directed networks: the twitter network of the uk riots journal of the royal society interface donald j. trump and the politics of debasement critical studies in media communication using machine learning to detect cyberbullying ahme sentiment analysis in data of twitter using pablo quantifying time-dependent media agenda and public opinion by topic modeling physica a: statistical mechanics and its applications a scalable tree boosting system proceedings of the nd acm sigkdd international conference on knowledge discovery and data mining didrik tree boosting with xgboost-why does xgboost winëverymachine learning competition? random search for hyper-parameter optimization comparing effect sizes in follow-up studies: roc area, cohen's d, and r law and human behavior permutation importance: a corrected feature importance measure jonny identifying communicator roles in twitter proceedings of the st international conference on world wide web use of machine learning to detect illegal wildlife product promotion and sales on twitter frontiers in big data analyzing mass media influence using natural language processing and time series analysis michael quantifying controversy in social media proceedings of the ninth acm international conference on web search and data mining sandeepa mining twitter for fine-grained political opinion polarity classification, ideology detection and sarcasm detection proceedings of the eleventh acm international conference on web search and data mining consensus clustering in complex networks scientific reports measuring polarization in twitter enabled in online political conversation: the case of us presidential election judgments and group discussion: effect of presentation and memory factors on polarization sociometry why do humans reason? arguments for an argumentative theory persuasive arguments theory, group polarization, and choice shifts personality and ingmar content and network dynamics behind egyptian political polarization on twitter proceedings of the th acm conference on computer supported cooperative work & social computing measuring political polarization: twitter shows the two sides of venezuela chaos jeffrey investigating political polarization on twitter: a canadian perspective policy & internet testing two classes of theories about group induced shifts in individual choice sergio massa of " pais" (former chief of the cabinet of ministers of cristina kirchner, then leader of the opposition against cristina kirchner in when he won his provincial election) and florencio randazzo of twitter keywords considering the previous subsection, the following terms were chosen as keywords for tweeter • candidates for senate of the main four parties: their name and official user on twitter topic decomposition the topic embedding obtained with non-negative matrix factorization: . president donald trump: the o president of the united states. . obamagate: the accusation that barack obama is conspiring against donald trump world health organization: president trump announcing the us will pull out of the world health organization thank you: individuals thanking president trump for this actions in regard to the covid- pandemic fake news: individuals discussing and claiming that certain news are fake president barack obama: the o president of the united states and his administration key: cord- - fjya wn authors: rogers, l c g title: ending the covid- epidemic in the united kingdom date: - - journal: nan doi: nan sha: doc_id: cord_uid: fjya wn social distancing and lockdown are the two main non-pharmaceutical interventions being used by the uk government to contain and control the covid- epidemic; these are being applied uniformly across the entire country, even though the results of the imperial college report by ferguson et al show that the impact of the infection increases sharply with age. this paper develops a variant of the workhorse sir model for epidemics, where the population is classified into a number of age groups. this allows us to understand the effects of age-dependent controls on the epidemic, and explore possible exit strategies. the global covid- pandemic has swept through the nations of the world with a frightening speed, and left governments struggling to cope with the situation. the initial responses have been directed towards limiting the death toll and ensuring that health services are not completely overwhelmed, as would be only too possible with an infection that can grow by a factor of one thousand in a month. as there is as yet no vaccine, no effective medication, and very imperfect understanding of the parameters of the epidemic, efforts have been directed towards containment, with decisions about return to normality being left until later. without vaccine or effective medical treatment, the only remaining strategies would appear to be either a policy of contact tracing and quarantining, or developing herd immunity. the first of these policies appears to have been applied successfully in south korea and singapore, and is generally regarded as the first line of public health defence. in the current pandemic, most countries have quickly found themselves overwhelmed by the scale and speed of the outbreak, and have been unable to apply contact tracing as rigorously and universally as is needed for the method to work. when it does work, contact tracing and quarantine will allow an outbreak to be snuffed out before it spreads widely, but it will of course leave a large population of susceptibles open to a new infection, so continuing vigilance is essential. as we have seen contact tracing overwhelmed, the goal of this paper is to explore the route to herd immunity, using age-dependent release from lockdown, and a gradual relaxation of social distancing rules. in section we present the model, which is in almost all respects a straightforward variant of the standard sir epidemic model. the equations contain terms for the controls which are available to modify the dynamics of the epidemic. the problem is a control problem, and for this we have to define the objective, which we do in section . the issue is of course that we have a conflict between the obvious cost of the numbers of citizens whose lives are ended prematurely, which is a concern for the next few months; and the damage that an extended lockdown will do to the economy, which will be a concern for many years if the aftermath of the financial crash is any guide. in setting up the cost structure, some relatively arbitrary (but hopefully reasonably realistic) assumptions have to be made; these are not in any way essential to the approach, and can easily be changed by any reader prepared to play with the jupyter notebook posted online . parameter values, or even the entire form of the costs, can be changed by anyone with a little knowledge of python. experts in health economics would doubtless be able to suggest values that better embody current thinking, and before any of the results of this paper can be relied on, such inputs will be necessary. in section we briefly discuss the datasources used, and in section we present the results of computation in various scenarios. a simple sir epidemic model is too crude to allow us to model and control the key features of the covid- epidemic; many infected individuals are asymptomatic, and the impact of the infection on different age groups is very different. so we will break down the population into j age groups, and let a j (t), i j (t), s j (t) denote the numbers of j-individuals at time t who are (respectively) asymptomatic infected, symptomatic infected, and susceptible. we will denote by n j (t) the total number of j-individuals in the population at time t, and allow this to change gradually with the influx of new births, visitors from other countries; this is to model the possibility that new infecteds come in from outside and reignite the epidemic. the most basic form of the evolution is governed by the differential equationṡ where ι j and σ j are known functions of time representing the arrival of new asymptomatic infec- https://colab.research.google.com/drive/ tbb usgia wehy-hviygdo mpnzu a tives and susceptibles respectively ; and the final term on the right-hand side of ( ) allows for the possibility that removed infectives may not in fact be immune, and some may return to the population ready for reinfection. the parameter p ∈ ( , ) appearing in ( ), ( ) is the probability that a susceptible becoming infected is symptomatic; and the parameter ρ > is the recovery rate. the infection rates λ j (t) are explicit non-linear functions of the state of the system that will be discussed shortly, but, aside from the terms involving λ, the evolution is linear. so if we stack the variables into a single vector the evolution ( )-( ) can be written aṡ where m is a j × j constant matrix, Λ is a simple matrix whose entries involve the λ j in the appropriate entries, and η is the vector of driving terms. [remark.the model ( )-( ) is the fluid limit of a markov chain model in which ρ is the rate that an individual jumps from an infected state to the removed state, and therefore the implicit (markovian) assumption is that the time spent in the infective state is exponentially distributed. this assumption does not fit well with observation, so we can allow for different distributions by the familiar trick of the method of stages (see, for example, [ ] ), in which a infected individual passes through a number of exponentially-distributed stages. in more detail, we can suppose that there are k x stages for the symptomatic infection, and that i k j (t) is the number of symptomatic j-individuals at stage k of the infection at time t, j = , . . . , j, k = , . . . , k x . making this change, the equation ( ) becomes the systemİ this corresponds to making the duration of symptomatic infection a sum of k x independent exponentials each with mean /ρk x , which has the same mean as an exponential of rate ρ but smaller variance. we could similarly decompose the asymptomatic infections, and indeed by further ramifications of the method of stages we could make the distribution of infected time approximate any desired distribution. there is a good reason not to take this too far, however; in the numerics, the differential equation has to be solved many times. it is remarkable that this can be done in a reasonable amount of time, but the more complicated the model, the slower this step becomes and ultimately the computation will be too slow. but however we do this, when we stack all the variables into a big state vector z, the evolution still has the form ( ), and the appropriate form of this is coded into the jupyter notebooks.] each individual spends part of the waking day at home, and part of the waking day outside . we shall denote by m o ij the mean number of contacts that an i-individual has per day with j-individuals when outside the home; and by m h ij the mean number of contacts that an i-individual has per day with j-individuals when inside the home. it is important to understand that m o ij is the mean number of contacts that an i-individual has with j-individuals if everyone spends their entire waking day outside the home. if the i-individual spends a fraction ϕ i of the waking day outside the home, and j-individuals spend a fraction ϕ j of the waking day outside the home, then the mean number of contacts per day which an i-individual has with j-individuals outside the home will be ϕ i m o ij ϕ j . each time an infected person has contact with someone, infection will be transmitted with probability β, though of course this will only result in a change if the person contacted was susceptible. thus the overall rate at which infection is passed in the outside world to j-individuals will be where ϕ i (t) is the fraction of time spent in the outside world by i-individuals, and δ ∈ [ , ] is the proportion of symptomatic infecteds who go into the outside world. in an ideal situation, this would be close to zero, but many people with the infection get only mild symptoms and may not self-isolate. the number of j-individuals at time t is n j (t), so the factor s j (t)/n j (t) on the right-hand side of ( ) is the probability that a contacted j-individual is susceptible. this may have the appearance of a conventional extension of an sir model, but one point to flag straight away is that the controls ϕ enter quadratically in the expression for the infectivity, whereas some authors use only a linear dependence. this is erroneous. what happens in the home is rather more difficult to deal with. we could simply take ( ) and change superscript o to h, and ϕ to − ϕ, but this would be incorrect, because an infected individual outside may go through the day and infect a large number of people, but within the home there are relatively few that could be infected, so the scope to spread infection is much reducedthis is after all the rationale for locking down populations. without the constraint on the number of infections imposed by the household size, a single infected i-individual in the home would be firing infection transmissions at j-individuals at rate thus if τ is the mean infective time, during the period of infectivity each infected i-individual in the home will fire a poisson(γ ij (t)τ ) number of infections towards j-individuals, and therefore will fire a possible z ∼ poisson(γ i (t)τ ) number of infections towards all others, where γ i (t) = j γ ij (t). however, the number of infections that can strike another individual cannot exceed n − , where n is the size of the household in which the infected i-individual lives. data from the office of national statistics allow us to deduce the distribution of n . the mean number of individuals at whom the infected i-individual fires infections is this is the mean number of infections the infected i-individual could fire at others during a period of mean length τ , so we will simply suppose that while infected the i-individual in the home will be firing infections at rate µ i (t)/τ . an infection fired at another will be supposed to strike a j-individual with probability p h ij (t) proportional to m h ij ( − ϕ j (t)); and given that it strikes a j-individual, the probability that a new infection results will be s j (t)/n j (t). thus the analogue of ( ) for new infections of j-individuals in the home will be we combine these to give finally [remark. these assumptions represent a compromise; any honest treatment of what goes on within households would appear to require a decomposition of the population into groups according to different household compositions by age, meaning the size of the statespace gets out of controlwhich would render the calculation impractical. ] it is worth emphasizing that there are just four controlling parameters in this model: β, the probability that a contact results in a transmission; p, the probability that an infected person is symptomatic; ρ, the reciprocal of the mean infective time; ε, the probability that a removed infective is still susceptible. other values which are needed for the calculations, such as the mean numbers m o ij , m h ij of contacts, can be found from published estimates. there are three components to the cost: the cost of lockdown, the cost of social distancing, and the cost of deaths. we take them in turn. there will be a normal levelφ j for the proportion of time spent by a j-individual outside the home; for the purposes of the computations, the assumption here is that of the waking hours of the week, are spent in school or work, are spent in social activities, and are spent at home, makingφ j equal to / for all age groups. if a j-individual is locked down at level ϕ j (s) at time s, we propose that the cost by time t should be proportional to for constant ϕ j , this will be convex in t, which seems realistic; a short lockdown (as for a public holiday) causes little damage, but as the time away from regular work stretches on, the damage suffered increases more rapidly, as businesses collapse and workers are made redundant. we will consider strategies where for some < u < v (which may depend on j) where ϕ j ( ) is the initial level of lockdown applied. at time u, this starts to be relaxed in a linear fashion, being fully relaxed by time v. integrating ( ) up to v gives the cost of a j-individual being locked down as for some constant c. if we think that the social cost of an individual being locked down for one year is sc , then the constant of proportionality in ( ) is fixed so that the cost will be this then has to be summed over all the members of the population, with a small reduction for retired people, who would presumably impact the economy less if they were prevented from going out. in the numerical implementation, we fix v = u + ; this reduces the number of free parameters, and in any case reflects the realistic situation that once an age group is freed from the lockdown restrictions they will quite quickly get back to normal activity. social distancing imposes costs; public transport will have to run at reduced capacity, as will restaurants and theatres. but these costs are steady ongoing frictions which do not keep people away from work for months on end. if the social distancing policy means that at time t the number of contacts outside the home are reduced to a fraction sd(t) ∈ ( , ) of the normal situation, then we propose that the cost of this policy by time t would be proportional to the form of sd is available to choose, and in the computations we suppose that sd rises from the initial value sd to final value in a piecewise-linear fashion through n sd stages. this allows for the possibility that social distancing could be gradually relaxed by opening more and more classes of business or public assembly. thus at some time u , sd starts to rise to the first staged value sd at time v , where it remains until u ; from there it rises to the next staged value sd at time v , and so on. we suppose that the levels of the stages are equally spaced, but this can easily be altered. if there is just one stage, the policy starts at some value sd and at time u starts to rise linearly to at later time v, so the overall cost will be by considering the effect of social distancing for a year, we fix the constant to give cost where θ sd ∈ ( , ) expresses the pain of social distancing relative to lockdown. in the calculations, we will allow the profile of social distancing to be a more general piecewise-linear continuous functions, permitting social distancing to be relaxed in stages and held at intermediate values. making an estimate of the cost of the death of an individual is ethically and procedurally quite a vexed issue. for the purposes of the calculations reported in this paper and as default values used in the jupyter notebook, the assumption is that the cost of the death of an individual is proportional to the expected number of further years that they would have lived; and that the constant of proportionality is of the same order as sc , the cost of an individual being locked down for one year. so the code has a parameter deathfactor which is used to scale sc for the calculations. this is only part of the story however. we need to calculate the number of deaths which will result from any particular policy, and this comes from the calculated stream of removed symptomatic infectives, coming at rate ρi j (t) in age group j. most of these will have recovered, but a percentage of these will need hospitalization, and of those a percentage will need critical care. the probabilities depend on the age of the patient, with older patients at much higher risk; estimates are given in [ ] and are quoted in [ ] . so we calculate the rate at which new critical care beds are required. based on an estimate for the number of days a critical care patient needs a bed (taken to be days), and knowing the total number of available critical care beds, we can keep a running count of the number of critical care beds in use, and then see how many of the incoming patients for critical care can be accommodated. those who can be accommodated survive with probability p cc (taken to be . ); those who cannot are assumed to die. it is assumed that younger patients always take priority in allocating limited resources. the code is built around the data assumptions in [ ] , who use nine age groups, - , - , - , - , - , - , - , - , and +. the probabilities of hospitalization and critical care need for these age groups are estimated by verity et al. [ ] . the population numbers for these age groups come from the statista web site (https://www.statista.com/topics/ /uk/). the number of critical care beds in england at the end of was around , with around more planned at the emergency nightingale hospitals, so as an optimistic figure we took to be the number. the mean infectious period was taken to be days, in line with values in [ ] , but it seems this can be highly variable. various values were tried for p, the probability of an infected person being symptomatic, but the baseline for this parameter was . . infectivity was taken to be . , in line with values proposed by [ ] , but again there appears to be quite a wide range of possible values, as we see from [ ] . the contact matrix values m o , m h are derived from [ ] ; they work with different age ranges, so some pre-processing of their data had to be done; the code for this is available from the author on request. the code for the calculations was written in python, and is available in the jupyter notebooks for the reader to scrutinize and experiment with. the first approach was to take the objective and minimize this using the scipy routine minimize, which acts as a wrapper to fourteen different methods, only a few of which were possibilities due to the constrained nature of the problem. the only routine which managed acceptable runtimes was slsqp, but it turned out that for virtually all randomly-chosen starting points, the end point was the same as the start point; so this suggested the method which is used in the jupyter notebook, which is simply to randomly generate control rules of the form discussed above, and focus on those which do best. it is of course impossible to present more than just a few cases, but we can explain what the default values for all the relevant parameters are, and then show how the outputs vary as some of as initial values, we assume there are asymptomatic infecteds in each of the age groups, and the initial vector ϕ is ϕ = [ , , , , , , , , ] * φ/ the costs of lockdown are supposed to be less severe for the older age groups, so we use qcost = [ , , , , , , . , . , . ] * sc as mentioned before, we took the number nbeds of critical care beds to be . we ran the calculation for days (except in the do-nothing example, which ran for days). we insisted that lockdown ends for all but the oldest age group ( +) by day , and we imposed the condition that social distancing reaches its end value s end by day . in this base case, we shall take sd = . and ϕ =φ, which is the situation where no social distancing and no lockdown happens. there are , deaths, and using the proposed cost parameters, the cost of deaths is bn, the cost of social disruption is . bn. in this scenario, the epidemic is short and massive; as we see from figure , everything is over in about days, with a peak number of new daily cases for critical care of , , and for hospital admissions of almost , . figure shows that the critical care provision is completely swamped, with nearly , critical care cases unable to get a critical care bed and therefore dying without the necessary care. it is hard to imagine how such a scenario could be thought acceptable. in this scenario, fairly tight lockdown and social distancing measure are applied from the beginning and gradually relaxed. the costs of lockdown and social distancing this time amount to bn, the death costs to . bn, and the total number of deaths was , . the load of new cases is much more manageable, with a peak of just over , new critical care cases, and about , new cases in all. all but the two oldest age groups are out of lockdown within days, but looking at figure we see that even after days the epidemic is far from over; once the oldest group is let out of lockdown and social distancing has come to an end, the epidemic starts to take off again. most worrying here is that from days on, every single critical care bed is taken by a covid- patient, and thousands of elderly patients needing a critical care bed are unable to obtain one. this supports the proposition that some form of social distancing will have to be maintained for a very long time if no treatment or vaccine can be found. next we see what happens if in fact the infectivity is higher than the middle case value of . suggested in [ ] . this time, lockdown and social distancing costs remain at around bn, death costs are about . bn, and the total number of deaths is , . the general picture looks like the previous situation but more accentuated; there is a clear second surge after the oldest age group is released from lockdown, and some , die without the critical care they need as the hospitals are submerged with cases. this time, saturation of the critical care facilities begins around day and keeps going. even maintaining social distancing at % is not sufficient to hold back the epidemic in the longer run. if the probability that an infective is symptomatic is reduced to . , the outcome is improved, with death costs around . bn, lockdown costs little changed, and total deaths reduced to , . figure shows two pronounced peaks to the infection, the second again coinciding with the final relaxation of restrictions. the critical care capacity only saturates at around day this time. the epidemic is on a smaller and more manageable scale; peak admissions to critical care are just over , peak hospital admissions just over . this is not surprising, since the proportion of those infected who are symptomatic (and therefore open to possible complications) is lower. however, there are more undetected asymptomatic infecteds going about in the population, so the number of deaths is higher than in the base case; it is clear from the pictures that towards the end the epidemic is beginning to get out of control. in this scenario, we find the costs of lockdown and social distancing to be reduced to bn, death costs around . bn. the number of deaths is , . what is most clear from figure is that from the time that the - age group is released from lockdown around day , the epidemic gradually gets more out of control, with critical care at full stretch from day onwards, and the numbers of older patients needing critical care and dying without it growing , at the end of the run. of course, it is only possible to display a few examples, which barely begins to explore the diversity of behaviour that will arise as parameters are varied. this is the purpose of the jupyter notebook which can be found at https://colab.research.google.com/drive/ tbb usgia wehy-hviygdo mpnzu a conclusions. this paper offers a simple model for the current covid- epidemic; no account is taken of spatial effects, which could make a big difference to any conclusions. the treatment of the spread of the infection in the home is an approximation, plausibly based perhaps, but still an approximation. nevertheless, the modelling assumptions are simple and compact, and permit rapid exploration of possible responses of a non-pharmaceutical nature. the calculations require assumptions about the initial state of the epidemic which are essentially guessed. even coming into the epidemic once it is under way, it would be hard to get reliable values for the numbers of asymptomatic, susceptible and immune people in the population, not least because there is at the time of writing no test to determine whether someone has had the infection and is now immune, and only a rather unreliable test whether an individual currently has the infection. no account is taken of parameter uncertainty. this is a natural area of enquiry, but at the moment it seems that the data that would support strong conclusions is not yet available. as it seems that the key parameters are known with very little precision, a highly detailed model, or a sophisticated story about statistical inference may help less than some rough exploration of possible parameter combinations; as the epidemic evolves around the world, we will undoubtedly learn more of its characteristics, which will allow us better to control it. infectious diseases of humans: dynamics and control networks of queues and the method of stages impact of non-pharmaceutical interventions (npis) to reduce covid mortality and healthcare demand early transmission dynamics in wuhan, china, of novel coronavirus-infected pneumonia projecting social contact matrices in countries using contact surveys and demographic data age-structured impact of social distancing on the covid- epidemic in india social contact patterns and control strategies for influenza in the elderly estimates of the severity of coronavirus disease : a model-based analysis. the lancet infectious diseases it is a pleasure to thank josef teichmann, kalvis jansons, ronojoy adhikari, rob jack, philip ernst and mike cates for illuminating discussions. as economists will insist on noting, they are not responsible for the errors herein. key: cord- - b esll authors: huang, ganyu; pan, qiaoyi; zhao, shuangying; gao, yucen; gao, xiaofeng title: prediction of covid- outbreak in china and optimal return date for university students based on propagation dynamics date: - - journal: j shanghai jiaotong univ sci doi: . /s - - - sha: doc_id: cord_uid: b esll on december , a novel coronavirus disease, named covid- , began to spread around the world from wuhan, china. it is useful and urgent to consider the future trend of this outbreak. we establish the + penta-group model to predict the development of the covid- outbreak. in this model, we use the collected data to calibrate the parameters, and let the recovery rate and mortality change according to the actual situation. furthermore, we propose the bat model, which is composed of three parts: simulation of the return rush (back), analytic hierarchy process (ahp) method, and technique for order preference by similarity to an ideal solution (topsis) method, to figure out the best return date for university students. we also discuss the impacts of some factors that may occur in the future, such as secondary infection, emergence of effective drugs, and population flow from korea to china. nomenclature c-the average number of contacts of an exposed person without isolation each day n-the number of individuals nd-the death toll ne-the number of exposed individuals ni-the number of infectious individuals nr-the number of recovered individuals ns-the number of susceptible individuals n -the total population of china p-intensity of isolation for exposed individuals r-correlation coefficient r -coefficient of determination t -moment when the government began to take measures t-outbreak duration α-incubation rate β-infectious rate of contacts of an exposed person γ-recovery rate μ-pneumonia mortality introduction on december , the first patient with unexplained pneumonia was admitted into the hospital in wuhan. since then, a novel coronavirus disease, named covid- , has spread around the world, and the number of infected patients has been growing exponentially. we have known that the novel coronavirus has certain infectivity and a good affinity with human respiratory tract cells. it can also be transmitted from person to person. thus, it is useful and urgent to predict the situation of this outbreak with mathematical modeling. besides, students still stay at home to prevent the spread of covid- . here we establish a model to predict the spread of covid- and infer the most suitable return date for university students. traditionally, the compartment model is used to predict the outbreak of infectious diseases. before building our model, we have an overview of related work. we classify the related work into two categories: models with external floating population and those without. in these papers, conventional models are the models of seir, seiar and seijr. they all have their advantages. for example, the seir model is easy to implement, and the seijr model accurately divides isolated individuals from other groups. however, there is a common disadvantage: the results of longterm prediction are not accurate because these models cannot fit the real situation for a long time. in this paper, we consider some factors that influence the covid- outbreak for a long time and establish the + penta-group model. on the basis of traditional seir model, we add a compartment, i.e., dead individuals, and take into account some parameters, such as the moment when the government began to take measures, and intensity of isolation for exposed individuals. moreover, for some parameters used in our model, we use the collected data to calibrate them in order to achieve as close as possible to the actual situation. then, we establish an analytical model, using simulation of the return rush (back), analytic hierarchy process (ahp) method and technique for order preference by similarity to an ideal solution (topsis) method, called bat model. through the combination of these two models, we can predict the development of the epidemic and draw the pros and cons of different return dates. existing work on prediction of the covid- outbreak can be classified into models without external floating population and those with. previous related work adopts differential equations as the basic form for simulation. the types of models without external floating population are the seir, seiar and seijr models, approximately. the comparison of these models and our model is shown in fig. seir as a traditional infectious disease model, the seir model describes the relationship between susceptible individuals, exposed individuals, infectious individuals, and recovered individuals. fan et al. [ ] , geng et al. [ ] , and zhou et al. [ ] proposed some of the most classic seir models. they directly applied traditional seir model [ ] without any changes to simulate the outbreak in wuhan and other areas. the seir model takes little account of the actual situation, so the long-term prediction is far from the actual value. seijr the seijr model is roughly the same as traditional seir model, but the population is divided into susceptible individuals, asymptomatic individuals during the incubation period, infectious individuals with symptoms, isolated individuals with treatment, and recovered individuals. read et al. [ ] adopted this idea. this model accurately separates isolated and other populations and it is more realistic about the status quo. nevertheless, precise data on each individual are hard to collect, making it difficult to calibrate parameters. therefore, the long-term prediction is far from the actual value. seiar in the seiar model, the difference from the seijr model is that there are no isolated individuals but asymptomatic individuals. bai et al. [ ] followed this approach, and this model has similar characteristics to the seijr model. in addition to these, we find an seir based model with external floating population, which considers the zoonotic force of infection and the daily number of travelers. wu et al. [ ] adopted this model. the simulation is already very close to the beginning of the epidemic. however, as the outbreak progresses, it is drifting away from reality, which makes it unsuitable for long-term forecasting. all of these models have their strengths, but none of them do well in long-term predictions due to the parameters or model accuracy. based on the above experience, our + penta-group model takes into account the long-term nature of the outbreak. we add the dead individuals, whose precise data can be collected to calibrate mortality, to our model and we also add the time of isolation initiation and the intensity of isolation to the model given the long-term impact of the measures that the government has taken. in general, we establish a model that can predict the long-term situation of the outbreak. we establish two models to predict the spread of covid- and figure out the most suitable return time. first, we establish the + penta-group model to predict the future trend of the covid- outbreak in china. then, we propose the bat model to simulate the return rush and consider some factors to obtain the best return time. model for the + penta-group model, we assume that there is no floating population, considering that the government has issued notices and taken measures to keep people at home. moreover, we assume that the recovery rate is positively correlated with the level of medical care, and the mortality is negatively correlated with the level of medical care. the + penta-group model includes six sub-models that describe the flow relationship of each population [ ] . it reflects the complete changes of five groups of people and the overall relationship. in this paper, we use differential equations to simulate the flow of people [ ] . the first model that reflects the change in susceptible individuals is ( ) the second model that reflects the change in exposed individuals is the third model that reflects the change in infectious individuals is the fourth model that reflects the change in recovered individuals is in this model, we separate n d from n r to predict the death toll precisely. moreover, we will discuss the effect of secondary infection in subsection . . this new compartment also benefits this section because secondary infections in dead individuals will never exist. the fifth model that reflects the change in dead individuals is and the sixth model that reflects the overall relationship is the bat model is composed of three parts: simulation of the return rush (back), ahp method and topsis method. first of all, we assume that the infectious rate is positively correlated with the population density, measured by the per capita floor space. on the first day of the spring festival travel rush, before the extended leave notice, people were sent at shanghai hongqiao railway station. moreover on february , people were at the same place. without extended holidays, the per capita area of million people will increase m times: m = . , estimated by data of shanghai hongqiao railway station. then we derive the impacted infectious rate and the number of contacts that would quadruple: β = mβ, and c = c. by replacing the original parameters, we get here we take into account the impact of both the epidemic situation and the delay to rework and return to school, and use ahp method to get the weight of each factor. factors considered in our analysis are the end date of the outbreak, the total number of cases, economic impact, and students' graduation. we establish a weight matrix for these factors, as shown in fig. . then we set up a scoring system to obtain the best return date using topsis method. when constructing the matrix of judgment, we compare factors in pairs using the consistent matrix method [ ] [ ] . the relative scale is adopted to minimize the difficulty of comparing various factors with different properties, to improve accuracy. through the analysis of the questionnaire results, the importance levels of the four relevant factors are determined in a score-based method from equally important (denoted as ) to extremely more critical (denoted as ), as shown in fig. . in terms of importance, relative to the end time, the scores of the number of cases, the economic impact and the end time are , and . , respectively. also, we set up a scoring system to obtain the best return date using topsis method [ ] [ ] . we first determine that both the economic impact and the students' graduation are related to the return time. it is evident that the delay of return will influence graduation of those students while do harm to the economic. then, the end time of the outbreak is subtracted from the original case to get a × matrix. furthermore, we normalize this matrix and add up the product of weight and value of each factor in the matrix. we consider the sum as the highest score. comparing those scores, we finally derive the most suitable return date. with the bat model, we can derive the most suitable return date. to realize the prediction of the future situation of the outbreak, we need to determine the specific values of the parameters in the + penta-group model [ ] . we set the time for the emergence of the first case as t = d. according to the time of the emergence of much news about covid- and the time when people started to pay attention, we set t as d (january , ). the mean time from symptoms onset to isolation is . d (interval: . - . d) [ ] , from which we obtain /α = . . under traffic control, considering the fact that people in hubei were forbidden to leave hubei, and the city's buses, subways, ferries, and long-distance passenger transport were suspended from : am since january , we assume that each person has only daily contact with family members at home, i.e., a census household size of . people per household (from the national data). the total population of china is n = , while the population in hubei is , so the average number of contacts is c = , which is calculated by employing a decentralized average and considered to be the number of people exposed to an exposed person without isolation. for the recovery rate and pneumonia mortality, we apply the latest data to eqs. ( ) and ( ) and get the variation of the recovery rate and pneumonia mortality. at the same time, we can see that these two parameters depend on the time t from at last, we use the nonlinear least square method to get β and p that best match the actual data. when the sum of the squares of the predicted value from the actual value is the smallest, we obtain β = . , p = . . until now, we have all the parameters, and then we set the initial condition as follows: with the initial conditions brought in, we obtain the predicted results of the infections of the covid- outbreak in china, as shown in fig. . to verify the validity of our model, we set the coefficient of determination and the correlation coefficient between the predicted curve and the actual data as the reliability evaluation criteria of the model. the closer the two coefficients are to , the higher the correlation is, which means the higher the reliability of the predicted results is. the final results are r = . and r = . ; both are greater than . , so the correlation is very high. eventually, our model can be considered to be highly reliable. from the prediction results, it is concluded that by the seven-day rule of no new infections, we know that the epidemic will end on may , and the total number of cases is . the number of exposed individuals peaked at on february . the number of infectious individuals peaked at on february . we assume that the general return rush lasts for seven days, and use bat model to evaluate sets of return date (starting from march to april ). finally, we obtain the best time to return to work or study is from march to march , which means universities will start on march . judging from the prediction results, we cannot relax our vigilance at this stage but should wait patiently for the epidemic to end, although the epidemic situation has passed its inflection point. in the following analysis, we assume that the government and people will continue to take strict precautionary measures. while the cured ones will all become susceptible individuals and share the same infectious rate and other equations remain the same, we rewrite eqs. ( ) and ( ) to comply with the presence of secondary infections: the new framework is shown in fig. . we apply eqs. ( ) and ( ) to get the results shown in fig. . the prediction model gives the outbreak prediction results and simultaneously evaluates the prediction of secondary infection at different time, and finally gets almost the same result, from which we can know that there is no need to panic if secondary infection occurs. as long as we continue to take protective measures, the overall situation will not be significantly affected. predictably, the emergence of effective therapies and specific drugs will significantly improve γ and reduce μ. furthermore, we assume that the influence of the emergence of effective drugs on the two parameters has the following three conditions: only the recovery rate increases, only the pneumonia mortality decreases, and both recovery rate and pneumonia mortality change. here, we increase the cure rate to . and reduce the pneumonia mortality by a tenth. we take three values as the possible time for effective drugs to appear: t = d (march , ) , t = d (march , ), and t = d (march , ) and get the results, as shown in table . while the improvement of the cure rate and the reduction in the mortality will increase the number of cured people and reduce the number of deaths, the delay in the presence of effective treatment and drugs will increase the number of deaths but decrease the number of cured individuals. these two parameters have a relatively small impact on the end of the outbreak and the total number of infections. we take the exchange between the first-tier city shanghai and the republic of korea as an example to discuss the influence of the population flow from japan and south korea on the covid- outbreak in china. south korea will suspend most flights to china, according to statements from major korean airlines. we regard the day february as the date of announcement as the time node, and the six routes still open after the time node, which means that flights can be taken. the previous routes have about flights. while the numbers of flights from shanghai to korea are and , we determine that the korean authorities allow only asymptomatic passengers on flights before and after the decision. moreover, in the context of a large population, we use foreign predictive case data to figure out the ratio of exposed people to susceptible people. on the basis of this ratio, the number of exposed and susceptible people arriving in china by plane is estimated. then, it is added to all kinds of people in shanghai to figure out the final prediction result. korean air usually uses boeing , which can carry people between and . we take the mid-value, people and obtain that the daily population flows of korea and shanghai around february are and , respectively. supposing the daily population flow is a, and the proportion of the latent population in the sum of latent population and susceptible population is k, for shanghai, the expressions are using the previous model, we change the data to the infection data of shanghai and obtain the results, and we compare the obtained results with the predicted results without considering the flow between korea and shanghai. by comparison, we find almost no difference in the results. the results differ only by two digit after the decimal point. therefore, we conclude that although the news will strongly report the entry of sick foreigners, it has a relatively small impact on overall epidemic control. we should not be panicked by such reports, nor should we be relaxed because there is no report. we should pay more attention to the protection against the exposed individuals, the main source of infection. in this paper, we establish the + penta-group model to predict the spread of covid- and infer the most suitable return date for university students using the bat model. firstly, we develop a basic seirbased model for predicting the spread of new viruses. secondly, with the help of methods such as ahp and topsis and taking into account various factors, we establish the bat model to obtain an optimal time for the return to work and study, which is of great practical significance. our estimates perform much better in the long run than the estimates of other forecasting models. we are very innovative in introducing the isolation strength parameter and set the isolation time; for example, dead population is added on the basis of seir model. the change of mortality and cure rate varying with time is obtained by fitting instead of a constant, which is scientific. seir-based novel pneumonia transmission model and inflection point prediction analysis analysis of the role of current prevention and control measures in the epidemic of new coronavirus based on seir model preliminary prediction of the basic reproduction number of the wuhan novel coronavirus -ncov global stability analysis on one type of seir epidemic model with floating population novel coronavirus -ncov: early estimation of epidemiological parameters and epidemic predictions early transmission dynamics of novel coronavirus pneumonia epidemic in shaanxi province nowcasting and forecasting the potential domestic and international spread of the -ncov outbreak originating in wuhan, china: a modelling study study on the stability of infectious disease dynamics model survey of transmission models of infectious diseases research on computation methods of ahp weight vector and its applications fuzzy analytic hierarchy process a review of the comprehensive multiindex evaluation method the improved method for topsis in comprehensive evaluation parameter identification for a stochastic seirs epidemic model: case study influenza modelling the epidemic trend of the -ncov outbreak in hubei province key: cord- - gljl n authors: brown, eric e.; kumar, sanjeev; rajji, tarek k.; pollock, bruce g.; mulsant, benoit h. title: anticipating and mitigating the impact of covid- pandemic on alzheimer's disease and related dementias date: - - journal: am j geriatr psychiatry doi: . /j.jagp. . . sha: doc_id: cord_uid: gljl n the covid- pandemic is causing global morbidity and mortality, straining health systems, and disrupting society, putting individuals with alzheimer's disease and related dementias (adrd) at risk of significant harm. in this special article, we examine the current and expected impact of the pandemic on individuals with adrd. we discuss and propose mitigation strategies for: the risk of covid- infection and its associated morbidity and mortality for individuals with adrd; the impact of covid- on the diagnosis and clinical management of adrd; consequences of societal responses to covid- in different adrd care settings; the effect of covid- on caregivers and physicians of individuals with adrd; mental hygiene, trauma, and stigma in the time of covid- ; and the potential impact of covid- on adrd research. amid considerable uncertainty, we may be able to prevent or reduce the harm of the covid- pandemic and its consequences for individuals with adrd and their caregivers. a novel coronavirus, severe acute respiratory syndrome coronavirus (sars-cov- ), was detected in late . it has been identified as the cause of covid- , a respiratory illness of varying severity. on , with covid- affecting countries or territories, the world health organization (who) declared covid- to be a pandemic of -alarming levels of spread and severity‖. while the situation is rapidly evolving, this pandemic has already disrupted the world in three major ways due its direct health impact, its impact on the health care system, and the social and economic consequences of the response to the pandemic. during normal times, individuals with alzheimer's disease and related dementias (adrd) are among the most vulnerable persons in society, depending on family or professional caregivers for their day to day survival. this pandemic exacerbates further their vulnerability, due to both the morbidity and mortality from covid- and the indirect effects of the pandemic on the social supports and the health care system on which they depend. an understanding and appreciation of the current and potential impact of the pandemic on individuals with adrd can help in their care. these considerations can also influence the decisions of caregivers, health professionals, institutions, and policymakers. thus, in the context of a rapidly evolving situation, this special article discusses and proposes mitigation strategies for six major issues: ( ) why individuals with adrd are at high risk for covid- and its associated morbidity and mortality; ( ) how covid- will impact the diagnosis and clinical several features of adrd may increase the risk of contracting covid- . some individuals with adrd may be unable to follow the recommendations from public health authorities to reduce the transmission of covid- : hand hygiene; covering one's mouth and nose when coughing; monitoring for and reporting symptoms of covid- ; maintaining physical distance from others; and self-isolating by remaining alone at home. some with mci or milder dementias may be unwilling or unable to comply due to apathy or depression. those with more severe dementias will not be able to understand, appreciate, or remember most of these recommendations due to the severity of their short-term memory loss and overall cognitive impairment. finally, behavioural and psychological symptoms of dementia (bpsd), such as motor agitation, intrusiveness, or wandering, may undermine efforts to maintain isolation. despite considerable uncertainty and variability in estimates of covid- outcomes, age and comorbid medical conditions have consistently been the most significant factors associated with a poor prognosis including hospitalization and death. [ ] [ ] [ ] age is the best established risk factor both for adrd and for symptomatic and severe illness and mortality from this is illustrated by the situation in italy where over a third of confirmed cases and approximately of deaths are occurring in individuals years and older. precise estimates of outcomes will only be known in time, but they seem to depend on local circumstances such as demographics and resources, in particular the ability of the health care system to cope. beyond age, increased morbidity and mortality is expected in patients with adrd due to the association of adrd with physical comorbidities and other features of adrd. individuals with dementia are more likely to have cardiovascular disease, diabetes and pneumonia compared to individuals of the same age without dementia. these conditions have been associated with poorer outcomes including death, in individuals with covid- . among cases of laboratory-confirmed covid- in china, pneumonia occurred in over % of cases. absent the pandemic, mortality from pneumonia has been reported to be twice higher in individuals with dementia compared to those without dementia. a rapid increase in the number of covid- cases is adversely affecting health systems and is causing a shortage of hospital beds and a strain on health care providers. increased demand on health systems may also result in the diversion of resources away from patients with chronic diseases, including those with adrd. the suspension of elective and non-urgent care is occurring in many affected areas. the availability of urgent and intensive care resources becomes compromised when the prevalence of severe cases of covid- exceeds local resources. individual with adrd may suffer disproportionally from constraints in resources due to the chronic nature of their illness and their specific care needs. the workup and diagnosis of adrd is vulnerable to disruption in several ways. as primary care providers and specialists are being redeployed to address medical emergencies, these physicians are not available to work up neurocognitive disorders. attending a clinic for one or more appointments and visits for blood work and neuroimaging expose frail individuals to risks that may exceed the benefits of timely evaluation and regular monitoring. in many jurisdictions, outpatient physicians have transitioned to providing virtual care, completing assessments and follow-ups by telephone or videoconferencing. these modalities may not be adequate to perform the physical and neurological examinations or some of the cognitive tests required when diagnosing mci or dementia or monitoring their progression. in some cases, it may be possible to provide an initial visit in person and follow-ups remotely. otherwise, diagnosis and care may have to be deferred or limited. the use of anticholinesterase inhibitors and memantine is common in patients with adrd. medications frequently used for the treatment of bpsd include antipsychotic, antidepressant, antiepileptic and other psychotropic medications. patients who are stable on medications may be impacted if the supply of their medication is disrupted due to missed visits, disruption of pharmacy pickup or delivery, or supply chain problems. initiating a new medication during the pandemic may be associated with higher risk, particularly if components of routine screening are disrupted such as in-person clinical assessments, blood work, or electrocardiogram, or the ability to follow up on adverse events in a timely manner. rare but serious adverse events associated with mediations used in the treatment of adrd and bpsd-e.g., bradycardia, gastrointestinal symptoms, falls, fractures, cardiovascular events, or strokes-carry higher morbidity and mortality if access to urgent care is impeded. in the context of social isolation, individuals with adrd who rely on family or health professionals for reminders or assistance with taking their medications are at risk for sudden discontinuation of medications. the risk-benefit ratio of some medications in dementia may shift towards harm if adequate prescribing and monitoring is not possible. common non-pharmacologic interventions for adrd in general, and bpsd in particular, involve social and physical contact such as social groups, exercise groups, and pet therapy. a limitation on resources and a need for physical distancing will not merely suspend these interventions, it will also result in increased isolation, a lack of physical exercise, decreased social engagement, and a suspension of purposeful activity. while confined at home, many people are now using technology to socialize and even exercise in group; individuals with adrd may not be able to use electronic tools and software (see below). resolution of the pandemic may be associated with an increased demand for care that was deferred. individuals with adrd and their family may also need assistance to resume care and address complications that arose from the lack of follow-up and monitoring or from the disruption in health-promoting interventions. the societal response to the pandemic includes travel restrictions and home confinement (-lockdowns‖). people are encouraged or required to isolate socially and not to leave their home. non-essential businesses are shut down. the extent and duration of these social distancing measures is uncertain, but it may be significant and prolonged in some jurisdictions. in this context, many resources upon which patients with adrd depend may become unavailable. depending on the severity of their illness, individuals with adrd live in various settings and rely on the availability and accessibility of various resources. in the context of the covid- pandemic, these settings may influence both the risk and impact of societal consequences of covid- . most individuals with milder adrd have minimal care needs and live in the community where they may have established robust supports. however, their ability to live in the community may be threatened if it depends on services that are disrupted by the pandemic. delivery services such as meals on wheels may be delayed or disrupted due to increased demand, closures, or supply chain failures. family or professional caregivers (e.g., home health care workers) providing in-home support for activities of daily living can also become unavailable due to increased demand, workers' illness, or required isolation due to exposure; some workers may also be prevented by their employer from working in multiple settings. individuals with adrd living in the community may be particularly vulnerable if they are unable to seek help should they fall ill. covid- can be associated with a sudden deterioration of respiratory status and cardiac complications. thus, symptomatic patients require frequent check-ins, while maintaining physical distance. many individuals with adrd who rely on personal savings and investments are also at risk of financial adversity due to the economic consequences of the pandemic. as younger people, they may need to access government programs for financial support. also, they are less likely to drive a personal vehicle, instead relying on mass transit or transportation services that increase their exposure and risk of infection. they may benefit from assistance in identifying safe means of transportation, and in reducing their need to leave home by facilitating deliveries and deferring non-essential travel. those living alone in the community may also suffer from loneliness due to increased isolation and disruption of group activities. creative ideas to incorporate alternative social physical activities safely within the home are needed. whereas people are turning to technology to stay socially connected and access services including health care, some individuals with adrd may have trouble using technology due to cognitive impairment. they need instruction and support to use of these tools. as with any disaster, individuals with adrd and their family need to make contingency plans for the provision of essential services. families' and caregivers' awareness of the potential risks and disruptions described above for patients with adrd living in the community may help mitigate their impact. potential mitigation strategies include increased support in the form of more frequent contact by telephone or video chat, problem solving to maintain delivery and caregivers' services, planning for potential disruption, or temporarily moving to a location where the required supports can be provided. paradoxically, some families may be able to temporarily provide support at home because they are unable to work due to lockdowns or other restrictions. many of the issues faced by individuals with adrd in the community also apply to those living in group and assisted living environments. in some cases, the increased risk of infection associated with large groups may shift the risk-benefit ratio towards returning to one's home, if it is an option. however, many individuals with adrd require a supportive living environment because of a decreased level of functioning. in these settings, physical touching and toileting, crowding and shared rooms, and staff working in multiple settings may further increase the risk of covid- transmission. as discussed above, features of moderate to severe dementia such as severe memory impairment, and bpsd such as wandering, and agitation may thwart attempts to promote the actions recommended to reduce risk of transmission. in the other direction, imposition of increased hand hygiene, isolation, or restriction of visitors and activities may worsen cognitive symptoms or bpsd, increasing further care needs and risks. individuals with adrd living in long term care (ltc) (-nursing homes‖) face all the challenges of those in supportive living environments, and additional risks. their higher dependence on caregivers and health care providers eliminates the possibility of physical distancing. in these settings, personal protective equipment (ppe) may be rationed for confirmed or suspected cases or even become unavailable. when covid- affects ltc homes, it can have a high attack rate and case fatality rate-for example, a case fatality rate of . %- fatalities among affected residents-has been reported in a washington state ltc. this home also experienced a significant disruption to staffing, with health care workers reported to be infected. many staff of ltc work at multiple facilities or in private homes increasing the risk of transmission and disruption of care beyond an impacted facility. patients with adrd are hospitalized due to bpsd, comorbid illness, or inability to care for themselves and lack of access to supportive services or ltc. hospitals present the same risks as ltc, with additional risks. hospital staff and physicians are highly vulnerable to contracting covid- : of the first , confirmed cases in china (as of february , ), , ( . %) were health care workers and professionals, as were , ( . %) of the first , confirmed cases in italy (as of march , ) . the risk of covid- nosocomial infection is high due to high staff ratios and turnover, high patient volumes, crowded rooms, rapid inflow of detected and undetected cases of covid- , and constrained supply of ppe. for reasons discussed above (age, comorbidities, behavioral and cognitive problems), individuals with adrd are among those at highest risk of nosocomial infection. in many communities affected by covid- , hospitals get strained or overwhelmed. hospitalized individuals with adrd may be particularly affected because they are less able to monitor their care or advocate for themselves. decreased nursing time has been shown to be associated with increased medical errors and adverse events in dementia. the need for hospitalization implies a more severe illness. patients with severe bpsd may be at even higher risk for the behaviours discussed above that elevate transmission of infection. on a south korean psychiatric ward, of inpatients were infected and died during a covid outbreak. upon admission, hospitals need to evaluate the risk to individuals with adrd and the risk to others, in the context of potential, suspected, or confirmed cases of covid- . planning for these situations is needed to clarify the ethical issues, local legal framework, and institutional policies that impact a decision with respect to the need for and use of locked seclusion, chemical and physical restraints, and end of life or palliative care in high risk situations. regardless of choices made by patients with adrd or their family members, health care interventions taken for granted may have to be rationed in some jurisdictions affected by the pandemic (see below). in addition to the usual settings in which patients with adrd receive care, the pandemic will force some patients into unexpected and suboptimal environments with their own challenges. hospitals dealing with or preparing for a surge in covid- patients are discharging or diverting some patients with milder cases to hotels, convention centres, tents, and shipping containers. while the physical needs of some medically stable patients with adrd may be met in these alternative settings, their cognitive and behavioral needs may not. during the pandemic, the perennial lack of availability of safe and adequate housing options for individuals with adrd, combined with an unprecedented strain on medical and social resources, could create its own crisis, leading to unprecedented levels of morbidity and mortality in this frail population. as most patients with adrd depend on caregivers, the impact of the pandemic on formal and informal caregivers need to be considered. in the best of time, the physical and mental health of some caregivers is precarious. during this pandemic, some caregivers may become ill, they may need to isolate and be unavailable, or they may develop anxiety and other mental health issues. as discussed above, due to the sudden unavailability of established services, family members may have to become caregivers for a relative with adrd. grief and its consequences are likely in family caregivers who have lost a loved one and in professional caregivers who have lost a patient. all of the above will lead to exhaustion and burnout. as discussed above, specific aspects of caring for individuals with adrd are incompatible with physical distancing. inadequate or unavailable ppe or training related to its use sets the stage for viral transmission. responding to agitation and threats of violence typically requires urgent interventions that impede proper ppe use and increase further the risk of viral exposure. many patients with adrd have -do not resuscitate‖ status, including advanced directives not to transfer them to an acute medical floor. as a result, in some settings, if these patients develop covid- , neurologists, geriatricians, geriatric psychiatrists, or primary care providers will have to practice out of their scope and care, managing the symptoms and distress associated with pneumonia. however, this issue goes beyond covid- and pneumonia. as discussed above, during this pandemic, many patients with adrd who want to receive the full spectrum of care, including intensive care and intubation, may not be able to access optimal acute care for any medical issue, not just covid- . all physicians may have to treat a variety of medical issues that would have otherwise been treated by specialists. preparatory discussions with patients and family members are needed to clarify the goals of care should these dire circumstances arise; they are particularly crucial if advance discussion of code status have not yet occurred or are not clearly documented. health care workers involved in adrd care are already exposed to suffering and deaths. their stress and anxiety may be further increased by the current risk to their own safety. the number of cases, deaths and societal impact of covid- has already exceeded those observed during the epidemic of severe acute respiratory syndrome (sars). as following sars, we need to be prepared to address the serious and long-term mental effects of covid- on health care workers, including post-traumatic stress disorder and depression. the covid- pandemic threatens to disrupt not the active care of individuals of adrd, but also the basic routines that promote their mental health. the pandemic and its social consequences may cause fear, anxiety, and anger. they will disrupt all forms of social interaction, possibly for a prolonged period of time. a lack of physical closeness may lead to increased loneliness and sadness. exercise is recommended generally and specifically for individuals with adrd, and confinement reduces access to exercise. sleep disturbances is common in adrd and sleep may be further disrupted due to anxiety and loss of social rhythms (-zeitgeists‖). in turn, lack of activities and sleep loss and stimulation may cause delirium in individuals with adrd, contributing further to morbidity and mortality. like health care workers, individuals with adrd may experience the loss of friends and family due to covid- . these losses may lead to grief, bereavement, or frank depression, a common feature of adrd. the pandemic and its consequences may also be experienced as a trauma, followed by post-traumatic stress disorder. in turn, stress and trauma can accelerate cognitive decline. age, illness, depression, trauma, and dementia are all risk factors for suicide. during the pandemic, individuals with adrd may be doubly stigmatized. stigma is already a pervasive issue in adrd. individuals with, or at risk of exposure to, covid- have been stigmatized. risks of stigma include ostracization and denial of health and social services, which comes at time of potential scarcity of resources to be allocated. rationing raises triage issues beyond some of the logistical issues discussed above. will older individuals with mild adrd be able to access intensive care beds? if they are already on a ventilator, will they be taken off to reallocate these scarce resources to younger patients? how will these decisions be made ethically? what will be the psychological impact of triage on health professionals? a response to these complex questions is beyond the scope of this paper. however, some ethicists have proposed a framework to address these issues in the unprecedented context of the covid- pandemic. the discussion above has focused exclusively on the immediate risks and impact of the as per the declaration of helsinki, -concern for the interests of the subject must always prevail over the interest of science and society.‖ therefore, all research activities such as observational studies in which participants are exposed a potentially lethal infection (e.g., through face-to-face contact with research staff) without the possibility of any direct benefit should be suspended unless they can be continued entirely remotely. when participation in a study entails provision of essential medical care (e.g., an intervention that is only available through a research trial), continuation of the study should be considered with the maximum possible mitigation of the risk of infection. the us food and drug administration (fda) has issued some guidance regarding continuation of research participation for intervention studies and how to mitigate the risks to participants and to the integrity of the research studies during the pandemic. adapting and protecting the integrity of research activities during a pandemic research activities have been and remain critical in advancing medical knowledge and alleviating the suffering for millions of future patients, particularly in the field of adrd, for which no new medication has been approved since . clinical investigators can explore creative ways to continue their studies while mitigating the risk of covid- infection both for research participants and staff. this may require modification of study protocols to collect safety and endpoint assessments remotely. some assessments (e.g., follow-up neuroimaging for a secondary outcome) may need to be deferred or missed. challenges in terms of selective retention, measurement errors, data missing not at random, and other confounds will need to be addressed in the analyses and reporting of the results. when a study cannot be done entirely remotely because it requires in-person visits (e.g., a trial requiring regular monitoring of safety lab tests), the increased risk of participation associated with in-person visits needs to be discussed explicitly with participants-or, in the cases of most studies involving participants with moderate to severe adrd, their substitute decision maker (sdm). the established relationship between participants (or their sdms) and the research staff will facilitate these discussions. institutional review boards (irbs) and data and safety management boards (dsmbs) would also need to be involved in reassessing the risk/benefit ratio of continuing participation in these studies. a few clinical trials may consider not just to continue following and monitoring current participants, but also to recruit new participants. except for some rare trials of purely psychosocial interventions, baseline assessments and safety lab tests would require in-person visits. again, this would require the involvement of the irb and dsmb and careful discussion with possible participants or their sdm and documentation of this consent process. as with any major crisis, the covid- pandemic will have a lasting impact on the way all clinical research, including adrd research, is carried out. the current challenging situation is forcing researchers to think how they could conduct most research procedures remotely. it will accelerate the adoption of technologies and tools that permit remote assessments. [ ] [ ] [ ] in the field of adrd research, we believe it will impact most the traditional neuropsychological and functional assessments on which most primary outcomes for adrd interventions trials are based. in the long term, adrd research will also benefit from these technological innovations because they should allow the recruitment and follow-up of much larger samples at reduced costs. finally, the covid- crisis may expedite the development of non-pharmacological interventions that can be delivered the home of participant, e.g., homebased cognitive training or physical exercise, or that use small portable devices that can be easily used in private homes, e.g., transcranial direct current stimulation and similar devices. the covid- pandemic is disrupting the world and its health care systems in unprecedented ways. this pandemic also threatens the integrity and viability of current and future adrd research. local impact will vary and evolve depending on specific factors, including the incidence of covid- , the associated death rates, the availability of resources, and the societal changes implemented to control the pandemic. these local variations combined with the heterogeneity of adrd make simple generic recommendations ineffectual. however, awareness of this possible impact and mitigation strategies adapted to individual and local circumstances may prevent or reduce the harm of this pandemic and its consequences for persons with adrd and their caregivers. eric brown: substantial contributions to the conception or design of the work and the acquisition, analysis, or interpretation of data for the work; drafting the work or revising it critically for important intellectual content; final approval of the version to be published; and agreement to be accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved. sanjeev kumar: substantial contributions to the conception or design of the work; the acquisition, analysis, or interpretation of data for the work; drafting the work or revising it critically for important intellectual content; and final approval of the version to be published bruce g. pollock: substantial contributions to the conception or design of the work; or the acquisition, analysis, or interpretation of data for the work; and final approval of the version to be published. tark k. rajji: substantial contributions to the conception or design of the work; or the acquisition, analysis, or interpretation of data for the work; and final approval of the version to be published. benoit h. mulsant: substantial contributions to the conception or design of the work and the acquisition, analysis, or interpretation of data for the work; drafting the work or revising it critically for important intellectual content; final approval of the version to be published; and agreement to be accountable for all aspects of the work in ensuring that 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during covid- pandemic. u.s. food and drug administration digital biomarkers for alzheimer's disease: the mobile/wearable devices opportunity sensing technology to monitor behavioral and psychological symptoms and to assess treatment response in people with dementia feasibility of remotely supervised transcranial direct current stimulation and cognitive remediation: a systematic review telephone-based screening tools for mild cognitive impairment and dementia in aging studies: a review of validated instruments front key: cord- -gpnaldjk authors: gomes, m. gabriela m. title: a pragmatic approach to account for individual risks to optimise health policy date: - - journal: nan doi: nan sha: doc_id: cord_uid: gpnaldjk developing feasible strategies and setting realistic targets for disease prevention and control depends on representative models, whether conceptual, experimental, logistical or mathematical. mathematical modelling was established in infectious diseases over a century ago, with the seminal works of ross and others. propelled by the discovery of etiological agents for infectious diseases, and koch's postulates, models have focused on the complexities of pathogen transmission and evolution to understand and predict disease trends in greater depth. this has led to their adoption by policy makers; however, as model-informed policies are being implemented, the inaccuracies of some predictions are increasingly apparent, most notably their tendency to overestimate the impact of control interventions. here, we discuss how these discrepancies could be explained by methodological limitations in capturing the effects of heterogeneity in real-world systems. we suggest that improvements could derive from theory developed in demography to study variation in life-expectancy and ageing. using simulations, we illustrate the problem and its impact, and formulate a pragmatic way forward. since the detection of aids in the early s, it has been evident that heterogeneity in individual sexual behaviours needed to be considered in mathematical models for the transmission of the causative agent -the human immunodeficiency virus (hiv) . much research has been devoted to measuring contact networks in diverse settings and by different methods, to attempt to reproduce transmission dynamics accurately [ ] [ ] [ ] . meanwhile other equally important sources of inter-individual variation were overlooked. for example, unmodelled heterogeneity in infectiousness and susceptibility led to over-attribution of hiv infectivity to the acute phase and, consequently, to concerns that interventions relying on treatment as prevention might be compromised. the problem of unaccounted heterogeneity in predictive models can be illustrated with the simplest mathematical description of infectious disease transmission in a host population. figure shows the prevalence of infection over time under three alternative scenarios: all individuals are at equal risk of acquiring infection (black trajectories [notice unrealistic time scale]); individual risk is affected by a factor that modifies either their susceptibility to infection (blue) or exposure through connectivity with other individuals (green). risk modifying factors are drawn from a distribution with mean one (blue and green density plots on the left) while the homogeneous scenario is sketched by assigning a factor one to all individuals (black frequency plot). as the virus spreads in the human population, individuals at higher risk are predominantly infected as indicated at endemic equilibrium (figure a, b , c, density plots on the right, coloured red) and after years of control (figure d, e, f). the control strategy applied to endemic equilibrium in the figure is the - - treatment as prevention target advocated by the joint united nations programme on hiv/aids whereby % of infected individuals should be detected, with % of these receiving antiretroviral therapy, and % of these should achieve viral suppression (becoming effectively non-infectious). ; distributed susceptibility to infection with variance (b, e); distributed connectivity with variance (c, f). in disease-free equilibrium, individuals differ in potential risk in scenarios b and c, but not in scenario a (risk panels on the left). the vertical lines mark the mean risk values ( in all cases). at endemic equilibrium, individuals with higher risk are predominantly infected (risk panels on the right, where red vertical lines mark mean baseline risk among individuals who eventually became infected), resulting in reduced mean risk among those who remain uninfected (black vertical lines). to compensate for this selection effect, heterogeneous models require a higher ! to attain the same endemic prevalence (a, b, c). interventions that reduce infection also reduce selection pressure, which unintendedly increases mean risk in the uninfected poll and in heterogeneous models, ( ) is a probability density function with mean and variance , and 〈 # 〉 denotes the th -moment of the distribution. gamma distributions were used for concreteness. figure shows that heterogeneous models that account for wide biological and social variation require higher basic reproduction numbers ( ! ) to reach a given endemic level and predict less impact for control efforts when compared with the homogeneous counterpart model. this holds true regardless of whether heterogeneity affects susceptibility or connectivity. at endemic equilibrium, individuals at higher risk are predominantly infected (red distributions have mean greater than one as marked by the red vertical lines), and hence those who remain uninfected are individuals with lower risk (blue and green distributions have mean lower than one as marked by the black vertical lines). thus, the mean risk in the uninfected but susceptible subpopulation decreases, and the epidemic decelerates (thin blue and green curves); higher values of ! are consequently required if the heterogeneous models are to attain the same endemic level as the homogeneous formulation (heavy blue and green curves). finally, interventions are less impactful under heterogeneity because ! is implicitly higher. indeed, these biases could help explain trends in hiv incidence data which lag substantially behind targets informed by model predictions, even in settings that have reached the - - implementation targets , . a novel severe acute respiratory syndrome coronavirus (sars-cov- ) isolated at the end of from a patient in china has spread worldwide causing the covid- pandemic, despite intensive measures to contain the outbreak at the source. countrywide epidemics have been extensively analysed and modelled throughout the world. initial studies projected attack rates of around % if transmission had been left unmitigated , while subsequent reports noted that individual variation in susceptibility or exposure to infection might reduce these estimates substantially risk distributions are simulated in three scenarios: homogeneous (black); distributed susceptibility to infection with variance (blue); distributed connectivity with variance (green). left panels represent distributions of potential individual risk prior to the outbreak, with vertical lines marking mean risk values ( in all cases). as the epidemic progresses, individuals with higher risk are predominantly infected, depleting the susceptible pool in a selective manner and decelerating the epidemic. the inset overlays the three epidemic curves scaled to the same height to facilitate shape comparison. right panels show in red the risk distributions among individuals who have been infected over months of epidemic spread (mean greater than one when risk is heterogeneous, as marked by red vertical lines) and the reduced mean in heterogeneous models, ( ) is a probability density function with mean and variance , and 〈 # 〉 denotes the thmoment of the distribution. gamma distributions were used for concreteness. as models inform policies, we cannot but stress the importance of representing individual variation pragmatically. while much is being discovered about sars-cov- and its interaction with human hosts, epidemic curves are widely available from locations where the virus has been circulating. models can be constructed with inbuilt risk distributions whose shape can be inferred by assessing their ability to mould simulated trajectories to observed epidemics while accounting for realistic social distancing interventions . variation in infectiousness was critical to attribute the scarce and explosive outbreaks to superspreaders when the first sars emerged in , but what we are discussing here is different. infectiousness does not respond to selection as susceptibility or connectivity do, i.e. models with and without variation in infectiousness perform equivalently when implemented deterministically and only differ through stochastic processes. the need to account for heterogeneity in risk to acquire infections is not restricted to aids and covid- but is generally applicable across infectious disease epidemiology models. moreover, similar issues arise in methods intended to evaluate the efficacy interventions from experimental studies as illustrated for vaccines in the sequel. individual variation in susceptibility to infection induces biases in cohort studies and clinical trials. vaccine efficacy trials offer a useful illustration of the problem and give insight into the potential solution. in a vaccine trial, two groups of individuals are randomised to receive a vaccine or placebo and disease occurrences are recorded in each group. as disease affects predominantly higher-risk individuals, the mean risk among those who remain unaffected decreases and disease incidence declines. in the vaccine group the same trend will occur at a slower pace (presuming that the vaccine protects to some degree). as a result, the two randomised groups become different over time with more highly susceptible individuals remaining in the vaccine group. the vaccine efficacy, described as a ratio of cases in vaccinated compared to control group, therefore appears to wane (figure ) , . this effect will be stronger in settings where transmission intensity is higher, inducing a trend of seemingly declining efficacy with disease burden . the concept is illustrated in figure by simulating a vaccine trial with heterogeneous and homogeneous models analogous to those utilised in figures and . selection on individual variation in disease susceptibility thus offers an explanation for vaccine efficacy trends that is entirely based on population level heterogeneity, in contrast with waning vaccine-induced immunity, an individual-level effect . as both processes may occur concurrently in a trial, it is important to disentangle their roles, as they lead to different interpretations of the same incidence trend. for example, vaccine efficacy might wane in all individuals, or it might be constant for each individual but decline at the population level due to selection on individual variation. to capture this in a timely manner requires multicentre trial designs with sites carefully selected over a gradient of transmission intensities (e.g. optimally spaced along the incidence axis in figure c, f) , and analyses performed by fitting curves generated by models that incorporate individual heterogeneity. an alternative and more tightly controlled approach would be to use experimental designs in human infection challenge studies where these are available to generate dose-response curves and apply similar models. these approaches have recently been successfully tested in animal systems . heterogeneities in predispositions to infection depend on the mode of transmission but play a role in all high-burden infectious diseases. in respiratory infections, heterogeneity may arise from a variation in exposure of the susceptible host to the pathogen, or the competence of host immune systems to control pathogenic viruses or bacteria. these two processes have multiple the mechanisms underpinning single factors for infection and their interactions determine individual propensities to acquire disease. these are potentially so numerous that to attain a full mechanistic description may be unfeasible. even in the unlikely scenario that a list of all putative factors may be available, the measurement of effect sizes would be subject to selection within cohorts resulting in underestimated variances . to contribute constructively to the development of health policies, model building involves compromises between leaving factors out (reductionism) or adopting a broader but coarse description (holism). holistic descriptions of heterogeneity are currently underutilised in infectious diseases. recently, measures of statistical dispersion commonly used in economics have been adapted to describe risk inequality in cancer , tuberculosis and malaria , offering a holistic approach to improve the predictive capacity of disease models. essentially, this involves stratifying the population into groups of individuals with similar risk, which may be as granular as individual level for frequent diseases, such as malaria or influenza. for infectious diseases which cluster by proximity, such as tuberculosis, stratification can use geographical units. familial relatedness pertains when there is a clear genetic contribution to risk, such as cancer. by recording disease events in each group, specific incidence rates can be calculated and ranked. unknown distributions of individual risk are then embedded in dynamic models and estimated by fitting the models to the stratified data. because they incorporate explicit distributions of individual risk, these models automatically adjust average risks in susceptible pools to changes in transmission intensity, occurring naturally or in response to interventions. not subject to the selection biases described above, this model approach inherently enables more accurate impact predictions for use in policy development. there is compelling evidence that epidemiologists could use indicators that account for the whole variation in disease risk. heterogeneity is unlimited in real-world systems and cannot be completely reconstructed mechanistically. inspired by established practices in demography and economics and supported by successful applications in both infectious and non-communicable diseases, the use and further development of these approaches offers a powerful route to build disease models that enable more accurate estimates of intervention efficacy and more accurate predictions of the impact of control programmes. an application of the theory of probabilities to the study of a priori pathometry, part i modeling infectious disease dynamics in the complex landscape of global health is the unaids target sufficient for hiv control in botswana? joint united nations programme on hiv/aids (unaids), global aids update 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superspreading and the effect of individual variation on disease emergence estimability and interpretability of vaccine efficacy using frailty mixing models apparent declining efficacy in randomized trials: examples of the thai rv hiv vaccine and caprisa microbicide trials clinical trials: the mathematics of falling vaccine efficacy with rising disease incidence seven-year efficacy of rts,s/as malaria vaccine among young african children design, recruitment, and microbiological considerations in human challenge studies vaccine effects on heterogeneity in susceptibility and implications for population health management understanding variation in disease risk: the elusive concept of frailty inequality in genetic cancer risk suggests bad genes rather than bad luck introducing risk inequality metrics in tuberculosis policy development modelling the epidemiology of residual plasmodium vivax malaria in a heterogeneous host population: a case study in the amazon basin key: cord- - pmts ui authors: nema, vijay title: microbial forensics: beyond a fascination date: - - journal: dna fingerprinting: advancements and future endeavors doi: . / - - - - _ sha: doc_id: cord_uid: pmts ui microbiology has seen a great transition from culture-based identification of microbes using various biochemical and microscopic observations to identify and functionally characterize the microbes by just collecting the dna and sequencing it. this advancement has not only moved in and around microbiology but has found its applications in fields which were earlier considered to be the remote ones. forensics is one such field, where tracing the leftover evidence on a crime scene can lead to the identification and prosecution of the culprit. when leftover microbes in the biological material or objects used by the culprit or the person in question are used to correlate the identity of the individual, it takes us to the new field of science—“microbial forensics.” technological advances in the field of forensics, molecular biology, and microbiology have all helped to refine the techniques of collecting and processing of the samples for microbiological identification using dna-based methods followed by its inference in the form of evidence. studies have supported the assumption that skin or surface microflora of an individual is somewhat related with the microflora found on the objects used by that individual and efforts are ongoing to see if this is found consistently in various surroundings and with different individuals. once established, this technique would facilitate accurate identification and differentiation of an individual or suspect to guide investigations along with conventional evidence. legal investigations are not only the field where microbial forensic could help. agriculture, defense, public health, tourism, etc. are the fields wherein microbial forensics with different names based on the fields are helping out and have potential to further support other fields. tracing the leftover evidences on a crime scene remained the only way of getting to the culprit. the history and evolution of forensic sciences has been very fascinating and interesting for even those who do not understand the science behind it. the journey started with william james herschel sometimes in when he recognized that the fingerprints remain unique to the individuals. it was used on legal and administrative documents then and was published in with all evidences and their analysis [ ] . it was gradually picked up for all possible uses including crime scene investigations. fingerprints remained the landmark evidence in all forensic investigations and are still playing important roles. additional techniques came in to support forensics in the form of dna fingerprinting, wherein dna matching became useful in various cases. dna fingerprinting is used to establish a link between biological evidence and a suspect in a criminal investigation [ ] [ ] [ ] [ ] [ ] . dnaor genetic-fingerprinting relies heavily on the principle that no two individuals share the same genetic code. recently, there has been a new discipline co-emerged with culture-independent techniques of identifying microbes. this new discipline looks for microbes and tries to co-relate them with individuals as like fingerprints or dna. there is a constant interaction of individuals with microbes in their surrounding, and they leave microbes into their surroundings. whenever there is a physical contact, bacteria hop across from the skin to the material used. the microbial communities attached with an individual's skin or other sites are being explored, and preliminary evidences suggest that they are unique and can identify individuals or the material used by them in a few cases [ ] [ ] [ ] . this became the base for coining of a new term "microbial forensics." however the field has other dimensions too and would be discussed in detail in this chapter. the microbial forensics rely on the inputs from various fields of basic and applied sciences. these include microbiology, genetics, bioinformatics, forensic science, immunology, population genetics, biochemistry, molecular biology, epidemiology, etc. along with the law enforcement, public health, policy, and intelligence communities. bacterial density on the human skin may be as high as cells/cm [ ] and can be freely transferred to surface which comes in contact. evaluating the traces of skin microbiome left on questioned objects may be useful for forensic identification. calculating the distances from samples and their donators, it seems possible to estimate whether items or palm prints belong to one specific person or not. this has become possible because of the culture-independent method of tracing all microbial species present in a given environment. this technique used here is called nextgeneration sequencing, and the population of microbes no matter cultivable or nonculturable is called microbiome. in this process, total dna of the given environment or object is taken out, and the specific gene for prokaryotes, i.e., srrna gene, is amplified. this gene has a property like a clock with fast-moving arm and slowmoving arm. this concept has been explained by the work of karl woose who named this gene as a biological clock [ ] [ ] [ ] [ ] . the gene contains highly conserved regions to identify the microbes with consistency and at the same time some variable regions to differentiate between closely related microbes. the technique has advantages over dna from individuals as the microbiome dna is abundant in touch dna, and these organisms are much more stable because of complicated cell wall structures. hence, it might be easier in certain instances to extract bacterial dna than human dna from surfaces target samples. another good reason for this is the higher abundance of bacterial cells on the skin and shed epidermal cells as compared to human cells. there are some surfaces like fabrics, smudged surfaces, or highly textured surfaces from where obtaining clear fingerprints is very difficult. bacterial dna can still be found there and can help in solving the purpose [ ] . microbiology and forensic science were always considered to be different fields, and establishing a link between the two for better investigative power was not thought of earlier. microbiology is simply defined as study of microorganisms wherein microorganisms are the organisms that exist as single cells or cell clusters and must be viewed individually with the aid of a microscope. microbiology classifies microbes into various groups, and based on their characteristics and physiology, they could be assigned different genera and species. most of the microbes, especially the saprophytic ones, depend on other substrates and interact specifically with their environment and habitat to gain important nutrients for their survival. this requirement remains very specific and unique with respect to one community of microbes and here comes a link with forensic sciences. forensic science explores about those unique things (belongings or body remains) which could be co-related with the career (criminal) of those things, for instance, fingerprints or dna. because microbial communities on a particular individual's body are expected to be unique, identifying that individual with leftover microbial traces on the material used by the individual is a possibility and is being confirmed using various experiments. however, culturing of all those microbes and identifying them is a near impossible task. the reason is that all microbes do not grow on known culture media, and some which can grow are sometimes overtaken by the competition with other microbes in the same community. hence collecting the total dna and amplifying for the microbial signature gene is a good solution ( fig. . ). this technique is called metagenomics. further, a sequencing technique that sequences the metagenome is called next-generation sequencing (ngs). ngs also known as high-throughput sequencing, represents different modern sequencing technologies for sequencing dna and rna much faster than sanger sequencing and with lower economical and technical inputs. identifying individuals is important in forensic science, and various developments have supported it from time to time. however, while making use of dna, its quantity becomes crucial for accurate detection with desired quality for prosecution of crime. a smart offender can be cautious enough to decrease or degrade the traces of biological leftovers like blood, semen, etc. along with the fingerprints from the crime scene, which can complicate offender detection. hence although fingerprints and dna fingerprints remain very precise techniques, the availability of raw material becomes limiting factor in their use. microbes can help in such scenario as their dna is not as easily destroyed as a human dna and remains available on surfaces at crime scene or on objects used. the pattern of bacterial dna is dictated by the surrounding environment and the individual's microbiome [ , ] . it is possible that the different bacterial patterns or the type of bacteria with typical physiology could discriminate individuals with different lifestyles. hence, bacterial dna analysis may serve as a complimentary technique in cases where standard dna identification is partially informative [ ] . along with this, technologies like pcr, real-time pcr, mlst (multilocus sequence typing), mlva (multilocus vntr analysis), fish (fluorescence in situ hybridization), and microarrays are being employed based on the need of the case or the availability of the infrastructure. additional new methodologies like matrix-assisted laser desorption/ionization-time of flight (malditof), gas chromatography-mass spectroscopy (gc-ms), and liquid chromatography-mass spectroscopy (lc-ms) are also well established in resolving minor difference in bacterial strains. investigation of a crime scene is not just potential application wherein microbial forensics can play an important role. bioterrorism, biosecurity, biometry, medical forensics, etc. are the upcoming fields wherein definitive detection of microbes and their correlations may help a lot. research on the transmission of microbes between human and surrounding environments has proved to be a property with potential for microbiome to be used in forensic investigations. in some cases, typical human microbial associations have been used to relate individuals to objects they have used [ ] . pattern of associated microbes with the surfaces at home and the family living and working with them have shown a predictive correlation to an extent that family's home and that individuals within a home can be differentiated [ ] . similar is the case with smartphones which rather remain in contact with specific individual and for longer durations [ ] . interestingly the microbial communities were different on the top and bottom of the phone differentiating the individuals and surface flora. an interesting property of the deposited microbiome is that it changes with a constant rate on a particular surface and can be utilized for forensic calculations. work by metcalf and co-workers have revealed that postmortem, the microbiome of animal hosts changes radically, but the pattern is much more predictable [ ] . this can help tracing the time and direction of the events. lax and co-workers worked to determine if the surface type and individuals have an effect on the microbial communities and have found that microbial community structure was determined both by surface type and participant. another aspect of microbial forensics is its role in bioterrorism. herein the microbial forensics could be defined as "the discipline of applying scientific methods to the analysis of evidence related to bioterrorism, biocrimes, hoaxes, or the accidental release of a biological agent or toxin for attribution purposes" [ ] . microbial forensics, while dealing with bioterrorism, concentrate on identification of the agent or toxin and/or the mode of its production and dissemination. in addition, traditional forensic methods are used in conjunction to reach the goal of identifying the perpetrators of the crime. around , microbial species or strains are listed as dangerous for humans [ ] . building individual diagnostic methods for these many numbers of agents is an impossible task, and hence ngs is the only tool to do massive parallel sequencing and to identify unknown pathogens, microorganisms modified to create panic, and pathogens in complex communities or samples with low abundance. with the global expansion of trade and communication, frequent movement of individuals from one country to other is unavoidable. in such scenario carriage of an endemic pathogen or drug resistance to a new geographical region is a looming threat. recent outbreaks and transmission incidents of sars and ebola have raised an alert. microbial forensic has a crucial role in such cases wherein the status is not declared by individuals, is not detected by routine quarantine, or is a new pathogen altogether. detection of microbial drug resistance or the emerging resistance is becoming increasingly important for human health. similar things are true in the case of plant pathogens and food borne diseases [ , ] . the foodborne diseases have always been a substantial global challenge to public health. a huge population worldwide become sick of foodborne illnesses every year with a substantial burden on public health as well as on economy. addressing this problem has many steps, out of which one age-old problem is the rapid identification of the food source of the contamination. in a classic laboratory study, we could trace back the source of the foodborne outbreak, but the finding could not be utilized in helping the troubled ones immediately [ ] . this is due to the infrastructural limitations and technical challenges in identifying the pathogens. a technology which was considered to be reliable and was used till recent past was pulsed-field gel electrophoresis (pfge). however its resolution in pinpointing the source of the outbreak has not been satisfactory. recent employment of whole-genome sequencing (wgs) in such investigations has shown promise. a retrospective study by us food and drug administration's center for food safety and applied nutrition (fda-cfsan) in could provide a far better resolution of the causal factors. all the isolates were sequenced on the illumina miseq. wgs using illumina could distinguish all of the isolates which looked exactly the same. ultimately they concluded that the isolates from the outbreak were most closely related to a -year-old historical isolate that was linked to a processing facility only km away from the source of the outbreak [ ] . this could not only allow newer findings but also traced back the source of contamination to further allow the rectification. such cases are sometimes accidental but are often criminal too, and tracing back the source would prevent such cases. in bio crimes, serious disease outbreak by natural occurrence or intentional may result in harm or death, causing disruption, creating fear, and affecting economic well-being. microbial forensics thus plays an important role in consumer protection, food security, and even in litigation. agriculture and agricultural goods are also the susceptible area for microbial interventions and hence are important in terms of microbial forensics. there could be deliberate misuse of microbes or their products affecting flora and fauna which is important for agriculture. this could be given a name such as "agroterrorism" [ ] . a field of investigation emerged against this threat for investigating into the violations and used scientific knowledge and technology to do so. this was given the name of bioforensics [ ] . another aspect of microbial forensic application to the foodborne pathogens is to trace pathogens in cash crops especially spices and other costly ones. van doren and co-workers have studied reported illness outbreaks from canada, denmark, england and wales, france, germany, new zealand, norway, serbia, and the united states which occurred due to consumption of pathogen-contaminated spice during - . the outbreaks were reported from a few developed countries only. the reason for not including other countries was that those countries did not have updated technology to investigate and report similar findings. it was reported that these outbreaks resulted in human illnesses, hospitalizations, and deaths. infants/children were the primary population segments impacted by % ( / ) of spice-attributed outbreaks [ ] . the economic aspect associated here is the detection of pathogens after shipment and then the recall of the material. this involved a huge cost. recent development in microbial forensics in agricultural sciences also aids in pest control as well as deliberate introduction of pests along with food imports or use of pathogens as anticrop bioweapons. different companies are coming up with molecular detection tools for rapid detection of specific pathogens in such products. for instance, hu and co-workers have compared and evaluated the effectiveness of the molecular methods ( m molecular detection system (mds) and ansr pathogen detection system (pds)) for the detection of salmonella in egg products and compared the same with culture methods to find that the molecular methods are the superior and faster ones [ ] . budowle and co-workers have established a criterion comprising a foundation for investigators to establish, validate, and implement high-throughput sequencing (hts) as a tool in microbial forensics [ ] . likewise, design principles for an effective microbial forensics program for law enforcement and national security purposes have been provided [ ] . microbial pathogens or toxins can be used to commit acts of terror; they can be used as weapons for execution of a crime. in biological warfare, transmissible lethal agents are used to attack the targeted populations. the impact of the bioterrorism was seriously considered after the anthrax attack in the united states in . this incidence in the united states helped the world understand that bioterrorism can have drastic and global impacts. microbial forensics has a role in such cases by applying scientific methods for the analysis of evidence from such a bioterrorism attack. microbial forensic in conjunction with epidemiology can try to decipher if an outbreak is natural, accidental, or intentional [ , ] . for instance, study by price and co-workers found that the bacillus anthracis injectional anthrax cases were originated from heroin users in scotland [ ] . ou and co-workers used molecular tracking of hiv to report for the first time about the passage of hiv infection from dentist to patient after invasive healthcare procedure [ ] . a spanish anesthetist infected patients with hepatitis c virus which could be found using phylogenetic and molecular clock analysis [ ] . in the ebola outbreak, the origin and transmission could be traced using bioforensic methods [ ] , etc. other important and relatively new aspect of microbial forensics in medicine and medicolegal field is "thanatomicrobiome" (thanatos-death) that studies the microorganisms found in internal organs and cavities upon death. the thanatomicrobiome tries to investigate the total microbial communities including bacterial and fungi from all the body locations of decomposing corpses. these studies are important in providing evidence in medicolegal death investigations [ ] . by doing this, the concept of human postmortem microbiome project (hpmp) has also been introduced which would create a consortium of research projects to identify and characterize the thanatomicrobiome and epinecrotic communities (e.g., epithelial tissues, body cavities, and the alimentary canal), relating to human decomposition with a potential of finding a state-of-the-art, more dependable, and molecular way of determining the time of death [ ] . it has been shown that typical characteristics and pattern of the human microbiome might identify individuals and remain constant in the individual but differ from the others [ , , ] . this means that individuals might be specifically and consistently identified using their microbiome. however microbiome-based identifiability is still a long way to go. franzosa and co-workers have suggested a few means to achieve the target of identifiability using microbes. the identification of a "metagenomic code" that remains unique for an individual for a longer duration of time and stands true for a sizable population is the key [ ] . hence microbiome establishment, structure, personalization, and temporal stability are the standard terms and areas to work upon. there are some untraveled avenues which start from microbial forensics. emergence of antimicrobial resistance, prediction and prevention of future outbreaks, etc. are some of the fields wherein a surveillance system making use of the principles of microbial forensics can help. antimicrobial resistance in microorganisms emerges naturally. however, antimicrobial exposure due to human practices in healthcare, agriculture, sanitation, industrial processes, travel, and other fields contributes significantly. timely detection of pathogens harboring resistance can mitigate the onward transmission among individuals and among different geographical locations. timely detection of pathogens like hiv, severe acute respiratory syndrome (sars) virus, and pandemic influenza could have avoided the big health emergencies which we have witnessed in recent past. similar is the case with the pandemic spread of sars coronavirus in and h n influenza in resulting in substantial economic loss. microbial forensics can play a crucial role in such cases by checking the emergence in real time and suggesting measures to prevent transmission. however, a lot of investment is required to place such services at all vulnerable points or check points. technological advances especially in the field of metagenomics have paved way for identification of potential human pathogens among other species and have attained good predictive power regarding transmissibility and virulence of the novel microbes. the science of microbial forensics is in its infancy and needs much more that what has already been done. a few things which needs to be taken care as preparation before we take this as a routine science are protocols and procedures for collecting specimens at the attack site, recognizing that an attack is occurring and diagnosing the disease, analysis of specimens in contained facilities, quality assurance and control. although microbial forensics involve techniques or methodologies from basic laboratory sciences, the problems in question, processes engaged in and expected outcomes need more than that. there are efforts and continuous need for validating all the tools and techniques involved which should be acceptable to peers and stakeholder from scientific, legal, and policy making side. the optimization of methods to answer key questions pertaining to investigative and legal needs is a must to satisfy the criterion of acceptability. meeting these challenges will allow the establishment of a complementary and reliable method to compensate for the lacuna of dna fingerprinting and fingerprinting as discussed earlier. meeting the challenges needs the consorted efforts from global communities of workers from basic sciences, epidemiologists, forensic experts, medical experts, legal experts, and a big team of technology developers. the most reliable technique till date for microbial forensics is metagenomics-a culture-independent approach for identifying and enumerating microbes. metagenomic have been an outstanding technique for sequencing the genomes of unculturable microbes, which represent the vast majority of microorganisms, particularly from environmental samples. however, technological advancement identifies the rare taxon is awaited. as microbial metagenomics is undergoing a formative phase as a diagnostic technique, optimization of methods and their validation remain a challenge. other aspects of this are the leadership role and generic availability of tools and techniques. countries with major resources would be able to take lead in basic research, while the resource-limited setting may not be able to adapt microbial forensics owing to its monitory needs. availability of equipment and techniques for rapid and precise molecular diagnosis is important for controlling and responding to the needs of microbial forensics. till date, next-generation sequencing is the only technology that seems promising for microbial forensics. but the instrument and the reagents remain very costly as compared to biochemical tests and a few basic molecular assays being used in forensic laboratories. moreover, expert workers and bioinformatics analysis of the huge data generated after massive parallel sequencing or next-generation sequencing require a devoted facility and expertise. microbial forensics may, in most of the cases, be associated with the detection of causal pathogen in cases of biological terrorism, but microbiome associated with individuals and objects used or touched by them at crime scenes may also be used as a tool in providing forensically relevant information. this science has got its diverse utility in the field of medicine, agriculture, trade especially in food articles, etc. as discussed in this chapter. the evidence and the literature available till date indicate a definitive linkage between an individual and microbial communities inhabiting that individual skin or other body parts. the science is progressing toward identifying these communities, next steps of which would be to see if these communities have something in common and that common character has something to do with the individual. later work in this field may identify chemical entities and their microbial connections to land up to the final conclusions about signature communities of microbes and their forensic potential. however, we may have to continue our search to see those days soon. the origin of fingerprinting dna 'fingerprinting' of captive family groups of common marmosets (callithrix jacchus) forensic application of dna 'fingerprints' application of dna "fingerprints" to paternity determinations the man behind the dna fingerprints: an interview with professor sir alec jeffreys demographic study of a wild house sparrow population by dna fingerprinting forensic identification using skin bacterial communities comparison of bacterial dna profiles of footwear insoles and soles of feet for the forensic discrimination of footwear owners forensic analysis of the microbiome of phones and shoes microbial ecology of human skin in health and disease microbiology's scarred revolutionary - ) phylogenetic structure of the prokaryotic domain: the primary kingdoms towards a natural system of organisms: proposal for the domains archaea, bacteria, and eucarya microbial forensic analysis of bacterial fingerprint by sequence comparison of s rrna gene cohabiting family members share microbiota with one another and with their dogs is human dna enough?-potential for bacterial dna longitudinal analysis of microbial interaction between humans and the indoor environment mobile phones carry the personal microbiome of their owners a microbial clock provides an accurate estimate of the postmortem interval in a mouse model system expansion of microbial forensics risk factors for human disease emergence practical value of food pathogen traceability through building a whole-genome sequencing network and database singleton sequence type , an emerging clonal group of listeria monocytogenes associated with three multistate outbreaks linked to contaminated stone fruit, caramel apples, and leafy green salad isolation and characterization of heat resistant enterotoxigenic staphylococcus aureus from a food poisoning outbreak in indian subcontinent tracing origins of the salmonella bareilly strain causing a food-borne outbreak in the united states a methodology for assessing the risk posed by the deliberate and harmful use of plant pathogens in characterization of the threat resulting from plant pathogen use as anticrop bioweapons: an eu perspective on agroterrorism foodborne illness outbreaks from microbial contaminants in spices evaluation of m molecular detection system and ansr pathogen detection system for rapid detection of salmonella from egg products validation of high throughput sequencing and microbial forensics applications designing an effective microbial forensics program for law enforcement and national security purposes microbial forensic investigation of the anthrax-letter attacks review of the scientific approaches used during the fbi's investigation of the anthrax letters molecular epidemiologic investigation of an anthrax outbreak among heroin users economou an ( ) molecular epidemiology of hiv transmission in a dental practice genomic variation landscape of the human gut microbiome the thanatomicrobiome: a missing piece of the microbial puzzle of death human thanatomicrobiome succession and time since death the long-term stability of the human gut microbiota molecular evolution in court: analysis of a large hepatitis c virus outbreak from an evolving source identifying personal microbiomes using metagenomic codes key: cord- -vytmwmoj authors: shah, nita h; suthar, ankush h; jayswal, ekta n title: control strategies to curtail transmission of covid- date: - - journal: nan doi: . / . . . sha: doc_id: cord_uid: vytmwmoj recently, the world health organization has declared the outbreak of a severe acute respiratory syndrome coronavirius as a pandemic, and declared it as public health emergency of international concern. more than , , positive cases and , deaths caused by coronavirus affecting countries and territories. this pandemic can transform into an extremely destructive form if we still do not take it seriously. in this present study, we propose a generalized seir model of covid- to study the behavior of its transmission under different control strategies. in december, , the pandemic outbreak of a novel coronavirus disease named covid- raised intense attention not only within china but internationally [ ] . doctors and scientists tested the previously developed drugs to treat the infected people, but that failed to succeed. then, in february, , the world health organization (who) declared the outbreak of this highly contagious covid- as pandemic globally [ ] . to control the human to human virus transmission, the central government of china as well as all local governments had tightened preventive measures. however, the virus had spread rapidly across most of the regions in china and in other countries and territories around the world. one major cause of the quick spread of covid- is the lack of information and awareness about the virus during its early stages of infection. as on march , , : gmt, has affected countries and territories around the world with , confirmed cases, of which , have passed away, and , are serious or critical (worldometers.info). still there is a possibility that spread of this virus could be more intense and cause high mortality. while the new year was enjoying their spring vacations, the outbreak of covid- has accelerated, as most of the people were on their way to hometown or else travelling to different places for relaxation. symptoms of covid- takes at least to days, which makes it is tough to isolate infected individuals during initial stage of the infection. the major symptoms of covid- include dry coughing, high fever with difficulties in breathing [ ] . the virus may spread in the environment through respiratory droplets of infected individuals when they cough or sneeze. further an unaffected population becomes infected when they are exposed by touching the infected surface or while breathing in an infected environment [ ] . during the initial stages of covid- outbreak, such human transmissions were taking place because, wide-range of public was unaware of these risk factors, and the infected individuals were also not isolated and were spreading the virus unknowingly to other individuals. moreover, the risk factor of contamination is very high since the virus can remain viable in environment for several days in favourable conditions [ , ] . several studies reveal that old-aged people, children and those with major diseases are having low immunity and tend to seriously affected once they become infected [ , ] . still, we lack with any proper treatment or vaccines as a cure for this disease. hence to control its transmission further, isolating the infected individuals in special quarantine cells has been implemented in most of the countries. despite of these prevention strategies, we are in danger as the transmission is still ongoing and the mortality due to the virus maintains a high level. to combat this situation, studies like mathematical modelling play a crucial role to understand the pandemic behaviour of the infectious disease. several studies have already been undertaken to analyse the covid- transmission dynamics. based on these database studies of covid- outbreak since st december, to th january, , wu et. al. ( ) introduced a seir-model to estimate the spread of the disease nationally as well as globally [ ] . proposed a compartmental model by dividing each group into two subpopulations, the quarantined and unquarantined. moreover, they re-designed their previous model by using diagnose and time-dependent contact rates, and re-estimated the reproduction ratio to quantify the evolution in better way [ , ] . peng et. al. ( ) planned a generalized seir model that suitably incorporates the intrinsic impact of hidden exposed and infectious cases of covid- [ ] . presented the incubation period behaviour of local outbreak of covid- by constructing a dynamic system [ ] . khan & atangana ( ) described brief details of interaction among the bats, unknown hosts, humans and the infections reservoir by formulating the mathematical results of the mathematical fractional model [ ] . chen et. al. in this work, a covid- model is constructed to study human to human transmission of the virus in section . optimal control theory is introduced and applied to the model to develop in section and in section , the model is simulated numerically to observe effect of control strategies on the model. to analyse the human to human transmission dynamics of covid- , a compartmental model is constructed. the model consists all possible human to human transmission of the virus. the covid- is highly contagious in nature and infected cases are seen in most of the countries around the world, hence in the model the susceptible population class is ignored and whole population is divided in five compartments, class of exposed individuals (t) e (individuals surrounded by infection by not yet infected), class of infected individuals by covid- i(t) , class of critically infected individuals by (t) c , class of hospitalised individuals (t) h and class of dead individuals due to covid- . cc-by-nc . international license it is made available under a author/funder, who has granted medrxiv a license to display the preprint in perpetuity. is the (which was not peer-reviewed) the copyright holder for this preprint rate at which hospitalised individuals get recovered and become exposed again . assumed β rate at which infected individuals recovered themselves due to strong immunity and again become exposed . assumed table parameters used in the model using the above depiction, dynamical system of set of nonlinear differential for the model is formulated as follows: . cc-by-nc . international license it is made available under a author/funder, who has granted medrxiv a license to display the preprint in perpetuity. is the (which was not peer-reviewed) the copyright holder for this preprint . https://doi.org/ . / . . . doi: medrxiv preprint b ei ed h ei e dt di ei i i i ei i dt dc i note that, all the parameters used in this covid- model are non-negative. consider the feasible region, ( , , , , ) : the region Λ is positively invariant, all the solutions of the system ( ) are remain in the feasible region ( ). by solving the above system ( ), we get two equilibrium points: ii. endemic equilibrium point: * basic reproduction number ( ) r for the model can be established using the next generation matrix method [ , ] . the basic reproduction number ( ) r is obtained as the spectral radius of matrix ( ) fv − at disease free equilibrium point. where f and v are as below: defined effective basic reproduction number is: control measures have made significant role to control the epidemic of covid- at certain level. in this control theory, five control variables are used as five possible control strategies. since the virus is highly contagious, it quickly infect any people come in contact with an infected individual. to avoid this situation we have taken u control variable to selfquarantine exposed individuals and u control variable as an isolation of infected individuals. moreover, to minimise mortality rate of covid- , u control variable is taken which helps to reduce critically infected cases by taking extra medical care of infected individuals. u and u control variables are taken to improve hospitalisation facility for infected and critically infected individuals respectively. purpose of this study of control theory is to protect people from the outbreak by applying control or treatment in each stage. objective function for the required scenario is, where, φ is a smooth function on the interval [ , ] . the optimal effect is found by using results of fleming and rishel ( ) [ ] . associated langrangian function with adjoint variable , , , , λ λ λ λ λ is given by, the partial derivatives of the lagrangian function with respect to each variable of the compartment gives the adjoint equation variables . cc-by-nc . international license it is made available under a author/funder, who has granted medrxiv a license to display the preprint in perpetuity. is the (which was not peer-reviewed) the copyright holder for this preprint hence, the optimal controls are given by and optimal conditions given as, ( ) this calculation gives analytical behaviour of optimal control on the system. numerical interpretation of optimal control theory is simulated in the next section. [ ] in this section, the covid- model is simulated numerically, wherein the parametric values for simulation are taken from recent pandemic outbreak of coronavirus (https://www.who.int/emergencies/diseases/novel-coronavirus- /situation-reports). . cc-by-nc . international license it is made available under a author/funder, who has granted medrxiv a license to display the preprint in perpetuity. is the (which was not peer-reviewed) the copyright holder for this preprint . https://doi.org/ . / . . . doi: medrxiv preprint figure variation in all compartments figure represents the variations in all the compartments of covid- model with respect to time. also, the pandemic behaviour of the covid- outbreak can be clearly seen here. we can say that, a large population of exposed individuals become infected before a week. moreover, the critically infected cases and hospitalisation cases also increase with matter of time. further, it clearly shows that after one week the mortality rate is also increased. . cc-by-nc . international license it is made available under a author/funder, who has granted medrxiv a license to display the preprint in perpetuity. figure . moreover, the figure also demonstrates which control can be applied at how much intensity to control covid- outbreak in seven weeks. the high fluctuation in u control variable at an initial stage suggests that it is very important to control infected individuals to move at critical stage to reduce mortality due to covid- . and, this can be achieved easily if an infected individual gets proper vaccination for this disease. since effective vaccination is not available for coronavirus, one should take proper care of infected individuals to improve their immunity so that their body becomes capable to fight against the virus and not reaching to a . cc-by-nc . international license it is made available under a author/funder, who has granted medrxiv a license to display the preprint in perpetuity. is the (which was not peer-reviewed) the copyright holder for this preprint . https://doi.org/ . / . . . doi: medrxiv preprint critical stage. moreover fluctuation in u control variable suggests that it is very important to isolate or quarantine infected individuals to control this pandemic outbreak. figure variation in each compartment under individual effect of control variables separate effect of control variables on each compartment can be observed in figure . from the figure, we can interpret that u control variable is highly effective to stabilise this epidemic situation. figure (b) depicts that population class of infected individuals is lowest under the influence of u control variable which suggests that rapid hospitalisation of . cc-by-nc . international license it is made available under a author/funder, who has granted medrxiv a license to display the preprint in perpetuity. is the (which was not peer-reviewed) the copyright holder for this preprint . https://doi.org/ . / . . . doi: medrxiv preprint infected individuals is an effective step to reduce infected cases of covid- . figure (c) suggests that to reduce critical cases of covid- , first we should make control on infected individuals to become critically infected and we should improve hospitalisation and medical facility for critically infected individuals to save their lives. figure (e) shows that mortality rate due to covid- can be reduced effectively within three weeks of outbreak by applying u , u and u control strategies. that means self-quarantine for an exposed individual, isolation of an infected individual and reducing critical cases by taking extra care of infected individuals are effective strategies to control further transmission of covid- . . cc-by-nc . international license it is made available under a author/funder, who has granted medrxiv a license to display the preprint in perpetuity. is the (which was not peer-reviewed) the copyright holder for this preprint . https://doi.org/ . / . . . doi: medrxiv preprint (c) figure scatter diagram for covid- outbreak figure demonstrates the scatter diagram representing chaotic situation created during covid- outbreak. figure (a), (b) and (c) shows periodic mortality from classes of exposed individuals, infected individuals and critically infected individuals respectively, when under hospitalisation. on comparison of figures (a) and (b), it can be interpreted that mortality ratio in class of infected individuals is higher and much quicker than in the class of exposed individuals. the chaotic figure (c) represents a very high mortality rate of critically infected individuals. hence, in the absence of vaccination for covid- , it becomes a challenging situation to cure critically infected individuals. in this study, a compartmental model is constructed to examine transmission of covid- in human population class. moreover, basic reproduction number is formulated to calculate threshold value of the disease. in order to develop strategies to prevent the epidemic of covid- , optimal control theory is applied to the model. further to advance control theory, five control variables are introduced in the model in the form of control strategies. these strategies include self-quarantine of exposed individuals, isolation of infected individuals, taking extra care of infected individuals to reduce critical case of covid- , increase hospitalisation facility for infected and critically infected individuals. distinctive and combined effects of these control variables on all the compartments are observed and examined graphically by simulating the covid- model. numerical simulation of the model reflects that quarantine and better medical treatment of infected individuals reduce the critically infected cases, which will further reduce the transmission risk and demises. https://www.who.int/emergencies/diseases/novel-coronavirus- /situation-reports . cc-by-nc . international license it is made available under a author/funder, who has granted medrxiv a license to display the preprint in perpetuity. is the (which was not peer-reviewed) the copyright holder for this preprint . https://doi.org/ . / . . . doi: medrxiv preprint a mathematical model for simulating the transmission of wuhan novel coronavirus a time delay dynamic system with external source for the local outbreak of -ncov novel coronavirus: where we are and what we know on the definition and the computation of the basic reproduction ratio r in models for infectious diseases in heterogeneous populations reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission stochastic differential systems, stochastic control theory and applications: proceedings of a workshop, held at ima modeling the dynamics of novel coronavirus ( -ncov) with fractional derivative the novel coronavirus outbreak-a global threat epidemic analysis of covid- in china by dynamical modeling pattern of early human-to-human transmission of wuhan the epidemiology and pathogenesis of coronavirus disease (covid- ) outbreak novel coronavirus (covid- ) outbreak: a review of the current literature world health organization declares global emergency: a review of the novel coronavirus (covid- ) an updated estimation of the risk of transmission of the novel coronavirus ( -ncov) estimation of the transmission risk of the -ncov and its implication for public health interventions breadth of concomitant immune responses prior to patient recovery: a case report of non-severe covid- a mathematical model for the novel coronavirus epidemic in wuhan a mathematical model for estimating the age-specific transmissibility of a novel coronavirus early prediction of the novel coronavirus outbreak in the mainland china based on simple mathematical model key: cord- - qcq soy authors: caravita, ruggero title: peopletraffic: a common framework for harmonizing privacy and epidemic risks date: - - journal: nan doi: nan sha: doc_id: cord_uid: qcq soy peopletraffic is a proposed initiative to develop a real-time, open-data population density mapping tool open to public institutions, private companies and the civil society, providing a common framework for infection spreading prevention. the system is based on a real-time people' locations gathering and mapping system from available g, g and g mobile networks operators, enforcing privacy-by-design through the adoption of an innovative data anonymizing algorithm inspired by quantum information de-localizing processes. besides being originally targeted to help balancing social distancing regulations during the phase- of the covid- pandemics, peopletraffic would be beneficial for any infection spreading prevention event, e.g. supporting policy-makers in strategic decision-making. the adoption of social distancing regulations, enforcing physical separation between individuals to limit population density and reducing individual-to-individual contacts, has been so far the most effective tool employed by national countries to mitigate the covid- pandemics cases' shock on their national sanitary systems [ ] . the effectiveness of these regulations was predicted by most epidemic models [ ] based on the hypothesis that individual-to-individual contact is the main transmission process driving infection spreading (see [ ] for a review). their strong corroboration by the observations lead to conclude that local population density in the proximity of an individual has a strong a-priori predictive power on the likeliness of that individual to get infected. civil society's response to these strict social distancing regulations and restrictions has been widely positive (i.e. with a high degree of acceptance) in most countries involved in the first phase of the covid- pandemic (e.g. ∼ % for the italian case, see [ ] ). this indicates that most people act according to regulations for their own and common interests, and also suggests that wide adoption of positive individual behaviours is likely if all citizens are given a set of good practices and tools to follow them. it became also clear, on the other hand, that strict social distancing regulations have profound impacts on countries' economies [ ] , and their partial to full relaxation becomes necessary to mitigate the adverse economical effects as soon as pressure on the sanitary systems is sufficiently relaxed. this marks the beginning of the co-existence period with the infection (the so-called pandemic phase- ), which is expected to last approximately until a vaccination becomes available to the mass public (estimated mid- for the covid- case). the main risk connected to relaxing social distancing measures is to increase the risk of epidemic resumption due to increased people individual-to-individual contacts. the possibility to differentiate, rather than relieve, social distancing policies in different contexts is likely to mitigate that risk and consequent novel shocks on national sanitary systems. in what forms this differentiation can take place, it is one of the most discussed themes at the moment by policy-makers of most countries involved in the epidemic, as the ability to efficiently tune social distancing rules in economic, social and personal life contexts (and rationally distribute the diffusion risk) could have a profound impact on each country economic performance during phase- . here we propose an initiative to develop a real-time, open-data population density and flux mapping system, hypothetically named peopletraffic, in an analogy to the well-known google traffic system for road traffic. the proposed system enforces privacy-by-design and allows privacy levels to be externally and transparently regulated through the use of an innovative anonymizing algorithm specifically designed for mapping applications and inspired by quantum information de-localizing processes. this tool relies on gsm, not bluetooth sensing. contrary to many other systems being developed that are based on direct proximity sensing via bluetooth, and subsequent notifications in case of proximity with a subsequently identified infected individual, this scheme relies on determining the average local area person density via gsm/umts/lte. it is meant to enable a winwin reduction of pandemic diffusion risks linked to people movements by supporting their autonomous risk prevention evaluations and decisions with the knowledge of real-time population density and fluxes. furthermore, it would allow social distancing to be adapted to a variety of contexts, providing valuable quasi real-time information to individuals and policy-makers in taking decisions (both at the individual and strategic levels) based on a clear view of people density, which has proved so far one of the most reliable a-priori predictors of infection spreading. finally, in the long-term, it could be a driver of innovation and economic activity, for instance as a tool for accurate flux and market analyses and business cases identification. in order for the population density and flux knowl-edge to be effective for individual-to-individual contact prevention, spatial and time resolutions close to the individual proximity (i.e. tens of meters and minutes) are necessary. this is key to allow virtuous behaviour orienting at the individual scale, like choosing the right means of transportation for commuting, or the right places and timing for necessary and leisure activities. this requires however the system to deal with individual privacy by design, preventing especially the risk of individual reidentification and tracing. bringing the knowledge of real-time population density and flux to everyone thus necessitates solving two main challenges: how to technically produce maps of sufficient resolution to be useful for individual-to-individual contact prevention, and a strong privacy risks mitigation approach enforcing full transparency and privacy-by-design to the data handling and sharing system. in this work, we review the possibilities offered by present-day technologies in constructing real-time population density and flux maps through the use of existing real-time locating system (rtls) with sufficient spatial and temporal resolutions to get close the individual scale. secondly, we approach the privacy concern in quantitative manner, i.e. describing a tunable algorithm providing privacy-by-design by preventing individuals' localization at the level of the each data provider. different levels of privacy could be transparently set (at the price of statistics necessary to reach a certain level of resolution) for effective policing to be allowed. last, we lay out the design of the information processing system, highlighting its principal implementation characteristics. the main positional data acquisition methods we considered here are these that can be obtained from real-time data analysis of nowadays capillary mobile networks (i.e. these adopting gsm, umts, and lte network technologies), i.e. not requiring any software to be installed on individual user equipment (ue). modern mobile networks, from the physical layer point of view, allow many of such techniques with varying accuracies and required computing power [ ] . what method can be implemented on each territory is thus mainly in the hands of each mobile network provider capabilities and data sharing policies. it's reasonable to assume that different accuracies would be obtained from different providers each adopting its own localization approach from the simplest to the most elaborated method demonstrated so far. here we consider the two limiting cases: a) the mere counting of number of connections per mobile network cell (also known as localization through cell identity, ci) and b) accurate individual ue positioning by the net-work via the highest accuracy available methods, e.g. rssi triangulation or observed time difference of arrival (otdoa). scenario a, i.e. counting the number of connections per network cell, has the advantage to be applicable to most network technologies, including public wifi hotspots. it is the simplest and most anonymous approach, based on data that most network providers already possess (and even sell for market analytics purposes in some cases [ ] ). its mapping accuracy is however limited by the size of deployed network cells. scenario b, i.e. measuring independently each ue position, can provide sub-cell resolution at the price of higher requirements in terms of complexity, data processing power and personal data handling. most network providers already developed all necessary infrastructures during the lte technology deployment phases to meet regulatory emergency call positioning requirements. indeed, the importance of accurately geo-locating emergency phone calls was recognized to be so socially impacting already that it was made part of the lte network standard: as of , % of emergency calls in the united states are positionally located within m [ ] . individual ue locating methods usually require a data anonymizing step after mapping is performed to comply to general data protection regulations (see privacy section). mapping and anonymizing algorithms have typically to be run by the network operators to avoid distributing non-anonymous data. as for the former case, achievable resolutions increase proportionally to mutual inter-distances between transceiver stations. expected positional accuracies of both scenario a and b are proportional to local densities of mobile network cells. thus, mapping them on country scales is necessary to evaluate the realizability of a mass rtls as the one here discussed in a realistic use-case scenario. we conducted a survey of existing cell locations and sizes to determine the granularities of gsm, umts and lte networks and estimate the positional accuracies that could be obtained by network operators adopting the two approaches discussed above. the study was conducted by merging all available cells identification codes and geo-locations from the opencel-lid [ ] and mozilla location services [ ] free databases. each cell is uniquely identified by its mobile country code (mcc), mobile network code (mnc), location area code (lac) and cell identification number (cid). it's worth summarizing, for the following discussions, how these databases are constructed. they are built upon big datasets of geo-tagged mobile connections to individual cells of the networks from physical people mobile phones participating in the mapping initiatives, logging and streaming their anonymous gps positions and connected network cells identification numbers while moving. each set of mobile phones' logged gps positions is then clustered on a per-cell basis, from which the centroid position is calculated by averaging all samples' positions. cell connection ranges are also estimated by the spatial spread of each cluster points. the number of samples available per cell is widely distributed due to this statistical acquisition modality, spanning from the < samples of infrequently visited cells up to the > samples of most frequently visited cells (fig. , top row) . ranges are similarly widely distributed, spanning from a few m to km (fig. , bottom row) . we applied a data quality cut to the dataset rejecting all these cells with < samples, giving rise to an nonphysical tail in the ranges distribution < m (fig. , dashed lines) . it is worth noting also that, despite the notable dimensions of these location databases, their statistical acquisition modality can give rise to systematic errors when comparing different contexts. a first issue is spatial nonuniformity in sampling/partial territorial coverage. this issue was mitigated analyzing territories with comparable amounts of acquired samples per unit surface (given in the databases). a second concern is the completeness of the databases for small or local mobile network providers in terms of actual active cells on the territory. for this reason, the analyses reported here are given separately per network provider and limiting to those with major shares of physical-people sim cards in italy: tim, vodafone and wind tre, covering . %, . % and . % market respectively [ ] . by this method, about . · unique mobile cells were listed on the italian territory (see fig. , showing with different color the density distribution of gsm, umts an lte cells). the list of cells was subsequently reduced to the scale of single urban territories. here we considered the two historical city centers of the cities of rome, a very large-sized town (fig. , right bottom), and of genoa, a large-sized town (fig. , right top). the former, being the reference case-study city used in [ ] , allows also direct spatial resolution comparisons between the methods, while the latter is an example of large-sized town with complex orography (seaside, rivers and hills) as typically found in italian provinces. in order to compare gsm, umts and lte network cell sizes, one has first to determine their expected spatial shapes (here referred to as connection domains) to be able to then reconstruct their size distributions. connection domains are here defined as those surface domains in whose boundaries single mobile devices can connect with a certain probability to that particular network cell. constructing connection domains associated to each cell thus implies accounting for the typical behaviour of mobile network devices to connect to their closest cell, when any is available, starting from the cell positions p i and ranges r i and evaluating any point in the surface. solving this problem in the general case is a genuine challenge, suggesting the use of a monte-carlo approach. here we adopted an approximated approach valid in the high network cell density limit. in this regime, cell inter-distances are much smaller than the maximum connection ranges allowed by the technology and observed ranges are set almost entirely by the transceiver positions p i (thus neglecting r i ). also, it implies that the surface is completely covered by connection domains, forming a tessellation set by p i . this type of arbitrary tessellations constructed upon a set of generating points p i are usually known as voronoi tessellations [ ] . voronoi tessellations are constructed from a set of generating positions p i as follows: the domain relative to the i-th point is defined by all points x j of the surface for which p i is the closest generating point, according at first glance, it may look like the use of voronoi tessellations with the euclidean distance for constructing connection domains is only grossly approximating the real process of mobile devices connecting to their most intense nearby transceiver. one might argue that this process implicitly assumes equal transmission power and reception sensitivity for all cell transceivers and uniform antenna angular emission patterns, and that nearby cells overlap each other to allow handovers. the first criticism would be correct if exact cell towers positions would be used for constructing the connection domains. here, however, cell positions x i taken from location databases are calculated as cluster centroids from the original geo-tagged user positions. voronoi tessellations with the euclidean distance are nothing but the graphical representations of the spatial domains associated to the clusters calculated by the well-known kmeans clustering algorithm. indeed, k-means clusters are obtained minimizing the sum-of-squares of all euclidean distances between n generating points (the cluster centroids) and the dataset samples, which is the same process to build a voronoi tessellation with the euclidean distance. the second criticism is correct in that it possible for a device to connect to a cell even on the outside of its connection domain. however, this is unlikely to happen frequently, as normally, when a mobile device leaves a cell connection domain, automatic handover occurs transferring the connection to the nearby cell with its better signal reception. for this to occur nonetheless, either the device has to move at high velocity or channel saturation has to occur, i.e. nearby cells handover connections having all connection channels used. the distributions of connection domains for the tim (mnc- ), vodafone (mnc- ) and wind tre (mnc- ) network operators were constructed using the subset of cells' position associated to each mnc code. their spatial distribution for the whole italian territory are omit- ted due to their complexity, while they are shown for the rome and genova historical city centers in fig. and fig. respectively. the statistical analysis of their surfaces are shown in fig. for the whole italian terri-tory and in fig. , fig. for the historical city centers of rome and genoa respectively. associated network cell radii r gsm , r umts and r lte (also reported in the figures) were calculated under the approximation of av- the distributions on the whole italian territory show that deployed gsm, umts and lte networks have increasingly higher spatial granularities as expected, with average cell radii of ≈ . km, ≈ . km and ≈ . km respectively and % fluctuations from network operator to network operator. average cell radii dramatically reduce while zooming on a single urban context. in the case of rome, a very large-sized town, these reduce to ≈ . km, ≈ . km and ≈ . km whereas in the case of genoa, a large-sized town, they similarly reduce to ≈ . km, ≈ . km and ≈ . km. an accurate estimate of positional accuracy of deployed lte networks can now be obtained by combining the measured cell radii with an evaluation of the intrinsic resolution of ci and otdoa localization techniques in a controlled test scenario including noise and threedimensional effects. here we considered the horizontal accuracy analyses reported in rydén et al. [ ] , which established that spatial resolutions of σ a lte = m and σ b lte = m (gaussian standard deviations at % error) can be obtained for scenario a and b respectively with regularly-spaced outdoor cells of m radius (i.e. / of the interdistance between transceivers considered in the study). the analysis of [ ] , in other words, reports that indirect ue position detection by cell identity has a resolution (at % error level) σ a lte ≈ . · r lte . these resolutions were scaled by the ratio of the cells radii to get the estimated ground resolutions of deployed networks. a summary of the obtained positioning resolutions for the different contexts is given in tab. i. by using anonymous ci data only and combining data of different lte network providers, resolutions up to ∼ m can be obtained in dense urban areas. using otdoa, a factor of in resolution is gained, bringing it down to ∼ m. the first experiments of population density measurements in urban contexts were conducted about years ago in rome by the senseable cities group of the mas-sachusetts institute of technology (see [ ] ) using telecom italia mobile (tim) gsm towers and its localizing and handling network event system (lochness) platform to measure in real-time people density and fluxes through the localization and mapping of each individual ue. indeed, the location method implemented in the platform combined measured signal strengths from serving transceiver stations, their neighboring ones and from each mobile device to triangulate their locations every ∼ . s, in a similar way to what otdoa does in the case of lte networks. a spatial resolution of m was obtained in rome's urban area with the available gsm network, increasing to m in the suburbs and to m in the extra-urban area [ ] . more recent experiments adopting time difference of arrival localization algorithms have also shown to be able to break the m barrier in an urban context using gsm only [ ] . scaling the lochness method resolution obtained in rome by the gsm cells sizes in the different territories by these of rome (see fig. ) allows to calculate the estimated resolution σ b gsm of gsm in a realistic scenario b. the estimate of gsm resolution in a realistic scenario a (cell identity only) was obtained with the same method used for lte, i.e. by considering the estimates in [ ] to define σ a gsm ≈ . · r gsm . a summary of the obtained positioning resolutions for the different contexts is given in tab. ii. results in scenario b are comparable between gsm and lte after being scaled by their different cell sizes, further suggesting that resolution is mostly set by geometrical disposition of the cells on the territory rather than technology-specific location protocols implementations. table i : estimated individual positioning accuracies in scenario a and b for different lte network providers in different territories, using the methods discussed in the text. all distances are given in km. the spatial resolution analysis here performed shows that anonymous number of connections data (scenario a) could provide reliable information about population density on the scale of hundreds of meters in most urban contexts, i.e. allowing only big crowds to be distinguished, unless further capillarization of the networks are made available. non-anonymous location data, on the other hand, would provide spatial resolutions in the order of the tens of meters (scenario b), i.e. the scale of small crowds and the individual proximity. the studies reported before [ ] underlined that significant improvements of the anonymous cell identity method can be obtained by deploying mini-and microcells inside buildings, enhancing the ci resolution to m. a further study from the same group [ ] showed also that indoor resolutions up to σ otdoa = . m can be reached by deploying indoor lte pico-cells combined with an enhanced, iterative otdoa approach. finally, gps-assisted ue locating (also known as a-gnss), a part of the lte standard, is also a solid possibility for resolution enhancement in outdoor contexts, reaching the scale of ≈ m. another possibility for the ci approach to reach the ∼ m resolutions would be to complement mobile location data with higher resolution local data sources, such as public wifi hotspots, public means of transportation locations, smart mobility devices locations, rf-noise lev-els monitoring tools. as these networks are much less homogeneous than mobile network between different urban contexts, calibration of the reconstructed density maps with mobile network devices would likely be necessary anyway. to date, no known protocols are available for individual users to contribute with their own access points to an hypothetical wifi collective monitoring network. levels of resolution in the m range would allow social distancing regulations to be enforceable at the individual scale, posing however the significant challenge of balancing the risks to individual privacy loss (see privacy section). practical use cases in means of public transportation, individual businesses, industries, offices and marketplaces would become a solid possibility, requiring only further capillarization of mobile network technologies -a trend that is already happening with the development of g networks. a summary of the identified methods per resolution provided is shown in tab. iii. the possibilities offered by existing technologies in mass locating people with spatial accuracies at the level of single individuals proximity, discussed in the above sections, raise privacy concerns that, if not properly handled, would prevent the adoption of a mass rtls as the one here proposed. on the one hand, as stated by fisher and dobson in [ ] , "each individual should be able to negotiate access by another person to information about their location. no one else should be able to circumvent that right". on the other hand, as discussed by ratti et al. in [ ] , there is general consensus that aggregated population density maps can be made to satisfy all requirements of data anonymity, i.e. without violating any personal data protection regulation. fisher and dobson also point out in [ ] that as long as personal data is not made available by mobile phone operators to third parties, most privacy concerns are avoided. here we first review the juridical literature on personal data privacy relevant for this matter, i.e. that defining law boundaries to data anonymity. then we take a quantitative approach to address the implementation of the privacy constraints, laying down the specifications of the second key part of the system: the user data anonymization and mapping algorithm. the boundaries of data anonymity are sketched by recital of regulation (eu) / of the european parliament and of the council of april on the protection of natural persons with regard to the processing of personal data and on the free movement of such data, and repealing directive / /ec (general data protection regulation) (see [ ] ), stating that: "the principles of data protection should therefore not apply to anonymous information, namely information which does not relate to an identified or identifiable natural person or personal data rendered anonymous in such a manner that the data subject is not or no longer identifiable". the boundaries of identifiability are also sketched in the same recital : "to ascertain whether means are reasonably likely to be used to identify the natural person, account should be taken of all objective factors, such as the costs of and the amount of time required for identification, taking into consideration the available technology at the time of the processing and technological developments". this formulation implies that technical analysis to evaluate the feasibility and the efforts required to identify the natural person to which data relate have to be carried out during the design phase of any information systems involving personal data, leaving open the data anonymization modality. aggregated data that can be proven to fall under these prescriptions can thus be declared anonymous; for these, the recital clearly states: "(the general data protection regulation) does not concern the processing of such anonymous information, including for statistical or research purposes". thus, if proper mitigation of the risk that a single person's identity can be retrieved is carried out, real-time population density maps can be considered anonymous data and thus publicly distributed. a standard adopted technique for anonymizing mapping data consists in introducing a minimal threshold on the number of individuals per cell, under which the cell is discarded from the map. this guarantees a high combinatorial cost for following single individuals on the map. for instance, if an average of individuals per map cell is present, in order to reconstruct the trajectory of one of them starting from a given cell in the map, the whole combinatorial tree of possible steps into nearby valid cells should be considered, whose number of branches grows by n where n being the number of steps. this is the principle beyond anonymizing by thresholding: making de-facto impossible the reconstruction of a single trajectory, and thus its de-anonimization, due to the very high number of equally-likely possible combinations. this method has a drawback: not all of the available information is used to generate the map, as that from a certain fraction of the individuals is discarded after thresholding. the amount of information lost is by construction highly non-linear in the number of people per cell, causing critical statistics losses when the size of the mapping cells is small enough for the average number of people per cell to be comparable or smaller than unity. in other words, the choice of the thresholding level imposes a minimal resolution to the mapping system, under which most of the information available is discarded. in the present case, this drawback would significantly limit the maximal resolution of the proposed system and its risk-prevention capability, as its goal is by construction to get as close as possible to the single individual scale. to avoid this thresholding inconvenience, we developed a position anonymizing system working independently from the spatial resolution scale choosen for mapping. it is based on preserving the key information necessary for prevention, i.e. mutual interdistance between individuals, with the highest accuracy, while anonymizing individuals' absolute positions. here for sake of simplicity we describe the approach in a mono-dimensional scenario; the bi-and tri-dimensional cases follow as its straightforward generalizations. are then generated following gaussian distributions g [x (n) ,σ (n) ] (x) centered on x (n) with standard deviations σ (n) . these generated positions x (n) take the name of anonymized position, whereas the coefficients σ (n) take the name of anonymization parameters. wave-packeting: the second step (see fig. . ) consists in constructing wave packets ψ (n) (x) relative to each anonymized position x (n) . each ψ (n) (x) is a complex-valued function with complexamplitude given by the same gaussian distribution used for generating anonymized positions, g [x (n) ,σ (n) ] (x), and complex-phase dependent upon the distance between each point of the grid x and the original individual position x (n) , exp(ik||x (n) − x||), where k = πm/l is the spatial sampling wavenumber, here chosen (following nyquist theorem) for a full wavelength to match times the map resolution d = l/m (l being the whole map size). all wave packets are summed up in a collective wave-function ψ(x) = n n= ψ (n) (x), which is then sampled over the m points p (m) of the regular grid chosen for mapping (here m ∈ [ , m ]) to build the aggregated complexvalued map ψ (m) ≡ ψ(p (m) ). ψ (m) takes the name of unmatched wavefunction since its phase reference is still arbitrary. it is no longer possible to reconstruct the original positions x (n) from ψ (m) to better than σ (n) , as each of the individual wave-functions are centered on the gaussianlyrandomized positions x (n) . whether this aggredated map can now be considered anonymous or not, it depends only on the choice of σ (n) rather than that of the mapping accuracy. if σ (n) coefficients in the anonymization step are chosen so that many individuals' wave-packets overlap with each other, combinatorial anonymization is again provided (see next sections) while surpassing the limitation of loosing information of anonymization by thresholding. this process thus allows constructing aggregated, anonymized complex-valued unmached wavefunctions from h localization system providers, ψ . common-phase matching: the third step (see fig. . ) is run by the system collecting all individual unmatched wavefunctions ψ (m) h received from the individual providers. a phase rotation exp(iφ h ) is applied to each of the unmatched wavefunction, allowing each one to be referenced to the same phase-referencing system and thus constructing phase-matched wavefunctions that can be now summed up constructively. unmatched wavefunctions are assumed here to be built on the same previously-set mapping grid p (m) . phase rotation coefficients allow, in other words, all individual maps to be cross-calibrated on the same positional referencing system. where, for notation simplicity, we set g ≡ g [x ( ) ,σ ( ) ] (x) and g ≡ g [x ( ) ,σ ( ) ] (x). taking the complex squared-modulo, one gets: the two gaussian terms g ( ) (x) and g ( ) (x) are centered in x ( ) and x ( ) , thus not allowing position deanonimizing from a single map, while their interference contains the oscillatory term cos(k(x ( ) − x ( ) )) which encodes in the oscillations the reciprocal distance between the individuals, referenced to the mapping grid and calculated with their original positions. the maximum amount of information that can be thus retrieved from the final map about the two individuals are the two anonymized positions, their mutual inter-distance and the expected area in which each of the individuals is with a given probability. this process thus protects individual privacy in the limit of a few people present in the map, an example of which is shown in fig. , first row, in which people are positioned at regular m distances in a km context being mapped with m resolution (fig. , top left) . the final population density distribution produced by the algorithm shows four gaussian functions centered on the anonymized positions and delocalized with σ = m. when the number of individuals grows to (fig. , second row) and (fig. , third row) , progressively all interference terms sum in phase and ultimately dominate over the stochastic gaussian terms, giving rise again to the original density distribution in the statistical limit of many people (compare fig. bottom row, red to blue distributions). in all these cases it is always impossible from the final distribution to retrieve the exact original positions, as the first stochastic anonymization cannot be inverted. it's worth noticing that this inversion cannot be performed exactly even considering many different realizations of the maps at different time instants, as the stochastic anonymizing process give different anonymized positions at each time. this task can be shown to be equivalent to retrieving the exact position of a quantum particle at rest obeying heisenberg's uncertainty principle. its exact position would be found only in the limit of infinite observations, and only if the particle is at rest all the time (i.e. with null average velocity). combining many observations over a long time of a well isolated single individual in quiet may still allow to reduce the positional uncertainty statistically down to an undesired high level of accuracy. several approaches are being investigated to prevent this from happening by design. the simplest one is the addition of a small amount of white noise to each of the complex maps. a more sophisticated approach is to introduce some combinatorial anonymization, obtainable in this context (without any loss of information) by selecting large enough σ (n) for several wavepackets to overlap with each other in any point of the map. here the challenge is to select the values of σ (n) following the local availability of statistics and adopting an optimal resolution-to-anonymization criterion. this approach is currently being investigated. a sketch of the proposed data processing system is shown in fig. . the system is composed of two main parts: a first data processing pipeline hosted in each data provider computing facility and a second anonymous data aggregation and post-processing pipeline hosted in a common computing infrastructure providing also open data publication. the first part of the data processing falls inevitably under the responsibility of each location data provider, as they must comply with the strict policies about personal data handling. this processing involves the collection of users' locations and their subsequent anonymization into a single anonymous, aggregated complex-valued map, following the algorithm described in the previous sections. each of these maps, being now anonymous and compliant with privacy regulations (also discussed in the previous sections), can now be transmitted to the common computing infrastructure that collects all of them from the different location providers participating in the initiative. the role of the common project infrastructure is to run the common-phase matching and mapping algorithms also discussed in the previous sections, to produce the final population density maps which are made available openly. the frequency of new maps generation has to lie in the range of minutes, in order to be effective for prevention on typical human time scales. this paper proposes the start of an initiative for developing a privacy-protecting real-time, open-data population density and flux mapping system, hypothetically named peopletraffic, designed to support citizens and public authorities in harmonizing epidemic diffusion risks whilst properly dealing with privacy concerns. in the specific, it is meant as a tool for aiding the management of the covid- pandemics phase- , which is expected to last approximately until either population herd immunity is obtained or a vaccination becomes available to the mass public. the proposed system is based upon recognizing that social distancing regulations, enforcing physical separation between individuals to limit population density and reducing individual-to-individual contacts, have been the most effective tool in mitigating the spread of epidemics driven by individual-to-individual contact (as covid- and most influenza viruses). the proposed system makes use of the nowadays capillary distributions of mobile network stations (i.e. these adopting gsm, umts, and lte network technologies) to construct real-time population density and flux maps with sufficient spatial and temporal resolutions to get close to the individual proximity scale. the construction of these maps includes an innovative approach to privacy-by-design, compliant with the current european privacy regulations which, thanks to a quantum-inspired delocalization process, preserves the key information necessary for prevention (i.e. mutual inter-distance between individuals) with the highest accuracy while anonymizing individuals' absolute positions. the proposed method is robust against incomplete cell phone possession or activation, intentional de-activation of cell phones by their owners or prevalence of specific providers in specific areas. in place of ex-post intervening when positive cases of infection are detected (which typically happens with some time-lag from the diffusion event), the hereobtained real-time people distribution maps support preventively orienting people towards safe behaviour allowing, e.g., choosing the timing and the means of transportation for commuting. they would also provide valuable information to policy-makers in taking decisions based on people density, which has proved so far one of the most reliable a-priori predictors of infection spreading. here we aim to thank all that contributed to the writing of this note. we acknowledge the important input and discussions from: under the responsibility of each location data provider (gray box): (a) individual users positions are detected and collected by the network provider data system; (b) the anonymization algorithm is run within the location data provider computing infrastructure in order to delocalize each users' position into quantum-like complex-valued wave packets; (c) all wave packets are combined into an aggregated, anonymized wave function; (d) several wave functions are obtained from different mobile network system providers and are distributed to a third-party for subsequent analyses; (e) all providers data are calibrated and combined in order to obtain the final density map dept. art therapy and cultural studies applied ecology and system dynamics lab alfonso fuggetta (politecnico di milano and cefriel) marcello scipioni (dept. of digital innovation, camera del lavoro di milano) scientific and ethical basis for social-distancing interventions against covid- modelling the covid- epidemic and implementation of populationwide interventions in italy airborne transmission route of covid- : why meters/ feet of inter-personal distance could not be enough social distancing in italy one month into the lockdown world economic outlook overview of mobile localization techniques and performances of a novel fingerprinting-based method enhanced time of arrival estimation and quantization of positioning in lte networks annual ieee interational symposium on personal, indoor and mobile radio communications mozilla foundation. mozilla location service real-time urban monitoring using cell phones: a case study in rome voronoi diagrams and delaunay triangulations. computing in euclidean geometry baseline performance of lte positioning in gpp d mimo indoor user scenarios real time rome database correlation method for gsm location who knows where you are, and who should mobile landscapes: using location data from cell phones for urban analysis. environment and planning b -planning and design regulation (eu) / of the european parliament and of the council of april on the protection of natural persons with regard to the processing of personal data and on the free movement of such data, and repealing directive / /ec (general data protection regulation key: cord- -zd v b authors: kawashima, kent; matsumoto, tomotaka; akashi, hiroshi title: disease outbreaks: critical biological factors and control strategies date: - - journal: urban resilience doi: . / - - - - _ sha: doc_id: cord_uid: zd v b disease outbreaks remain a major threat to human health and welfare especially in urban areas in both developed and developing countries. a large body of theoretical work has been devoted to modeling disease emergence, and critical factors that predict outbreak occurrence and severity have been proposed. in this chapter, we focus on biological factors that underlie both theoretical models and urban planning. we describe the sars – pandemic as a case study of epidemic control of a human infectious disease. we then describe theoretical analyses of disease dynamics and control strategies. an important conclusion is that epidemic control will be strongly dependent on particular aspects of pathogen biology including host breadth, virulence, incubation time, and/or mutation rate. the probability, and potential cost, of future outbreaks, may be high and lessons from both past cases and theoretical work should inform urban design and policy. interdisciplinary collaboration in planning, swiftness of information dissemination and response, and willingness to forgo personal liberties during a crisis may be key factors in resilience to infectious disease outbreaks. infectious diseases pose an ever-present danger to human societies. despite tremendous advances in medical care, roughly one quarter of worldwide human deaths are attributed to infectious and parasitic disease (mathers et al. ) . several seemingly unalterable aspects of urban life, including long-distance travel and dense human contact networks, facilitate outbreaks from both known and newly evolved pathogens. epidemics are defined as widespread occurrences of infectious disease in a community at a particular time, and the th century bubonic plague, or "black death", was the most devastating epidemic in human history (benedictow ) . death rates were as high as - % in europe, africa, and asia from a disease caused by a bacterial infection (yersinia pestis) that persists in rodent populations and is transmitted by fleas to humans. close contact between humans and rats and worldwide travel contributed to the global impact of bubonic plague which appears to have originated in asia and traveled to europe via trade routes (especially rat-infested ships). the most destructive modern pandemic was the influenza that infected one third of the world's population (about million) and killed - million between january and december (taubenberger and morens ) . "spanish influenza", as the disease was named, is caused by the h n virus which is endemic in pigs and birds and often transitions into human populations. the lethality of the strain was high and showed an unusual relationship between lethality and patients' age: % of deaths were in the - age group which is the opposite pattern for milder flu strains (higher mortality among the very young and the aged). this partly reflected the impact of wwi where contagion was passed among troops both in training facilities as well as during warfare. however, the strain also had an unusual and lethal property; virulence was enhanced by a human immune over-reaction called a "cytokine storm" which causes the lungs to fill with liquid. some important aspects of the epidemic were: a deadly pathogen arose from a jump from animal to human (close between-species interactions were important in the origin of the virus), a few mutations were sufficient to confer strong lethality for the virus, and human travel allowed rapid spread (close quarters and massive troop movements helped to spread the virus and allowed new mutations to spread quickly). this chapter will focus on biological factors that are relevant for understanding and controlling epidemics. we will briefly describe some pathogens that cause human disease and their transmission mechanisms before analyzing the sars - epidemic as a case study of a modern urban epidemic. disease models will be discussed with a goal of determining how human societies can prepare to minimize the impact of future disease outbreaks. infectious diseases can be classified into two broad categories based on their pattern of transmission (table ) . "long-range" infectious diseases are infections that do not require close contact for transmission. for example, water-borne diseases, such as cholera, can rapidly spread throughout the community when the supply of drinking water becomes contaminated with the pathogen vibrio cholerae through poor sanitation or hygiene practices. food-borne infections follow a similar transmission pattern to water-borne diseases. transmission through contaminated food and water is also known as "fecal-oral transmission" because fecal matter is often the source of contamination while oral ingestion is the primary route for infection (mount sinai hospital ) . diseases transmitted by an animal vector, such as bubonic plague, are also considered long-range infections because a vector facilitates the spreading of the pathogen and direct contact is not necessary. one interesting aspect of some vector-borne infections is that direct contact with an infected individual cannot transmit the infection without the help of the vector. for example, dengue fever, caused by a mosquito-borne virus, can only be transmitted through the bite of an infected mosquito (us centers for disease control and prevention ). in contrast, plague, caused by bacteria living in fleas of rodents, is primarily transmitted through flea bites, but contact with contaminated body fluids like blood can also lead to plague bacterial infection (us centers for disease control and prevention a). in general, fecal-oral and vector-borne diseases are infections transmitted through an environmental (water, food) or a biological (animal) carrier that extends transmission range to large distances, but other routes are also possible depending on the specific pathogen. compared to long-range diseases, "short-range" infectious diseases are infections that transmit over limited distances and may require close or direct physical contact with an infectious individual. examples of short-range infections are pathogens that infect via contaminated airborne particles or expectorated droplets, and diseases that require contact with skin or bodily fluids such as blood or semen. infections capable of airborne transmission have the widest range among short-range infections and are caused by pathogens that spread through minute solid or liquid particles suspended in the air for an extended period of time (mount sinai hospital ) . in addition, the pathogen must be resistant to desiccation to remain viable for long periods of time outside its host. respiratory diseases are commonly believed to spread via airborne transmission of contaminated particles expectorated from coughing and sneezing. however, many respiratory pathogens do not have the capacity to withstand dry environments. instead, these pathogens transmit via "droplets"-expectorated moisture particles that are too big to indefinitely remain suspended in the air-to ensure ample moisture while outside the host. transmission occurs when contaminated droplets from an infected individual come in contact with surfaces of the eye, nose, or mouth. this mode of transmission is called "droplet contact". although diseases spreading via droplet contact have a more limited range than truly airborne infections, in the later sections, we will show how environmental factors can extend the range of droplet transmission. finally, diseases that transmit via direct contact generally have the most limited transmission range and some have stringent requirements for transmission. in the case of ebola, the disease is transmissible only via direct exposure of broken skin or mucous membranes with contaminated body fluids like blood, urine and semen, and excretions such as vomit and feces (us centers for disease control and prevention c). sexually transmitted diseases like hiv/aids are a special form of direct contact infection that requires sexual intercourse or sharing contaminated needles for exposure (us centers for disease control and prevention b). thus, short-range infections are characterized by some dependence on distance for infection and can be transmitted directly without a carrier. distinguishing between these two classes is important because measures to alleviate and control the spread of long-range infections are not applicable for short-range cases and vice versa. for instance, targeting the carrier or vector of the disease to control the spread of long-range infections (e.g., decontaminating or blocking off access to contaminated water or food) and reducing exposure to vectors of the disease, are irrelevant for mitigating the spread of short-range infections. in contrast, measures to control short-range diseases such as limiting person-to-person contact and imposing quarantine procedures do little to help alleviate the spread of water-borne or vector-borne illnesses. thus, identifying the mode of transmission is crucial to controlling the spread of any contagious infection. however, we will show that the distinction between long-and short-range transmissions is not always clear-cut. in this chapter, we focus on the emergence and spreading of severe acute respiratory syndrome or sars; the first worldwide pandemic in the age of globalized air travel and telecommunications. through theoretical analyses and data gathered from the epidemic, we examine how globalization exacerbates the problem of containing epidemics and show how urban environments can be especially prone to epidemics. the emergence and control of the sars epidemic is extensively documented. research on both the origin and epidemiology of the outbreak as well as the biological underpinnings of the disease making them excellent cases to determine methods to enhance urban resilience to epidemics. the history of the - global outbreak of severe acute respiratory syndrome (sars) provides key lessons on biological and policy factors that should be of general importance in designing resilient cities. we will summarize the history of the epidemic, with a focus on biological factors, before our discussion of disease models. according to the world health organization (who), over worldwide sars cases and over deaths occurred in different countries, mostly over a period of about four months (kamps and hoffmann ) . the severe, "atypical" pneumonia originated in guangdong province in southern china in mid-november . most of the early cases appear to have occurred among those who kill and sell animals and meat as well as food preparers and servers (breiman et al. ) . by mid to late january , the disease began to spread rapidly within the province, but a combination of symptoms difficult to distinguish from pneumonia (fever, dizziness, muscle soreness, coughing) and government policy to discourage coverage delayed the reporting of the epidemic until february . the initial communication reported cases (including > healthcare workers) and mortalities, but claimed that the epidemic was under control (enserink ) . the role of "superspreaders" and amplification in hospitals remained characteristics of sars as it spread to a worldwide epidemic. the first of several superspreading (generally defined as ten or more transmissions from a single infected individual) events occurred in hong kong on february , (braden et al. ). the index case was a physician from guangdong who stayed at the hotel metropole. the physician had treated sars patients in guangdong (although the disease was still unrecognized) and showed symptoms before his trip. he stayed only one night at the hotel before being hospitalized with severe symptoms but the short stay was sufficient to spread the infection to or more of the guests from the same floor of the hotel as well as a hong kong resident who visited one of the guests. eventually, over (almost half) of the documented sars cases could be traced to this "index" case. remarkably, there was no known direct contact in most of the transmissions among the hotel guests and visitors. the hong kong resident who visited a friend in the hotel subsequently infected over others at the prince of wales hospital in hong kong. others were business/holiday travelers who spread the pathogen to canada, vietnam, and singapore. as we will discuss below, this high transmission rate with little close contact in the metropole hotel remains mysterious. rapid recognition of a new epidemic was aided by a who disease expert, carlo urbani, who was asked to examine patients in a hanoi hospital. the affected included one of the metropole guests and roughly hospital staff who became affected not long after his admission. urbani recognized a severe, and possibly new, disease and warned who headquarters as well as the hospital and vietnam government before contracting, and eventually dying from, the disease (bourouiba et al. ) . response time is a critical parameter in epidemic control and his efforts played a large role in the effort to subdue the epidemic. who designated a new disease, "severe acute respiratory syndrome" (sars), on march and issued a global health alert on march followed by an emergency travel advisory on march . the etiological agent of sars was later discovered to be a novel coronavirus and was named sars-associated coronavirus (sars-cov). this discovery, in late march , came as a surprise to disease experts as previous human coronaviruses were only known to cause mild illness. in animals, related viruses were known to cause fatal respiratory as well as neurological diseases but coronaviruses are usually highly species-specific (kamps and hoffmann ) . forensic analysis of the metropole hotel in late april revealed physical components of sars in the common areas of the th floor including the corridor and elevator hall. however, no bacteria were found inside the guest rooms of the infected guests (the ventilation systems employed positive pressure within the guest rooms so that air was not shared among rooms). respiratory droplets, or suspended small particle aerosols generated by the index case-patient, are the most likely transmission mechanism (braden et al. ) . sars and other respiratory infections are considered to undergo short-range (approximately m) transmission via pathogen-infected droplets from host coughing or sneezing. such transmission requires "close contact", physical proximity between infected and susceptible individuals who can be infected when large droplets spray enter their bodies via air or touch. however, minute droplets or even solid residues that can arise via evaporation (droplet nuclei) may allow potential indirect and/or long-range transmission (bourouiba et al. ) . for example, contaminated gas clouds that form during coughing/sneezing may have carried the pathogen and extended its transmission range, removing the distinction between droplet contact and airborne modes of transmission. aerosol transmission probably caused high infection rates in an airline flight (air china ) from hong kong to beijing in which a single -year old individual infected at least others (olsen et al. ) . this feature of the disease may be highly relevant for medical and urban policy. long-range aerosol/nuclei transmission does not require direct contact between infected and uninfected individuals and can greatly elevate the number of "contacts" for a given infected individual. interestingly, genetic analysis showed that several sars strains entered hong kong, but only the hotel metropole index case was associated with the subsequent global outbreak (guan et al. ) . a related superspreading event occurred at a crowded high-rise residence, the amoy gardens, in hong kong. many of the infected individuals inhabited vertically placed apartments (in contrast to transmissions on a common floor at the metro hotel case). sanitary drainage fixtures that were malfunctioning and allowing air and sars-contaminated aerosols to flow back into resident bathrooms may have been the main driver of infection spread in the condominium (stein ) . the superspreader was likely a medical patient undergoing treatment for a kidney problem including hemodialysis, a medical treatment that inhibits immune capacity (stein ) . the index case carried a high viral load and suffered from diarrhea. an important feature of this event was again, a lack of direct contact between the spreader and the individuals he infected, and the "opportunity" for the pathogen to be exposed to a large number of individuals through airborne transmission (yu et al. ) . at the amoy gardens, more than individuals showed symptoms of sars almost simultaneously. high rates of hospital (nosocomial) transmission were an important and disturbing characteristic of the sars outbreak. the large fraction of infections among healthcare workers probably reflects a combination of contact from respiratory secretions from patients who were at a highly contagious stage (critically ill individuals also were the most infectious) as well as from medical procedures that inadvertently generated aerosol contamination. a single patient appears to have transmitted infections to over hospital staff in a span of two weeks at the prince of wales hospital in hong kong (see below). two other superspreader events occurred in hospitals in other countries (braden et al. ) . one infected patient (the son of one of the hotel metropole guests) infected over cases among patients, visitors, and healthcare workers at the acute care hospital in toronto, canada. finally, although taiwan instituted strict port entry screening and isolation of potentially exposed travelers entering the country, there was an outbreak in the ho ping hospital which spread into the community. in spite of a lock-down quarantine of over people in the hospital (included a large fraction of uninfected individuals), over cases emerged before the outbreak was contained. the initial rapid spread of sars caused widespread concern and panic and the epidemic seemed unstoppable. however, the disease was eventually contained within several months through efforts coordinated by the who. although advances in biomedical science and cooperative efforts among laboratories played key roles in isolating the infectious agent, "classic" epidemiological practices of patient isolation (separation of infected individuals from the general population), contact tracing, and large-scale quarantine (isolation of non-symptomatic individuals who have had contact with the infectious agent) were the main elements that halted the epidemic ). the - sars pandemic was caused by a moderately transmissible viral infection that produced . new cases for every infection (riley et al. ) and yet it spread to over countries across three continents potentially exposing tens of thousands of people in the span of only a few months. several studies have shown that the vast majority of infected cases had very low infectivity and that a few outliers were responsible for a disproportionate number of new infections riley et al. ; lipsitch et al. ; wong et al. ). in fact, riley et al. ( ) and lipsitch et al. ( ) found that early in the epidemic, an infected individual would only produce approximately three new infections when outliers are excluded. in singapore, % of the first probable sars cases showed no evidence of transmitting the infection yet cases appeared to have transmitted the disease to or more individuals (lipsitch et al. ) . shen et al. ( ) found a similar pattern in beijing where out of the confirmed cases did not infect others whereas four cases were responsible for infecting eight or more. the rapid spreading of sars despite only moderate average infectiousness has revived interest in the concept of superspreading events and heterogeneity in pathogen transmission. the transmission potential of an infectious disease is often described by the parameter r, the average number of new infections that infected cases produce over the course of their infection. r is the transmission potential of an infected individual within an otherwise completely susceptible population (dietz ) . however, population-based summary statistics may obscure individual variation of infectiousness and other types of heterogeneities. woolhouse et al. ( ) have shown that heterogeneities in infectiousness exist such that only % of the host population contributes at least % of a pathogen's transmission potential. these individuals who significantly transmit more than the average are called superspreaders. in hong kong, apart from the incident at hotel metropole, at least two large clusters of infection were attributed to superspreading events (riley et al. ) . data from the sars pandemic showed the effect that superspreaders and superspreading events could have on the trajectory of the epidemic. given their crucial role in intensifying an outbreak, we review the risk factors that facilitate superspreading events. co-infection and the presence of a comorbid disease could be risk factors for turning infected individuals into superspreaders (stein ) . studies on hiv/aids transmission showed that co-infection with another sexually transmitted pathogen increased the urethral shedding of hiv in infected individuals. moss et al. ( ) demonstrated that urethral hiv infection is associated with gonococcal infection and treatment for urethritis may reduce the risk of hiv transmission. in the case of sars, peiris et al. ( ) reported that other viral respiratory pathogens such as human metapneumovirus were detected in confirmed sars cases. in addition, the index case in the prince of wales hospital superspreading event was described to have a "runny nose" , an uncommon symptom for a lower-respiratory tract infection such as sars. these observations have led to the hypothesis that co-infection or presence of a comorbid condition could endow an infected individual with characteristics or behaviors that increases their infectiousness (bassetti et al. ) . for example, rhinovirus, the major cause of common colds, can cause swelling of nasal tissues that can elevate airflow speed and contribute to aerosol production (sherertz et al. ) . rhinovirus co-infection with more serious, but less transmissible respiratory ailments, such as sars, could be an important factor contributing to high infectivity. environmental factors also play an important role in facilitating superspreading events (stein ) . in the sars superspreading event at the prince of wales hospital, the index case was placed on a nebulized bronchodilator four times daily for one week (kamps and hoffmann ) . nebulized bronchodilators are often used to deliver drugs to the lungs of respiratory patients but may have inadvertently aerosolized the virus and left infected droplets in the immediate surroundings leading to extensive dissemination of the pathogen (tomlinson and cockram ) . tracheal intubation, which involves placing a flexible tube into a patient's windpipe to maintain an airway to deliver drugs, may also have inadvertently spread sars within hospitals. patients often emit respiratory secretions during the procedure. an outdated ventilation system and overcrowding likely also contributed to the spreading of the virus at the prince of wales hospital (riley et al. ; tomlinson and cockram ) . through a case-control study of hospitals treating sars patients, yu et al. ( ) confirmed overcrowding as one of the general risk factors of hospital-based sars superspreading events. the case-control study performed included wards in hospitals in guangzhou and wards in five hospitals in hong kong and showed that the main risk factors included closely arranged beds (less than m apart), a workload of more than two patients per healthcare worker, hospital staff that continued working despite experiencing symptoms of the disease, and lack of washing or changing facilities for staff. despite the explosive growth and global distribution of the sars outbreak, the pandemic was largely contained through isolation and quarantine, increasing social distance, and social behavioral adjustments (bell and world health organization working group on prevention of international and community transmission of sars ). isolation and quarantine were shown to significantly interrupt transmission of sars in several countries including hong kong (riley et al. ) , china (pang et al. ) , singapore (lipsitch et al. ) , taiwan (twu et al. ) , and canada (svoboda et al. ). in general, symptomatic cases were immediately placed in isolation while contacts of confirmed infected cases were placed in some form of quarantine. in some cases, contacts were not immediately confined but instead were monitored for the disease and isolated only when symptoms emerged. confinement was usually at home but designated facilities were available in countries like taiwan (twu et al. ) . in some cases, individuals under quarantine were allowed to travel with the permission from the local health authorities provided they wore masks and refrained from using public transportation or visiting crowded places. to further reduce the chance of transmission, hong kong and singapore also closed schools and public facilities, and canceled mass gatherings to "increase social distance". people were also required to wear masks when using public transport, entering hospitals, or in jobs where interacting with numerous people is unavoidable such as in restaurants (bell and world health organization working group on prevention of international and community transmission of sars ). the concerted effort has been marginally associated with the rapid reduction of new sars cases in several countries. however, because of the simultaneous introduction of these measures, it is difficult to evaluate the effectiveness of each. several characteristics of the infectious agent were important factors in controlling the sars epidemic. the incubation period from contact with the infectious agent to onset of symptoms was, on average, . days. importantly, peak infectivity coincided with clinical symptoms and often required an additional days or more ). thus, infectious individuals tended to be hospitalized before peak transmissibility. in addition, the two-week interval from exposure to high infectivity gave epidemiologists critical time to perform contact tracing to identify and quarantine potentially infected individuals before they reached high infectivity. this feature, in combination with moderate transmission rates (except in special cases), contributed to making sars a relatively controllable outbreak. in the next section, we present current theories on the emergence and spreading of epidemics and review the theoretical underpinnings behind control measures used to contain outbreaks. we briefly highlight different mathematical models used to describe epidemic dynamics in populations. we explain the factors that govern the emergence and transmission of diseases as well as the evolution of pathogens that cause them. finally, we examine how control measures such as isolation, quarantine, and vaccination mitigate the spread of infections. mathematical models have played an important role in our understanding of disease propagation. if biological factors can be accurately incorporated, such models may have predictive power to evaluate control strategies and guide policy. a key parameter in epidemic models is the total number of new infections that arise from a single affected host, the reproduction number, r. this value determines the outbreak potential of the infection; if r = , the infection will be maintained at a constant level (if we ignore random effects). r > leads to disease spread and r < predicts eventual extinction. however, r is not an intrinsic property of the pathogen. variability of the reproductive number across pathogens, hosts, and environments over time must be understood to accurately model disease. in the following three subsections, we discuss theoretical results on three important aspect of disease outbreak: ( ) the effect of "superspreaders" on the probability of outbreak, ( ) the impact of control strategies such as isolation and quarantine, and ( ) factors that affect the evolution of pathogen virulence. the - sars epidemic was characterized by the large impact of "superspreaders" on disease propagation. in theoretical models, superspreaders can be treated as individuals with large number of connections to other individuals. individual-based simulations incorporating network structures can efficiently address this topic and, in this subsection, we introduce three theoretical studies focused on the effect of network structure on disease outbreak. lipsitch et al. ( ) studied the effect of superspreaders on outbreak probability using the estimated parameters from the sars outbreak in singapore. the authors first estimated the distribution of the parameter r, which expresses the number of new infections from an infected host. probabilities of outbreak (persistence of initially introduced pathogen lineages) were determined for r distributions with a fixed mean but differing in variance. the authors found that large variance in r distribution greatly decreased the probability of outbreak (fig. ) . contrary to the expectation of the importance of superspreaders, their result showed that distributions strongly clustered around the mean had higher probabilities of outbreak than distributions that included superspreaders (right-hand tail outliers). one reason of this apparent inconsistency might be the assumption of a fixed mean r. under this assumption, increased variance in the r distribution increases both the numbers of individuals with extremely high r and low r. individuals with low r are essentially "dead ends" in disease infection and high numbers of such individuals will decrease outbreak risk. a similar result was obtained in meyers et al. ( ) . this study also focused on the case of sars outbreak in asian countries and used parameters estimated from the case study in individual-based simulations. meyers and co-workers examined differences in the probability of outbreak among three different networks among individuals. in the first network, termed "urban", many individuals have numerous contacts at public places including schools, hospitals, shopping centers and workplaces, and have more limited numbers of contacts at their home. the second network was a power law network, in which the distribution of the number of connections has a long right-hand tail. in such a distribution, a small fraction of people have large numbers of connections but most people have only a few connections. the third network was a poisson network, in which the majority of the people have numbers of connections close to the mean number. if the existence of superspreaders increases the probability of outbreak, then power law networks should show the highest outbreak probability. however, similar to lipsitch et al. ( ) , power law networks showed the lowest probabilities of outbreak. the reason might be similar to what we discussed above; in a power law network, the numbers of individuals with extremely small numbers of connection are elevated compared with the other two networks. pathogens cannot spread if they infect such individuals and will go extinct before they have a chance to infect superspreaders. fig. theoretically estimated probability that a single introduced pathogen persists after infinite time under a markov process with different mean (e) and variance (v) in the r distribution. in lipsitch et al. ( ) this persistence probability is considered as probability of an outbreak. modified from lipsitch et al. ( , fig. a) the two studies above indicated reduced probabilities of outbreak for populations that include superspreaders, but this conclusion may be strongly sensitive to model assumptions. networks with more total connections (including superspreaders) may realistically model urban environments (this relaxes the assumption of constant mean connectedness). fujie and odagaki ( ) modeled superspreaders as individuals with higher infection rates (strong infectiousness model) or more connections including connections with distant individuals (hub model). they calculated the probability of outbreak under different fractions of superspreaders in a population and showed that, as the fraction of superspreaders increases, the probability of outbreak increases greatly (fig. ) . they also analyzed several features of outbreaks like speed of disease spread and infection path between the two models and suggested that the hub model is consistent with data from the sars outbreak in singapore. these contrasting results highlight the need to validate model assumptions for applications to human society. higher outbreak probabilities with larger numbers of connections may seem obvious but this may be a realistic scenario for human society. a key issue is whether the number of connections of one person statistically affects that of others in human society. if not, the comparison between different fraction of number of superspreaders like fujie and odagaki ( ) would fig. theoretically estimated "percolation" probability of a single introduced pathogen under different fraction of superspreaders and population density in a hub model. in fujie and odagaki ( ) this percolation probability of percolation theory, in which a pathogen that has infected an individual in the bottom of × grid finally reaches an individual in the top of the grid, is considered the probability of an outbreak. as density becomes lower, distance between individuals becomes longer. the results for different fraction of superspreaders (λ) are shown in different markers. modified from fujie and odagaki ( , fig. ) more realistically predict the effect of superspreaders on the probability of outbreak. however, if higher number of connections of one person necessitates reduced numbers for others, the results in lipsitch et al. ( ) and meyers et al. ( ) could be more applicable for human society. in either case, models should focus on both outbreak probability as well as the nature (explosiveness) of disease spread. lloyd-smith et al. ( ) demonstrated that many previous human epidemics appear to have spread through superspreaders (although not to the same extent as sars). they showed that, although pathogen extinction probability increases with variance in reproductive number, populations with superspreaders experienced more rapid infection spread in cases of pathogen survival. under their model, host populations may suffer greatly from improbable epidemics. the first step to control the rise of any infectious disease is to understand how it transmits between hosts. often, we imagine these infections as readily communicable illnesses that can be caught by even the most fleeting contact. but as we have shown, exposure and transmission depends on the route the infectious disease pathogen takes. this means that some diseases can be transmitted even without direct or close contact with an infected individual. we have also shown how particular conditions can make a close-range disease transmit over extended distances, as is the case with sars transmission in the amoy gardens condominium complex. aside from mode of transmission, the timing between infectiousness and showing symptoms of the disease is another crucial factor to consider. an infectious disease is an illness caused by the presence of a pathogen within the host as well as the host's response to the invading pathogen. upon entry into the host, the pathogen begins to increase its numbers by redirecting resources to itself. after a certain time, its presence and the damage it has done to the host raises an internal host response to thwart the infection. it is at this stage of the infection that overt symptoms appear and the infection can be observed. the time elapsed between exposure to the pathogen and observing the initial signs and symptoms of the disease is called as the "incubation period" of the disease. the length of the incubation period varies among diseases and is affected by several factors such as dose and route of infection, and host susceptibility and ability to respond to the pathogen. because of these considerations, incubation period is described as a range of values depicting how short or how long it takes before an infection would show symptoms. during this period, the infected individual may or may not be contagious depending on the type of disease and the individual's health state. the disparity between the time we observe the symptoms of the infection and consider an individual ill and the time the individual is contagious are important aspects to consider in modeling as well as in prescribing infection control measures. the timings vary widely depending on the infectious disease (fig. ) . in the simplest scenario, the entire time an infected individual is contagious occurs after the first symptoms of the disease and ends well before the symptoms disappear. a completely overlapping timing where all symptomatic individuals are infectious would simplify identification and make control measures more effective. this timing pattern can be easily modeled by assuming that newly infected individuals simultaneously start to cause new infections to other individuals. and because the disease spreads specifically through a single class of individuals, control measures can simply identify symptomatic individuals to prevent new infections. in the case of sars, peak infectiousness occurs - days following the onset of disease symptoms and correlates with viral load over the course of the infection ). many believe this pattern helped contain the sars pandemic (chau and yip ; diamond ; fraser et al. ) despite exponential growth of the epidemic that quickly spread to multiple continents. in contrast, diseases such as hiv/aids have completely different infectious and symptomatic periods. the first signs of aids do not appear until the infecting pathogen has significantly damaged the host yet the infected individual is contagious throughout the asymptomatic phase and peak infectivity occurs before the onset of symptoms ). modeling diseases with disconnected infectious and symptomatic periods requires splitting the "infectious" class into "asymptomatic infectious" and "symptomatic infectious" classes to more accurately reflect the clinical characteristics of the disease. though sars and hiv/aids have significantly different timing patterns, the relationship between peak infectivity and symptomatic period is clear. however, some diseases exhibit partially overlapping contagious and symptomatic periods that make their outbreaks more difficult to stop. identifying the precise period that infected individuals are contagious is difficult because the values are affected by anderson et al. ( ) numerous factors such as susceptibility of the host, mechanism of infection, and immune response (baron ) . individual variation in incubation periods further complicates the problem. in dealing with diseases that exhibit partially overlapping periods such as pandemic influenza, it is best to rely on conservative measures that consider both exposed and likely infected individuals as targets of containment measures. note that it is possible to harbor an infection yet not show any signs or symptoms of the disease. called a "subclinical infection", this asymptomatic state may be a result of the pathogen infection strategy and the host's ability to tolerate an infection instead of purging it (baron ) . asymptomatic cases that are infectious can help spread the contagion despite strict control measures by being misclassified as uninfected individuals. asymptomatic cases are usually discovered by chance or by reviewing epidemiological data after an epidemic (baron ) . modeling asymptomatic cases requires adding an "asymptomatic infectious" class that is capable of exposing and transmitting the disease. containing the spread of an infectious disease suspected to have a high proportion of asymptomatic infected individuals is difficult but procedures such as contact tracing may reveal some of these asymptomatic carriers and quarantining of exposed and high-risk individuals can minimize their impact. most emerging infections have no available vaccine or treatment. thus the only way to control the spread of these diseases is to prevent exposure and further transmission. isolation and quarantine are two control measures that help block transmission by isolating the individuals who have, or may have, the contagious disease. "isolation" describes separating sick individuals (symptomatic) from people who are not sick (naïve) while quarantine pertains to the practice of separating and restricting the movement of asymptomatic individuals who may have been exposed to the disease to see whether they become sick. these control measures aim to progressively reduce the number of new secondary infections until the disease is eradicated from the population. formally, we can measure the effect of isolation and quarantine by taking a survey of new infected cases and deriving the basic reproduction number r of the infectious disease for each step of the outbreak. without any intervention, r is expected to eventually decrease as the number of susceptible individuals decreases in a finite population without migration. however, by the time the rate decreases to r < , a large proportion of the population has already been infected with the disease. by "removing" potentially infected individuals from the population, isolation and quarantine can more rapidly decrease r below by reducing the incidence of the disease, leading to fewer new infected cases capable of transmitting the infection. isolating symptomatic individuals prevents new cases by separating individuals spreading the pathogen from the host population. given a clearly defined set of symptoms to diagnose the disease, this strategy is intuitive and straightforward to implement from a public health point of view. a precise case definition also reduces misdiagnoses and prevents unnecessary isolation of non-target cases. however, many diseases share symptoms and may occur in combination with other infections so case definitions are not always precise. in the sars epidemic, infected individuals showing atypical symptoms were a major source of transmission, partly because co-infection may have elevated transmission rates (kamps and hoffmann ) . modern biomedical research may serve to quickly identify new pathogens and providing diagnostic tests may be the most important function of initial research (vaccines and treatments generally require months or years and may not be helpful for new diseases). isolating symptomatic individuals is most effective if peak infectivity occurs after observing the first symptoms of the disease and transmission only occurs in symptomatic cases ). while diseases like sars have shown such properties, other infections such as influenza appear to be transmissible even prior to showing overt symptoms. when peak infectivity occurs before the onset of symptoms, quarantine for symptomatic individuals may have little impact on dampening the spread of the infection . even for infectious diseases that transmit only after symptoms emerge, infected individuals may not immediately practice self-isolation or report to a healthcare facility. during the lag time between diagnosis and isolation, the pathogen can still spread to susceptible hosts undermining isolation as a way to control the spread of the infection. on the other hand, quarantining individuals that have been exposed to the disease addresses the shortcomings of isolation as a control measure. identifying exposure is dependent on how the pathogen spreads from one host to another. if the pathogen transmits via airborne droplets, then people present in the same room with an infected individual are considered "exposed". however, if the pathogen spreads only through sexual contact, then only individuals who have had sexual relations with the infected case are considered exposed. when the transmission mechanism is unknown, scenarios such as airborne transmission or via physical contact that lead to the most conservative outcome may be used instead. because the criteria to select individuals are independent of disease status, this strategy sacrifices sensitivity but works regardless of timing of infectivity and does not suffer from the lag time problem. such a conservative strategy is well suited for emerging infections, especially when the mechanisms of transmission and pathogenesis have yet to be revealed. in a perfect quarantine, all exposed individuals are expected to undergo quarantine regardless of whether they develop the disease or not, and during the quarantine period, exposed individuals do not transmit the disease. however, tracing all contacts is often problematic especially when an infected individual has traveled to numerous locations and when exposure occurred in public spaces and mass transit. compared to isolation, quarantine sometimes faces more resistance from expected participants especially from those who have been exposed but appear to be in a healthy condition. during the sars epidemic, mass quarantines were implemented in many countries. over , potentially exposed individuals were quarantined in taiwan, but in retrospect, the action may have spread panic among uninfected individuals and may not have been an effective strategy (university of louisville school of medicine ). in reality, quarantines are never perfect. compliance to the procedures is often problematic: quarantined individuals do not reduce their geographical movement or they only abide by the procedure for a short period. formal quarantines have good compliance rates but are costly and difficult to manage for a large number of cases. therefore a majority of quarantines are made voluntarily or with less monitoring than formal quarantines, but these suffer from reduced compliance and are less effective overall. knowledge about potential superspreaders to identify candidates for isolation can greatly enhance the efficacy of quarantines with much lower numbers of required isolations (diamond ) . although such knowledge may be rare at the beginning of an epidemic, rapid epidemiological analyses may play a critical role in reducing the costs of epidemic control. a critical aspect of human pathogens is their virulence or extent of damage to host. high virulence infectious disease such as hiv, plague or smallpox can be a great threat to human society, and the number of cases of pathogens that have been reported to have evolved virulence and/or resistance against drugs is alarming (altizer et al. ; holden et al. ). understanding the factors which affect the evolution of virulence in human society is an important issue. if it is possible to control these factors in urban design, human society can be more resilient against serious disease outbreaks. several classic theoretical studies on the evolution of virulence concluded that reduced virulence is generally adaptive and should evolve among pathogens. low virulence allows infected host individuals to survive, and pathogens can have more chance to spread to other host individuals. if pathogens have high virulence, they can propagate within an infected host individual, but risk killing the infected host and limiting their spread to other hosts. trade-offs between reproduction within a host and transmission among hosts is a well-studied explanation for the evolution of reduced virulence (anderson and may ; alizon et al. ). however, the balance (or equilibrium) of this trade-off can differ depending on biological characters of pathogens. ewald ( ) discussed how transmission mechanisms of pathogens can alter the predicted trajectory of virulence evolution. highly virulent diseases tend to immobilize hosts in early stage of infection. therefore, if pathogens are mainly transmitted by contacts between hosts, higher virulence would greatly decrease chances of new transmission. however, if pathogens can survive outside of the host and can be transmitted by air, water or vectors in which they are not virulent, host immobility should have less effect on the chances of new transmission. ewald ( ) noted that such pathogens, such as smallpox, tuberculosis or diphtheria, are often more virulent than pathogens that depend more directly on hosts for transmission. other factors can affect the balance of the trade-off and allow evolution of high virulence (galvani ) . for example, if multiple pathogen strains infect simultaneously and compete within individual hosts, high reproduction rate within a host (leading to high virulence) may be favored. in sexually-transmitted diseases, frequent exchange of sexual partners makes transmission of pathogens between hosts easier and as a result cause high virulence. this may be the case of hiv in human society (lipsitch and nowak ) . host population structure also affects the transmission of pathogens and therefore, has a large impact on the evolution of virulence. because urban planning and design can create or alter population structure by its use of the the environment, in the following paragraphs, we introduce two studies focused on the effect of host population structure on evolution of virulence. these studies are based on relatively simple models that may yield general insights. boots and sasaki ( ) incorporated a grid-like spatial structure of "sites" at which individuals can exist. each site can have one of three states: empty, occupied by susceptible individual, or occupied by infected individual. in the spatial structure, connections between individuals were divided into two types, those between neighbors and those between randomly chosen individuals. randomly chosen individuals can be in distant sites, and in such cases, pathogens can be transferred to distant locations. they found that pathogen virulence is favored as contact between hosts living in distant places becomes more common. in this model, a site becomes empty after death of an occupant. therefore, higher virulence is more likely to create a situation in which pathogens kill all susceptible hosts around them and can no longer spread. however, long-distance transfer allows pathogens to spread to new locations where they are surrounded by susceptible hosts. long distance transportation in human society allows contact between distant individuals and may be an important factor that facilitates the spread of outbreaks and favors pathogen virulence. boots and sasaki ( ) did not consider host immunity in their model. immune (infection-resistant) hosts can block pathogen spread and may have a large impact on the evolution of virulence. this question was theoretically addressed by the same authors. boots et al. ( ) incorporated the immune state after the recovery assuming a negative correlation between recovery rate and virulence and found that evolutionary trajectories could lead to low, or even extremely high, virulence depending on host population density. in host populations with high density, pathogens can easily find susceptible hosts and therefore, low virulence which increases the opportunity of infection to a new host evolves. on the other hand, in host populations with low density, immune hosts around a newly infected host efficiently block pathogen spread. in this case, highly lethal pathogens which kill infected hosts and make open spaces can spread more efficiently compared with pathogens with low virulence which induce immunity in hosts. even after killing some hosts, pathogens still have a chance to spread by infecting new susceptible hosts that emigrate to the open spaces. in boots and sasaki ( ) , infected hosts are assumed to be susceptible just after they recover and therefore, lower virulence pathogens spread more efficiently. however, in boots et al. ( ) , immune hosts block pathogen spread and create scenarios where highly lethal pathogens evolve. the results in boots and sasaki ( ) and boots et al. ( ) reveal scenarios in which low virulence can evolve to higher virulence depending on the structure of host populations. a key point is that outcomes are sensitive to the scenarios of population structure, transmission mechanisms, and host immunity. because of their short generation times and high genetic mutation rates, pathogens like rna viruses may evolve rapidly, even over the course of an outbreak. influenza virus, norovirus or dengue virus are well known examples of rna viruses that infect humans. because these viruses cause epidemics every year, controlling their impact is a very important aspect of urban resilience. as mentioned above, the models in boots and sasaki ( ) and boots et al. ( ) may be too simple to directly apply for particular diseases. theoretical studies under more realistic conditions based on structures that closely resemble actual human society and biological characteristics relevant to particular pathogens will be valuable to prevent and control outbreaks of high virulent diseases. important points to consider include parameters and assumption sensitivity for aspects of both host populations and pathogens. in addition, the definition of "connection" differs depending on the transmission mechanism of the pathogen. the concept of "network" must take the view of the pathogen and different networks may need to be considered for different diseases in the same human populations. many of the major human infectious diseases are zoonotic infections that have crossed over from animals into humans (wolfe et al. ). bubonic plague (schmid et al. ) , influenza (palese ) , hiv (gao et al. ) , ebola (marí saéz et al. ) , sars (lau et al. ; li et al. b ) and mers (memish et al. ; wang et al. ) have all been shown to have originated from animals before infecting humans. wolfe et al. ( ) surveyed major infectious diseases ranked by highest mortality and/or morbidity to identify patterns in their animal origins and geographical spreading. all the diseases they surveyed appeared to have originated from the old world (africa, asia, europe) and a remarkable proportion of causative pathogens arose from warm-blooded vertebrates while the remaining were attributed to birds. interestingly, the purported geographical origin of the disease was correlated with the type of animal to which the pathogen originally infected. for example, many diseases that trace back to tropical regions have come from wild non-human primates whereas diseases attributed to temperate regions often emerged from domestic animals. although the exact reason for this pattern is unknown, wolfe et al. ( ) suggested that, because livestock and pets were domesticated in the old world, ancestral pathogens had more opportunity to infect humans compared to more recently domesticated new world animals. for the disparity between old world and new world monkeys, they believe that closer genetic relatedness between human and old world monkeys may have aided in cross-species transmission. these results stress the importance of considering both environmental and biological factors as key determinants of cross-species transmission of infectious diseases. recent spreading of human population by urbanization exposes us to novel pathogens that were previously isolated from human society. the risk of zoonotic infections may be increasing and it is notable that many novel pathogens appear to have high virulence in human (reads ; schrag and wiener ) . during their long evolutionary history, pathogens and their original hosts may have been recurrently co-evolving by which hosts evolve to be resistant against the pathogens, and pathogens evolve to evade the resistant system (little ; woolhouse et al. ) . this means if hosts are exposed to a novel pathogen, it is highly possible that the hosts do not yet have immune resistance against the pathogen and are affected by high virulence (longdon et al. ) . there are also cases in which infections of novel pathogens cause inappropriate immune response and as a result, increase their virulence (graham and baric ). as introduced above, these highly virulent pathogens can spread in a host population depending on host spatial structure. however, it is important to note that not all novel pathogens have high virulence for human. highly virulent pathogens are more likely to be detected and studied and therefore, the patterns may result from ascertainment bias (alizon et al. ; longdon et al. ) . in any case, careful surveillance of both human and animal populations in regions of high human-animal contact may be an important component to defending against novel disease (woolhouse et al. ) . finding the original animal host of a new human pathogen requires scientific rigor but also guesswork and luck. the search for the animal reservoir of the sars pathogen first identified the himalayan palm civet (paguma larvata) after sars-like coronaviruses (sl-covs) were isolated from civets in live-animal markets in guangdong, china (guan et al. ) . however, tu et al. ( ) showed that while civets in live-animal markets were infected with sl-covs, civets on farms did not possess antibodies against the virus, which indicated that they have never been exposed to the pathogen. moreover, palm civets infected with sars-cov showed signs of illness contrary to the expectation that animal reservoirs should be clinically asymptomatic (calisher et al. ) . this observation and that other animals in the same live-animal markets were also infected by the virus (guan et al. ) indicated that the palm civets were infected in live-animal markets rather than being the ultimate source of the pathogen. surveillance of wild animals in the region later lead to the serendipitous discovery that chinese horseshoe bats (rhinolophus sinicus) are the original animal host of the coronavirus that became sars-cov (lau et al. ; li et al. b) . the focus on bats may have been inspired by outbreaks of nipah and hendra virus a decade before that were also traced back to these mammals (normile ). in addition, li et al. ( b) stated that the use of bat products in food and traditional medicine in southern china led them to investigate bats as a potential reservoir. interestingly, bats appear to harbor many human pathogens and have been implicated as the animal reservoir of nipah virus, hendra virus, ebola virus, and sars-cov. even mers-cov, initially transmitted from camels, have been traced back to bat through phylogenetic analysis and biochemical studies (wang et al. ; yang et al. ) . while sars-cov infection primarily affected the respiratory system, high concentrations of coronavirus were observed in bat feces and recovery from the small and large intestines indicate that replication is primarily through the excretory system (drexler et al. ) . lau et al. ( ) speculated that the use of bats in traditional medicine, especially bat feces, may have played a crucial role in the cross-species transmission of the virus. bat meat is also considered a delicacy and many chinese believe it possess therapeutic activity, which led to bat trade in live-animal markets such as those in guangdong, china. exposure between the pathogen reservoir and the new potential host species is a key factor dictating the probability of successful cross-species transmission. for example, hiv- and - seem to have transferred multiple times to humans since based on phylogenetic analysis, but only after was there a significant spreading of the infection (heeney et al. ) . one explanation suggests that the limited interactions between humans and primates created a barrier for the transference of the virus and insufficient interhuman encounters of infected cases delayed the rise of the epidemic (parrish et al. ) . to describe this phenomenon, let us model the underlying host contact network as a network of nodes (individuals) and connections (exposure). assuming a heterogeneously connected network such as human social network and contact networks (eubank et al. ) , we find that the probability of a new infection becoming extinct by chance is very high both because the pathogen may be poorly adapted to transmit in the new host (parrish et al. ; daszak et al. ; dobson and foufopoulos ) and because cross-species transmission events tend to occur in sparsely connected rural areas (tibayrenc ) . the limited connections inhibit emergence of the disease and only the few that avoid stochastic extinction proceed to produce an epidemic in the host population (lloyd-smith et al. ; eubank et al. ). this may explain why spillover events of animal infections, such as h n avian influenza, fail to take hold in the human population despite the hundreds of human cases and deaths that have been reported (parrish et al. ) . while distribution is skewed towards fewer connections in these networks, it is still possible that the cross-species transmission event occurs at a highly connected portion of the network. such an outcome will only make it more likely that the infection will take hold to produce an epidemic due to the presence of highly connected hubs that can spread the disease to a disproportionate number of hosts (rock et al. ) . lloyd-smith et al. ( ) expand this concept to show that any type of individual variance, for example infectiousness, produces the same effect. high individual variance increases the probability of extinction of an invading disease regardless of the strength of mean infectiousness. when the host population has a highly heterogeneously connected network, emergence of disease may be rare, but infections that survive stochastic extinction produce "explosive" epidemics similar to the case of sars in . these findings show that host population structure and demography significantly affects the probability of cross-species transmission as well as the subsequent epidemic that may follow. host factors also play a significant role in determining the success of new infections in novel hosts, especially for viruses. to infect a host, a virus must be able to interact with the host's cellular receptors to gain entry into cells and hijack the cell's machinery to replicate itself. at the same time, the pathogen must survive against the host's defense mechanisms. the initial interaction between the virus and host receptors is a critical step that determines host specificity and host range. for example, in sars as well as in other coronaviruses, the viral structure responsible for viral entry is the spike glycoprotein, which also appears to be the key determinant of host specificity (graham and baric ) . in humans, the receptor-binding domain on the spike glycoprotein interacts with a cell surface metalloproteinase called human angiotensin-converting enzyme (ace) to gain entry and infect lung epithelial cells (li et al. ) . however, ren et al. ( ) showed that sl-covs found in bats do not interact with palm civet or human ace receptors implying that changes must have occurred to gain this new interaction. in fact, there appears to be a sizeable difference between coronaviruses isolated from the putative bat reservoir and sars. sl-covs from bats were found to be at most only % similar compared to sars-cov (li et al. b) . later, ge et al. ( ) were able to isolate and characterize a sl-cov that utilizes the ace for cell entry in bats, palm civets and humans. this finding argues that ace utilization may have evolved prior to any cross-species transmission event. while gaining the ability to bind to a novel receptor appears to be a complicated process, in some instances, even a few amino acid changes may confer the ability to recognize a new species. initial studies comparing sars-cov isolated at different time points in the pandemic revealed the spike protein of viruses taken from palm civets and early human cases bind less efficiently than those from later on in the epidemic (yang et al. ) . further genetic and biophysical studies demonstrated that two amino acid changes had an enormous effect on the binding affinity of the sars spike protein to human lung epithelial cells (li et al. a, c; qu et al. ) . in most palm civet samples, lysine at position and serine at position of the spike protein were observed whereas asparagine and threonine were present in human samples. li et al. ( a) found that replacing lysine with asparagine removed the electrostatic interference with the histidine residue on the receptor while replacing serine with threonine provided a methyl group capable of filling in a hydrophobic pocket at the interface of the human ace receptor. although the structural changes appear to be subtle, these substitutions caused a thousand-fold increase in binding affinity to the human ace and lead to enhanced human transmission. however, li et al. ( a) also found that some civet specimens have asparagine instead of lysine at position yet this did not affect binding to the civet ace receptor. changes that are neutral to the original host but advantageous in the new host may have played a critical role in facilitating cross-species transmission between palm civets and humans. once a pathogen has evolved to reliably infect the new host's cells, the innate immune response is the host's first line of defense against the infection. when a virus successfully infects a cell, cytoplasmic enzymes that detect the production of double-stranded rna, a hallmark of virus replication, activate the expression and release of interferons from the cell. interferons act as an early-warning signal to other cells nearby by activating their intracellular antiviral response to combat viral infection and replication (roy and mocarski ) . because of the importance of this immune response against viral infection, many viruses have evolved features to subvert interferon signaling. for example, the influenza virus prevents the infected cell from detecting viral replication by using its ns protein to sequester double-stranded viral rna (lu et al. ) . another method to interfere with the innate immune response is to prevent interferons from activating antiviral mechanisms. nipah virus produces two proteins that prevent stat from translocating into the nucleus as well as another protein that sequesters stat present in the nucleus, obstructing the activation of interferon-stimulated genes (shaw et al. ). in the case of sars, kopecky-bromberg et al. ( ) found that sars-cov nucleocapsid and accessory proteins inhibit both the expression of interferon and associated transcription factors, as well as inhibiting cellular response to interferon by subverting the jak/stat activation of intracellular antiviral mechanisms. while infection with sars-cov did not induce production of interferons, coinfection with another virus did produce interferons. it appears that sars-cov does not induce interferon expression, yet does not shut down the whole pathway as interferon signaling continues to work when other stimuli are present (frieman et al. ) . by antagonizing the induction and response to interferons, the pathogen blocks the activation of more than interferon-stimulated genes which prevents the cell from going into an "antiviral state" (de lang et al. ). under the antiviral state, inhibitors are activated to prevent cell division, enzymes that digest proteins initiate programmed cell death, and proteins that present viral particles to activate the adaptive immune response are upregulated. blocking interferon signaling causes a general decrease of both innate and adaptive immune system response, allowing sars-cov to infect cells unimpeded and potentially cause a more serious disease. the rate at which a pathogen evolves is another biological factor that may determine risk of cross-species transmission. most recent emerging infections have been caused by rna viruses such as hiv (gao et al. ) , ebola virus (gire et al. ) , dengue virus (gubler ) , sars-cov (lee et al. ) and mers-cov (de groot et al. ) . rna viruses have an extremely high mutation rate because their rna polymerase, the enzyme that copies their genome, lacks proofreading activity which leads to error-prone replication. mutation rates for rna viruses range from − to − substitutions per nucleotide per cell infection, two orders of magnitude higher, on average, than dna viruses (sanjuán et al. ). at those rates, about out of , nucleotide changes every time an rna virus replicates itself. this may not seem high but note that hundreds of millions of viral particles may be produced during a single infection (haase ) , which gives the virus numerous opportunities to explore potentially advantageous mutations. although high mutation rates helps rna viruses to rapidly adopt advantageous changes and alter phenotype, deleterious mutations are also produced at an elevated rate. lauring et al. ( ) have demonstrated that viruses mitigate the effects of deleterious phenotypes by outcompeting and quickly purging these low-fitness variants. the ability of viruses to incorporate functional components made by other functional viruses within the same cell appears to also mitigate the negative effects of high mutation rates (makino et al. ). indeed, studies have shown that raising the mutation rate through mutagens can be used to create large numbers of dysfunctional mutants that rapidly leads to the extinction of the viral population (pathak and temin ; loeb et al. ; domingo ) . interestingly, in the case of sars, the coronavirus that caused the disease did not have a very high mutation rate relative to other rna viruses. coronaviruses have the largest genomes (approximately , nucleotides) among rna viruses and genome size and mutation rate appear to be negatively correlated (sanjuán et al. ) . one reason behind the relative stability of coronavirus genomes could be the presence of proofreading enzymes that guard against mutagenesis. in the case of sars-cov, smith et al. ( ) showed that the exoribonuclease domain in non-structural protein had proofreading activity and was responsible for protecting the viral genome against mutagenesis. although high mutation rates appear to facilitate adaptation of rna viruses to new environments, diseases of animal origin are not always caused by the fastest evolving rna viruses. the discussions above have introduced how several aspects of urban life, including high connectedness of individuals (including connections among distant individuals) and regions of high human/animal contact, are likely to elevate the risk of future epidemics. because these properties may be intrinsic to urban life and difficult to alter or control, monitoring and preparedness are critical for urban resilience to disease outbreak. opportunities for the evolution of new or variant human pathogens are difficult to limit and may, in fact, be increasing in modern societies. each contact between microbe and host can be considered a "trial" for a potential pathogen with random mutations in their genomes that may confer new functions or specificities. thousands of such trials occur daily in many regions and are likely spawning candidate emerging pathogens with the ability to reproduce within humans and possibly also to transmit from person to person. the trajectory of pathogen evolution depends strongly on the numbers of contacts (potential transmissions) among individuals in the host population as well as on chance. the vast majority of potential new pathogens are likely to be lost early in their histories. however, given continuous opportunities, the chance event of pathogen emergence is simply a matter of time. in guangdong province, several recent outbreaks of bird influenza (h n ) have led to limits on live poultry markets, but consumer preference for freshly slaughtered poultry and wild animals remain an impediment to regulating the high-risk concentration of multiple species (pig, poultry, dog, cat, rabbit, as well as reptiles, fish and numerous wild game) in close contact with one another (and often in poor health) as well as with humans. regions of recent human expansion where wild animal populations are in close proximity to high density human settlements must also be monitored carefully for new zoonotic diseases. new strains of swine and bird influenza are currently monitored as candidates for outbreaks but pathogen emergence is unpredictable and may come from completely unexpected sources. regardless of the source of new infectious agents, a major concern is that future pathogens may have properties that will make control much more difficult than sars. shorter incubation times and pre-symptomatic transmission strongly limit the efficacy of isolation and quarantine and may allow rapid disease spread. in this chapter, we have focused on biological factors that are central to disease emergence and control. policy prescriptions have been discussed extensively (university of louisville school of medicine ; beaglehole et al. ) and we highlight selected topics below. one of the important lessons from the sars crisis was the need for a rapid and organized response, even in the case of a relatively controllable disease. recognition of new epidemics through surveillance and global warnings and travel advisories are obvious critical factors but the necessary infrastructure has been difficult to implement, especially in developing regions. given the likely lag-time between the start of an outbreak and pathogen isolation and development of diagnostics, well-trained physicians and epidemiologists at the frontlines of the epidemic play a critical role in initial response. for an infected individual, the numbers of contacts and possible and actual transmissions increase rapidly with time so diagnosis and contact tracing are time-critical events. finally, communicating with, and educating the public and controlling panic are major concerns especially in the context of false reports and rumors. establishing trusted sources of information prior to emergencies should be a major objective for cities/regional governments. issues with coordination among government agencies or between medical and government agencies were strong obstacles in the response to sars in most affected regions (university of louisville school of medicine ). high transmission in medical care settings was one of the prominent features of both the sars and mers outbreaks. because infected individuals with weakened immune systems or co-infections may be the most difficult to diagnose and may show high infectiousness, proper training in pathogen containment is a critical element of epidemic preparation. similar basic techniques (proper use of gloves, gowns, masks, and goggles) were successful for sars and ebola suggesting that many practices will be of general value but specifics for particular transmission mechanisms (e.g. airborne versus vector transmission) are also critical. intervals between outbreak occurrences may be large, so regular confirmation of preparedness is important. low margins in health care are strongly linked to overcrowding and government and private organization incentives (e.g., increased funding for hospitals that rate highly on infection control training and preparedness) can greatly enhance hospital safety (committee on the future of emergency care in the united states health system ). the importance of patient isolation in limiting disease spread is clear from recent sars, ebola and mers outbreaks; hospitals must have containment facilities and "surge capacity" to limit superspreading events. although public health measures were sufficient to eventually control sars, additional measures including antiviral drugs and rapid vaccine development and production may be necessary for stronger pathogens. the economic impact of epidemics, roughly billion usd ( % of regional gdp) for east asia from sars and potentially over billion usd for pandemic influenza (the economist ) should help to justify the costs of outbreak preparation. informed sanitation (water purification, sewage treatment) and building regulations/inspections (e.g. airflow control) policies can play a key role in preventing disease emergence and spread. the sars example illustrates the need for extensive interdisciplinary efforts, combining expertise from physics (fluid mechanics), biology (especially understanding mechanisms of disease transmission), and building design for resilience to future outbreaks. isolation and quarantine were critical to controlling sars in hong kong, singapore, taiwan, china, vietnam and canada. compliance rates appeared to be high in all regions (university of louisville school of medicine ) perhaps partly because the "cultural" value placed on solidarity and cohesion was relatively high in these regions. more severe movement restrictions may be necessary for more transmissible and/or virulent pathogens. it is unclear whether similar measures 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co-evolution of pathogens and their hosts receptor usage and cell entry of bat coronavirus hku provide insight into bat-to-human transmission of mers coronavirus evasion of antibody neutralization in emerging severe acute respiratory syndrome coronaviruses evidence of airborne transmission of the severe acute respiratory syndrome virus why did outbreaks of severe acute respiratory syndrome occur in some hospital wards but not in others key: cord- - yivxfi authors: robertson, christopher t; schaefer, k aleks; scheitrum, daniel; puig, sergio; joiner, keith title: indemnifying precaution: economic insights for regulation of a highly infectious disease date: - - journal: j law biosci doi: . /jlb/lsaa sha: doc_id: cord_uid: yivxfi economic insights are powerful for understanding the challenge of managing a highly infectious disease, such as covid- , through behavioral precautions including social distancing. one problem is a form of moral hazard, which arises when some individuals face less personal risk of harm or bear greater personal costs of taking precautions. without legal intervention, some individuals will see socially risky behaviors as personally less costly than socially beneficial behaviors, a balance that makes those beneficial behaviors unsustainable. for insights, we review health insurance moral hazard, agricultural infectious disease policy, and deterrence theory, but find that classic enforcement strategies of punishing noncompliant people are stymied. one mechanism is for policymakers to indemnify individuals for losses associated with taking those socially desirable behaviors to reduce the spread. we develop a coherent approach for doing so, based on conditional cash payments and precommitments by citizens, which may also be reinforced by social norms. in the medium-term time horizon until a vaccine is developed, and perhaps thereafter, management of the covid- pandemic will largely depend on broad behavioral changes at the population level. under a strategy of social distancing, lockdown, or quarantine, individuals are directed or suggested to exercise precautions including staying home, closing businesses, wearing masks, and avoiding physical proximity to other persons. presymptomatic patients are a reservoir for spread, but such precautions depend on them believing that spread is both important and preventable. individuals have inherent incentives to undertake such measures, because they are self-protective, reducing the chance of the actor herself becoming infected and suffering. accordingly, policymakers can expect a substantial degree of voluntary compliance, as long as the public receives, and believes, accurate information about the risk. that is, regrettably, a nontrivial assumption, but that problem is not our focus here. notwithstanding the self-protective effects of these measures, microeconomic analysis suggests a likely market failure, due to heterogeneity in the population. part of the heterogeneity is biological-some individuals (eg younger persons and women) appear less likely to suffer harm from infection, whereas other individuals (eg older persons, men, and those with other medical conditions) face greater risk of harm if infected. the costs of precaution are also heterogeneous. for individuals who would otherwise be actively building careers or businesses, searching for romantic partners, or providing for dependents including children, the costs of staying at home are much more substantial, compared with others who are already retired from work, settled with spouses and partners, and no longer have dependents. certainly, the consequences of loss of life are more dire for the younger as they have more years of life to lose. however, younger people tend to discount the future more heavily than older individuals and may not place much value on the additional years of life at risk. perhaps most important, the greatest risk to individuals in this younger group, particularly teenagers, is the loss of the social interactions through school, sports, and other activities that are essential to combat depression, among other risk factors for health. suicide and suicide attempts in younger individuals dwarf the magnitude of risk from covid- , which makes the pandemic precautions particularly burdensome for this population, even if yielding spillover benefits for everybody else. perilously, young people are starting to venture into 'covid- parties' organized, so that people can mingle with infected people to get the illness 'out of the way' and carry on with life. in rough terms, for the age gradient in particular, these observations suggest a stark misalignment of incentives-younger persons personally receive the fewest benefits from precautions, but suffer the greatest costs of taking them. on the margin, some individuals will see the personal costs of taking a precaution to be greater than the personal benefits. the heterogeneity in the population suggests a classic market failure, known in the law and economics literature as an 'externality' . those who do not comply with precautions disproportionally impose the costs of noncompliance on others, who are more likely to suffer from infection. similarly, for seasonal flu where vaccination is a primary precaution, the rate of vaccination in the - age bracket has not in recent years exceeded %, which is just over half the rate of older adults. in a recent survey, young millennials were the least well informed about influenza, and the most likely to believe anti-vaccine rhetoric. accordingly for covid- , we can expect that for those who can get infected without bearing healthcare costs, suffering, or unemployment, precautions may seem unnecessary. this is especially true given that persons have private information about their preventive measures, but may not possess information about whether they are infected. how can governments effectively regulate this situation in the complex environment of an infectious disease, like covid- ? we make the nontrivial assumption that governments can promulgate policies about what activities may be optimal at a given point in time (ie whether to return to work), but we focus on mechanisms of compliance, recognizing that many micro-level decisions are difficult for the government to monitor, much less to enforce. from a normative perspective, the goals are clear: to minimize the net harm to aggregate social welfare caused by the pandemic, accounting for both the public health losses (mortality and morbidity, and the costs of treating or suffering with the same) and the economic losses associated with taking precautions (lost wages and forgone consumption of welfare-enhancing goods and services). we generally assume, for the sake of argument, that certain levels of specific precautions are worthwhile from this social utility perspective. yet, for the reasons just stated, the costs and benefits of taking those precautions are poorly distributed. we do not offer a normative theory of optimal distribution, but rather a behavioral one: how to align the costs and benefits of precautions so that the precautions will be sustainably undertaken. one mechanism to address that problem is for policymakers to indemnify individuals for losses associated with taking those socially desirable behaviors to reduce the spread. we discuss a coherent mechanism for encouraging the taking of costly precautions, which may also be reinforced by social norms. the concept of 'moral hazard' is that individuals are more likely to take risky or costly behaviors when those costs are borne by others. in health policy, most of the focus on moral hazard has been in the design of health insurance policy, using deductibles and copays, to insure that once ill or injured, a patient does not wastefully consume healthcare. that form of moral hazard is sometimes distinguished as 'secondary', or 'ex post', after the illness arises. notwithstanding an overwhelming emphasis in health policy, the literature suggests that 'ex post' moral hazard is a relatively small driver of healthcare consumption for several reasons, including patients' lack of agency in making many of their own healthcare choices in practice. accordingly in the covid- infectious disease context, where underconsumption is a greater risk than overconsumption, congress provided that tests be covered without cost exposures and insurance companies have largely covered associated treatments. in contrast, 'primary', or 'ex ante', moral hazard applies where individuals who have healthcare costs largely externalized to the insurance pool may undertake risky behaviors (eg smoking or skydiving) increasing chances of having an injury or illness in the first place. for health insurance design, primary moral hazard may have a relatively small effect on risk-taking behavior, because individuals personally suffer many of the other risks associated with illness or injury (including pain, suffering, lost work, chance of death). these other costs are likely more salient to a person selecting a risky behavior than is the fact that some of the healthcare costs will be insured. for the policy of managing infectious disease, primary moral hazard is likely to be a more important driver of behavior where the chance of suffering any disutility whatsoever is heterogeneous. in this case, although the risk does not approach zero, it is as if relative youth provides partial indemnity insurance against not only the healthcare costs, but also the pain, suffering, lost work, and chance of death that are associated with covid- infection. traditional health insurance policy has conceived healthcare as a cost when a risk materializes, but healthcare is often itself a precaution against a greater future risk. baicker and colleagues have coined the term 'behavioral hazard' to refer to the phenomenon of people declining to consume worthwhile healthcare. this body of research in the health insurance domain demonstrates the more general phenomenon of how policy may strike the wrong balance, for example, if actors are biased away from optimal precaution-taking decisions, because the immediate costs of care (eg copayments for insulin) seem more salient than the longer-term costs (eg treating neuropathy for uncontrolled diabetes). of course, that problem is exacerbated if the costs of precaution are so high that individuals simply cannot afford to take them, even if they would prefer to do so. accordingly, the affordable care act now requires coverage of certain preventive services without cost exposure at all-indemnifying the cost of precaution-an approach that may improve welfare and reduce spending overall. in the recent past, few global diseases in human health have been comparable to covid- with respect to the simultaneous level of transmissibility and pathogenicity. yet policymakers are not 'flying blind' . in other infectious disease contexts, moral hazard and risk-seeking behavior have been confirmed empirically. for example, in the uk, policymakers have struggled to manage an outbreak of bovine tuberculosis. the primary policy mechanism is a surveillance program, where agricultural agents visit farms and test animals for the disease. if it is discovered, the animal is killed, and the farm is put on a disease-restricted status (like a quarantine or lockdown) for days. the farmers are able to take various costly precautions (eg maintaining fences, disinfecting trailers) to reduce the risk of infection. one might suppose that the risks of having beef purchasers reject infected meat, of having an infected animal discovered and slaughtered, and having the farm put on lockdown would be sufficient to induce optimal rates of precaution-taking. however, the policy also includes a provision to indemnify the farmer for the loss of the infected animal that must be destroyed by law. forthcoming empirical work shows that higher levels of indemnity may lead to higher rates of infection likely because farmers take fewer precautions when facing larger indemnities. in this case, the government has in part exacerbated the moral hazard problem, by paying an indemnity that lowers the farmer's risk exposure, reducing the inherent incentive he would otherwise have to keep his cattle healthy. this indemnity is similar to the young, female, otherwise healthy human in the age of covid- , who may be less likely to suffer adverse effects of infection, and thus has reduced inherent incentives to take precautions. as in human health, a farm experiencing a disease breakdown generates a negative externality for its neighbors through spatial disease transmission. by taking steps to minimize the likelihood of a breakdown on her own farm, the farmer also reduces the likelihood of infection for her neighbors. the indemnity payment relieves the farm of a portion of the costs of contracting the disease and, by doing so, reduces the incentive to invest in on-farm biosecurity. consequently, not only do high indemnity rates lead to higher rates of disease, directly, by disincentivizing precautionary steps, but also the spatial feedback effect runs the risk of generating further infections in the surrounding area. again, the example of animal disease management echoes the human experience. in the agricultural settings, the unfortunate policy of indemnifying farmers against the costs of their failing to take precautions may reflect a constitutional, legal, or political limit to governmental enforcement. the payment of an indemnity may reflect a political bargain, allowing a relatively intrusive regulatory mechanism, such as mandatory testing, to be agreeable to the agricultural lobby, if accompanied by a payment from the treasury to offset some of the costs thereof. similarly, under the us constitution's due process clause, the government must generally compensate individuals for 'takings' of their property. moreover, under international commercial agreements, businesses may enjoy a remedy against excessive regulatory interventions that cause economic injury. more generally, the us constitution limits the powers of the state and federal governments to restrict certain liberties, but the supreme court has generally upheld reasonable public health interventions, especially in times of emergency. in the case of jacobson v. massachusetts, for example, the supreme court upheld a local massachusetts law requiring smallpox vaccination. the courts have, however, struck down public health enforcement actions that were motivated by racial animus, or which were not appropriately tailored to the risks at hand. nonetheless, the government has broad powers in this domain. accordingly, to enforce orders for social distancing, or staying at home in particular, some governmental actors made strict orders backed by the coercive power of the state. on april , for example, police officers throughout the state of california began issuing citations for those who refused to close businesses or maintain social distance on beaches. if these sorts of citations, or more severe sanctions such as imprisonment, have a deterrent effect, they may solve the collective action problem. however, deterrence theory suggests that to be effective, enforcement has to find the optimal mix between detecting noncompliance and then sanctioning it once found. for a rational actor, the risk of suffering the sanction is the product of these two variables. although it may be relatively easy for the police to detect and enforce against business operators and beach goers, it will be much more difficult to detect individuals who meet to have sex, for example. similarly the war on illicit drugs has been stymied by such difficulties of detection. whether such black markets can be kept small enough to keep infection rates at manageable levels, is a key question. in this case, deterrence is also stymied by the realities of an infectious disease, such as covid- . law enforcement typically employs escalating consequences for violations, starting with the threat of fines and culminating with imprisonment as the ultimate consequence short of death. yet, fines may affect communities that have already been hit hard by the pandemic and are generally hard to enforce, when individuals have little or no funds to pay (a problem known as 'judgment proofing'). indeed, the power to fine is ultimately backed by the power to imprison those who refuse to pay. moreover, prisoners are particularly vulnerable to covid- due to overcrowding, poor ventilation, unsanitary facilities, and poor access to healthcare services. prisons easily become epicenters of disease, threatening the health and safety of the inmates as well as the surrounding community. inmates from prisons to home confinement. some prisoners have reportedly even tried to get themselves infected, as a basis for then getting early release. thus, governments are hamstrung in how they are able to enforce compliance with social distancing and quarantine requirements. fines are regressive and imprisoning an individual violating quarantine guidelines would be counterproductive as they could introduce the disease into a particularly vulnerable population where the chance of spread is high. governors and law enforcement agencies have dramatically reduced arrests. by may , some local governments were already refusing to enforce 'stayat-home' orders for political, ideological, or other reasons. hence, governments will have to look beyond the threat of fines and imprisonment to compel compliance with precautionary measures. these difficulties may explain why, in march and april , the usa saw private actors merely encouraging people to take precautions, and even some governmental actors, such as state governors, who had the power to exercise the coercive role of the state, declined to do so, in favor of mere exhortation and encouragement. the literature on 'private ordering' and the broader literature on social norms, together suggest that individuals may provide socially desirable behaviors, even when it is not compelled to do so under strict rationality. economics literature suggests the possibility of repeated interactions with individuals and the threat of social retaliation may be sufficient to establish and uphold social norms (ie 'don't burn bridges'). for instance, adherence to government recommendations to social distance may be achieved simply through the universal fear of loss of status or reputations if one is discovered to disregard recommended behavior. in hong kong and elsewhere, internet users shamed people they believed had flouted lockdown orders, traveled, or socialized recklessly during the pandemic. vendors may also voluntarily embrace precautions to burnish their own reputations for safety. for covid- , government directives were initially crude-just a binary decision to allow businesses to remain open (if essential) versus mandate closure (if not). yet, the market responded innovatively: in some 'essential' stores, there were no limits on the number of shoppers in the store, no systematic disinfection of carts or baskets or checkout counters, no masks or other protective equipment of store personnel, and the like. conversely, some stores voluntarily created waiting lines outside the store, with tape demarcating foot intervals, allowing entry into the store only with exit of another shopper, thoughtful distancing of carts from other shoppers on checkout, a designated position for the customer while items are scanned, and more. stores may have enacted voluntary precautions in hopes of boosting business by being seen as a safe place to shop, reducing liability exposure in the event of infected employees, or simply to minimize the chance of disease spread for safety reasons. eventually, governments may catch up to prescribing the sort of granular policies for managing covid- as they have, for example, for handling food-borne illness in foods. yet, reputational sanctions tend to work best when used against members within identifiable groups, such as a close-knit religious or ethnic community, but can cut against compliance of formal rules. in communities in which government authority conflicts with strong social norms or fear of loss of status or reputations, governmental orders can also be harder to enforce. it has been reported that an important factor contributing to the outbreak in south korea included mistrust by a close-knit community. economic and behavioral insights are powerful for understanding the problems inherent in managing a highly infectious disease, but what do they recommend as solutions? the overarching principle is to make it easier (ie less costly) for individuals to take reasonable precautions than to not take reasonable precautions. in this essay, we are primarily focused on regulatory mechanisms prior to a vaccine becoming available. however, the american experience with vaccine mandates is illustrative of our economic and behavioral analysis so far. consider a parent's choice about whether to vaccinate her child prior to covid- . her state may nominally require vaccination unless an exemption applies, but an indifferent or harried parent may find it easier to scribble her name on an exemption form rather than go to the hassle of finding a pediatrician, making an appointment, and securing the vaccination. indeed, scholars have found that vaccination rates vary substantially depending on the proce- dure required to invoke such an exemption. for example, in washington state implemented a requirement that parents have a counseling session with a physician prior to securing such an exemption, and exemption rates went down by %. in addition to any information delivered, these requirements function as behavioral speed bumps for the parent, with the inconvenience (ie non-monetary cost) serving to ration the scarce resource of non-vaccinated parents. in this way, the precaution is made less costly than not taking the precaution. for covid- , when a vaccine is available, it may begin as a scarce resource to be rationed across many people desiring it, but once it achieves a certain saturation, there will likely remain a minority of persons who resist vaccination, unless properly incentivized. the usa has generally focused only on childhood vaccinations, but strategies for incentivizing adults will then be required as well. for example, participating in some valuable but risky activities, such as airline travel, could be conditioned on vaccine compliance. returning to our focus on the prevaccine era, in order to diminish the negative impact on the economy and citizens' finances, some governments are considering issuing 'immunity certificates' to individuals who have recovered from the disease and are presumed to be immune from reinfection as well as unable to spread disease. these individuals with immunity certificates would then be able to re-enter society and resume their employment as well as patronize businesses and continue participating in the economy. assuming that fundamental questions regarding immunity can be answered affirmatively by medical science, and that a technological solution can be employed to ensure validity over counterfeiting concerns, such a policy could then receive support in judicial review, as discriminating against those with and without immunity, not unlike the way extant and potential policies discriminate against those who are unvaccinated. still, this sort of certificate policy could backfire, especially as it creates an incentive to contract the disease-a 'get-out-of-jail-free' card, creating a risk of community spread, prior to the hypothesized benefit of immunity being secured. intentionally seeking out disease like in the form of 'covid- parties' has precedents in the form of 'chicken pox parties' in order to obtain immunity as a young child as well as the concept of 'gift giving', the intentional transmission of hiv. unless the infection is secured in controlled conditions (eg exposure followed by weeks of quarantine), the net effects may be negative overall. this analysis suggests that the immunity certificates policy could exacerbate the same moral hazard problem, which already discourages some people from taking reasonable precautions. this problem may be overstated, to the extent that individuals are already actively flouting stay-at-home orders, immunity certificates may do little to alter their private risk calculus toward less precaution. thus, the primary concern is the population on the margin, who otherwise would have abided by shelter-in-place and social distancing, but due to immunity certificates, will be tipped toward reckless behavior. those who are extremely financially insecure, those who perceive themselves to not be at risk of serious adverse consequences of the disease, or those who believe contracting covid- is inevitable have an incentive to eschew precautionary measures and seek out the disease in order to shorten the length of time they are out of work. this problem reinforces the more fundamental need, discussed below, to further indemnify individuals who are taking precautions, including through substantial increase in unemployment compensation, as already beginning in the cares act (discussed below). speaking more broadly, while the immunity card solution allows identification of individuals who are no longer disease susceptible, it fails to solve the primary imperfect information problem-identifying who is contagious. expanded testing capacity and faster tests would allow for more direct targeting of the moral hazard problem. improved testing would dramatically reduce the need for population-wide 'shelter in place' strategies. under this scenario, quarantine restrictions could be limited only to individuals that test positive and their contacts. this strategy imposes the economic costs of contagion on precisely the right individuals-those that are contagious. and unlike the immunity card strategy, it does not create a perverse incentive to become infected, but rather imposes the costs of quarantine on those who become infected. note that such an analysis need not suggest that all individuals who become infected are in some way at 'fault' for having become infected (though some may have been, if they failed to take reasonable precautions to avoid infection). once infected due to any cause, in economics jargon, the infected individuals generate a negative externality, and, thus, they are the appropriate population to be isolated. regardless of the source of infection, it may then be unreasonable for such a person to engage in activities that risk harm to others. we also emphasize below that the individuals under targeted quarantine could be compensated for the private costs of quarantine through private or public insurance programs. a test-and-quarantine strategy would allow the economy-susceptible and immune individuals alike-to resume normal life while actively and effectively mitigating the spread of the disease. of course, this targeted quarantine strategy still requires compliance with guidelines to stay at home on the part of the covid- -positive individuals. compliance may be achieved more easily in this scenario as subjects of quarantine will know the restrictions are temporary. additionally, because those quarantined have tested positive or come in contact with a positive case, they will face more severe social pressure to avoid contact with others. however, unless widespread testing could be implemented and made mandatory (at least conditional on certain risky behaviors), other imperfections in the healthcare system confound this strategy. if tests were not mandatory, symptomatic individuals could simply avoid testing so as not to be detected as a positive case and removed from employment. for instance, those who are financially insecure and without any sickleave program that would provide compensation during the quarantine period would have incentive to avoid the test to prevent loss of income. for covid- across all these particular policy tactics, the fundamental mechanism must be to reduce the costs associated with individuals taking precautions, so that the net individual cost of precaution is lower than not taking the precaution. the most costly form of precaution is to stay home from work. one obvious solution is to effectively indemnify persons who lose income due to lost work. prior to the covid- crisis, this was a weakness of us policy, compared with other industrialized countries, which tend to have robust provisions for paid sick leave and unemployment insurance. for people who actually lose their jobs, unemployment insurance in the usa pays for up to weeks and is even then capped to cover only a portion of prior income. in one study, those receiving unemployment insurance only recouped half of their lost wages on average. the $ trillion package passed by congress in mid-march provides a one-time payment at about $ plus $ per child for most families (and less or none for others). it is worthwhile that these payments went to both workers and nonworkers, because even nonworkers face substantial disutilities in complying with social distancing protocols. however, for workers at least, the payments are far from sufficient to indemnify the costs of precaution: the median american family would need about $ , to compensate for a single lost month of work. additionally, the usa has increased weekly unemployment benefits by $ . even with the increased weekly payment for the unemployed, the benefit may end in the near future and it does not scale with income to the detriment of those living in high cost-of-living areas. this suggests that noncompliance will remain a very substantial problem (not to mention the substantial disutility suffered by those under the current income shock and the larger economic effects due to contraction). of course, with broader public spending on income replacement and broader compensation for taking precautions, someone must pay those costs. as younger persons today may be disproportionately taking precautions for the sake of protecting older persons (as we suggest in the introduction), it may not be sensible to use deficit financing, where younger persons would ultimately bear those costs. however, we set aside the point of intergenerational justice. behaviorally, it may be more sensible to distribute the burdens across current taxpayers more rationally. current us tax policy is relatively flat, unlike the wartime era of the s, when marginal tax rates went as high as % for the highest-income earners. we cannot here make a comprehensive case for the optimal tax policy, recognizing complications like tax avoidance. however, it remains true that wealthier individuals suffer less disutility for each dollar expropriated through taxation, compared with poorer individuals who suffer greater deprivations on the margin. this 'diminishing marginal utility' of money (as it is known in the economics literature) suggests a substantial opportunity to reallocate the costs of precaution to minimize the disutility. most importantly, this special pandemic situation inverts some of the classic arguments against progressive taxation as undermining incentives to work. here, the rush to get back to work may impose more social costs (in terms of infections) than social benefits (in terms of economic productivity). in this way, government payments to those who are complying with social distance or quarantine protocols are designed to indemnify them against the costs of taking those prosocial precautions. of course there is a risk of mismatch-people receiving the payments who are nonetheless not complying with distancing/quarantine guidelines. to make the bargain more explicit, the payments could be made conditional on agreeing to comply with stay-at-home or social distancing orders. given the extensive literature on the deep evolutionary basis of reciprocity for human behavior, we hypothesize (subject to testing) that such an explicit promise to comply as a reciprocal condition of accepting funds (a 'carrot' strategy) may have behavioral advantages over other ('stick') forms of enforcement, such as fines or imprisonment. our point is not about the cost of noncompliance (assume equal probability of detection and an equal-size penalty), and we are not suggesting a differential framing according to prospect theory (in both cases it may be framed as a loss conditional on noncompliance, rather than a gain). rather, asking individuals to explicitly commit to compliance as a condition of accepting payment reinforces a social norm of compliance. moreover, the breaking of the promise creates a cognitive dissonance, which itself may be experienced as a disutility. the explicit promise and size of these payments are likely to make them more effective than the sorts of small fines that may have perverse effects. in addition to self-policing by people feeling motivated to keep their own promises, compliance may be buttressed by other members of the public shaming those who do not comply or even reporting them to authorities, because they represent not only a hypothetical risk for infection but also expropriation of public funds. in this way, the noncompliance can also be connected to standard law enforcement mechanisms, where an individual convicted of violating a legitimate order suffers revocation of the payment as a penalty, with full due process protections of course. even with such a standard (rational) deterrence theory, the explicit promise to forfeit the funds upon noncompliance may make that risk seem more salient to the citizen and thus increase compliance. overall, these economic and behavioral principles suggest that to manage a pandemic prior to dissemination of a vaccine, policymakers should use conditional payments to encourage compliance with social distancing, stay-at-home, and quarantine directives. the key is to make compliance easier and cheaper than noncompliance, especially for those that would otherwise feel the greatest compulsion to not comply. adolescents are paying a high price for covid- prevention (suicide is the second leading cause of death for individuals - years of age new source of coronavirus spread: 'covid- parties', nytimes fatal tradeoffs: public and private responsibilities for risk flu vaccination coverage insurance coverage of emergency care for young adults under health reform families first coronavirus response act health insurance providers respond to coronavirus (covid- ) anticipatory ex ante moral hazard and the effect of medicare on prevention, health econ health insurance increases preventive care, not risky behaviors diabetes outpatient care and acute complications before and after high-deductible insurance enrollment: a natural experiment for translation in diabetes (next-d) study. the theory of demand for health insurance effects of a cost-sharing exemption on use of preventive services at one large employer, health aff bovine tb strategy review: summary and conclusions, department for environment food & rural affairs actions once tb is suspected or confirmed, tb hub cruel to be kind: moral hazard in british animal disease management memorandum on prioritization of home confinement as appropriate in response to covid- pandemic inmates tried to infect themselves with the coronavirus to get early release, los angeles county sheriff says portland police will not take misdemeanor arrests to jail during the covid- outbreak, to avoid overcrowding, willamette week northam encourages police to avoid arrests, imprisonment in wake of covid- virus coronavirus: officers make fewer arrests during covid- emergency two arizona sheriffs say they will not enforce governor's stay-at-home order, the hill to-know-about-face-masks-and-staying-home-as-virus-spreads#transcri pt (national institute for allergies and infectious diseases director anthony fauci interviewed: 'q. but when lives are at stake, why aren't command measures requiring people to do this appropriate now? a. that generally is not the way things operate in the relationship between the federal government and the states order without law: how neighbors settle disputes credible commitments: using hostages to support exchange social norms and community enforcement medical-exemptions-questions-and-answers/ (a california law allows the health department to report physicians to the medical board if they issue too many such exemptions can rationing through inconvenience be ethical? vaccines and airline travel: a federal role to protect the public health. covid- see robertson supra note chickenpox transmission, ctrs. for disease control & prevention the intentional transmission of hiv by hiv-positive men to their hiv-negative sex partners, automobile accidents, tort law, externalities, and insurance: an economist's critique introduction to unemployment insurance senate passes $ trillion coronavirus relief package, npr budget office, average household income, by income source and income group extra $ unemployment benefits will start flowing as early as this week for a lucky few unemployment benefits will be reduced after federal individual tax rates history, nominal dollars joel slemrod & shlomo yitzhaki, tax avoidance, evasion, and administration, in handbook of public economics social welfare and the rate structure: a new look at progressive taxation, cal. l. rev. ( ) (arguing that the diminishing marginal utility of money makes it efficient to take more from higher-paid individuals); see also leo p. martinez see generally, philippe choné & guy laroque, optimal incentives for labor force participation the case for a progressive tax: from basic research to policy recommendations, perhaps the most remarkable aspect of evolution is its ability to generate cooperation in a competitive world thus, we might add 'natural cooperation' as a third fundamental principle of evolution beside mutation and natural selection erc: a theory of equity, reciprocity, and competition prospect theory: an analysis of decision under risk applying behavioral economics to public health policy: illustrative examples and promising directions, legal promise and psychological contract the neural circuitry of a broken promise numerous psychological and economic experiments have shown that the exchange of promises greatly enhances cooperative behavior in experimental games fine enough or do not fine at all, a fine is a price. the authors thank andrea sharp and jacqueline salwa for research assistance, and bert skye for administrative support. the manuscript benefited from two anonymous peer reviewers. key: cord- -r en s authors: watanabe, chiho title: health impact of urban physicochemical environment considering the mobility of the people date: - - journal: health in ecological perspectives in the anthropocene doi: . / - - - - _ sha: doc_id: cord_uid: r en s most of the current environmental health researches assumes that exposure to the environmental agents occurs either in the residence or workplace, neglecting the mobility of the people due to commuting and daily activities. mobility of the people varies in terms of spatial and temporal range, that is, from momentary short ones to generation-scale long ones. focusing on the daily movement of the people, various methods for grasping the mobility, which also range from simple observational methods like time allocation to methods with advanced technology like global navigation satellite systems, will be reviewed. referring environmental health studies examining the health effects of either air pollution or heat, importance of the mobility of the people is discussed. assessing the mobility will open a new research avenue for the study of infectious diseases as well as noncommunicable diseases. depending on the media (most of the case, relevant media should be food, water, air, soil, etc.) as well as the agent of concern, a variety of the methods exists to evaluate the exposure, and exposure evaluation has been recognized as an independent research field. the procedure for exposure evaluation can be largely classified into two categories, that is, measuring environment and measuring organism; these are the procedures called as environmental monitoring and biological monitoring. depending on the media and the agent, one or both of these methods are utilized. for example, both (organic) mercury from fish and cadmium from rice are heavy metals exposed through food consumption. therefore, by monitoring the concentration of these metals in respective major food source, combined with food consumption data, exposure (ingested amount of mercury/cadmium) could be estimated. biological monitoring for these metals is also possible by measuring the concentration of mercury in the hair (which reflects the concentration in the blood, and approximates the concentration in the brain) or cadmium in urine (which reflects the concentration in renal cortex). detailed discussions about these two categories of monitoring are beyond the scope of this book, and interested readers should refer to existing textbooks. unlike the case for arsenic in water or mercury in the fish, many of the major "classical" air pollutants like nox, sox, co, pms (either . or ) do not have appropriate biological exposure markers, and we need to rely on the environmental monitoring. this is also true for the exposure to temperature or to noise, both of which are associated with atmospheric exposure. in conventional environmental health study or environmental epidemiology, environmental monitoring of the outdoor atmosphere at the residential area of the participants has been used as surrogates for individual/population exposure to the agents of concern. implicit assumption here is that people would stay in their residence, and variation of the exposure due to their daily mobility is, if any, negligible. although this assumption is not realistic at all, this approach has been successful in a sense evidenced by the existence of numerous epidemiological findings in this area in the past. in fact, exposure to pollutants or physical factors associated with air/atmosphere is heavily influenced by the location of the individual. assume we would like to estimate an individual's exposure to nitric oxides, most of the case, individuals would not stay in the home whole day, particularly in urban settings, commuting into city center or business districts for workplace or for schooling, thereby exposing themselves to environments that are different from their own residential neighborhoods. in this sense, kwan [ ] has suggested that research involving geographical components should reconsider conventional methods to estimate the exposure, referring to environmental health/epidemiology (together with the research on segregation or on the issue of accessibility). richardson et al. [ ] pointed out that due to the accumulation of highly sophisticated spatial and spatiotemporal technology like gis, gps, remote sensing, and computer cartography, collectively termed as geographic information science, it becomes possible to model the disease process involving multiple spatiotemporal data obtained in different disciplines. likewise, the exposure to environmental factors could be evaluated using such spatiotemporal data. spatial resolution of various types of environmental data becomes so high that heterogeneity within the area of commuting distance could be documented. in addition, recent technical progress in downscaling of the climate models (see [ ] ) enables the researchers to predict differential impact of climate change within relatively small areas. health? apart from the environmental data, to consider the mobility of the people, we need to collect the information on the mobility of people with enough spatiotemporal resolution. mobility of people can mean wide variety of phenomenon in terms of time, space, and context as listed in fig. . . time scale of the mobility can range from moment to moment as exemplified by the ecological momentary assessment (later in this chapter) to years, even including hundreds of centuries (like out of africa, the expansion of our ancestors)! duration of the sojourn time should be considered as an independent factor and can also range from few seconds to generations; for example, workplace exposure to hazardous substances (including radioactive materials) would be evaluated in terms of minutes, while the effects of regional migration fig. . schematic classification of various type of human mobility by "relevant" spatial and temporal scales. for example, "migration' takes place with relatively long time, ranging from months to multiple generations and traveling relatively long distance, while "outdoor/indoor" discrimination is needed even a couple of meters apart. 'ema' stands for ecological momentary assessment (see text) may emerge after several generations. accordingly, spatial scale could range from a few meters to thousand kilometers. a few meter matters when micro-scale environments such as indoor (including air-conditioning) vs. outdoor, inside and outside of vehicle are considered, for example. at larger scale, proximity to major roads or any combustion facility could exert significant influences on exposure to noise or air pollutants. far larger scale can change the environment as a whole; an important aspect in today's environmental health is that people can make a global scale travel within h. mobility of people also entails the change in the context; by changing the location, the socioeconomic and cultural aspects of the neighborhood would change, which may affect the meaning of material environment and, in turn, health status of the moving individuals. at the same time, change in location means the change in activities of the individuals; for example, individuals working at outside road construction site might have much higher physical activity levels (and increased ventilation rate) and higher exposure to heat, dust, and noise than staying at home. while it is fairly difficult to consider all of these potential factors, in case of atmospheric exposure, geographical location of the individual should be the factor to consider in the first place, since it does provide the basis of the air which she or he inhales in every moment. in this chapter, main focus will be on daily mobility of people for commuting and for other daily life activities. geographical location is crucial for some physicochemical environmental factors other than air pollutants. one such example is heat environment, which consists of temperature, humidity, air flow, and radiation, and varies even with a very small scale, reflecting the variation of land use or land cover, local topography (layout of surrounding buildings, for example), or elevation. in addition, numerous heat sources are found in human-built environment, including exhaust gases, waste heat, etc. as a result of combined effects of these factors, most of the urban centers have warmer environment, compared to the surrounding areas, termed as heat island. mobility of individuals has been dealt with in many research areas. in urban planning, grasping mobility of individuals is crucial to create an appropriate layout for transportation, public space/facilities, and private houses. in public health, mobility of individuals sometimes play key role in the spread of diseases (described later). also, mobility has been one of a classical topic in the area of human ecology since it is associated with the question of how a population utilizes the environment spatially as well as temporally (time allocation studies). mobility is also associated with energetics (utilization of somatic energy) as a part of physical activities in general. as such, many methods to grasp the mobility of individuals have been developed (table . ), which will be discussed below. the simplest method is field observation. time allocation studies observe the individuals in the targeted field and record the location and type of activity for a given period, which is useful to answer some of the basic questions in human unlikely large ecology or other related fields as noted above. while this method is in a sense "perfect" since the observer can obtain whatever details she or he wants, obvious disadvantages include time-labor intensiveness, biased behavior due to the presence of observing researcher. a simplified variation of the time allocation is the spot-check method, in which researcher will observe the people's activity in certain fixed location(s) (e.g., see [ ] ). despite its simplicity and easiness, spot-check method could provide valuable quantitative information. activity diary is another classical method, which relies on the self-recorded diary. this would solve the issue of laborintensiveness for researcher and could cover much larger number of individuals, but like other self-reporting methods, reliability and accuracy of the record are the main problems to be considered. activity diary is useful when researchers are interested in qualitative aspects of the moving behavior. person-trip is another method, which has long been utilized especially urban planning as well as urban studies (e.g., see ( [ , ] )). person-trip uses a predetermined, formatted questionnaire to be either self-recorded or recorded by interviewers, through which location of the individual, purpose of travel (translocation), and method of travel (either walk, bicycle, private car, public transportations) for a given period will be obtained. while this method has problem of bias and/or inaccuracy due to recall, brevity and simplicity made this method popular, particularly when a large population needs to be covered. many governmental (both national and local levels) surveys utilize this method to quantify the volume of mobility, for example, traffic volume of vehicles. gps (global positioning system) has been used as if it was a generic term, but actually gps is a name of a system developed in usa. generic name for the systems is global navigation satellite systems (gnss), which is referring to any system that locates specific targets by use of the combination of signal-detecting device and a group of satellites. in this book, the "targets" are basically human individuals, but they could be animals (so-called activity logger) or traffic vehicles. spatial resolution of contemporary gps is fine enough to locate individuals for many study fields, and it solves the issues of time-labor intensiveness and false or biased report. thus, this has been used in various research areas including anthropology, human ecology, and presumably sociology, and urban studies (see [ , ] ). another advantage is that gps uses electrical data processing, which also alleviates the risk/errors associated with data transfer. on the other hand, in some area like inside building or underground malls the signal for gps are generally weak and difficult to detect. although the gps could provide very rich and useful information regarding the mobility, individuals rarely own the device, and researchers need to provide and distribute it to the participants. this has been overcome by the recent propagation of gpsequipped mobile phones and alike. mobile phone per se can be also utilized as a tool in capturing the location of individuals without using gps device since every call made by mobile phone is registered by nearby relay station, hence generating a record regarding approximate location of the mobile phone users at the time of the call. by collecting such records of local calls, researcher can trace or reconstruct the translocation of individuals. major advantage of this method is the fact nowadays a large proportion of populations own the mobile phone even in developing countries and in very remote areas. on the hand, researchers need to negotiate with mobile phone company to obtain such record, and the major barriers for such negotiation are as following: ( ) conflict with the protection of privacy information (even when the information is provided in anonymous manner) may arise, ( ) often there are two or more mobile phone companies operating in a given area, and ( ) since the information is provided in anonymous manner, demographic parameters of the mobile owner are not known to the researcher. effort has been made to overcome the last point, in which an algorism has been developed to estimate the demographic attributes of a mobile phone owner through the pattern of mobility, although the feasibility as well as the accuracy of estimated attributes needs further investigation (arai, shibasaki, in preparation). wesolowski et al. [ ] compared the mobility data obtained by a person-trip type survey with the one obtained by mobile phone; both conducted in kenya over the same period. reflecting the nature of the methods, numbers of the participants were and , in the survey and mobile phone analyses, respectively. while the person-trip type survey was cross-sectional in nature, the mobile phone records followed the movement of the people for months. while the resultant two data sets agreed in some aspects of the travels such as ( ) most visited areas (in terms of districts) or ( ) overall relative frequency of individuals with different number of travels, they disagree other aspects such as the number of mobile phone subscribers in the area as much as ten times. in this section, a couple of examples will be presented that incorporates the mobility of the individuals/groups in estimating exposure to physicochemical factors in the air. as the physicochemical factors, air pollutant and heat will be discussed. in the final part, a rather classical, different approach to trace individual exposure will be also introduced. a relatively large spatial scale study has been conducted covering approximately × km area in belgium [ ] , which compared regional exposure estimates for two representative air pollutants, nox and ozone, under two alternative assumptions. first, exposure assumed to occur in the residential place of the participants (static exposure), that is, the mobility of the participants is neglected. second, mobility of the people was taken into account in estimating exposure (dynamic exposure). information on mobility was obtained through activity diaries collected from residents, which is then extrapolated to a synthetic (but reflecting the demographic structure of actual) population of approximately millions. the target geographical region consisted of zones ( municipalities) whose average area was km , and the location of each individual has been predicted for week ( days) by -hr interval. pollutant concentrations are estimated for no and ozone using air pollution models (i.e., an emission model combined with a dispersion model) for a year by h interval and × km resolution with finer resolution along major roads. based on the location data and pollution data, time-weighted exposure estimate was calculated under two conditions: with and without taking peoples' mobility into account. to estimate the municipality-wise health impacts of the exposure to these air pollutants, the time-weighted exposure estimate was converted into the respiratory mortality using the information of existing epidemiological data, which is then converted into years of life lost (yll) following the burden of diseases framework by who. the analyses revealed the pollutant-specific regional difference in the pollutant concentration; that is, for no , urban zones had higher concentrations than rural zones regardless the age and gender, and for ozone, it was vice versa. as expected, urban and industrial zones have much larger population in daytime, which was in contrast with the surrounding zones. as the results, dynamic exposure for no for the whole population was slightly higher than static exposure, while for ozone it was vice versa. while the difference between static and dynamic exposure were statistically significant, the difference was small and reached only up to %. in terms of health impact, again the difference between the two methods was statistically significant but small ( . % increase for no and . % decrease for ozone). at the municipality level, the maximum difference between the two approaches reached as large as %, where dynamic was higher than static, and larger differences were usually observed in rural areas. for ozone, maximum difference was only % (dynamic was lower than static). while the extent of impacts shown in this study might not be so remarkable, the results demonstrated that mobility of people could have significant impact on the estimate of health impact by air pollution and that such an impact could be more remarkable at smaller scale. as pointed out by the authors, considering the mobility of people in air pollution issue inevitably connects the issue of transportation (and urban planning) with health issues, which is also commended from the viewpoint of eco-health. similar dynamic-vs-static comparison was conducted with much smaller sample size in western new york, and as naturally expected the difference between the two approaches depended on the pattern of spatiotemporal pattern of air pollutants, pm . , as well as on that of behaviors [ ] . the human early-life exposome (helix) is a multi-country (eight countries), multi-cohort project in europe to characterize early life exposure to various chemical and physical environmental factors and to associate them with health consequences in early life ( [ ] project url: http://www.projecthelix.eu/en). involving , mother-child pairs, the project would try to grasp the whole picture about the exposure as much as possible, and the use of time-space activity information is planned, which will be utilized to estimate the participants' exposure to not only air pollutants but also noise, uv radiation, temperature, and built environment/green space etc. basically, the environmental data is collected from (ground) monitoring stations and/or remote sensing. in addition, smartphone-based "personal exposure monitoring kit" has been developed that enables to capture not only the location of mothers and children but also their physical activities and air pollution by built-in accelerometer and sensors for uv and pm . . recent progress of this project can be found at the following url: https://www.isglobal.org/en/web/guest/healthisglobal/-/custom-blog-portlet/prova/ / . helix is an ambitious attempt, which needs large amount of budget ( . m euro, according to the web page), time, and manpower. considering the nature of current "environmental exposure," that is, long term, multiple species, and mild to moderate (rather than severe) level, probably such an extensive effort is required to elucidate the relationship between environmental agents and health consequences. heat is another environmental factor, which might have some relevance to the mobility issue, since urban heat, or heat island, is a ubiquitous phenomena common to most of the big urban areas, which would pose additional heat burden to urban dwellers as well urban commuters under the influence of climate change (global warming). usually, effects of heat are considered to be immediate or short, which is different from those of air pollutants, whose effects can be both short term and long term. although not involving mobility assessment, laaidi et al.'s study on the heatmortality relationship [ ] is worth to be discussed here. this study analyzes the relationship between all-cause mortality among the elderlies living in paris, france, or nearby area and land-surface temperature captured by satellites for a period of a heat wave occurred in august . based on a case-control study of pairs of mortal-alive elderly people (age > ), they found elevated odds ratio of mortality with increased land surface temperature (lst) of the residence area. of noteworthy, the elevated odds ratio was associated with minimum (night time) lst averaged over either days (whole observation period) or days preceding the reported deaths but not with any lsts averaged over days preceding deaths or the day of death. this result suggested that the effect of heat might not be limited to immediate effects but might be "cumulative" to some extent. also, approximately . °c of increase in temperature was associated with a significantly elevated odds ratio more than two, showing relatively potent effect of temperature on mortality. in this study, spatial resolution of the lst was km , and the case and control are matched, in addition to age and sex, for residential area, which contains - pixels, allowing the temperature comparison between the case and control. targeting the elderlies, mobility would be less important than in younger generations. we have conducted a study in which mobility of the people is considered in heat exposure issue in a subtropical urban area. this particular issue will be discussed in the next chapter. in the area of industrial health, exposures of the factory workers to air-borne chemicals peculiar to the factory are monitored with device, which is "worn" by each worker. many types of such devices have been developed for various solvents or gaseous pollutants, among which the γ-radiation monitor is the best known. cumulative exposure of each individual to the target chemical/radiation is quantified by analyzing the amount of chemical collected/absorbed by the device. such personal device has been used for appropriate control of worker's exposure to hazardous chemicals, but which could be extended into surveys in general population. while this method provides the estimate of individual exposure, if used in general population, distribution and retrieval of the device could be labor taking, and the quantified results would not give any hint of the potential sources of the exposure, since it only provides the cumulative exposure rather than temporally tracing the individual exposure. potential use of mobility information would not be confined to the issues that have been discussed in this chapter so far. these examples will be discussed in this section. many infectious diseases are transmitted through direct or indirect human-to-human contact. mobility information has been utilized in the development of the models for propagation of some of the infectious diseases like influenza (direct) or malaria (indirect). in developing models, however, most of the attempts have based on simulations under plausible assumptions about the parameters, and not so much have been done using actual mobility data. malaria is one of the diseases that will be propagated by mosquitoes (indirect human contact). propagation of the malaria agent (plasmodium) occurs when a mosquito (anopheles) sucked blood from an infected human individual and then bites an intact individual. since the range of area that traveled by a mosquito is relatively limited (approximately - km/day for anopheles) [ ] , mobility of infected human individuals should play some roles in the propagation of the agent, particularly for long distance propagation. wesolowski [ ] tried to elucidate the role of human mobility in the propagation of malaria in kenya. based on mobile phone records (either call or text) of about million people for year, they reconstructed the mobility patterns of the people and combined this information with spatial prevalence data of malaria cases. location of the people (mobile users) is followed based on approximately , cell towers located in settlements in kenya. travels (change of the location) beyond the border of each participant's "primary settlement" (presumably where the residence is located) was counted and used for data analyses. a malaria prevalence map with km resolution for has been used to classify the settlements according to their prevalence, then, combining the two types of information, that is, travels and prevalence observed in various settlements, they have estimated the proportion of the infected travels, which actually transported the malaria from one settlement to another. in this way, they could identify the source areas and the sink areas; the former supply the malaria, while the latter accept it. with such an analyses, they could show there were several distinct sources and sinks for malaria in kenya. nairobi, the capital, and the area around the victoria lake were serving as the most remarkable sink and the source, respectively. also, they observed that travel of people reflected the regional population density and regular travel, which is different from the travel of the parasites, where the lake regions serve as the primary source of the parasites, which flew into its surrounding areas and the capital area. based on these observations, the authors suggested that the elimination program must take the imported case into account for the program to be successful. in addition, they demonstrated that this method could identify the "hot spot" (settlement), which shows distinct export and import of malaria incidence compared to adjacent settlements and that it can also provide useful information for elucidating the mechanisms of smaller scale transmission. such an analysis provides a good example demonstrating the huge potential of using spatial analyses in the area of disease propagation. they applied the same approach to model and predict the dengue epidemics in pakistan [ ] . mobility of approximately million subscribers was followed for months in across tehsils (small politically defined areas in pakistan), and analyzed with more than , reported cases observed in tehsils over months in . focus of the analyses was the spread of the disease from southern region, where the warm climate supports the existence of vector mosquito throughout the year, to the northern regions with greater seasonality that limits the transmission. the authors calculated the "dengue suitability" of each region mainly based on daily temperature, which was combined with the probability of importing the infection by travelers from epidemic area to estimate the regional (spatiotemporal) risk of dengue epidemic. the results considering the mobile phone data are compared with those obtained from conventional "gravity" model, in which the travel volume of the people depends on the population sizes of and distance between the two regions (beginning and end of the travel). the results of the two models sometimes differ widely; among the two regions that experienced real dengue epidemics in , import of infection could not be predicted by the gravity model, while the model with mobile phone information could. also, the risk map generated for entire pakistan showed substantially different pictures between the two models. part of the reason of such differences is related with the observation that contrary to conventional mobility model, the mobile phone data showed no decay of travel volume with increasing distance of the regions. overall, this research demonstrated the importance of grasping mobility based on real observational data to understand the spread of infectious disease at the level of a country. for the diseases that are propagated through direct human-to-human contact, mobility of individuals among the population at stake should be much more crucial than the case of malaria as described above. for example, in the outbreaks of sars and mers, identifying the "index case" would be important. many quantitative models have been proposed to explain the spread of disease, but many of them have not taken the spatial information into account. as explained in this section, modeling with peoples' mobility for infectious diseases has not been explored so much, while it is a promising field for the future. at a larger spatial scale, spread of infectious diseases is associated with international travels. using the data for international airline travelers, potentially "hot" areas for the spread of zika virus have been identified. potential threat of importation of the virus from americas to africa and asian countries was demonstrated [ ] . relative importance of noncommunicable diseases (ncds) has been increasing both in developed and developing countries; to name a few, ischemic heart diseases, stroke, diabetes mellitus, and various types of cancer are the big ones in this category. it has been quite well established that obesity and hypertension are associated with higher risk of these diseases, which in turn are associated with imbalance in the energetics. numerous reports have been published regarding metabolic aspects of individuals at high risks for the ncds. in these reports, activities are mainly evaluated with activity diary, pedometer, or accelerometer wore by the subjects. while these lines of information would provide valuable data to demonstrate the association between inactivity and risk factors of ncds, a major defect is that it would not easily identify where in the daily life of the individual potential problem lies (i.e., leverage point). gps information or mobile phone call record might be useful in reconstructing daily activity of individuals, since they can provide the information regarding the speed of the translocation, by which researcher can make a reasonable guess if the individual moved actively (i.e., walking or bicycling) or passively (i.e., driving a car, using public transportations). this is a relatively unexplored area, which might bear potential public health importance both in developed and developing countries. ecological momentary assessment (ema) refers to the methods of collecting data from individuals, who are in their daily lives (thus, ecological), providing real-time data (thus, momentary) repeatedly [ ] . this is often enabled by using ict devices that can prompt a series of questions to participating individuals to report their physical and/or mental conditions to the researchers. the devices can be also connected with sensors for physiological or clinical information like heart rate, blood pressure, or body temperature, blood glucose, or blood oxygenation [ ] , thereby health "events" like arrhythmia, asthma attack, and panic episodes can be recorded. in addition, ema device has been connected with physical sensors to air pollution. with this kind of device, chronological data, which can be associated with special health events, can be collected, accumulated, and later be related with physiological and environmental conditions (like air pollution) where the individual was in, revealing hidden association between the health event and certain patterns of preceding environmental and/or behavioral conditions. this methodology has been successful in clinical settings, particularly highlighted in clinical psychology, and its application to environmental health may generate a unique opportunity to grasp individual's "dose" and "response" simultaneously. by combining with environmental monitoring information provided by satellites as well as ground monitoring stations, potential of using ema will be greatly enhanced in the area of environmental health. as noted in the beginning of this chapter, environmental health concerns the relationship between environmental condition and health consequences, spatial information is an indispensable component of this field. conventional environmental health studies have dealt with the spatial aspects as represented by administrative units, which is basically a qualitative variable and black box so to speak, in nature. more quantitative aspect of the spatial distribution is worth to be focused in environmental health, and recent progress in information and communication technology including data processing enables us to develop a new type of research. in this way, spatial information becomes much more manipulative in the analyses with its implication being much clearer. refining spatial information is only a method to improve the accuracy of exposure estimate, hence, associated with other progresses in this field. for example, conventional environmental health study only focused on a very limited number of environmental factors, most often only a single factor, and the dose-response relationship was evolved around this single factor. this is most likely due to the fact that problems in the past were mostly associated with a single environmental agent like one chemical species. contemporary issues, however, involve multiple factors that are converged on a single endpoint. in such a case, approach adopted in the helix study might be useful, although we yet to know what can be obtained with this approach. refining exposure estimate should be considered in such a context to characterize comprehensive exposure. while potential of this field is enormous, especially to be combined with other relevant techniques like ema, there are a couple of issues that needs constant attention. first, as the technology (both hard and soft) advances, more attention should be paid for the importance of the issue of privacy. this is not only saying that full attention should be paid to protection of privacy, but also ( ) considering the benefit for the people obtained through such information and ( ) letting people know both aspects (goods and bads) of mobility information, thereby enabling them to choose appropriate reaction towards such investigation. finally, it should be emphasized that mobility information obtained in the ways described in this chapter might evoke a new discussion about what "true" exposure is and to what extent we need to know about the exposure. as partially discussed before, if you would like to quantify the exposure of an individual as much as possible, you need to actually chase this individual to see how the individual and the environment at a given moment is faced with each other. for example, merely wearing a fine-pore mask would substantially change the exposure to certain air pollutants, which could not be picked up by the approaches discussed in this chapter. after all, required fineness of the quantitative evaluation totally depends on the objectives of the specific research. potential for zika virus introduction and transmission in resource-limited countries in africa and the asia-pacific region: a modelling study downscaling climate models health impact assessment of air pollution using a dynamic exposure profile: implications for exposure and health impact estimates issues of commuter transport in developing countres flight performance of the malaria vectors anopheles gambiae and anopheles atroparvus beyond space (as we knew it): toward temporally integrated geographies of segregation, health, and accessibility the impact of heat islands on mortality in paris during the august heat wave urban form and the ecological footprint of commuting. the case of barcelona gender difference in daily time and space use among bangladeshi villagers under arsenic hazard: application of the compact spot-check method health and the mobile phone spatial turn in health research ecological momentary assessment the human early-life exposome (helix): project rationale and design quantifying the impact of human mobility on malaria quantifying travel behavior for infectious disease research: a comparison of data from surveys and mobile phones impact of human mobility on the emergence of dengue epidemics in pakistan geospatial estimation of individual exposure ot air pollutants: moving form stati monitoing to activity-based dynamic exposure assessment key: cord- -s knxdne authors: perra, nicola; gonçalves, bruno title: modeling and predicting human infectious diseases date: - - journal: social phenomena doi: . / - - - - _ sha: doc_id: cord_uid: s knxdne the spreading of infectious diseases has dramatically shaped our history and society. the quest to understand and prevent their spreading dates more than two centuries. over the years, advances in medicine, biology, mathematics, physics, network science, computer science, and technology in general contributed to the development of modern epidemiology. in this chapter, we present a summary of different mathematical and computational approaches aimed at describing, modeling, and forecasting the diffusion of viruses. we start from the basic concepts and models in an unstructured population and gradually increase the realism by adding the effects of realistic contact structures within a population as well as the effects of human mobility coupling different subpopulations. building on these concepts we present two realistic data-driven epidemiological models able to forecast the spreading of infectious diseases at different geographical granularities. we conclude by introducing some recent developments in diseases modeling rooted in the big-data revolution. historically, the first quantitative attempt to understand and prevent infectious diseases dates back to when bernoulli studied the effectiveness of inoculation against smallpox [ ] . since then, and despite some initial lulls [ ] , an intense research activity has developed a rigorous formulation of pathogens' spreading. in this chapter, we present different approaches to model and predict the spreading of infectious diseases at different geographical resolutions and levels of detail. we focus on airborne illnesses transmitted from human to human. we are the carriers of such diseases. our contacts and mobility are the crucial ingredients to understand and model their spreading. interestingly, the access to large-scale data describing these human dynamics is a recent development in epidemiology. indeed, for many years only the biological roots of transmission were clearly understood, so it is not surprising that classical models in epidemiology neglect realistic human contact structures or mobility in favor of more mathematically tractable and simplified descriptions of unstructured populations. we start our chapter with these modeling approaches that offer us an intuitive way of introducing the basic quantities and concepts in epidemiology. advances in technology are resulting in increased data on human dynamics and behavior. consequently, modeling approaches in epidemiology are gradually becoming more detailed and starting to include realistic contact and mobility patterns. in sects. . and . we describe such developments and analyze the effects of heterogeneities in contact structures between individuals and between cities/subpopulations. with these ingredients in hand we then introduce state-of-the-art data-driven epidemiological models as examples of the modern capabilities in disease modeling and predictions. in particular, we consider gleam [ , ] , episims [ ] , and flute [ ] . the first model is based on the metapopulation framework, a paradigm where the inter-population dynamics is modeled using detailed mobility patterns, while the intra-population dynamics is described by coarse-grained techniques. the other tools are, instead, agent-based model (abm). this class of tools guarantees a very precise description of the unfolding of diseases, but need to be fed with extremely detailed data and are not computationally scalable. for these reasons their use so far has been limited to the study of disease spread within a limited numbers of countries. in comparison, metapopulation models include a reduced amount of data, while the approximated description of internal dynamics allows scaling the simulations to global scenarios. interestingly, the access to large-scale data on human activities has also started a new era in epidemiology. indeed, the big-data revolution naturally results in real time data on the health related behavior of individuals across the globe. such information can be obtained with tools that either require the active participation of individuals willing to share their health status or that is mined silently from individuals' health related data. epidemiology is becoming digital [ , ] . in sect. . we introduce the basic concepts, approaches, and results in this new field of epidemiology. in particular, we describe tools that, using search queries, microblogging, or other web-based data, are able to predict the incidence of a wide range of diseases two weeks ahead respect to traditional surveillance. epidemic models divide the progression of the disease into several states or compartments, with individuals transitioning compartments depending on their health status. the natural history of the disease is represented by the type of compartments and the transitions from one to another, and naturally varies from disease to disease. in some illnesses, susceptible individuals (s) become infected and infectious when coming in contact with one or more infectious (i) persons and remain so until their death. in this case the disease is described by the so-called si (susceptible-infected) model. in other diseases, as is the case for some sexual transmitted diseases, infected individuals recover becoming again susceptible to the disease. these diseases are described by the sis (susceptible-infected-susceptible) model. in the case of influenza like illnesses (ili), on the other hand, infected individuals recover becoming immune to future infections from the same pathogen. ilis are described by the sir (susceptible-infected-recovered) model. these basic compartments provide us with the fundamental description of the progression of an idealized infection in several general circumstances. further compartments can be added to accurately describe more realistic illnesses such as smallpox, chlamydia, meningitis, and ebola [ , , ] . keeping this important observation in mind, here we focus on the sir model. epidemic models are often represented using chart such as the one seen in fig. . . such illustrations are able to accurately represent the number of compartments and the disease's behavior in a concise and easily interpretable form. mathematically, models can also be accurately represented as reaction equations as we will see below. in general, epidemic models include two type of transitions, "interactive" and "spontaneous." interactive transitions require the contact between individuals in two different compartments, while spontaneous transitions occur naturally at a fixed rate per unit time. for example, in the transition between s to i, susceptible individuals become infected due to the interaction with infected individuals, i.e. sci ! i. the transition is mediated by individuals in the compartment i, see fig. but how can we model the infection process? intuitively we expect that the probability of single individual becoming infected must depend on ( ) the number of infected individuals in the population, ( ) the probability of infection given a contact with an infectious agent and, ( ) the number of such contacts. in this section we neglect the details of who is in contact with whom and consider instead individuals to be part of a homogeneously mixed population where everyone is assumed to be in contact with everyone else (we tackle heterogeneous contacts in sect. . ). in this limit, the per capita rate at which susceptible contract the disease, the force of infection , can be expressed in two forms depending on the type of population. in the first, often called mass-action law, the number of contacts per individual is independent of the total population size, and determined by the transmission rateǎ nd the probability of randomly contacting an infected individual, i.e. dˇi=n (where n is the population size). in the second case, often called pseudo massaction law, the number of contacts is assumed to scale with the population size, and the transmission rateˇ, i.e. dˇi. without loss of generality, in the following we focus on the first kind of contact. the sir framework is the crucial pillar to model ilis. think, for example, at the h n pandemic in , or the seasonal flu that every year spread across the globe. the progression of such diseases, from the first encounter to the recovery, happens in matters of days. for this reason, birth and death rates in the populations can be generally neglected, i.e. d t n Á for all times t. let us define the fraction of individuals in the susceptible, infected, and recovered compartments as s; i, and r. the sir model is then described by the following set of differential equations: where dˇi Áˇi n is the force of infection, and d t Á d dt . the first equation describes the infection process in a homogeneous mixed population. susceptible individuals become infected through random encounters with infected individuals. the second equation describes the balance between the in-flow (infection process, first term), and the out-flow (recovery process, second term) in compartment i. finally, the third equation accounts for the increase of the recovered population due to the recovery process. interestingly, the sir dynamical equations, although apparently very simple, due to their intrinsic non-linearity cannot be solved analytically. the description of the evolution of the disease can be obtained only through numerical integration of the system of differential equations. however, crucial analytic insight on the process can be obtained for early t t and late times t ! . under which conditions a disease starting from a small number, i , of individuals at time t is able to spread in the population? to answer this question let us consider the early stages of the spreading, i.e. t t . the equation for the infected compartment can be written as d t i d i.ˇs /, indicating an exponential behavior for early times. it then follows that if the initial fraction of susceptible individuals, s d s =n, is smaller than =ˇ, the exponent becomes negative and the disease dies out. we call this value the epidemic threshold [ ] of the sir model. the fraction of susceptibles in the population has to be larger than a certain value, that depends on the disease details, in order to observe an outbreak. typically, the initial cluster of infected individuals is small in comparison with the population size, i.e. s i , or s . in this case, the threshold condition can be re-written asˇ= > . the quantity: is called the basic reproductive number, and is a crucial quantity in epidemiology and provides a very simple interpretation of the epidemic threshold. indeed, the disease is able to spread if and only if each infected individual is able to infect, on average, more than one person before recovering. the meaning of r is then clear: it is simply the average number of infections generated by an initial infectious seed in a fully susceptible population [ ] . for any value of > , the sir dynamics will eventually reach a stationary, disease-free, state characterized by i d d t i d . indeed, infected individuals will keep recovering until they all reach the r compartment. what is the final number of recovered individuals? answering this apparently simple question is crucial to quantify the impact of the disease. we can tackle such conundrum dividing the first equation with the third equation in the system . . we obtain d r s d r s which in turn implies s t d s e r r t . unfortunately, this transcendent equation cannot be solved analytically. however, we can use it to gain some important insights on the sir dynamics. we note that for any r > , in the limit t ! , we must have s > . in other words, despite r , the disease-free equilibrium of an sir model is always characterized by some finite fraction of the population in the susceptible compartment, or, in other words, some individuals will always be able to avoid the infection. in the limit where r we can obtain an approximate solution for r (or equivalently for s d r ) by expanding s d s e r s at the second order around r . after a few basic algebraic manipulations we obtain in the previous sections we presented the basic concepts and models in epidemiology by considering a simple view of a population where individuals mix homogeneously. although such approximation allows a simple mathematical formulation, it is far from reality. individuals do not all have the same number of contacts, and more importantly, encounters are not completely random [ ] [ ] [ ] [ ] . some persons are more prone to social interactions than others, and contacts with family members, friends, and co-workers are much more likely than interactions with any other person in the population. over the last decade the network framework has been particularly effective in capturing the complex features and the heterogeneous nature of our contacts [ ] [ ] [ ] [ ] [ ] . in this approach, individuals are represented by nodes while links represent their interactions. as described in different chapters of the book (see chaps. , , and ), human contacts are not heterogeneous in both number and intensity [ ] [ ] [ ] [ ] ] but also change over time [ ] . this framework naturally introduces two timescales, the timescale at which the network connections evolve, g and the inherent timescale, p , of the process taking place over the network. although the dynamical nature of interactions might have crucial consequences on the disease spreading [ ] [ ] [ ] [ ] [ ] [ ] , the large majority of results in the literature deal with one of two limiting regimens [ , ] . when g p , the evolution of the network of contacts is much slower than the spreading of the disease and the network can be considered as static. on the other hand, when p g , the links are said to be annealed and changes in networks structure are much faster than the spreading of the pathogen. in both cases the two time-scales are well separated allowing for a simpler mathematical description. here we focus on the annealed approximation ( p g ) that provides a simple stage to model and understand the dynamical properties of epidemic processes. we refer the reader to chap. face-to-face interactions for recent approaches that relax this time-scale separation assumption. let us consider a network g .n; e/ characterized by n nodes connected by e edges. the number of contacts of each node is described by the degree k. the degree distribution p .k/ characterizes the probability of finding a node of degree k. empirical observations in many different domains show heavy-tailed degree distributions usually approximated as power-laws, i.e. p .k/ k ˛ [ , ] . furthermore, human contact networks are characterized by so-called assortative mixing, meaning a positive correlation between the degree of connected individuals. correlations are encoded in the conditional probability p .k jk/ that a node of degree k is connected with a node of degree k [ , ] . while including realistic correlations in epidemic models is crucial [ ] [ ] [ ] they introduce a wide set of mathematical challenges that are behind the scope of this chapter. in the following, we consider the simple case of uncorrelated networks in which the interdependence among degree classes is removed. how can we extend the sir model to include heterogeneous contact structures? here we must take a step further than simply treating all individuals the same. we start distinguishing nodes by degree while considering all vertices with the same degree as statistically equivalent. this is known as the degree block approximation and is exact for annealed networks. the quantities under study are now i k d i k n k ; s k d s k n k , and r k d r k n k , where the i k ; s k , and r k are the number of infected, susceptible, recovered individuals in the degree class k. n k instead describes the total number of nodes in the degree class k. the global averages are given by i d using this notation and heterogeneous mean field (hmf) theory [ ] , the system of differential equations ( . ) can now be written as: the contact structure introduces a force of infection function of the degree. in particular, k d k k where is the rate of infection per contact, i.e.ˇd k, and k describes the density of infected neighbors of nodes in the degree class k. intuitively, this density is a function of the conditional probability that a node k is connected to any node k and proportional to the number of infected nodes in each class in the simple case of uncorrelated networks the probability of finding a node of degree k in the neighborhood of a node in degree class k is independent of k. in this case k d d p k .k / p .k / i k =hki where the term k is due to the fact that at least one link of each infected node points to another infected vertex [ ] . in order to derive the epidemic threshold let us consider the early time limit of the epidemic process. as done in sect. . . . let us consider that at t t the population is formed mostly by susceptible individuals. in the present scenario this implies s k i k and r k k. the equation for the infected compartment then becomes d t i k d k i k . multiplying both sides for p .k/ and summing over all values of k we obtain d t i d hki i. in order to understand the behavior of i around t let us consider an equation built by multiplying both sides of the last equation by .k / p .k/ =hki and summing over all degree classes. we obtain d t d . hk i hki hki / . the fraction of infected individuals in each value of k will increase if and only if d t > . this condition is verified when [ ] : giving us the epidemic threshold of an sir process unfolding on an uncorrelated network. remarkably, due to their broad-tailed nature, real contact networks display fluctuations in the number of contacts (large hk i) that are significantly larger than the average degree hki resulting in very small thresholds. large degree nodes (hubs) facilitate an extremely efficient spreading of the infection by directly connecting many otherwise distant nodes. as soon as the hubs become infected diseases are able to reach a large fraction of the nodes in the network. real interaction networks are extremely fragile to disease spreading. while this finding is somehow worrisome, it suggests very efficient strategies to control and mitigate the outbreaks. indeed, hubs are central nodes and play a crucial role in the network connectivity [ ] and by vaccinating a small fraction of them one is able to quickly stop the spread of the disease and protect the rest of the population. it is important to mention that in realistic settings the knowledge of the networks' structure is often limited. hubs might not be easy to easily known and other indirect means must be employed. interestingly, the same feature of hubs that facilitates the spread of the disease also allows for their easy detection. since high degree nodes are connected to a large number of smaller degree nodes, one may simply randomly select a node, a, from the network and follow one of its links to reach another node, b. with high probability, node b has higher degree than a and is likely a hub. this effect became popularized as the friend paradox: on average your friends have more friends than you do [ ] . immunizing node b is then much more effective than immunizing node a. remarkably, as counter-intuitive as this methodology might seem, it works extremely well even in the case of quickly changing networks [ ] [ ] [ ] . the next step in the progression towards more realistic modeling approaches is to consider the internal structure of the nodes. if each node in the network represents a homogeneously mixed sub-population instead of a single individual and we consider the edges to represent interactions or mobility between the different subpopulations, then we are in the presence of what is known as meta-population. this concept was originally introduced by r. levins in [ ] for the study of geographically extended ecological populations where each node represents one of the ecological niches where a given population resides. the metapopulation framework was later extended for use in epidemic modeling by sattenspiel in . in a landmark paper [ ] sattenspiel considered two different types of interactions between individuals, local ones occurring within a given node, and social ones connecting individuals originating from different locations on the network. this idea was later expanded by sattenspiel and dietz to include the effects of mobility [ ] and thus laying the foundations for the development of epidemic models at the global scale. metapopulation epidemic models are extremely useful to describe particle reaction-diffusion models [ ] . in this type of model each node is allowed to have zero or more individuals that are free to diffuse among the nodes constituting the network. in our analysis, as done in the previous section, we follow the hmf approach and consider all nodes of degree k to be statistically equivalent and write all quantities in terms of the degree k. to start, let us define the average number of individuals in a node of degree k to be w k d where n k is the number of nodes with degree k and the sum is taken over all nodes i. the mean field dynamical equation describing the variation of the average number of individuals in a node of degree k is then: where p k and p kk represent, respectively, the rate at which particles diffuse out of a node of degree k and diffuse from a node of degree k to one of degree k . with these definitions, the meaning of each term of this equation becomes intuitively clear: the negative term represents individuals leaving the node, while the positive term accounts for individuals originating from other nodes arriving at this particular class of node. the conditional probability p .k jk/ encodes all the topological correlations of the network. by imposing that the total number of particles in the system remains constant, we obtain: that simply states that the number of particles arriving at nodes of degree k coming from nodes of degree k must be the same as the number of particles leaving nodes of degree k. the probabilities p k and p kk encode the details of the diffusion process [ ] . in the simplest case, the rate of movement of individuals is independent of the degree of their origin p k d p for all values of the degree. furthermore, if individuals that are moving simply select homogeneously among all of their connections, then we have p kk d p=k. in this case, the diffusion process will reach a stationary state when: where w d w=n, w is the total number of walkers in the system, and n the total number of nodes. the simple linear relation between w k and k serves as a strong reminder of the importance of network topology. nodes with higher degree will acquire larger populations of particles while nodes with smaller degrees will have proportionally smaller populations. however, even in the steady state, the diffusion process is ongoing, so individuals are continuously arriving and leaving any given node but are doing so in a way that maintains the total number of particles in each node constant. in more realistic settings, the traffic of individuals between two nodes is function of their degree [ ] : in this expression  modulates the strength of the diffusion flow between degree classes (empirical values are in the range : Ä Â Ä : [ ] ), where w is a constant and t k d w hk c i=hki is the proper normalization ensured by the condition in eq. ( . ). in these settings, the diffusion process reaches a stationary state when: note that for  d this solution coincides with the case of homogeneous diffusion [eq. ( . )]. combining this diffusion process with the (epidemic) reaction processes described above we finally obtain the full reaction-diffusion process. to do so we must simply write eq. ( . ) for each state of the disease (e.g., susceptible, infectious, and recovered for a simple sir model) and couple the resulting equations using the already familiar epidemic equations. the full significance of eq. ( . ) now becomes clear: nodes with higher degree have higher populations and are visited by more travelers, making them significantly more likely to also receive an infected individual that can act as the seed of a local epidemic. in a metapopulation epidemic context we must then consider two separate thresholds, the basic reproductive ratio, r , that determines whether or not a disease can spread within one population (node) and a critical diffusion rate, p c , that determines if individual mobility is sufficiently large to allow the disease to spread from one population to another. it is clear that if p d particles are completely unable to move from one population to another so the epidemic cannot spread across subpopulations and that if p d all individuals are in constant motion and the disease will inevitably spread to every subpopulation on the network with a transition occurring at some critical value p c . in general, the critical value p c cannot be calculated analytically using our approach as it depends non-trivially on the detailed structure of the network and the fluctuations of the diffusion rate of single individuals. however, in the case of uncorrelated networks a closed solution can be easily found for different mobility patterns. indeed, in the case where the mobility is regulated by eq. ( . ) we obtain: interestingly, the critical value of p is inversely proportional to the degree heterogeneity in the network, so that broad tailed networks have very low critical values. this simple fact explains why simply restricting travel between populations is a highly ineffective way to prevent the global spread of an epidemic. the mobility patterns considered so far are so-called markovian: individuals move without remembering where they have been nor they have a home where they return to after each trip. although this is a rough approximation of individuals behavior, markovian diffusion patterns are allowed to analytically describe the fundamental dynamical properties of many systems. recently, new analytic results have been proposed for non-markovian dynamics that include origin-destination matrices and realistic travel routes that follow shortest paths [ ] . in particular, the threshold within such mobility schemes reads as: the exponent Á, typically close to : in heterogeneous networks, emerges from the shortest paths routing patterns [ ] . interestingly, for values of Â Ä : , fixing Á d : , p c in the case of markovian mobility patterns is larger than the critical value in a system subject to non-markovian diffusion. the presence of origindestination matrices and shortest paths mobility lower the threshold facilitating the global spreading of the disease. instead, for values of  > : the contrary is true. in these models the internal contacts rate is considered constant across each subpopulation. interestingly, recent longitudinal studies on phone networks [ ] and twitter mention networks [ ] point to the evidence that contacts instead scale super-linearly with the subpopulation sizes. considering the heterogeneity in population sizes observed in real metapopulation networks, the scaling behavior entails deep consequence in the spreading dynamics. a recent study generalized the metapopulation framework considering such observations. interestingly, the critical mobility thresholds, in the case of mobility patterns described by eq. ( . ), changes significantly being lowered by such scaling features of human contacts [ ] . despite their simplicity, metapopulation models are extremely powerful tools in large scale study of epidemics. they easily lend themselves to large scale numerical stochastic simulations where the population and state of each node can be tracked and analyzed in great detail and multiple scenarios as well as interventions can be tested. the state of the art in the class of metapopulation approaches is currently defined by the global epidemic and mobility model (gleam) [ , ] . gleam integrates worldwide population estimates [ , ] with complete airline transportation and commuting databases to create a world wide description of mobility around the world that can then be used as the substrate on which the epidemic can spread. gleam divides the globe into transportation basins. each basin is defined empirically around an airport and the area of the basin is determined to be the region within which residents would likely use that airport for long distance travel. each basin represents a major metropolitan area such as new york, london, or paris. information about all civilian flights can be obtained from the international air transportation association (iata) [ ] and the official airline guide (oag) [ ] that are responsible for compiling up-to-date databases of flight information that airlines use to plan their operations. by connecting the population basins with the direct flight information from these databases we obtain the network that acts as a substrate for the reaction diffusion process. while most human mobility does not take place in the form of flights, the flight network provides the fundamental structure for long range travel that explains how diseases such as sars [ ] , smallpox [ ] , or ebola [ ] spread from country to country. to capture the finer details of within country mobility further information must be considered. gleam uses census information to create a commuting network at the basin level that connects neighboring metropolitan areas proportionally to the number of people who live in one are but work in the other. short-term short-distance mobility such as commuting is fundamentally different from medium-term long-distance airline travel. in one case, the typical timescale is work-day ( h) while in the other it is day. this timescale difference is taken into account in gleam in an effective, mean-field, manner instead of explicitly through a reaction process such as the one described above. this added layer is the final piece of the puzzle that brings the whole together and allows gleam to describe accurately the spread from one country to the next but also the spread happening within a given country [ ] . in fig. . we illustrate the progression in terms of detail that we have undergone since our initial description of simple homogeneously mixed epidemic models in a single population. with all these ingredients in place we have a fine grained description of mobility on a world wide scale on top of which we can finally build an epidemic model. within each basin, gleam still uses the homogeneous mixing approximation. this assumption is particularly suited for diseases that spread easily from person to person through airborne means such as ili. gleam describes influenza through an seir model as illustrated in fig. . . seir models are a modification of the sir model described above that includes a further compartment, exposed, to represent of the remaining symptomatic individuals, one half is sick enough to decide to not travel or commute while the remaining half continue to travel normally. despite their apparent complexity, large scale models such as gleam are controlled by just a small number of parameters and ultimately, it's the proper setting of these few parameters that is responsible for the proper calibration of the model and validity of the results obtained. most of the disease and mobility parameters are set directly from the literature or careful testing so that as little as possible remains unknown when it is time to apply it to a new outbreak. gleam was put to the test during the h n pandemic with great success. during the course of the epidemic, researchers were able to use official data as it was released by health authorities around the world. in the early days of the outbreak there was a great uncertainty about the correct value of the r for the /h n pdm strain in circulation so a methodology to determine it had to be conceived. one of the main advantages of epidemic metapopulation models is their computational tractability. it was this feature what proved invaluable when it came to determine the proper value of r . by plugging in a given set of parameters one is able to generate several hundreds or thousands of in silico outbreaks. each outbreak contains information not only about the number of cases in each city or country as a function of time but also information about the time when the first case occurs within a given country. in general, each outbreak will be different due to stochasticity and by combining all outbreaks generated for a certain parameter set we can calculate the probability distribution of the arrival times. the number of times that an outbreak generated the seeding of a country, say the uk, in the same day as it occurred in reality provides us with a measure of how likely the parameter values used are. by multiplying this probability for all countries with a known arrival time we can determine the overall likelihood of the simulation: where the product is taken over all countries c with known arrival time t c and the probability distribution of arrival times, p c .t/ is determined numerically for each set of input values. the set of parameters that maximizes this quantity is then the one whose values are the most likely to be correct. using this procedure the team behind gleam determined that the mostly likely value of the basic reproductive ratio was r d : [ ] , a value that was later confirmed by independent studies [ , ] . armed with an empirical estimate of the basic reproductive ratio for an ongoing pandemic, they then proceeded to use this value to estimate the future progression of the pandemic. their results predicting that the full peak of the pandemic would hit in october and november were published in early september [ ] . a comparison between these predictions and the official data published by the health authorities in each country would be published several years later [ ] clearly confirming the validity of gleam for epidemic forecasting in real time. indeed, the model predicted, months in advance, the correct peak week in % of countries in the north hemisphere for which real data was accessible. in the rest of cases the maximum error reported has been weeks. gleam can also be further extended to include age-structure [ ] , interventions and travel reductions. the next logical step in the hierarchy of large scale epidemic models is to take the description of the underlying population all the way down to the individual level with what are known as abm. the fundamental idea behind this class of model is a deceptively simple one: treat each individual in the population separately, assigning it properties such as age, gender, workplace, residence, family structure, etc: : : these added details give them a clear edge in terms of detail over metapopulation models but do so at the cost of much higher computational cost. the first step in building a model of this type is to generate a synthetic population that is statistically equivalent to the population we are interested in studying. typically this is in a hierarchical way, first generating individual households, aggregating households into neighborhoods, neighborhoods into communities, and communities into the census tracts that constitute the country. generating synthetic households in a way that reproduces the census data is far from a trivial task. the exact details vary depending on the end goal of the model and the level of details desired but the household size, age, and gender of household members are determined stochastically from the empirically observed distributions and conditional probabilities. one might start by determining the size of the household by extracting from the distribution of household size of the country of interest and selecting the age and gender of the head of the household proportionally to the number of heads of households for that household size that are in each age group. conditional on this synthetic individual we can then generate the remaining members, if any, of the household. the required conditional probability distributions and correlation tables can be easily generated [ ] from high quality census data that can be found for most countries in the world. this process is repeated until enough synthetic households have been generated. households are then aggregated into neighborhoods by selecting from the households according to the distribution of households in a specific neighborhood. neighborhoods are similarly aggregated into communities and communities into census tracts. each increasing level of aggregation (from household to country) represents a decrease in the level of social contact, with the most intimate contacts occurring at the household level and least intimate ones at the census tract or country level. the next step is to assign to each individual a profession and work place. workplaces are generated following a procedure similar to the generation of households and each employed individual is assigned a specific household. school age children are assigned a school. working individuals are assigned to work places in a different community or census tract in a way that reflects empirical commuting patterns. at this point, we have a fairly accurate description of where the entire population of a city or country lives and works. it is then not entirely surprising that this approach was first used to study in detail the demands imposed on the transportation system of a large metropolitan city. transims, the transportation analysis and simulation system [ ] , used an approach similar to the one described above to generate a synthetic population for the city of portland, in oregon (or) and coupled it with a route planner that would determine the actual route taken by each individual on her way to work or school as a way of modeling the daily toll on portland's transportation infrastructure and the effect that disruptions or modification might have in the daily lives of its population. episims [ ] was the logical extension of transims to the epidemic world. episims used the transims infrastructure to generate the contact network between individuals in portland, or. susceptible individuals are able to acquire the infection whenever they are in a location along with one or more infectious individuals. in this way the researchers are capable of observing as the disease spreads through the population and evaluate the effect that measures such as contact tracing and mass vaccination. more recent approaches have significantly simplified the mobility aspect of this kind of models and simply divide each h period into day time and nighttime. individuals are considered to be in contact with other members of their workplace during the day and with other household members during the night. in recent years, modelers have successfully expanded the large scale agent based approach to the country [ ] and even continent level [ ] . as the spatial scale of the models increased further modes of long-range transportation such as flights had to be considered. these are important to determine not only the seeding of the country under consideration through importation of cases from another country but also to connect distant regions in a more realistic way. flute [ ] is currently the most realistic large scale agent-based epidemic model of the continental united states. it considers that international seeding occurs at random in the locations that host the largest international airports in the us by, each day, randomly infecting in each location a number of individuals that is proportional to the international traffic of those airports. flute is a refinement of a previous model [ ] and it further refines the modeling of the infectious process by varying the infectiousness of an individual over time in the sir model that they consider. at the time of infection each individual is assigned one of six experimentally obtained viral load histories. each history prescribes the individuals viral load for each day of the infectious period and the infectiousness is considered to be proportional to the viral load. individuals may remain asymptotic for up to days after infection during which their infectiousness is reduced by % with respect to the symptomatic period. the total infectious period is set to days regardless of the length of the symptomatic period. given the complexity of the model the calibration of the disease parameters in order to obtain a given value of the basic reproductive ratio, r requires some finesse. chao et al. [ ] uses the definition of r to determine "experimentally" its value from the input parameters. it numerically simulates instances of the epidemic caused by a single individual within a person fully susceptible community for each possible age group of the seeding individual and use it to calculate the r a of each age group a. the final r is defined to the average of the various r a weighted by age dependent attack rate [ ] . the final result of this procedure is that the value of r is given by: where is the infection probability per unit contact and is given as input. flute was a pioneer in the way it completely released its source code, opening the doors of a new level of verifiability in this area. it has successfully used to study the spread of influenza viruses and analyze the effect of various interventions in the los angeles county [ ] and united states country level [ ] . the unprecedented amount of data on human dynamics made available by recent advances technology has allowed the development of realistic epidemic models able to capture and predict the unfolding of infectious disease at different geographical scales [ ] . in the previous sections, we described briefly some successful examples that have been made possible thanks to high resolution data on where we live, how we live, and how we move. data availability has started a second golden age in epidemic modeling [ ] . all models are judged against surveillance data collected by health departments. unfortunately, due to excessive costs, and other constraints their quality is far from ideal. for example, the influenza surveillance network in the usa, one of the most efficient systems in the world, is constituted of just providers that operate voluntarily. surveillance data is imprecise, incomplete, characterized by large backlogs, delays in reporting times, and the result of very small sample sizes. furthermore, the geographical coverage is not homogeneous across different regions, even within the same country. for these reasons the calibration and test of epidemic models with surveillance data induce strong limitations in the predictive capabilities of such tools. one of the most limiting issues is the geographical granularity of the data. in general, information are aggregated at the country or regional level. the lack of ground truth data at smaller scales does not allow a more precise selection and training of realistic epidemic models. how can we lift such limitations? data, data and more data is again the answer. at the end of almost billion of people had access to the internet while almost billion are phone subscribers, around % of which are actively using smartphones. the explosion of mobile usage boosted also the activity of social media platforms such as facebook, twitter, google+ etc. that now count several hundred million active users that are happy to share not just their thoughts, but also their gps coordinates. the incredible amount of information we create and access contain important epidemiologically relevant indicators. users complaining about catching a cold before the weekend on facebook or twitter, searching for symptoms of particular diseases on search engines, or wikipedia, canceling their dinner reservations on online platforms like opentable are just few examples. an intense research activity, across different disciplines, is clearly showing the potential, as well as the challenges and risks, of such digital traces for epidemiology [ ] . we are at the dawn of the digital revolution in epidemiology [ , ] . the new approach allows for the early detection of disease outbreaks [ ] , the real time monitoring of the evolution of a disease with an incredible geographical granularity [ ] [ ] [ ] , the access to health related behaviors, practices and sentiments at large scales [ , ] , inform data-driven epidemic models [ , ] , and development of statistical based models with prediction power [ , [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] . the search for epidemiological indicators in digital traces follows two methodologies: active and passive. in active data collection users are asked to share their health status using apps and web-based platforms [ ] . examples are influenzanet that is available in different european countries [ ] , and flu near you in the usa [ ] that engage tens of thousands of users that together provide the information necessary for the creation of interactive maps of ili in almost real time. in passive data collection, instead, information about individuals health status is mined from other available sources that do not require the active participation of users. news articles [ ] , queries on search engines [ ] , posts on online social networks [ , [ ] [ ] [ ] [ ] , page view counts on wikipedia [ , ] or other online/offline behaviors [ , ] are typical examples. in the following, we focus on the prototypical, and most famous, method of digital epidemiology, google flu trends (gft) [ ] , while considering also other approaches based on twitter and wikipedia data. gft is by far the most famous model in digital epidemiology. launched in november together with a nature paper [ ] describing its methodology, it has continuously made predictions on the course of seasonal influenza in countries around the world. the method used by gft is extremely simple. the percentage of ili visits, a typical indicator used by surveillance systems to monitor the unfolding of the seasonal flu, is estimated with a linear model based on search engine queries. this approach is general, and used in many different fields of science. a quantity of interest, in this case the percentage of ili visits p, is estimated using a correlated signal, in this case the ili related queries fraction q, that acts as surrogate. the fit allows the estimate of p as a function of the value of q: logit .p/ dˇ cˇ logit .q/ c ; ( . ) where logit .x/ d ln x x ,ˇ andˇ are fitting parameters, and is an error term. as clear from the expression, the gft is a simple linear fit, where the unknown parameters are determined considering historical data. the innovation of the system lies on the definition of q that is evaluated using hundreds of billions of searches on google. indeed, gft scans all the queries we submit to google, without using information about users' identity, in search of those that ili related. this is the paradigm of passive data collection in digital epidemiology. in the original model the authors measured the correlation of millions search queries with historic cdc data, finding that of them were enough to ensure the best correlation between the number of searches and the number of ili cases. the identity of such terms has been kept secret in order to avoid changes in users' behavior. however, the authors provided a list of topics associated with each one of them: were associated with influenza complications, to cold/flu remedies, to general terms for influenza, etc. although the search for the terms has been performed without prior information, none of the most representative terms were unrelated to the disease. in these settings gft showed a mean correlation of : with real data and was able to predict the surveillance value with - weeks ahead. gft is based on proprietary data that for many different constraints cannot be shared with the research community. other data sources, different in nature, are instead easily accessible. twitter and wikipedia are the two examples. indeed, both systems are available for download, with some limitations, through their respective apis. the models based on twitter are built within the same paradigm of gft [ , [ ] [ ] [ ] ] . tweets are mined in search of ili-related tweets, or other health conditions such as insomnia, obesity, and other chronic diseases [ , ] , that are used to inform regression models. such tweets are determined either as done in gft, or through more involved methods based on support vector machine (svm) or other machine learning methods that, provided an annotated corpus, find disease related tweets beyond simple keywords matches [ , [ ] [ ] [ ] ] . the presence of gps information or other self-reported geographical data allows the models to probe different granularities ranging from countries [ , , , ] to cities [ ] . while models based on twitter analyze users' posts, those based on wikipedia focus on pages views [ , ] . the basic intuition is that wikipedia is used to learn more about a diseases or a medication. plus, the website is so popular that is most likely one of the first results of search queries on most search engines. the methods proposed so far monitor a set of pages related to the disease under study. examples are influenza, cold, fever, dengue, etc. page views at the daily or weekly basis are then used a surrogates in linear fitting models. interestingly, the correlation with surveillance data ranges from : in the case of ebola to : in for ilis [ , ] , and allows accurate predictions up to weeks ahead. one important limitation of wikipedia based methods is the lack of geographical granularity. indeed, the view counts are reported irrespective of readers' location but the language of the page can be used as a rough proxy for location. such approximation might be extremely good for localized languages like italian but it poses strong limitations in the case of global languages like english. indeed, it is reported that % of pages views for english pages are done in the usa, % in the uk, and the rest in australia, canada and other countries [ ] . besides, without making further approximation such methods cannot provide indications at scales smaller than the country level. despite these impressive correlations, especially in the case of ilis, much still remains to be done. gft offers a particular clear example of the possible limitations of such tools. indeed, despite the initial success, it completely failed to forecast the h n pandemic [ , ] . the model was updated in september to increase the number of terms to , including the terms present in the original version. nevertheless, gft missed high out of weeks in the season - . in gft predicted a peak height more than double the actual value causing the underlying model to be modified again later that year. what are the reasons underlying the limitations of gft and other similar tools? by construction, gft relies just on simple correlations causing it to detect not only the flu but also things that correlate strongly with the flu such as winter patterns. this is likely one of the reasons why the model was not able to capture the unfolding of an off-season pandemic such as the h n pandemic. also, changes in the google search engine, that can inadvertently modify users' behavior, were not taken into account in gft. this factor alone possibly explains the large overestimation of the peak height in . plus, simple auto-regressive models using just cdc data can perform as well or better than gft [ ] . the parable of gft clearly shows both the potential and the risks of digital tools for epidemic predictions. the limitations of gft can possibly affect all similar approaches based on digital passive data collection. in particular, the use of simple correlations measures does not guarantee the ability of capturing the phenomena across different scales in space and time with respect to those used in the training. not to mention that correlations might be completely spurious. in a recent study for example, a linear model based on twitter simply informed with the timeline of the term zombie was shown to be a good predictor of the seasonal flu [ ] . despite such observations the potential of these models is invaluable to probe data that cannot be predicted by simple auto-regressive models. for example, flu activity at high geographical granularities, although very important, is measured with great difficulties by the surveillance systems. gft and other spatially resolved tools can effectively access to these local indicators, and provide precious estimates that can be used a complement for the surveillance and as input for generating epidemic models [ , ] . the field of epidemiology is currently undergoing a digital revolution due to the seemingly endless availability of data and computational power. data on human behavior is allowing for the development of new tools and models while the commoditization of computer resources once available only for world leading research institutions is making highly detailed large scale numerical approaches feasible at last. in this chapter, we present a brief review not only of the fundamental mathematical tools and concepts of epidemiology but also of some of the state-of-the-art and computational approaches aimed at describing, modeling, and forecasting the diffusion of viruses. our focus was on the developments occurring over the past decade that are sure to form the foundation for developments in decades to come. essai dune nouvelle analyse de la mortalité causée par la petite vérole et des advantages de l'inocoulation pur la prévenir. mémoires de mathematique physique de l infectious diseases in humans the role of the airline transportation network in the prediction and predictability of global epidemics modeling the spatial spread of infectious diseases: the global epidemic and mobility computational model modelling disease outbreaks in realistic urban social networks flute, a publicly available stochastic influenza epidemic simulation model digital disease detection: harnessing the web for public health surveillance digital epidemiology the mathematical theory of infectious diseases modeling infectious diseases in humans and animals a contribution to the mathematical theory of epidemics networks: an introduction scale-free networks complex networks: structure, robustness and function dynamical processes on complex networks computational social science linked: how everything is connected to everything else and 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analysis global capacity for emerging infectious disease detection web-based participatory surveillance of infectious diseases: the influenzanet participatory surveillance experience assessing vaccination sentiments with online social media: implications for infectious disease dynamics and control you are what you tweet: analyzing twitter for public health forecasting seasonal outbreaks of influenza forecasting seasonal influenza with stochastic microsimulations models assimilating digital surveillance data the use of twitter to track levels of disease activity and public concern in the us during the influenza a h n pandemic validating models for disease detection using twitter national and local influenza surveillance through twitter: an analysis of the - influenza epidemic towards detecting influenza epidemics by analyzing twitter messages detecting influenza epidemics using search engine query data detecting epidemics using wikipedia article views: a demonstration of feasibility with language as location proxy wikipedia usage estimates prevalence of influenzalike illness in the united states in near real-time guess who is not coming to dinner? evaluating online restaurant reservations for disease surveillance satellite imagery analysis: what can hospital parking lots tell us about a disease outbreak? public health for the people: participatory infectious disease surveillance in the digital age google flu trends using twitter to estimate h n influenza activity a content analysis of chronic diseases social groups on facebook and twitter. telemedicine and e-health reassessing google flu trends data for detection of seasonal and pandemic influenza: a comparative epidemiological study at three geographic scales predicting consumer behavior with web search acknowledgements bg was partially supported by the french anr project harms-flu (anr- -monu- ). key: cord- -jqh authors: nan title: next generation technology for epidemic prevention and control: data-driven contact tracking date: - - journal: ieee access doi: . /access. . sha: doc_id: cord_uid: jqh contact tracking is one of the key technologies in prevention and control of infectious diseases. in the face of a sudden infectious disease outbreak, contact tracking systems can help medical professionals quickly locate and isolate infected persons and high-risk individuals, preventing further spread and a large-scale outbreak of infectious disease. furthermore, the transmission networks of infectious diseases established using contact tracking technology can aid in the visualization of actual virus transmission paths, which enables simulations and predictions of the transmission process, assessment of the outbreak trend, and further development and deployment of more effective prevention and control strategies. exploring effective contact tracking methods will be significant. governments, academics, and industries have all given extensive attention to this goal. in this paper, we review the developments and challenges of current contact tracing technologies regarding individual and group contact from both static and dynamic perspectives, including static individual contact tracing, dynamic individual contact tracing, static group contact tracing, and dynamic group contact tracing. with the purpose of providing useful reference and inspiration for researchers and practitioners in related fields, directions in multi-view contact tracing, multi-scale contact tracing, and ai-based contact tracing are provided for next-generation technologies for epidemic prevention and control. outbreaks of infectious diseases could cause huge losses in human lives. the spanish pandemic in led to over million deaths [ ] . as of , approximately . billion people worldwide are at risk of malaria, and every seconds one patient dies due to malaria infection [ ] . the death rate of tuberculosis has exceeded aids, becoming the most deadly infectious disease in the world. about % of people in south africa have latent tuberculosis and there were , cases of tuberculosis in alone [ ] . along with the serious threat to human lives, infectious diseases also bring huge economic losses. statistically, malaria causes an economic loss of billion us dollars every year in african countries [ ] . seasonal influenza in the us causes an annual economic burden of billion us dollars [ ] . the developments in vaccines and drugs have enabled us to combat infectious diseases and have greatly reduced the harm brought to human society. however, the sudden emerging infectious diseases caused by the drug resistance and the inherent variability of viruses still remains to be a serious global problem that often leaves us in an unprepared and vulnerable situation. for example, the h n flu in mutated to become the h n flu in and the h n flu in . the h n virus began to spread through contact networks in hong kong in january , and lives were taken in just one month [ ] . the death toll rose to after three months. thus, in the fight against various kinds of infectious diseases, relying solely on vaccine development is far from enough. a more effective ''active prevention and control'' method is desperately needed so as to rapidly detect and block figure . the spatial distribution of h n cumulative cases in the early stage of the outbreak in mainland china in [ ] . in this case, infected cases are recorded with the information of location and time, while the contact information dominating transmission remains unknown. the transmission paths of new infectious diseases, detaining the disease to a minimum spread until its eradication. many infectious diseases are transmitted through personto-person ''contact''. in computational epidemiology, a contact is simply defined either as a direct physical interaction (e.g. sexual contact) or proximity interaction (e.g. to people being within m of each other, or being in the same room) [ ] . human contact interactions constitutes a ''contact network'' of virus transmission. in this network, nodes represent individuals, and links represent contact relationships. the structure of the contact network significantly affects the spatiotemporal patterns of virus spread. for example, in the case of respiratory infections that spread through droplets, interactions like face-to-face communication, shaking hands, crowd gathering, and sharing vehicles enable the spread of diseases and increase the possibilities of transmission from infected to susceptible persons. tracking the contact interactions of individuals can effectively restore the ''invisible'' virus transmission paths, quickly locate and isolate high-risk individuals who were in contact with infected persons, and can aid in quantitative analysis of the transmission paths, processes, and trends of the infectious diseases, all leading to the development of corresponding effective epidemic control strategies. the biggest obstacle in contact tracking is obtaining data that directly describes contact behaviors. because contact interactions between individuals are diverse and often subtle, they are difficult to be directly observed and recorded. in other words, it is hard to obtain first-hand high-quality data for contact tracking. when a disease is spreading, the impact of the disease could be observed, instead of the underlying direct interactions between individuals. for example, during the outbreak of h n bird flu, it is difficult to identify who were infected due to contacts with certain infected people. as shown in fig. , only new h n cases and the number of deaths in different time and space can be observed. many epidemiology scholars and computer scientists have conducted research on how to accurately capture individuals' contact behavior data as well as how to indirectly infer the contact network from other data sources. many methods have been proposed, most of which utilize intelligence data analytics related technologies, such as intelligent sensing, network modeling and analysis, data visualization, multi-source heterogeneous data mining, data-driven reverse engineering, machine learning, and multi-agent simulation, among others. based on the granularity of contact modeling, the existing methods can be classified into four categories: static individual contact tracking, dynamic individual contact tracing, static group contact tracking, and dynamic group contact tracking. each of these methods are described and discussed separately in following sections. individual contact tracking records fine-grained ''individualto-individual'' contact information, such as contact time, location, frequency, duration, etc. the most common ways to gather contact information are non-automatic methods, e.g., offline and online questionnaires [ ] , [ ] , [ ] , and automatic methods, e.g., mobile phone, wireless sensors, rfid, and gps [ ] , [ ] , [ ] , [ ] . offline questionnaire has been used for many years in some counties to trace sexual contacts of sexually transmissible infections (stis), particularly for hiv [ ] . in recent years, hiv has killed more than million people. currently, there are still million newly infected hiv individuals and half of them will be died every year [ ] , [ ] . to reveal the spread patterns of hiv infection and aids in the u.s., fay et al. analyzed the patterns of same-gender sexual contact among men using the data developed from a national sample survey in and , respectively. they found that at least . percent of adult men have had sexual contact with another man in life, and never-married men are more likely to have same-gender sexual contacts [ ] . similarly, merino et al. [ ] sampled homosexual men from colombia as volunteers to answer questionnaires on sexual practices. analysis of these questionnaires suggests two significant risk factors for hiv- infection: ) having sexual contact with foreign visitors; ) having more than ten homosexual partners. they suggest that the spread of hiv- infections should be monitored at the international level and more attention should be paid to these subgroups with high transmission rates. in general, most of us tacitly approve that unsafe sexual behavior would be more prevalent among individuals with optimal viral suppression. in the swiss cohort study on april , , wolf et al. [ ] investigated the unsafe behavior among hiv-infected individuals by selfreported questionnaire. however, after adjustment for covariate, it reported that unsafe sex is associated with other factors, e.g., gender, age, ethnicity, status of partner, having occasional partners, living alone, etc. in recent years, researchers designed questionnaires to measure the validity and reliability of sexual abstinence and avoidance of highrisk situations. for example, najarkolaei et al. [ ] sampled female undergraduate students from tehran university, iran, and assessed the validity and reliability of the designed sex, behavioral abstinence, and avoidance of high-risk situation. zhang et al. [ ] surveyed hiv-positive persons on their socio-demographic characteristics and sexual behavior, and traced hiv infection status of persons who had heterosexual contact with the hiv carriers. among these persons, were hiv-positive, i.e., the secondary attack rate was . %. therefore, they appeal to improve the knowledge about hiv/aids, enhance psychological education, and promote the use of condom, so as to suppress the transmission of hiv. in addition to hiv, offline questionnaire has also been used to trace the contact between individuals to investigate other infectious diseases such as chlamydia trachomatis infection, zika, and flu. to seek the view of patients with chlamydia trachomatis infection on legislation impinging on their sexual behavior, an investigation was performed on patients at std clinics in stockholm, sweden in . during the past months, men ( %) were more likely to have sexual intercourse with occasional partners than women ( %), and the mean number of men and women was . and . , respectively [ ] . the zika virus is primarily transmitted by aedes species mosquitoes. however, by reviewing the travel experience and sexual intercourse of infected individuals in the us, researchers confirmed that there were cases of zika virus infection were transmitted by sexual contact [ ] . for instance, a person in texas was getting infected with the zika virus after sexual contact with someone who had acquired the infection while travelling abroad [ ] . in , molinari et al. [ ] investigated the contact interactions of , students in a high school through questionnaires. a local campus contact network was established based on information such as the length of contact time and contact frequency. the outbreak process of flu was then simulated based on this established contact network. they found that the classroom is the location with the most campus contact and that class break and lunch break are the times with the most campus contact. offline questionnaire is an efficient way to trace private contact interactions such as sexual practice between individuals. however, it needs to find target participants one by one within a specific region, which is time consuming and needs more physical labor. moreover, data collected by this method is usually time delayed and incomplete. with the purpose of collecting more timely and low-priced data of various kinds of contact behaviors, online questionnaires such as online survey and web-based survey have been extensively applied. in , a national online survey was constructed in adolescent males, using computer-assisted self-interviewing (audio-casi) technology. comparing with traditional selfadministered questionnaire, the prevalence of male-male sex with intravenous drug users estimated by audio-casi was higher by more than % [ ] . influenza-like illness (ili) outbreaks on a large scale every year in many countries, recording and detecting ili are important public health problems. flutracking, a weekly web-based survey of ili in australia, has been used to record the past and current influenza immunization status of participants in winter influenza seasons for many years [ ] . it only takes the participants less than seconds to complete the survey, including documenting symptoms, influenza vaccination status, and mobility behaviors such as time off work or normal duties. in , the peak week detected by flutracking was august, which was contemporaneous with that in other influenza surveillance systems [ ] . for the first three years being applied, the participants increased from to and , in , , and , respectively, due to its convenience in completing the survey and its accuracy in detecting the peak week of influenza activity. flutracking also provides vaccine effectiveness analysis by investigating the status of vaccinated and unvaccinated participants. in , the ili weekly incidence peaked in mid-july in the unvaccinated group, month earlier than vaccinated group confirmed by national influenza laboratory [ ] . in recent years, by cooperating with the health department, organizational email systems, and social media, flutracing gained over new participants each year by sending invitations from existing participants. as a result, the number of online participants in flutracing has exceeded , in [ ] . contact information collected through an online questionnaire is more timely and low-priced than offline questionnaire. however, it still cannot record real-time contact information, and, moreover, contact information collected online sometimes inaccurate or even false [ ] . because people on the internet are usually anonymous, which is incapable to verify the information of their real name, age, place of residence, etc. individual contact information obtained through offline or online questionnaires is usually time delayed, incomplete, and inaccurate. with the aim to collect dynamic, complete, and accurate individual contact information, some researchers began to use mobile phone, wireless sensors, rfid, and gps devices to track individual contact behaviors. in recent years, the application of mobile phones has become increasingly universal, providing a convenient way to record real time location information [ ] , [ ] . in , yoneki [ ] developed the first contact pattern discovery software, fluphone, which could automatically detect and record the contact behavior between users by mobile phone. the researchers collected the contact information of users on the cambridge university campus with this software and established the contact network between different users at different times. then, they simulated an influenza outbreak on this network using a seir model. in view that the large power consumption of gps and bluetooth resulted in short standby time of mobile phones, yoneki and crowcroft [ ] further developed a new contact tracking application, epimap, using wearable sensors, which had lower power consumption and longer standby time. epimap thoughtfully transmits and stores data by satellite, as many high-risk areas are in developing countries where there often are not enough wireless communication facilities to support contact tracking. wearable wireless sensors can record individuals' contact events such as time, location, and duration continuously and accurately, and gradually becomes a useful tool for collecting high-precision contact data in small areas [ ] . it has been applied to discover contact patterns in various kinds of social settings such as hospitals and campuses. for example, mit media lab researchers nathan eagle and alex pentland proposed the reality mining method as early as . this method suggests the use of wearable wireless sensors to record people's daily activities [ ] , [ ] . they developed an experimental system to record the activities of several mit students in a teaching building over time, and then established a small social network describing their contact relationships [ ] . salathé et al. [ ] collected the contact interactions of students in a high school in the united states for one day using wireless sensors, and they established an individual-based campus contact network. it was found that the campus contact network had high density connectivity and a small-world structure [ ] . however, it is costly to trace contact interactions using wearable wireless sensors, especially when the number of individuals being monitored is large. moreover, people wearing wearable wireless sensors are very conspicuous, participants are unwilling to wear such devices due to privacy concerns especially for patients. radio frequency identification (rfid) is a non-contact automatic identification technology, by which the contact behavior can be recorded when individuals carrying a small non-contact chip getting closer. in , olguin et al. [ ] collected , contacts among people (including medical staff, children in critical condition, and nursing staff) in a children's hospital in the united states using radiofrequency identification devices (rfid), and established a contact structure for the hospital. similarly, yoneki [ ] collected students' contact data from a french primary school using radiofrequency identification devices. more recently, in october , ibm researchers kurien and shingirirai from africa labs invented a radio tag designed to extend tracker working distance, and implemented it in tracking tuberculosis ( fig. ) [ ] . each tag contains a tiny sensor, figure . an ibm researcher holds a micro-radio tuberculosis tracker [ ] . in october , ibm researchers from johannesburg, south africa, released their latest research update: using cheap radio tags to anonymously track the contact transmission paths of tuberculosis. this study is an important step for ibm in helping who eliminate tuberculosis. a storage device, and a battery. radio tags can communicate with each other, allowing individuals' contact interactions to be recorded when two tags are in close proximity. the contact data collected by the radio tags is presented in a three-dimensional visualization system. using of the intelligent data analysis method provided by the system, medical staff can view the spatiotemporal distribution of tuberculosis patients in real time, track the transmission paths of tuberculosis, and find high-risk populations. because of the high cost of tuberculosis vaccines, contact data can also aid in the determination of high-priority vaccinations. however, the traditionally used radiofrequency tracker has a limited transmission and receiving range and only works within a small area. gps (global positioning system) has the capability of long-distance positioning, which has been widely used for tracing indoor and outdoor mobility behaviors and physical activities [ ] , [ ] . with the aged tendency of population, tracing mobility behavior is critical for measuring, describing, and comparing mobility patterns in older adults. for example, hirsch et al. [ ] investigated the mobility patterns using gps tracing data collected from older adults in vancouver, canada, with the goal of understanding neighborhood influences on older adults' health. they found that participants who were younger tend to drive more frequently and live far from their neighborhoods. gps devices have also been used for tracing physical activities of adolescents in school and other social settings [ ] - [ ] . for instance, rodriguez et al. [ ] sampled adolescent females in minneapolis and san diego, usa, and traced their physical activity and sedentary behaviors by gps every s in different settings. physical activities were more likely to occur in parks, schools, and places with high population density during weekend, less to occur in places with roads and food outlets. besides, tracing animals in the sea or on the land using gps devices can obtain detailed spatiotemporal data regarding the movement patterns. for instance, dujon et al. [ ] traced a green turtle travelling more than km across the indian ocean and obtained more than , locations. moreover, by tracing the whole-body motion dynamics of a cheetah using gps devices, patel et al. [ ] illuminated the factors that influence performance in legged animals. although detailed individual contact information can be collected through non-automatic methods, e.g., offline and online questionnaire, and automatic methods, e.g., mobile phone, wearable wireless sensors, rfid, and gps devices. these methods are mostly limited to small-scale population experiments due to high cost and short range collection. they have not been applied to large areas or large-scale contact behavior studies. group contact tracing captures contact interactions of human beings with similar characteristics (e.g., age, occupation, hobbies) in different social settings from the macroscopic level. static group contact behavior can be traced by large-scale questionnaire and simulated by multi-agent models. dynamic group contact behavior can be inferred by data mining method like tensor deconvolution. in recent years, a composite group model that can characterize population heterogeneity and model epidemic spreading dynamics, overcoming the difficulty of obtaining fine-grained individuals' data has attracted much attention. such models not only simulate the transmission process, but also depict the contact structure of a larger population. the composite group model divides the population into several meta-populations by age or spatial location, so that individuals within a meta-population have similar biological characteristics (such as susceptibility, infectivity, latent period, and recovery period). then, the process of epidemic transmission can be modeled using group contact interactions among meta-populations instead of individuals' contact interactions [ ] . based on this model, the infection and spread of epidemics can be described as a reaction-diffusion process. ''reaction'' characterizes the process of individual infection within a meta-population. ''diffusion'' characterizes the transfer process of epidemic diseases between different meta-populations through the group contact structure (fig. ). in addition, there is a practical significance in establishing contact networks for composite groups because control strategies for epidemic diseases are usually oriented towards composite populations, for example, vaccination groups are usually sectioned by age when planning vaccine allocation strategies. [ ] . the diffusion process is illustrated from a macroscopic perspective, i.e., the transmission among different meta-populations, whereas the reaction process is illustrated from a microscopic perspective, i.e., the individual infection within a meta-population. the composite group contact network was first established using questionnaires. in , mossong et al. [ ] conducted the polymod research project in europe, in which they organized a wide-range survey on contact behaviors, involving volume , , participants from eight european countries. a total of , contact records were collected. they found that contact interactions have significant spatial heterogeneity, with most individual contacts occurring at home ( %), work ( %), school ( %), places of entertainment ( %), and while using transportation ( %). further, contact structures under different scenarios have obvious differences. there are some age-related contact patterns: in many scenarios (such as in schools), individuals are more likely to contact people of similar age; most of the contact between children and their parents occurs at home, while most contacts for adults occur in workplaces. the researchers thus divided the population into several meta-populations, establishing a composite group model based on age. interaction probabilities between different age groups were estimated according to questionnaire data (fig. ) , and a contact network based on composite groups was established. the simulation method based on multi-agent models is also applied to the establishment of contact networks. this generally involves combining the questionnaire survey with population census data to establish the contact structure of composite groups. iozzi et al. [ ] modeled a virtual society with the characteristics of italian society based on questionnaire data from , people. human daily migration behaviors were simulated by a virtual community, and a contact matrix of the composite group was obtained. based on this matrix, the outbreak process of italian b (human parvovirus) was successfully simulated. similarly, eubank et al. [ ] simulated the movement of individuals within a city by large-scale agent system, and then modeled a group contact structure based on their simulation. the data they used included population census data, land usage, population migration, and other daily behavior data. constructing contact matrix for meta-population requires large-scale even nationwide questionnaire survey, which is quite costly and time delayed. multi-agent method simulates human mobility behaviors in the virtual world based on the contact matrix constructed using the data from the real world of the past [ ] . it doesn't consider the changes of existing contact patterns caused by human self-awareness and epidemic-control strategies in the future. most of the above studies focus on static properties of contact behaviors, such as the contact object (who is contacting), scene (where this contact happens), frequency, and duration. in other words, the aforementioned studies assume that the contact patterns of the individual remain stationary. however, contact interactions usually change with time, and show different temporal and spatial patterns. for example, contact interactions can change periodically with the weather and season, vary significantly between workdays, weekends, and holidays, and may be adjusted in response to the threat of an epidemic disease and during the outbreak by reducing travel or wearing face masks [ ] , [ ] . additionally, governmentimposed epidemic-control strategies can significantly change individuals' contact patterns [ ] , [ ] , [ ] , [ ] . for example, during the outbreak of h n flu in hong kong in , interventions, such as flight reductions, school closures, and vaccination efforts, significantly altered individuals' contact interactions [ ] - [ ] . dynamic contacts between individuals are more difficult to be observed and recorded than static contacts because of the limitations of existing contact tracing methods. offline and online questionnaires are incapable of recording real-time contact information, and usually time delayed to receive feedback from participants. automatic contact tracing methods such as mobile phone, wearable wireless sensor, rfid, and gps devices can collect continuous mobility information [ ] , [ ] . however, all these methods are limited to monitoring mobility behaviors for small-scale population, due to the large consumption of power, short range of positioning, high cost of money, etc. besides, most people cannot be expected to agree to have their dynamic contact interactions monitored in real time because of privacy issue. for example, wearing a tracker can also be equated to declaring one's self an infectious disease patient. tuberculosis patients in african countries are branded with social prejudice, making wearing an identifier a sensitive issue [ ] . in light of these obstacles, a new path that does not ''directly'' capture and record individuals' dynamic contact behaviors, but ''indirectly'' infers the dynamic contact model of a large-scale population from other readily available data sources must be found. infectious disease surveillance, like that depicted in fig. , expands everyday with the vast applications of information technology in the medical field. surveillance data record spatiotemporal information related to the spread of infectious diseases, which is the result of the spread model acting on the real contact network, as shown in fig. (a) . such surveillance data can be regarded as an external manifestation of the implicit contact network, suggesting that the dynamic contact network could be ''inversely'' inferred from infectious disease surveillance data, as shown in fig. (b) . essentially, this is a complex inverse engineering problem: using the observed dynamics phenomenon to determine the dynamic structure that leads to the phenomenon. in other words, determining time-dependent contact interactions using the timedependent spread trend of infectious diseases. based on the idea of inverse engineering, yang et al. [ ] proposed a novel modeling and inference method for constructing a dynamic contact network based on tensor model. they described the spatiotemporal patterns of composite group contacts as a tensor, modeled the inference of the dynamic contact network as low-rank tensor reconstruction problem, and proposed a tensor deconvolution based inference method by fusing compression perception, sparse tensor decomposition and epidemic propagation models. this method makes it possible to determine the dynamic contact network of the large-scale composite group from population census data and surveillance data of many epidemic diseases. using this method, composite group dynamic contact networks for hong kong and taiwan were established using population census data and surveillance data of a variety of infectious diseases (such as h n , influenza, measles, mumps, etc.) for these two areas. the temporal and spatial evolution patterns of individuals' dynamic contact interactions were analyzed. based on the established dynamic contact network, they further studied the spread law, and prevention and control strategies of h n epidemic disease. they arrived at two important conclusions: ( ) in the h n outbreak in hong kong in , if the beginning of the new semester was delayed two to six weeks, the total number of infections would have been reduced by % to %; ( ) the best strategy for prevention and control of h n spread is vaccination of school-age children in the first few days of the new semester. contact tracking based on intelligent information processing technology represents an active prevention and control strategy for infectious diseases. its main functions are to achieve early detection and timely intervention of infectious diseases. research on contact tracking methods not only expands the options for preventing and controlling infectious diseases, but also further improves people's understanding of their own contact behaviors. contact tracking has become an increasingly mature datadriven technology for disease prevention and control, evolving from individual tracking to group tracking. individual tracking attempts to capture more detailed contact interactions for accurate locating of infected patients and high-risk susceptible populations. traditional offline questionnaire is a practical method for tracing private contact interactions between individuals such as sexual practice. however, it is quite costly and time delayed to find target participants and receive feedback from them. comparatively speaking, online questionnaire serves a low-priced way to collect feedback from participants timely. however, it cannot record the time exactly when contact occurs. meanwhile, offline and online questionnaires sometimes provide inaccurate information of human mobility. for example, klous et al. [ ] surveyed participants in a rural in the netherlands using questionnaire and gps logger, respectively. investigations on walking, biking, and motorized transport duration showed that time spent in walking and biking based on questionnaire was strongly overestimated. the use of automatic contact tracing methods enabled researchers to obtain continuous and accurate individual contact information, e.g., time, location, duration, etc. mobile phone and wireless sensors were widely used to trace mobility behaviors of students in campus and patients in hospital. then, small-scale contact network within the tracing regions can be constructed and the diffusion process of infectious volume , disease such as influenza can be simulated and analyzed in detail. however, the use of mobile phone is limited to tracing short-term contact behavior because of large power consumption of gps and bluetooth. wearable wireless sensors can only be applied to small-scale population due to its high cost and privacy concerns. rfid devices are convenient carrying which solves privacy concerns very well, but it only can be used for short range collection. gps device has the advantage of long-distance positioning. however, it is costly to capture indoor mobility behaviors due to the requirement of communication stations [ ] . all these automatic contact tracing methods have not been used for studies of large-scale individual contact so far. group tracking replaces individual contacts with the contact probability of meta-populations, which, to some extent, overcomes the obstacles of individual tracking. using a contact matrix of meta-population, contact patterns regarding people with similar features can be depicted from the macroscopic level. however, the contact matrix is usually constructed using the data collected from a nationwide questionnaire, which is static and can only represent the contact patterns of the past. to explore dynamic contact patterns of meta-population, a data-driven ai (artificial intelligence) method was adopted, i.e., tensor deconvolution [ ] . based on this method a dynamic evolutionary model of the group contact was constructed and dynamic contact patterns were inferred inversely through insights into the time-dependent nature of the infectious disease surveillance data. nevertheless, it should be noted that although it can characterize a wider range of dynamic contact behaviors, it cannot be used to accurately locate unique contact events because of the coarse granularity of the captured contact behaviors. exploring social contact patterns for epidemic prevention and control is an every promising research direction, and some potential future development directions are illustrated as follows. a. multi-view contact tracing data obtained from different views can give expressions to different patterns of mobility behaviors. for example, offline and online questionnaire can accurately record contact events occurred in places that individuals frequently visited [ ] . gps devices can record indoor and outdoor contact events happened occasionally [ ] . heterogeneous contact network constructed by various kinds of information can provide a new way for analyzing and simulating the spread of epidemics. therefore, tracing mobility behaviors and analyzing contact patterns from multi-views to get new insight into what heterogeneous contact patterns like will be a new direction in the future. existing studies focus on either individual level or group level contact tracing, presenting independent contact patterns from microscopic and macroscopic scales, respectively. however, group contact patterns are formed by collaborative behaviors of individual mobility, while individual mobility behaviors can be influenced by others in the same group. revealing hidden interactions between individual contact and group contact will be helpful to identify influential individuals as sentries for disease monitoring. therefore, discovering hidden interactions from multi-scale contact patterns that tunneling individual contact and group contact will be a new opportunity for early epidemic detection. dynamic mobility behaviors lead to complex contact patterns, which are usually hidden and cannot be directly traced by non-automatic or automatic methods. a better way to infer dynamic contact patterns is adopting ai-based methods using heterogeneous real-world data. existing studies such as tensor deconvolution consider the combination of contact probabilities within real-world social settings like school, home, and workplace as linear [ ] . however, hidden dynamic contact patterns within these social settings could be more complicated than linear models can characterize. therefore, exploring advanced ai-based contact tracing methods, e.g., multi-view learning [ ] - [ ] , deep learning [ ] , broad learning [ ] , etc., will be the next generation technology for epidemic prevention and control. in this paper, we introduced current studies on contact tracing and its applications in epidemic prevention and control. this paper covered research directions, i.e., individual contact and group contact, which were introduced from both static and dynamic aspects. non-automatic tracing methods like offline and online questionnaires record static individual contact information, while automatic tracing methods like mobile phone, wearable wireless sensor, rfid, and gps devices collect dynamic contact events. static group contact patterns can be depicted by a coarse granularity contact matrix constructed by large-scale questionnaire data, dynamic contact patterns, however, can only be inversely inferred using data-driven ai technologies. both individual and group contact tracing are promising research directions and filled with challenges, especially for dynamic contact tracing. collecting contact data from multi-views and analyzing contact patterns from multi-scale mobility interactions will be new directions in the future. moreover, exploring advanced ai-based contact tracing methods using heterogeneous and multi-source data will provide new opportunities for epidemic prevention and control. hechang chen received the m.s. degree from the college of computer science and technology, jilin university, in , where he is currently pursuing the ph.d. degree. he was enrolled in the university of illinois at chicago as a joint training ph.d. student from to . his current research interests include heterogenous data mining and complex network modeling with applications to computational epidemiology. bo yang received the b.s., m.s., and ph.d. degrees in computer science from jilin university in , , and , respectively. he is currently a professor with the college of computer science and technology, jilin university. he is currently the director of the key laboratory of symbolic computation and knowledge engineer, ministry of education, china. his current research interests include data mining, complex/social network modeling and analysis, and multi-agent systems. he is currently working on the topics of discovering structural and dynamical patterns from large-scale and time-evolving networks with applications to web intelligence, recommender systems, and early detection/control of infectious events. he has published over articles in international journals, including ieee tkde, ieee tpami, acm tweb, dke, jaamas, and kbs, and international conferences, including ijcai, aaai, icdm, wi, pakdd, and asonam. he has served as an associated editor and a peer reviewer for international journals, including {web intelligence} and served as the pc chair and an spc or pc member for international conferences, including ksem, ijcai, and aamas. updating the accounts: global mortality of the - 'spanish' influenza pandemic plasmodium ovale: a case of notso-benign tertian malaria the global burden of respiratory disease impact of the large-scale deployment of artemether/lumefantrine on the malaria disease burden in africa: case studies of south africa, zambia and ethiopia high-resolution measurements of face-to-face contact patterns in a primary school tracking tuberculosis in south africa the annual impact of seasonal influenza in the us: measuring disease burden and costs updated situation of influenza activity in hong kong little italy: an agent-based approach to the estimation of contact patterns-fitting predicted matrices to serological data the tencent news what types of contacts are important for the spread of infections? using contact survey data to explore european mixing patterns estimating within-school contact networks to understand influenza transmission reality mining: sensing complex social systems time-critical social mobilization capturing individual and group behavior with wearable sensor fluphone study: virtual disease spread using haggle epimap: towards quantifying contact networks and modelling the spread of infections in developing countries a high-resolution human contact network for infectious disease transmission collective dynamics of small world networks close encounters in a pediatric ward: measuring face-toface proximity and mixing patterns with wearable sensors computing urban traffic congestions by incorporating sparse gps probe data and social media data modeling human mobility responses to the large-scale spreading of infectious diseases modelling dynamical processes in complex socio-technical systems social contacts and mixing patterns relevant to the spread of infectious diseases characterizing and discovering spatiotemporal social contact patterns for healthcare outbreaks in realistic urban social networks skip the trip: air travelers' behavioral responses to pandemic influenza the effect of risk perception on the h n pandemic influenza dynamics quantifying social distancing arising from pandemic influenza behavioral responses to epidemics in an online experiment: using virtual diseases to study human behavior an evaluation of an express testing service for sexually transmissible infections in low-risk clients without complications hiv/aids: years of progress and future challenges reflections on years of aids prevalence and patterns of same-gender sexual contact among men hiv- , sexual practices, and contact with foreigners in homosexual men in colombia, south america prevalence of unsafe sexual behavior among hiv-infected individuals: the swiss hiv cohort study sexual behavioral abstine hiv/aids questionnaire: validation study of an iranian questionnaire study on the risk of hiv transmission by heterosexual contact and the correlation factors a survey of patients with chlamydia trachomatis infection: sexual behaviour and perceptions about contact tracing transmission of zika virus through sexual contact with travelers to areas of ongoing transmission-continental united states zika virus was transmitted by sexual contact in texas, health officials report adolescent sexual behavior, drug use, and violence: increased reporting with computer survey technology insights from flutracking: thirteen tips to growing a web-based participatory surveillance system flutracking: a weekly australian community online survey of influenza-like illness in flutracking weekly online community survey of influenza-like illness annual report mobility assessment of a rural population in the netherlands using gps measurements generating gps activity spaces that shed light upon the mobility habits of older adults: a descriptive analysis what can global positioning systems tell us about the contribution of different types of urban greenspace to children's physical activity? out and about: association of the built environment with physical activity behaviors of adolescent females a study of community design, greenness, and physical activity in children using satellite, gps and accelerometer data the accuracy of fastloc-gps locations and implications for animal tracking tracking the cheetah tail using animal-borne cameras, gps, and an imu examining the spatial congruence between data obtained with a novel activity location questionnaire, continuous gps tracking, and prompted recall surveys using global positioning systems in health research: a practical approach to data collection and processing mobile sensing in environmental health and neighborhood research feasibility and acceptability of global positioning system (gps) methods to study the spatial contexts of substance use and sexual risk behaviors among young men who have sex with men in new york city: a p cohort sub-study strengths and weaknesses of global positioning system (gps) data-loggers and semi-structured interviews for capturing fine-scale human mobility: findings from iquitos using mobile phone data to study dynamics of rural-urban mobility inferencing human spatiotemporal mobility in greater maputo via mobile phone big data mining gps tracking in neighborhood and health studies: a step forward for environmental exposure assessment, a step backward for causal inference? multi-view clustering with graph embedding for connectome analysis a self-organizing tensor architecture for multi-view clustering mmrate: inferring multi-aspect diffusion networks with multi-pattern cascades inferring diffusion networks with sparse cascades by structure transfer partially observable reinforcement learning for sustainable active surveillance broad learning: an emerging area in social network analysis key: cord- - mw k yu authors: wang, wei; liang, qiaozhuan; mahto, raj v.; deng, wei; zhang, stephen x. title: entrepreneurial entry: the role of social media date: - - journal: technol forecast soc change doi: . /j.techfore. . sha: doc_id: cord_uid: mw k yu despite the exponential growth of social media use, whether and how social media use may affect entrepreneurial entry remains a key research gap. in this study we examine whether individuals’ social media use influences their entrepreneurial entry. drawing on social network theory, we argue that social media use allows individuals to obtain valuable social capital, as indicated by their offline social network, which increases their entrepreneurial entry. we further posit the relationship between social media use and entrepreneurial entry depends on individuals’ trust propensity based on the nature of social media as weak ties. our model was supported by a nationally representative survey of , adults in china over two years. as the first paper on the role of social media on entrepreneurial entry, we hope our research highlights and puts forward research intersecting social media and entrepreneurship. social media, defined as online social networking platforms for individuals to connect and communicate with others (e.g., facebook), has attracted billions of users. an emerging body of literature suggests that social media enables entrepreneurs to obtain knowledge about customers or opportunities, mobilize resources to progress their ventures, and manage customer relationships after venture launch (cheng & shiu, ; de zubielqui & jones, ; drummond et al., ) . further, social media allows entrepreneurs to efficiently manage their online relationships and reinforce their offline relationships (smith et al., ; thomas et al., ; wang et al., ) . despite much research on the impact of social media on the launch and post-launch stages of the entrepreneurial process (bird & schjoedt, ; gruber, ; ratinho et al., ) , there is little research on the impact of social media on the pre-launch stage, the first of the three stages of the entrepreneurial process (gruber, ) . despite the popularity of social media, it remains unclear whether and how social media affects individuals at the prelaunch stage of the entrepreneurial process, given social media consists of weak ties and substantial noise from false, inaccurate or even fake information, which may or may not benefit its users. in this study, we aim to contribute to the literature by investigating whether individuals' social media use affects their entrepreneurial entry based on social network theory. we argue that a higher social media use will allow an individual to develop a larger online social network and accumulate a greater amount of social capital, which facilitates entrepreneurial entry. a larger social network may facilitate individuals' information and knowledge seeking activities (grossman et al., ; miller et al., ) , which have a significant impact on their ability to generate and implement entrepreneurial ideas in the pre-launch stage (bhimani et al., ; cheng & shiu, ; orlandi et al., ) . social media, unlike offline face-to-face social networks, allows a user to develop a large social network beyond their geographical area without incurring significant effort and monetary cost (pang, ; smith et al., ) . the large social network arising from social media further enables social media users to build larger offline networks beyond their geographical proximity. hence, we argue that individuals' social media use has a positive impact on their offline network, which facilitates their entrepreneurial entry. however, social media is dominated by weak ties, and individuals with low trust propensity may not trust other online users easily so they are cautious about online information and knowledge. thus, we propose that trust propensity, an individual's tendency to believe in others (choi, ; gefen et al., ) , moderates the relationship between social media use and entrepreneurial entry. fig. displays the proposed model. we assessed the proposed model on a publicly available dataset of china family panel studies (cfps), which consists of a sample of nationally representative adults. our findings reveal that social media use https://doi.org/ . /j.techfore. . received august ; accepted september has a positive impact on entrepreneurial entry with individuals' offline network serving as a partial mediator. further, the findings confirm that individuals' trust propensity moderates the relationship between their social media use and entrepreneurial entry, with the relationship becoming weaker for individuals with high trust propensity. our study makes several important contributions to the literature. first, we contribute to the emerging entrepreneurship literature on an individual's transition to entrepreneurship by identifying factors contributing to the actual transition (mahto & mcdowell, ) . the identification of social media use addresses mahto and mcdowell's ( ) call for more research on novel antecedents of individuals' actual transition to starting entrepreneurship. to the best of our knowledge, this is the first study on the role of social media on individuals' entrepreneurial entry using social network theory. the research on social media in entrepreneurship area has focused on post-launch phases of entrepreneurship (cheng & shiu, ; drummond et al., ; mumi et al., ) , while research on individuals at the pre-launch stage of the entrepreneurial process is lacking. second, our study specified a mechanism for the impact of individuals' social media use on entrepreneurial entry via their offline network and used instrumental variables to help infer the causality. yu et al. ( yu et al. ( , p. noted that "specifying mediation models is essential to the advancement and maturation of particular research domains. as noted, mathieu et al. ( : ) write, 'developing an understanding of the underlying mechanisms or mediators (i.e., m), through which x predicts y, or x → m → y relationships, is what moves organizational research beyond dust-bowl empiricism and toward a true science.'" third, we contribute to the limited stream of research in the entrepreneurship literature on the networking of individuals in the prelaunch phase which has focused on networking offline (dimitratos et al., ; johannisson, ; klyver & foley, ) . instead, we offer a clearer picture of networking for entrepreneurship by connecting the literature on online social media use (fischer & reuber, ; smith et al., ) with offline social networks and entrepreneurial entry. the paper is organized as follows. the next section, section , provides an overview of the social capital theory and associated literature used to construct arguments for hypothesis development. section , data and methods, reports the context, method, and the variables. section reports the results of the statistical analysis, instrumental variable analysis to address endogeneity concerns, and an assessment of robustness checks. section discusses the study findings, outlines key study limitations, and provides guidance for future research and section concludes. social capital theory (rutten & boekema, ) is a popular theoretical framework among management scholars. more recently, the theory has been increasingly used by entrepreneurship scholars to explain behaviors at the levels of both the individual (e.g., entrepreneurs) and firm (e.g., new ventures) (dimitratos et al., ; klyver & foley, ; mcadam et al., ) . according to the theory, the network of an individual has a significant influence on an individual's behavior (e.g., seeking a specific job) and outcomes (e.g., getting the desired job). in the theory, the network represents important capital, referred to as social capital, that produces outcomes valued by individuals (mariotti & delbridge, ) . social capital allows an individual to obtain benefits by virtue of their membership in the social network. the underlying assumption of social capital is, "it's not what you know, it's who you know" (woolcock and narayan ( ) , p. ). for example, people with higher social capital are more likely to find a job (granovetter, ) or progress in their career (gabby & zuckerman, ) . for firms, social capital offers the ability to overcome the liability of newness or resource scarcity (mariotti & delbridge, ) . in entrepreneurship literature, scholars have used social capital to explain resource mobilization and pursuit of an opportunity by both entrepreneurs and small firms (dubini & aldrich, ; stuart & sorenson, ) . at the individual level, entrepreneurs embedded in a network are more likely to overcome challenges of resource scarcity and act promptly to launch a venture to capitalize on an opportunity (klyver & hindle, ) . for example, high social competence entrepreneurs establish strategic networks to obtain information, resources and more strategic business contacts (baron & markman, ) . mahto, ahluwalia and walsh ( ) supported the role of social capital by arguing that entrepreneurs with high social capital are more likely to succeed in obtaining venture capital funding. further, entrepreneurship scholars have argued that social networks influence entrepreneurs' decisions and the probability of executing a plan (davidsson & honig, ; jack & anderson, ; ratinho et al., ) . in women entrepreneurs, the presence of a robust social network is a key determinant of success (mcadam et al., ) . research suggests that the extent of a social network determines which resources entrepreneurs can obtain (jenssen & koenig, ; witt, ) . in the entrepreneurial context, scholars have also examined the influence of social networking at the firm level. for example, new and small firms often use a strong social network to overcome the liability of newness or smallness to pursue growth opportunities (galkina & chetty, ; mariotti & delbridge, ) . entrepreneurial ventures with limited resources often rely on their networks to obtain information and knowledge about consumers, competitors and networks in a foreign market (lu & beamish, ; wright & dana, ; yeung, ) . in the internationalization context, it is almost impossible for entrepreneurial firms to enter a foreign market without a robust social network (galkina & chetty, ) . it is well documented that new firms commonly use strategic networking for resources and capabilities (e.g., research and development) unavailable within the firm. the research on social networks in the entrepreneurship area is robust, but is focused almost exclusively on traditional offline social wang, et al. technological forecasting & social change ( ) networks with limited attention to the dominant online social media. as offline social networks and online social networks differ significantly in terms of strength of ties (i.e., weak ties vs. strong ties) between network associates (filiposka et al., ; rosen et al., ; subrahmanyam et al., ) , empirical findings from traditional offline social networks may not be applicable to online social networks because offline social networks are dominated by strong ties while online social media are dominated by weak ties (filiposka et al., ) , and strong ties are based on a high degree of trust and reciprocity while weak ties have low trust and reciprocity. this significantly limits our understanding of entrepreneurial phenomena in the context of online social media. further, the research on social networks has also paid limited attention to the pre-launch phase of the entrepreneurial process, focusing mostly on entrepreneurs and established entrepreneurial ventures. finally, as offline social networks, which have strong ties, are the main context of the literature, the role of individual trust propensity remains unexplored as well. this offers a unique opportunity to investigate the role of social media and individuals' trust propensity in the pre-launch phase of the entrepreneurial process. the widespread adoption of the internet has led to an exponential growth in social media around the world. we refer to social media as "online services that support social interactions among users through greatly accessible and scalable web-or mobile-based publishing techniques" (cheng & shiu, , p. ) . social media, using advanced information and communication technologies, offers its users the ability to connect, communicate, and engage with others on the platform (bhimani et al., ; kavota et al., ; orlandi et al., ) . some of the most popular social media companies in the world are facebook, twitter, qq, and wechat. the large number of users coupled with other benefits of social media platforms, such as marketing, engagement, and customer relationship management, have attracted firms and organizations to these platforms. for example, firms have used social media to build an effective business relationship with their customers (steinhoff et al., ) , create brand loyalty (helme-guizon & magnoni, ), and engage in knowledge acquisition activities (muninger et al., ) . firms have also started adopting social media to enhance their internal operations by strengthening communication and collaboration in teams (raghuram et al., ) . thus, social media and its impact on firms and their environment has intrigued business and management scholars driving growth of the literature. recently, entrepreneurship scholars have begun exploring the impact of social media on entrepreneurial phenomena. limited research on social media in entrepreneurship suggests that social media allows entrepreneurial firms to enhance exposure (mumi et al., ) , mobilize resources (drummond et al., ) , and improve innovation performance (de zubielqui & jones, ) . this limited research, while enlightening, is devoted almost entirely to the post-launch stage of the entrepreneurial process, where a start-up is already in existence. the impact of social media on other stages of the entrepreneurial process, especially the launch stage (i.e., entrepreneurial entry), remains unexplored and is worthy of further scholarly exploration. for example, even though we know that social media can offer new effectual pathways for individuals by augmenting their social network, whether social media influences entrepreneurial entry or offline social networks remains unexplored. thus, our goal in this study is to address the gap in our understanding of the impact of social media on entrepreneurial entry. a social network refers to a network of friends and acquaintances tied with formal and informal connections (barnett et al., ) , that can exist both online and offline. social media is useful for creating, expanding and managing networks. research suggests social media can be used to initiate weak ties (e.g., to start a new connection) and manage strong ties (i.e., to reinforce an existing connection) (smith et al., ) . similar to social interactions in a physical setting, people can interact with others and build connections in the virtual world of social media, which eliminates the need for a physical presence in the geographical proximity of the connection target. the lack of requirement for geographical proximity with the in-built relationship management tools in social media allows a user to connect with a significantly larger number of other users regardless of their physical location. the strength of relationships among connected users in social media is reflected by the level of interaction among them; users in a strong connection have a higher level of interaction and vice versa. however, given the probability of a much larger number of connections in social media, dominance of weak ties is accepted. when connected users, either online or offline, in a network reinforce their connection by enhancing their level of interaction in both mediums (i.e., offline and online), they strengthen ties. for example, when two connected users in social media engage in offline activities, they may enhance their offline social tie through the joint experience . research also informs that social media use helps reinforce or maintain the strength of relationships among offline friends (thomas et al., ) . social media allows people to communicate with their offline friends instantly and conveniently without the need to be in geographical proximity (barnett et al., ) . the opportunity to have a higher level of interaction at any time regardless of physical location offers social media users the ability to manage and enlarge their offline social network. further, social media can also be used to initiate offline ties directly. in the digital age, users can connect their friends and acquaintances to other friends and acquaintances on social media. social media platforms also recommend connections to users based on their user profile, preferences, and online activities to generate higher user engagement. for example, in china, when a user intends to connect with a person known to their friends or connections, they can ask their friends for a wechat name card recommendation. once connected online, users can extend their connection to their offline networks as well. as a result, higher social media use may enhance a user's offline social network. thus, we hypothesize: h . social media use of a user is positively associated with their offline social network. entrepreneurship, a context-dependent social process, is the exploitation of a market opportunity through a combination of available resources by entrepreneurs (shane & venkataraman, ) . the multistage process consists of: (a) the pre-launch stage, involving opportunity identification and evaluation, (b) the launch stage, involving business planning, resource acquisition, and entrepreneurial entry, and (c) the post-launch stage, involving venture development and growth (gruber, ) . our focus in this study is on entrepreneurial entry, which is the bridge between the pre-launch and launch stages of the entrepreneurial process, representing the transition from an individual to an entrepreneur (mahto & mcdowell, ; yeganegi et al., ) . entrepreneurial entry requires a viable entrepreneurial idea (i.e., opportunity) and resources (ratinho et al., ; ucbasaran et al., ) . individuals' social networks are important for researching and assessing entrepreneurial ideas (fiet et al., ) and accumulating valuable resources for entrepreneurial entry (grossman et al., ) . research suggests that networks play a crucial role in the success of entrepreneurs and their ventures (galkina & chetty, ; holm et al., ) . social networks allow individuals to access information and resources (chell & baines, ) . a larger social network allows entrepreneurs and smes to overcome resource scarcity for performance enhancement and expansion, especially international expansion (dimitratos et al., ; johannisson, ). although enlightening, the prior research on social networks in entrepreneurship has focused only on the traditional offline networks. in the digital age, social media has emerged as the key networking tool and enhanced individuals' ability to significantly enlarge their network and draw a higher social capital. these platforms allow entrepreneurs to efficiently manage both their online and offline networks and relationships . social media has significantly expanded the ability of individuals to network by removing geographical, cultural and professional boundaries. it allows people, separated by physical distance, to overcome the distance barrier to network and manage relations effectively (alarcóndel-amo et al., ; borst et al., ) . this is especially beneficial for an individual searching for entrepreneurial ideas that may be based on practices, trends, or business models emerging in the geographical locations of their network associates. as an example, jack ma of alibaba did not have to travel to the us to stumble upon the idea of an online commerce platform. social media allowed him to observe and obtain that information through network associates. while social media enlarges the social network of an individual with associates located beyond their geographical location, critics of the platform argue that such networks are mostly made up of weak ties lacking the strong ties of an offline network. however, individuals can still obtain useful and valuable information from abundant weak ties in such social networks (granovetter, ) . when accessing the network, the individuals have access to knowledge and information from various domains to inform their entrepreneurial ideas. further, the efficiency of social media allows for more effective and easy communications with distant individuals (alarcón-del-amo et al., ) . the improved communication with distant network associates allows individuals to strengthen their ties and obtain richer and reliable information. individuals may also obtain valuable access to new resources or new associates, who may support the formation of their new entrepreneurial venture. the distant network associates could also offer individuals additional resources in the form of entrepreneurial connections to new partners, buyers, suppliers, or talent, which all improve the chance of launching new ventures. it is well known that people, especially venture capitalists and investors, tend to minimize their risk by investing in known entrepreneurs rather than unknown entrepreneurs . thus, we believe social media use is beneficial for entrepreneurial entry. h . social media use is positively associated with entrepreneurial entry. social media significantly enhances individuals' capability to expand their networks by removing cultural, geographical, and professional boundaries, to manage and strengthen offline social relationships. according to prior research, offline networks can provide the spatially proximate information and resources relevant to entrepreneurial entry (levinthal & march, ; miller et al., ) . social media enhances the efficiency and reduces the transaction cost of communication with offline network associates, allowing individuals to use them for information, knowledge and resource search. a recombination of information and knowledge is key to generating and then evaluating entrepreneurial ideas for entrepreneurial entry. in an offline social network, an individual has a stronger relationship with network associates because of their face-to-face interactions and collective experience in geographical proximity. further, geographical proximity in an offline social network facilitates relationships in real life by augmenting face-to-face interactions via virtual means (kim et al., ) . the additional channel of communication via virtual social media allows individuals to obtain timely and richer information, which may help them benefit from the collective wisdom and capability of their higher social capital (orlikowski, ) to develop entrepreneurial opportunities. the richer information and better access to knowledge and resources all benefit their entrepreneurial entry. thus, with higher social media use, individuals will have an expanded offline social network, which provides them the resources needed for successful entrepreneurial entry. therefore, we propose: h . the offline social network mediates the relationship between social media use and entrepreneurial entry. trust propensity refers to an individual's tendency to trust others (choi, ; gefen et al., ) . trust propensity is a stable personality trait formed early in life through socialization and life experience (baer et al., ; warren et al., ) . like other ingrained personality traits, it affects an individual's behaviour, especially trust, in many situations (baer et al., ; friend et al., ) . for example, a customer with a high trust propensity is more likely to trust a salesperson without doubting their integrity (friend et al., ) . while trust propensity enables trust, it may leave individuals vulnerable due to reduced monitoring and reduced flow of new ideas (molina-morales et al., ) . furthermore, an individual with a high trust propensity may be inclined to obtain information from others indiscriminately and be locked into relationships. this may influence the individual's information processing capability. in the literature, trust propensity has attracted the attention of scholars seeking to explain not only the offline behavior of individuals, but also online behavior in social media platforms and virtual communities (lu et al., ; warren et al., ) . in social media, network associates are mostly connected through weak ties representing lack of trust and reciprocity. the existence of significant weak ties in social media makes the role of individual trust propensity critical. we believe trust propensity in social media moderates the impact of individuals' social media use on entrepreneurial entry by influencing their ability to network with strangers and known associates. further, prior findings in the literature suggest that trust influences entrepreneurial information searching and processing (keszey, ; molina-morales et al., ; wang et al., ) . this supports the possibility of trust propensity as the moderator of the link between social media use and entrepreneurial entry. in social media, the trust propensity of an individual influences their interaction and behavior (lu et al., ) . accordingly, an individual with a high trust propensity is more inclined to trust others. however, the trust in the relationship may not be mutual as the transacting party may lack the same trust propensity. as a result, the individual may fail to generate identical trust from the other individual thereby limiting the benefits of the relationship. with the aid of social media, an individual has the ability to access a large network of weak ties with remote individuals. this may allow the individual to obtain and validate information crucial to formalizing and finalizing an entrepreneurial idea. however, the advantage of higher social capital from access to a large network on social media may be eroded when individuals have a high trust propensity due to multiple factors. first, the network associates of individuals on social media vary significantly in terms of their trust propensity. the variations in the trust propensity of associates may result in them providing information via social media that may not always be reliable. in particular, network associates with low trust propensity may be reluctant to share valuable information. individuals with high trust propensity will treat a network associate and the information they provide with trust and without suspicion (peralta & saldanha, ; wang et al., ) . as a result, social media users may be exposed to both true and false information from associates. thus, such individuals are more likely to experience greater obstacles in distinguishing reliable information from unreliable noise, thereby incurring significantly higher information and resource search costs. the higher cost may hinder formation and finalization of an entrepreneurial idea and may hamper entrepreneurial entry. alternatively, individuals with low trust propensity are more likely to be more cautious (choi, ) . such individuals, due to their cautious attitude, are less likely to experience noise in their information and resource search, and thus may find it easier to distinguish reliable information from w. wang, et al. technological forecasting & social change ( ) unreliable information. as a result, the cost (i.e., monetary, labor, and time) of obtaining information and resources for such individuals is lower, which may significantly enhance the probability of entrepreneurial entry. second, in social interactions and transactions trust may trigger a lock-in effect (molina-morales et al., ) . the lock-in effect refers to a scenario where high trust propensity individuals interact only with a few trusted associates on social media. the lock-in effect prevents the individuals from benefiting from a higher social capital on social media. thus, a lock-in effect may significantly limit individuals' information and resource search to a limited number of associates, which may significantly impair development and formation of their entrepreneurial idea, and ultimately entrepreneurial entry. however, individuals with low trust propensity are less likely to suffer from the lock-in effect thereby increasing their probability of entrepreneurial entry. thus, we hypothesize: h . trust propensity moderates the relationship between social media use and entrepreneurial entry. we tested our proposed model on a sample of adults in china, a country with the world's largest population and the second highest total gross domestic product. china provides a rich setting for examining the link between social media and entrepreneurial entry for multiple reasons. first, china has experienced exponential growth in entrepreneurship and private enterprise development unleashed by economic transition (he et al., ) . the resulting entrepreneurial intensity provides a suitable context for investigating entrepreneurial phenomena including entrepreneurial entry. second, in china the adoption and use of social media is widespread with the world's largest number of users of internet (li et al., ) . the major american-based social media platforms, such as facebook, twitter, and instagram, were inaccessible in china at the time of the study (makri & schlegelmilch, ) , and people in china use other social media, such as wechat, qq, and sina weibo, which mirror or are similar to the american social media platforms (li et al., ) . our data is from the surveys of china family panel studies (cfps). cfps is a nationally representative longitudinal survey conducted every two years since by the institute of social science survey at peking university (xie & hu, ) . the cfps covers % of the chinese population in provinces, providing extensive individual-and familylevel economic and social life information. the data from cfps has been validated and used for research in entrepreneurship (barnett et al., ) and other fields (hou et al., ; sun et al., ) . the survey, first conducted in , had three follow-up waves in , , and . our study used data from the and waves, which started including variables on internet activities. the survey contains , observations from , families. we matched the samples in and through a unique identifier of the respondents. as our study focuses on the transition of an individual to an entrepreneur, we excluded respondents who had entrepreneurial entry, and our final study sample had , observations. entrepreneurial entry. the cpfs survey followed existing literature to operationalize entrepreneurial entry, an individual's entry into entrepreneurship, by whether (s)he started a business or became selfemployed (barnett et al., ; eesley & wang, ) . accordingly, in the study, entrepreneurial entry refers to whether the respondents became entrepreneurs within the two years between the and surveys. specifically, the cpfs surveys had a multiple choice question on employment information, where participants chose their current employment status among: (a) agricultural work for your family, (b) agricultural work for other families, (c) employed, (d) individual/private business/other self-employment, and (e) non-agricultural casual workers. we used option d to operationalize entrepreneurial entry, following barnett et al. ( ) . if the respondent did not choose option d in year but chose option d in year , (s)he transitioned to self-employment in those two years, and we dummy coded this individual on entrepreneurial entry. social media use. a primary use of social media on the internet is socializing (bhimani et al., ; hu et al., ) . social media is the main online platform where people connect to each other and share information (bahri et al., ) . the cpfs survey measured social media use by asking, "in general, how frequently do you use the internet to socialize?". the respondents selected an option from the following: ( ) everyday, ( ) - times per week, ( ) - times per week, ( ) - times per month, ( ) once per month, ( ) once per a few months, and ( ) never. as the scale was inverted, we reverse recoded it as minus the selected option to obtain the measure of social media use. offline social network. offline social network refers to an individual's network of associates in the real world. scholars have used a variety of measures to assess the social network of an individual, including the cost of maintaining the relationship (du et al., ; lei et al., ) . in china, the context of our study, a social network is composed primarily of family, friends, and close acquaintances (barnett et al., ) . an important means of maintaining such relationships is through exchanging gifts during important festivals, wedding and funeral ceremonies, and other occasions. thus, scholars have used gift expenses and receipts in the previous year to assess social networks in china (barnett et al., ; lei et al., ) . we focused only on expenses incurred on gifts as the cost of maintaining an offline social network. hence, we operationalized offline social networks by the question on "expenditure on gifts for social relations in the past months" from the cpfs survey. given that the expenditure is an amount, we transformed it using its natural log (ln (expenditure + )) (lei et al., ) . trust propensity. following the guidance of previous studies (chen et al., ; volland, ) , the cpfs survey assessed trust propensity by a single item scale that asked the extent to which a respondent trusts others. the respondents indicated their preference on a - scale. the data for trust propensity is from the survey. controls. in statistical analysis, we controlled for respondent demographics such as gender, age, and education. as age can correlate to people's resource availability, experience, and willingness to assume risk in a nonlinear fashion, we followed prior research to include the squared term of age as a control variable (belda & cabrer-borrás, ) . given the possibility of personal and family income influencing an individual's ability to finance a start-up (cetindamar et al., ; edelman & yli-renko, ) , we included it as a control variable in the analysis. all control variables are from the survey. we report descriptive statistics along with correlations among the study variables in table . table shows there is significant correlation among study variables, with most of the correlation coefficients below . . the negative correlation between age and social media use, at . , is the only exception. given the reported correlation among study variables, we rule out the possibility of multicollinearity in the sample. we further confirmed our inference by calculating variance inflation factors (vif), which were well below the threshold level of with the highest vif being . . w. wang, et al. technological forecasting & social change ( ) we used stata and spss to test our hypotheses. in the regression models, we used ordinary least squares regression to predict offline social network and logit regression to predict entrepreneurial entry. we report the results of hypothesis testing in table . in the table, model shows the impact of social media use on offline social network. the regression coefficient suggests that social media use has a positive and significant (β= . , p< . ) influence on the offline social network consistent with hypothesis h . thus, it provides support for h . in table , models and provide support for hypotheses h and h . the results of model show the main effect of social media use on entrepreneurial entry is significant (β= . , p< . ), thus providing support for h . in model , when we add offline social network, the coefficient of social media use decreases (β= . , p< . ) and the coefficient of offline social network becomes significant (β= . , p< . ). meanwhile, the chi-squared statistics suggest that the model improved significantly (Δχ = . , p< . ). the results offer preliminary support for hypothesis h (baron & kenny, ) . we further confirm h by using the bootstrapping method due to its inherent advantages (hayes, ; kenny & judd, ; preacher & hayes, ) over the technique of baron and kenny ( ) . we apply bootstrapping with model in spss process (hayes, ) . with bootstrapping samples, the results show that social media use has an indirect effect on entrepreneurial entry (β= . , % confidence interval: . - . ) while the direct effect is also significant (β= . , % confidence interval: . - . ). thus, the results support hypothesis h . the moderating effect of trust propensity is also reported in model of table . in the table, the interaction of social media use and trust propensity is significant and negative (β=- . , p< . ) along with a significant change from model to model (Δχ = . , p< . ). this notes: n refers to the sample size. ⁎ p < . ; ⁎⁎ p < . ; ⁎⁎⁎ p < . . notes: n refers to the sample size. standard errors in parentheses. ⁎ p < . , ⁎⁎ p < . , ⁎⁎⁎ p < . w. wang, et al. technological forecasting & social change ( ) provides support for hypothesis h . in fig. , we depict the moderating effects, where social media use of high trust propensity individuals has a weaker impact on entrepreneurial entry. additionally, model displays the results for all study variables, suggesting it is robust. we performed additional robustness checks by using alternative measurements for social media use and trust propensity. first, as social media is a communication channel on the internet, we used an item measuring the degree of importance of the internet as a communication channel as an alternative measure of social media use. the results of the analysis with alternative measures are in table and are largely consistent with our original analysis except for the moderating effect of trust propensity. second, because a high trust propensity individual is more likely to trust others, and vice-versa for a low trust propensity individual, we used an alternative dichotomous measure of whether people are mostly trustworthy or cautious when getting along with others for trust propensity. the results of the analysis with the alternative measure of trust propensity are reported in table and offer support for the moderating effect of trust propensity. we assessed endogeneity issues using the two-stage least squares instrumental variables ( sls-iv) approach. there is a possibility that social media use may not be fully exogenous and could be under the influence of certain unobservable characteristics that also influence offline social network. following prior literature (semadeni et al., notes: standard errors in parentheses. the sample size n varies because less missing values on the alternative measurement. social media use is measured with the item "how important is the internet as a communication path?" the answer is scored on a - scale from "very unimportant" to "very important". ⁎ p < . , ⁎⁎ p < . , ⁎⁎⁎ p < . w. wang, et al. technological forecasting & social change ( ) ), we treated social media use as an endogenous variable and reassessed our results on offline social network. in our model, we identified two instruments to investigate potential endogeneity issues. to investigate endogeneity, we used two instrumental variables (iv): ( ) online work and ( ) online entertainment. we operationalized the two ivs through the frequency of using the internet to work and the frequency of using the internet to entertain, respectively. first, as people can work or entertain on social media, we suggest that these two ivs are correlated with social media use and satisfy the correlation with the endogenous variable. second, the ivs should not be directly correlated with the error terms of estimations on offline social network because learning and entertainment are not the direct social activity but instead the users aim to learn and to entertain. hence, online learning and entertainment should not directly impact offline social network in a strong manner. empirically, in the first stage result in model , the results of the instruments on the potentially endogenous variable are, by and large, significant, suggesting the relevance of the instruments. also, the results of cragg-donald f-statistics show that the instruments are strong (f= . ). moreover, the results of overidentification estimations suggest that the instruments are exogenous (sargan statistics p= . ) (semadeni et al., ) . thus, the results statistically suggest that both ivs satisfy the conditions of qualifications as ivs. last but not least, both durbin (p< . ) and wu-hausman (p< . ) tests confirm the endogeneity. the results of the iv estimation, reported in table , are similar to the previous result. the outcomes of the two-stage estimations are consistent with the regression outcomes in the previous analysis. these outcomes empirically confirm that social media use positively affects offline social network, even after considering the endogeneity issues. despite social media being dominated by weak ties and the substantial noise of false, inaccurate or even fake information, our findings reveal that individuals with higher social media use tend to conduct entrepreneurial entry. it is consistent with the positive benefits of higher social capital or a larger social network (galkina & chetty, ; johanson & vahlne, ). our results suggest that higher social media use indicates a higher probability of a larger social media (online) network, which provides higher social capital that benefits entrepreneurial entry. our findings that the positive influence of offline social network on entrepreneurial entry is also due to the network effect extends the research on the offline social networks of entrepreneurs (chell & baines, ; dubini & aldrich, ; klyver & foley, ) . the literature suggests that social networks influence entrepreneurs' decision making and actions, and entrepreneurs require a strong social network to succeed in the entrepreneurial process (jenssen & koenig, ; witt, ) . our findings, using instrumental variable analysis, suggest that higher social media use enhances individuals' offline social networks. this finding is consistent with past evidence that users often used social networking sites to connect with family and friends (subrahmanyam et al., ) . unlike past studies that simply indicate an overlap between social media and offline network associates (mcmillan and morrison ( ) ), our instrumental variable analysis helps to establish the impact of online networks on offline networks, suggesting social media enhances offline networks and subsequently entrepreneurial entry. specifying mediation models is essential to the advancement of research domains and hence this study helps research on social media in entrepreneurship to further develop beyond its nascent stage (yu et al., ) . finally, our finding that trust propensity moderates the influence of social media use on individuals' entrepreneurial entry suggests that social media, which is dominated by weak ties and substantial noise from false, inaccurate or even fake information, is in fact beneficial to entrepreneurial entry. such benefit may be smaller for people who are notes: standard errors in parentheses. the sample size n varies because less missing values on the alternative measurement. trust propensity is measured with the item "in general, do you think that most people are trustworthy, or it is better to take greater caution when getting along with other people?". we code for the answer "most people are trustworthy" and for "the greater caution, the better". ⁎ p < . , ⁎⁎ p < . , ⁎⁎⁎ p < . table the results of instrumental variable analysis (n = , ). more trusting. specifically, our findings indicate that an individual's trust propensity plays a critical role in their use of social media and the outcome they experience. our results have important implications for practice. first, as social media can help individuals build networks that help with business resources and information both locally and remotely, people can target social media to help refine and validate entrepreneurial ideas and secure much needed resources for entrepreneurial launch. second, as individuals' trust propensity enhances or hinders the positive role of social media on entrepreneurial entry, potential entrepreneurs may specifically aim to apply more caution to their online contacts to obtain higher benefit from social media use for entrepreneurial entry. finally, given the role of social media in entrepreneurship, social media platforms may more specifically promote and facilitate networking of individuals to increase the level of entrepreneurial activity that can be enhanced via social media. our study has limitations and offers opportunity for further inquiry. first, theoretically, we used social network theory, and another theoretical framework may identify other possible mechanisms. for instance, an identification based theory may argue that social media use's influence on entrepreneurial entry could also be attributed to identity change in individuals due to network associates as theorized by mahto and mcdowell ( ) . however, given the lack of information about network associates on social media, identity change may be a remote probability. empirically, we operationalized offline social networks using gift expenses that serve as a proxy for the offline social network. the large nationally representative survey we used contained only expenditure on family relationships, yet individuals also need to expend similarly on gifts, eating out, etc. to maintain relationships with work acquaintances, partners, clients, former school mates, distant relatives, etc. hence, the expenditure on other relationships may mirror the expenditure on family relationships captured by this survey. we acknowledge these limitations and call for future research to search for alternative measures of social networks in other datasets. third, we caution readers in generalizing the findings of our study outside of china due to the study sample. china is different from other countries in terms of its cultural, legal, and social environment, which may affect respondent behavior on social media and entrepreneurial launch. thus, we suggest scholars empirically examine our model in other cultures. our study addresses the effect of social media on the entrepreneurship process, especially the pre-launch phase, by assessing the link between social media use and entrepreneurial entry. we use social capital theory to explain the link between social media use and entrepreneurial entry. we further argue that this relationship is contingent on individuals' trust propensity. thus, individuals with low trust propensity are more likely to benefit from social media use for entrepreneurial entry compared to individuals with high trust propensity. we also find that social media use strengthens individuals' offline social networks, which further aids their entrepreneurial entry. in conclusion, a key message is that social media can help individuals' transition to entrepreneurship. and practice, journal of applied psychology, journal of small business management, and family business review, etc. raj serves on editorial review boards of family business review and international entrepreneurship and management journal. he is also an associate editor of the journal of small business strategy and journal of small business management. wei deng is a phd candidate major in organization management at school of management, xi'an jiaotong university. his research interests include social entrepreneurship, entrepreneurial bricolage, and female entrepreneurship. his research has been published in journal of business research, asia pacific journal of management, and others. stephen x. zhang is an associate professor of entrepreneurship and innovation at the university of adelaide. he studies how entrepreneurs and top management teams behave under uncertainties, such as the impact of major uncertainties in the contemporary world (e.g. covid- and ai) on people's lives and work. such research has also given stephen opportunities to raise more than us$ . million of grants in several countries. prior to his academic career, stephen has worked 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introduction to the china family panel studies (cfps). chin individual-level ambidexterity and entrepreneurial entry entrepreneurship in international business: an institutional perspective consequences of downward envy: a model of selfesteem threat, abusive supervision, and supervisory leader self-improvement key: cord- - brblfq authors: mao, liang title: modeling triple-diffusions of infectious diseases, information, and preventive behaviors through a metropolitan social network—an agent-based simulation date: - - journal: appl geogr doi: . /j.apgeog. . . sha: doc_id: cord_uid: brblfq a typical epidemic often involves the transmission of a disease, the flow of information regarding the disease, and the spread of human preventive behaviors against the disease. these three processes diffuse simultaneously through human social networks, and interact with one another, forming negative and positive feedback loops in the complex human-disease systems. few studies, however, have been devoted to coupling all the three diffusions together and representing their interactions. to fill the knowledge gap, this article proposes a spatially explicit agent-based model to simulate a triple-diffusion process in a metropolitan area of million people. the individual-based approach, network model, behavioral theories, and stochastic processes are used to formulate the three diffusions and integrate them together. compared to the observed facts, the model results reasonably replicate the trends of influenza spread and information propagation. the model thus could be a valid and effective tool to evaluate information/behavior-based intervention strategies. besides its implications to the public health, the research findings also contribute to network modeling, systems science, and medical geography. recent outbreaks of infectious diseases, such as the h n flu, bird flu, and severe acute respiratory syndrome (sars), have brought images of empty streets and people wearing face masks to television screens and web pages, as fear of unknown diseases swept around the globe (funk, salathé, & jansen, ) . these images depict three basic components of epidemics, namely infectious diseases, information about diseases, and human preventive behavior against diseases. from a perspective of diffusion theory, each of the three components can be viewed as a spreading process throughout a population. the disease could be transmitted through person-to-person contact, the information is circulated by communication channels, and the preventive behavior can spread via the 'social contagion' process, such as the observational learning. the interactions among these three diffusion processes shape the scale and dynamics of epidemics (funk & jansen, ; lau et al., ; mao & yang, ) . mathematical and computational models have been extensively used by health policy makers to predict and control disease epidemics. a majority of existing models have been focused on the diffusion of diseases alone, assuming a 'passive' population that would not respond to diseases (bian et al., ; eubank et al., ; longini, halloran, nizam, & yang, ) . this is rarely the case because it is natural for people to protect themselves when realizing disease risks (eames, tilston, brooks-pollock, & edmunds, ; ferguson, ) . to improve, there has been much recent interest in modeling two diffusion processes in an epidemic, either a behavior-disease diffusion (house, ; mao & bian, ; vardavas, breban, & blower, ) , or an information (awareness)-disease diffusion (funk, gilad, watkins, & jansen, ; kiss, cassell, recker, & simon, ) . these 'dual-diffusion' models have made a remarkable progress toward the reality, but none of them consider all the three diffusion processes together. the third diffusion process has often been neglected or simplified. in the current literature, few modeling efforts have been devoted to explicitly representing all the three components, their spreading processes, and interactions. the lack of such models prevents researchers from unveiling a full picture of an epidemic, and inevitably introduces biases into the deep understanding on human-disease systems. for epidemiologists, it is of difficulty to explore how one diffusion process influences the other two, and what key factors govern the three diffusion processes. without a complete model, health policy makers would not be able to systematically evaluate social-network interventions for disease control, such as mass-media campaigns and behavior promotion strategies. as in the age of information, the fusion of diseasebehavior-information in epidemic modeling becomes a pressing task in public health. to fill the knowledge deficit, this research proposes a conceptual framework to integrate the three diffusion processes, and develops a triple-diffusion model in a realistic urban area. following sections discuss the conceptualization, formulation, and implementation of the model, and evaluate the simulation results. the proposed model conceptualizes a typical epidemic as one network structure, three paralleling diffusion processes, and three external factors (fig. ) . first, the contacts among individuals form a network structure as a basis for diffusion and interaction. second, infectious diseases are transmitted through direct contacts among individuals (the middle layer). disease control strategies, such as vaccination program, case treatment and isolation, pose external effects on the disease diffusion. third, the diffusion of diseases prompts the "word-of-mouth" discussion among individuals, which disseminates the information concerning diseases and prevention (the upper layer). the outbreak of diseases may also stimulate various mass media, such as tv, newspapers, and radio, to propagate relevant information, thus accelerating the diffusion of information. fourth, people being informed start to consider and make a decision toward the adoption of preventive behaviors. the adoptive behavior of individuals also influences their network neighbors to adopt, widely known as the "social contagion" effects (the lower layer). the diffusion of preventive behaviors, in turn, limits the dispersion of diseases and speeds the diffusion of information. behavioral interventions, as an external factor, can be implemented by health agencies to promote preventive behaviors, such as educational, incentive and role-model strategies. during an epidemic, these three diffusion processes interact with one another and form negative/positive feedbacks loops in the human-disease system, shown as arrows between layers in fig. . manipulated by the three external factors, these three diffusion processes, hereinafter named as the triple-diffusion process, determine the spatial and temporal dynamics of an epidemic. the conceptual model is formulated by an agent-based approach, which has gained its momentum in epidemic modeling during the last decade huang, sun, hsieh, & lin, ) . different from classic population-based models, each individual in a population is a basic modeling unit, associated with a number of attributes and events that change the attributes. to represent the contact network, individuals are modeled as nodes and are linked to one another through their daily contacts (as network ties). the individualized contacts are assumed to take place during three time periods in a day at four types of locations (mao & bian, ) , namely the daytime at workplaces, the nighttime at homes, and the pastime at service places or neighbor households (fig. ) . individuals travel between the three time periods and the four types of locations to carry out their daily activities, thus having contact with different groups of individuals and exposing themselves to disease infection. these contacts link all individuals into a population-wide network. two types of individual contacts are modeled in terms of the contact duration and closeness. one type is the close contacts (solid-line ovals in fig. ) that happen at homes (with family members), workplaces (with co-workers), and neighbor households (with friends). this type of contacts last for sufficient time to enable disease transmission. the other type refers to the occasional contacts (dash-line ovals in fig. ) that only happen at service places (with clerks and other consumers). in this case, an individual encounters only a limited number of individuals for a short time period, and thus the contact is less effective for infection. the diffusion of infectious diseases is formulated following the concept of classic susceptible-infectious-recovered (sir) model (anderson & may, ) . each individual possesses a serial of infection states and events as shown in fig. (the red dash-line box, in the web version). the progress of an infectious disease starts with a "susceptible" individual, who may receive infectious agents if having contact with an infectious neighbor in the network. the receipt event triggers a "latent" state, during which the disease agents develop internally in the body and are not emitted. the end of latent period initiates an "infectious" state, in which this individual is able to infect other susceptible neighbors and sustain the cascade of infection in the network. during the infectious period, individual may manifest disease symptoms ("symptomatic") or not ("asymptomatic"). for either state, this individual remains infectious but would be unaware of the infection if asymptomatic. after the infectious period, this individual gets recovered and is assumed to be immune to infection during this epidemic. two disease events connect the disease diffusion with other diffusions. first, the event of symptom manifestation will motivate individuals to discuss disease information, and prompt their social contacts to adopt preventive behavior by posing infection risks. the second event is the receipt of disease agents, which is affected by the diffusion of preventive behavior. specifically, the adoption of preventive behavior reduces the probability of disease transmission p, as specified in equation ( ): and e prevention are three model parameters varying in [ , ]. e contact indicates the effectiveness of a contact to transmit diseases, dependent on the physical closeness of the contact. its value can be calibrated based on the observed characteristics of a disease, such as the basic reproductive number r . i age is an age-specific infection rate, specifying the likelihood of receiving disease agents by age group, such as children, adults and seniors. e prevention indicates the efficacy of a preventive behavior in reducing infection. the parameterization is discussed later in the model implementation (simulating the diffusion of disease section and simulating the diffusion of preventive behavior section) when a specific disease and a specific preventive behavior are selected. regarding to the diffusion of information (blue dash-line box in fig. , in the web version), individuals are initially "unaware" of the disease, but can be "informed" through two channels: the word-ofmouth discussion and the mass media. the former circulates the information locally through the contact network, while the latter disseminates the information globally in the population, both modeled as probabilistic events. first, an informed or symptomatic individual will discuss the disease with each network neighbor at a rate g discussion , as formulated in equation ( ): where t is the current time step and t is the starting time of being informed or manifesting symptoms. the discussion rate g discussion decays nonlinearly as time proceeds, i.e., an individual is more likely to talk about the disease within a few days after being informed or feeling sick. turning to the mass media, the probability of an individual being informed g mass is formulated as a function of total symptomatic case number n s (t) at time step t (equation ( )): the more individuals get sick during the time t, the higher the intensity of mass-media propagation, and thus the greater chance for an individual being informed. the constant b is a scaling parameter that controls the intensity of mass-media propagation, and a small b results in a large g mass . a mass-media campaign then can be modeled by varying the b, the timing of campaign (when to start), and the frequency of campaign (time intervals between two broadcastings). once informed by either the discussion or the mass media, individuals will become decision makers toward the adoption of preventive behavior. in such a manner, the diffusion of information is coupled with the diffusion of disease and that of preventive behavior. individuals being informed start to evaluate and make a decision toward the adoption of preventive behavior (green dash-line box in fig. , in the web version). the decision depends on individuals' own characteristics and inter-personal influence from their social networks. this research uses a threshold behavioral model (granovetter & soong, ) to formulate the decision process. specifically, each individual has two adoption states, and the change of state is calculated based on equation ( ) for a given time step t, individual i will evaluate the proportion of adopters in i's personal network, as the peer pressure of adoption a i (t). once the peer pressure reaches a threshold t p;i (called the threshold of adoption pressure), an individual will decide to adopt. meanwhile, individual i also evaluates the proportion of symptomatic individuals in the personal network, as the perceive risks of infection m i (t). if the perceived risk exceeds another threshold t r;i (termed the threshold of infection risk), an individual will also adopt. the individualized thresholds (t p;i and t r;i ) reflect personal characteristics of individuals, while the events of evaluation represent the inter-personal influence between individuals. in such a way, the diffusion of disease elevates the perceived risks of individuals, and stimulates them to adopt preventive behavior. in turn, the adoption of preventive behavior impedes the diffusion of disease, forming a negative feedback loop in the human-disease system. the proposed triple-diffusion model is implemented in the greater buffalo metropolitan area, ny, usa, with a population of , (according to census ) . each individual is programmed into a software agent with attributes and events (table ) . besides a unique identifier, each individual has groups of attributes, including the network, demographic, spatiotemporal, infection, adoption, and information attributes. the events change the values of corresponding attributes. the social network is realized by a previously developed algorithm that assigns values to the demographic and network attributes of individuals (mao & bian, ) . the value assignment involves a large amount of geo-referenced data, including census data, business location data, land parcel data, transportation network, and results of a household travel survey. statistical distributions derived from these datasets, such as distributions of family size, workplace size, and household daily trips, are used to ensure the validity of value assignments. to differentiate the weekdays and weekends, individuals are not assigned to work (or schools) at weekends except those who work in service-oriented businesses (such as restaurants and grocery stores). those who do not work during the weekends would have increased trips to service-oriented businesses. the completion of assignments forms three linked populations, including a nighttime population at homes, a daytime population at workplaces, and a pastime population at service places or neighbor households. the three populations represent the same set of individuals, but at different locations and time periods of a day. individuals have contact with a number of other individuals at a same time period and same location, forming a spatio-temporally varying network. the simulated network has an average of . daily contacts per person, consistent with the observed number ( . ) from empirical studies (beutels, shkedy, aerts, & van damme, ; edmunds, ; fu, ) . the seasonal influenza is selected as an example due to its natural history has been well understood. a number of influenza parameters are either adopted or calibrated from existing literature as shown in table . the product of i age and e contact determines the transmission probability through one contact (equation ( )), which is used to simulate individuals' transition from susceptible to latent state as a stochastic branching process. the latent, incubation, and infectious periods control the sequential transitions from latent to infectious, symptomatic, and recovered states. two groups of parameters are set to simulate the word-ofmouth discussion and the mass-media effects, respectively. the parameter values are calibrated from the model evaluation later but are reported here. for the word-of-mouth discussion, the initial discussion rate g discussion ( ) in equation ( ) is set to . , and then the g discussion (t) is updated as the time goes by. for the mass media, the scaling parameter b in equation ( ) is specified as , based on which the probability of being informed by mass media g mass can be computed at every time step. the mass-media campaign is assumed to be triggered when the total symptomatic individuals exceed & of the total population, and the frequency of broadcasting follows a weekly basis. with these two probabilities, a monte-carlo simulation is used to determine whether an unaware individual will be informed or not at each time step. the use of flu prophylaxis (e.g., oseltamivir) is taken as a typical example of preventive behavior, because its efficacy is more conclusive than other preventive behaviors, such as hand washing and facemask wearing. three parameters are specified to simulate the behavioral diffusion and couple it with the diffusion of influenza. first, the model assumes that symptomatic individuals has a % likelihood to adopt flu prophylaxis to mitigate the symptoms and reduce their infectivity (mcisaac, levine, & goel, ) . second, the preventive efficacy of flu prophylaxis (e prevention in equation ( )) is set to % and % for susceptible and infectious individuals, respectively, indicating that their likelihood of being infected or infecting others can be reduced by such amount (hayden, ; longini et al., ) . third, the two adoptive thresholds of individuals t p;i and t r;i (in equation ( )) are generated from their statistical distributions using a monte-carlo method. those statistical distributions were derived based on a health behavioral survey, whose details are provided in the supplementary document. each individual is assigned to random numbers from those statistical distributions as their adoptive thresholds. for each time step, the model computes the peer pressure and perceived risk for every informed individual, and updates his/her adoption state using the threshold model. the triple-diffusion model is simulated over days, covering a general flu season (from december to may). at the beginning of simulation, all individuals are assigned susceptible and unaware states. to consider a background immunity before the epidemic, the model randomly selects . % of seniors, . % of adults, and . % of children according to the national immunization coverage (euler et al., ; molinari et al., ) , and directly moves them to the adopted and recovered states. all unselected individuals are set as non-adopters. to initialize the disease diffusion, five infectious individuals are randomly introduced into the study area at the first day. the simulation takes a tri-daily time step and runs the three diffusion processes concurrently in each time step. to stabilize the final outcomes, the model has been implemented by realizations. in each realization, the background immunity, the first five infectious individuals, their contacts, and the infection, awareness, and adoption of these contacts are randomized. the final outcomes are three diffusion curves, namely the epidemic curve (the weekly number of new cases), the adoption curve (the weekly number of new adopters), and the awareness curve (the weekly number of newly informed), all averaged from model realizations. two independent data sources are used to evaluate the model results and calibrate model parameters. one is the weekly reports of laboratory confirmed specimens in the e in buffalo, ny, issued by the new york state department of health (nysdoh, ) . the simulated epidemic curve is compared to the weekly reported data to show the validity of modeling disease diffusion. the other data source is the weekly statistics from google flu trends of the study area (google, ) , which summarizes the number of online flu-related inquires as a tool for monitoring influenza outbreaks (ginsberg et al., ) . relevant to this research, the weekly flu trend data could be a reliable representation to the real diffusion of influenza-related information (fenichel, kuminoff, & chowell, ) , and is compared to the simulated awareness curve from the model. model result evaluation fig. displays the simulated weekly number of newly infected individuals, compared to the actual number of weekly labconfirmed cases during the e influenza season. the shape and peak time of the predicted curve correspond well with those of the reported epidemic, although the magnitude of simulated cases is much larger than the reported data. the first possible reason is that many sick people may choose self-care instead of seeing a doctor, and thus cannot be reported. second, for those who seek healthcare, only a small portion of their specimens were submitted for laboratory testing. therefore, the number of influenza cases is often highly under-reported, and a complete data is rather difficult to collect. the laboratory data, so far, is the best available touchstone for model validation. in this sense, the model performs well in predicting the trend, and at least allows the estimate of a worse case result. fig. compares the simulated weekly number of newly informed people to the excessive weekly google flu search statistics that indicate the amount of online searching behavior relevant to influenza epidemic during the e flu season. the excessive weekly search statistic (the left y axis) is the difference between the observed statistics and its long-term average ( ), which removes searches of influenza in a normal day but not caused by the epidemic. the temporal course of the information diffusion is well predicted. since the two measurements are not in a same unit (primary and secondary axis in fig. ), their magnitudes are not comparable but are highly correlated. to my knowledge, both comparisons show a level of consistency that has rarely been achieved by other epidemic models (ferguson et al., ; funk et al., ; kiss et al., ; vardavas et al., ) . a majority of previous models cannot validate themselves by observed facts, particularly for the information diffusion. the triple-diffusion model, thus, could provide a reliable foundation to devise much-needed control and intervention strategies for infectious diseases, such as behavior promotion strategies and massmedia campaigns. fig. shows how the diffusion of influenza motivates people to adopt preventive behavior. the two diffusion processes take a similar shape, but there is a time lag about week between their peak times. as the number of influenza cases rises, individuals perceive increasing risks, which motivate them to adopt preventive behavior. their adoptive behavior further influences surrounding individuals to adopt. the time lag between the epidemic and adoption curves is possibly the time individuals need to be informed and take preventive actions. fig. also suggests that monitoring the real-time flu prophylaxis sales could detect the epidemic peak about week ahead of the traditional disease surveillance networks, such as the cdc sentinel network, which take up to weeks to collect, process, and report disease cases registered at health centers. the diffusions of influenza and its related information also take a similar bell-shape, but the information peaked approximately one week earlier than the disease (fig. ) . a possible reason is the wide coverage of modern mass media over the population, enabling a faster spread of information than the disease. at the beginning of the epidemic, only a few influenza cases occurred and a vast majority of people were unaware of the disease. as the diffusion of influenza took off (january nde th), individuals started to notice the disease problem and discuss with each other. when the epidemic became more sensational and drawn attention from the mass media (january the th), the awareness curve climbed steeply and reached the peak in four weeks. fig. implies that overseeing the diffusion of disease information, such as the google flu trend, could warn the public e week earlier before the epidemic peak actually occurs. in addition to forecasting the timeline of the three diffusion processes, this spatially explicit model allows the prediction of geographic distributions over time. fig. maps the spatial distributions of simulated infection (square), adoption (circle), and awareness (triangle) are mapped. for the purpose of clarity, only the downtown area is presented. the spatial distributions on days , , and are displayed in order to present different stages of the epidemic. on day the epidemic is on the rise, day is around the peak time, and on day , the epidemic is in decline. still in its infancy, the triple-diffusion model has several limitations in its design and implementation. first, the contact network used in the model could be further refined into three different but partially overlapping networks, namely an infection network, information network, and influential network, each channels a diffusion process. admittedly, the model would be more realistic, but building these networks requires extensive social survey to collect relevant data, which is often costly and time consuming. recent work on extracting social networks from facebook and twitter may be a promising method to address this issue (lewis, kaufman, gonzalez, wimmer, & christakis, ) . second, the effects of mass media is formulated as a simple formula, but could be more complicated if further considering various types of media and their corresponding coverage. probably, a sophisticated function could depict the human communications better, such as an exponential decay or a power-law decay function. life style data of individuals may be helpful to identify their preferred media and delineate the media coverage. third, the discussion rate is assumed homogenous over the study area. this rate may vary between age groups, occupations, and personalities. a health behavior survey may need to estimate discussion rates for different groups of individuals. fourth, there would be a certain amount of uncertainty if the model was used to predict the future influenza outbreaks. if new census data and travel survey data were filled in, this model could reasonably predict the timeline and scale of a future outbreak of seasonal influenza. however, for a pandemic influenza, such as the new h n , most of the model parameters should be adjusted to account for the highly infectious virus, the faster circulation of information, and possibly distinct response of individuals toward preventive behaviors. all these limitations warrant a future study. after all, the goal of modeling is not to predict what exactly happen during an epidemic, but rather to observe how the epidemic may proceed and encourage appropriate questions. in this sense, the model results provide valuable knowledge regarding city-wide epidemics. this article presents an original triple-diffusion model for epidemiology, and discusses its conceptual framework and design. the conceptual framework integrates three interactive processes: the diffusion of influenza, the diffusion of information, and that of preventive behavior, upon a human social network. the agentbased approach, network model, theories from epidemiology, information and behavioral sciences are used to formulate the conceptual framework into a working model. for illustration purposes, the model is implemented in an urbanized area with a large population. compared to the reported data, the proposed model reasonably replicates the observed trends of influenza infection and online query frequency. the model, thus, could be a valid and effective tool for exploring various control policies. there are two key contributions of this research to the literature body of network diffusion theory, public health, and agent-based modeling. first, the proposed triple-diffusion framework is a significant advancement to previous disease-only models and dualdiffusion models, such as bian and mao's work. the fusion of disease, information, and human behavior allows a more comprehensive d cubic view of the human-disease system, which can only be studied from a d planar perspective before. the increase of one dimension exposes much more details of an epidemic and thus enables a deeper understanding of this complex system, for example, the interactive mechanisms among the three diffusion processes. the proposed modeling framework can flexibly accommodate the mobile phone tracking data and the latest census data to improve the accuracy of modeled daytime and nighttime populations. the online social networking data (from facebook and twitter) can also be included to modify the way of communications between individuals, as well as the personal influence between them. second, this model can be further developed into a virtual platform for health decision makers to test disease control policies in many other metropolitan areas. particularly, since the model explicitly represents the diffusion of information and human preventive behavior, it permits a systematic evaluation of disease control policies that have not been well studied before, such as the mass-media campaigns and behavioral incentive strategies. the evaluation results will enrich the family of disease control polices, and help the public health overcome the socio-economic challenges posed by potential influenza outbreaks. infectious diseases of humans: dynamics and control social mixing patterns for transmission models of close contact infections: exploring self-evaluation and diary-based data collection through a web-based interface modeling individual vulnerability to communicable diseases: a 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framework for epidemic modeling visits by adults to family physicians for the common cold transmissibility of pandemic influenza the annual impact of seasonal influenza in the us: measuring disease burden and costs can influenza epidemics be prevented by voluntary vaccination supplementary data related to this article can be found at http:// dx.doi.org/ . /j.apgeog. . . . key: cord- -vcm v ix authors: pollmann, michael title: causal inference for spatial treatments date: - - journal: nan doi: nan sha: doc_id: cord_uid: vcm v ix i propose a framework, estimators, and inference procedures for the analysis of causal effects in a setting with spatial treatments. many events and policies (treatments), such as opening of businesses, building of hospitals, and sources of pollution, occur at specific spatial locations, with researchers interested in their effects on nearby individuals or businesses (outcome units). however, the existing treatment effects literature primarily considers treatments that could be assigned directly at the level of the outcome units, potentially with spillover effects. i approach the spatial treatment setting from a similar experimental perspective: what ideal experiment would we design to estimate the causal effects of spatial treatments? this perspective motivates a comparison between individuals near realized treatment locations and individuals near unrealized candidate locations, which is distinct from current empirical practice. furthermore, i show how to find such candidate locations and apply the proposed methods with observational data. i apply the proposed methods to study the causal effects of grocery stores on foot traffic to nearby businesses during covid- lockdowns. how can we do causal inference with spatial treatments? in the setting of this paper, a spatial treatment, such as the opening of a "million dollar plant" (greenstone and moretti, ; greenstone et al., ) occurs at a geographic location, and the outcome of interest, such as earnings, is measured for separate individuals who are located nearby. this distinction between units of treatment assignment and outcome units has received little attention in theoretical work in causal inference. in the absence of guidance from theoretical work, most recent empirical studies using highly-detailed location data rely on adaptations of the familiar difference-in-differences method. unfortunately, these adaptations to the spatial treatment setting implicitly either rely heavily on functional form assumptions or on partly incongruent nonparametric assumptions to identify causal effects. this is in stark contrast to settings with individual-level treatments, where many researchers prefer causal inference based on quasi-experimental methods with simpler, more transparent assumptions, that obtain credibility by emulating an "ideal experiment" the researcher wished to have run. in this paper, i propose (quasi-) experimental methods for spatial treatments that are motivated by an ideal experiment where the spatial locations of treatments are random. these methods are based on a simple insight: suppose the ideal experiment randomly chooses some locations from a larger set of candidate locations. then quasi-experimental methods should compare individuals near locations that are chosen to individuals near locations that were not chosen for treatment. for a formal characterization of estimands and estimators, i extend the potential outcomes framework for individual-level treatments to allow treatments to be randomized across space and to directly affect nearby individuals. within this framework, i derive finite sample design-based standard errors similar to those of neyman ( neyman ( , for randomized experiments with individual-level treatment assignment for a fixed population. in the "million dollar plant" example, my proposals using micro location data are analogous to the approach greenstone and moretti ( ) take with aggregate data, while most current empirical work takes a conceptually distinct approach. suppose we want to estimate the average effect of a million dollar plant on individuals who are, say, mile away. the method employed by most recent empirical work compares individuals on an "inner ring" around the million dollar plant with radius mile to individuals on an "outer ring," who are, say, miles away from the same million dollar plant. since many observable and unobservable characteristics correlate with distance from any one point in space (lee and ogburn, ; kelly, ) , this comparison of inner and outer ring is often unattractive: if treatment always occurs in the city center, the inner ring, or treated, individuals are urban individuals, while the outer ring, or control, individuals are suburban and rural individuals. researchers attempt to ameliorate this issue by adding a pre vs. post comparison in a difference-in-differences approach, where outcomes for urban and suburban individuals are allowed to be on different levels, but must evolve along parallel trends. in contrast, greenstone and moretti ( ) take a different approach with data aggregated at the county level. they compare counties that "won" the bidding war for a million dollar plant to "runners-up" counties that were also very seriously considered as locations for million dollar plants, but ultimately "lost" (greenstone and moretti, ) . in short, the methods i propose compare individuals who are mile away from the million dollar plants to individuals who are mile away from locations that would have been chosen for the plants in the losing counties. since these counterfactual locations are rarely known in observational studies, i show how to find suitable candidate locations in practice. with micro location data, the methods then estimate the same detailed estimands targeted by the difference-in-differences approach. they have an attractive quasi-experimental interpretation and are valid by design if the choice of treatment location is as good as random within a set of plausible candidate locations. the difference-in-differences approach of current empirical practice relies on either partly incongruent nonparametric or functional form assumptions that are not guaranteed to be satisfied even in a true randomized experiment. the comparison of individuals on an inner ring to those on an outer ring inherently makes two assumptions: first, the treatment must not affect individuals on the outer ring directly. this is most easily achieved by choosing an outer ring with large radius, such that these "control" individuals are far away. second, the individuals on inner and outer rings must be comparable. this is most easily achieved by choosing an outer ring close to the inner ring, in conflict with the first assumption. even when the differences in levels between inner and outer ring are differenced out with individual fixed effects in panel data, the parallel trends assumption is particularly strong in spatial treatment settings. suppose, for instance, that treatment only occurs in city centers. then the assumption may require individuals living in downtown areas to be on parallel trends to those on the outskirts of the city. furthermore, researchers typically estimate the effect not just at one distance but at multiple distances, typically using the same outer ring control group. this effectively requires that individuals at all distances up to the outer ring are on the same parallel trend, with additively separable time fixed effects. these assumptions are not just approximations to make finite sample analysis feasible where asymptotically an analogous nonparametric specification identifies treatment effects: identification in this approach rests upon the functional form assumptions even asymptotically, and even with experimental data. instead, i recommend estimators that are formally valid under the quasi-experimental variation in treatment location sometimes used to informally justify the assumptions of the difference-in-differences approach. the difference-in-differences approach generally yields the most credible estimates if the treatment is known not to have an effect past a short, known, distance. then individuals on the outer ring are likely to be comparable. sometimes, these comparisons are then justified by the fact that the exact location of the treatment was as good as random. for instance, (linden and rockoff, , p. ) , referencing bayer et al. ( ) , argue that for their treatment, sex offenders moving into neighborhoods, "the nature of the search for housing is also a largely random process at the local level. individuals may choose neighborhoods with specific characteristics, but, within a fraction of a mile, the exact locations available at the time individuals seek to move into a neighborhood are arguably exogenous." the estimators proposed in this paper allow researchers to make use of such credible identifying variation directly, rather than relying on an ultimately arbitrary outer ring. i demonstrate the quasi-experimental methods i propose in an application studying the causal effects of grocery stores on foot-traffic to nearby restaurants during covid- lockdowns in april of . in this application, i observe the exact spatial locations of grocery stores as well as other businesses in the san francisco bay area. i show how to find "control" neighborhoods that are similar to neighborhoods of actual grocery stores except for the absence of one marginal grocery store. the outcome of interest, foot-traffic to restaurants, is measured as the number of customers whose smarthphone location is shared with safegraph. i find that restaurants at distances of less than . miles from a grocery store have substantially more weekly customers than restaurants near counterfactual grocery store locations in comparable neighborhoods lacking the marginal grocery store. this suggests a positive externality of grocery stores on nearby businesses, akin to anchor stores in shopping malls, at least when customer mobility is reduced as during the covid- pandemic. while i argue in favor of a design-based, quasi-experimental approach in this paper, the difference-in-differences approach has its own advantages, such that both approaches are complementary. specifically, the comparison with an "outer ring" effectively removes time-specific noise that is shared within a larger region but distinct across regions. in contrast, the methods proposed in this paper focus mostly on eliminating confounding due to differences in the spatial neighborhoods, such as population density, of treated and control individuals. whether spatial variation, temporal variation, or functional form assumptions yield the most credible estimates of causal effects depends on the particular empirical setting. researchers may find studies particularly credible if several distinct identification strategies lead to similar conclusions. doubly-robust estimators (e.g. robins and rotnitzky, ; belloni et al., ) , which model both the outcome (conditional expectation) and assignment process (propensity score), may offer an attractive bridge between approaches. the framework developed in this paper allows me to extend the proposed methods to settings where multiple treatment locations are close to one another, as in the application to foot-traffic caused by grocery stores, which are often near other grocery stores. the existing difference-in-differences approach, in contrast, is not applicable when treatment locations are too close to one another. in the framework of this paper, i can allow for such interference between spatial treatments and illustrate the complications it causes. in recent work, zigler and papadogeorgou ( ) and aronow et al. ( ) specifically study such interference in a spatial treatment setting. they derive average effect estimands that are identified despite interference. in the present paper, i instead define the estimands of interest based on an ideal experiment that rules out interference by design. in extensions that complement the work by zigler and papadogeorgou ( ) and aronow et al. ( ) , i then discuss assumptions under which these estimands are identified even when there is interference. in addition, i demonstrate how to find additional candidate treatment locations, where treatment could have occurred but did not, with observational data, increasing the number of settings the proposed methods can be applied to. furthermore, i view the framework developed in this paper as particularly helpful for deriving standard errors of estimators of the effects of spatial treatments. by providing formulas for finite sample design-based standard errors, i sidestep the often difficult decisions regarding clustering and "spatially correlated errors" (e.g. conley, ) that arise in practice for virtually any application using spatial relationships between observations. aronow et al. ( ) also provide some design-based standard errors, but focus on asymptotic normality and sampling-based variances in the style of conley ( ) for the estimator most similar to the ones proposed in this paper. the results in their work therefore complement those in this paper. the interpretation of the standard errors i propose is simple: they reflect the variation in the estimator that arises from randomizing treatment locations, holding the individuals in the sample fixed. this is the same variation that is needed for internal validity of the causal effect estimates (abadie et al., ) . in the baseline setting, the variance estimators i derive are similar to clustering at the level of treatment assignment (abadie et al., ) . the approach i take in this paper, generalizes straightforwardly to settings with a contiguous region or multiple treatments close to one another. clustering, in contrast, is based on sharp, sometimes arbitrary, boundaries and the absence of interference between clusters. finally, the framework highlights nuances in interpretation that have received little attention in the literature thus far. most recent empirical work estimates the effects of spatial treatments at multiple distances. however, the average effects at different distances are not generally comparable. since some individuals are often more likely -before realization of treatment assignment -to be close to treatment locations, their treatment effects typically get more weight in average effect estimands at shorter distances, and less weight in average effect estimands at longer distances. in other words, we cannot generally interpret effect-by-distance curves or the change in effect between distances as average within-individual effects. even the aggregate weight placed on individuals near any one treatment location varies with distance. both of these effects can lead to estimates of average treatment effects that increase in distance, even though individual-level treatment effects are decreasing in distance for every individual. the framework in this paper allows me to characterize estimators with alternative weights on individuals to mitigate such issues. in addition, in this framework i can show how to aggregate individual-level treatment effects to estimate the aggregate effects of treatment at a location on all nearby individuals. the framework and methods discussed in this paper may also prove useful for causal inference questions not directly related to spatial treatments. first, other non-spatial settings also feature "treatments" that are not directly assigned to individuals but affect them based on some measure of distance. in this paper, i briefly discuss bartik ( ) -, or shift-share, instruments, where for instance industry-level shocks affect all cities depending on industry composition. the perspective taken in this paper resembles that of borusyak and hull ( ) , with non-random distances from candidate treatment locations but random variation in which candidate locations are realized. second, i develop an approach to finding suitable unrealized candidate locations in observational data based on flexible machine learning methods. this approach may extend to other settings with dependency between observations where it is sometimes challenging to find (good) control observations, such as event studies and other time series settings. third, separating treatment assignment and outcome individuals in this framework further clarifies distinctions between design-based and sampling-based inference (abadie et al., ) . while design-based inference captures variation in treatment locations, sampling-based inference can reflect sampling of individuals at fixed locations, within fixed regions (infill asymptotics (cressie, ) in the spatial statistics literature), of a growing contiguous space (expanding domain asymptotics (cressie, ) ), or of independent regions (clustering). the present paper focuses on design-based inference specifically; in-depth comparisons of different modes of inference are beyond its scope. my current analysis is limited in at least three important ways. first, i assume that outcome individuals have fixed locations. this is problematic if individuals move, or migrate, strategically in response to the treatment. second, the framework is not directly applicable to settings where we are interested in the causal effects of spatially correlated characteristics of places, such as in the literature on social mobility (e.g. chetty et al., ) . instead, the present paper focuses on treatments that occur at discrete locations in space. while the ideal experiment of randomizing treatment locations also creates a spatially correlated covariate of interest (distance from treatment), the randomization distribution it induces is much simpler to characterize. third, alternative estimators that are more robust or more efficient in certain settings may exist. while i attempt to offer theory and estimators for a variety of spatial treatment settings, the primary focus of this paper lies in developing a coherent conceptual framework that allows me to characterize, discuss, and exploit the ideal experiment with spatial treatments. in particular, the present paper provides no formal justification for the use of methods from the literature on sample splitting and double robustness (e.g. chernozhukov et al., ) . the need to consider many relative spatial locations for finding suitable unrealized candidate locations makes this a high-dimensional estimation problem in observational settings, suggesting the importance of methods and insights from that literature. the remainder of this paper is organized as follows. the final part of the introduction highlights the wide range of empirical applications for which this work is relevant, as well as connections to the theoretical literature. section develops a potential outcomes framework for spatial treatments. section contains the main results on identification, estimation, and inference under the ideal experiment. section discusses how to extend these results to additional settings of empirical relevance. section shifts the focus from experimental to observational data, proposing assumptions and methods that allow researchers to emulate the ideal experiment. section shows how to apply these methods in practice. in the conclusion, i discuss limitations of the present paper and fruitful directions for future research on causal inference for spatial treatments. empirical relevance the methods i propose are relevant for a diverse range of questions from many applied fields in economics and other social sciences. recent studies estimating the effects of spatial treatments using individual-level outcome and location data include stock ( stock ( , ; linden and rockoff ( ) ; currie et al. ( ) ; aliprantis and hartley ( ) ; sandler ( ); diamond and mcquade ( ) ; chalfin et al. ( ) ; rossin-slater et al. ( ) . notably, dell and olken ( ) explicitly consider counterfactual treatment locations in a quasi-experimental setting, as well as the permutation distribution based on counterfactual assignments. much more existing empirical work studying spatial treatments is limited to aggregated outcome data. if micro location data had been available for these studies at the time, researchers would likely have asked questions that can be answered using the methods i propose in this paper. experimental and observational studies of spatial treatments in economics using aggregate data fitting into the framework of this paper include duflo ( ) ; miguel and kremer ( ) ; cohen and dupas ( ) in development economics, greenstone et al. ( ); feyrer et al. ( ) public and labor economics, (jia, ) in industrial organization, and environmental economics (keiser and shapiro, ) . furthermore, a recent literature has documented large geographic variation in a diverse range of outcomes (for instance chetty et al., ; chetty and hendren, ; finkelstein et al., finkelstein et al., , bilal, ) . many potential sources or causes of this inequality, as well as many potential remedies such as place-based policies, involve spatial treatments. related theoretical literature this paper sits at the intersection of the literatures on causal inference, spatial statistics and econometrics. a small number of recent theoretical papers has similarly studied spatial treatments, albeit with a different focus. most closely related zigler and papadogeorgou ( ) , aronow et al. ( ), and imai et al. ( ) focus on settings with interference between treatment locations and show that only some average treatment effects are identified without additional semiparametric assumptions. in contrast, i define estimands of interest in a setting without interference, and discuss application-specific assumptions to retain identification of these estimands under interference. furthermore, i discuss a broader range of estimands and estimators, in particular for observational data where unrealized candidate treatment locations are rarely known. the simpler baseline setting also highlights interpretation and weighting issues that are obscured in the presence of interference. papadogeorgou et al. ( ) take a conceptually different approach. they develop a framework based on spatial point patterns (cf. cressie, ) rather than fixed units of observation to answer a distinct question. for them, the locations of outcome units vary with the treatment assignment, and the number of outcome units is the object of interest. instead of contrasting different treatment assignments to define effects, their estimand contrasts entire assignment mechanisms (stochastic interventions, muñoz and van der laan, ) . mcintosh ( ) proposes an estimator for settings where individuals known to be unaffected by the treatment exist as a natural group group. pouliot ( ) also studies a setting where the locations of outcomes and covariates are spatially misaligned, but not in the context of spatial treatments and causal inference. within the causal inference literature, the setting of this paper most closely relates to work on interference and networks. some work in causal inference explicitly considers spatially correlated treatments (delgado and florax, ; druckenmiller and hsiang, ) , but is not directly applicable to the patterns generated by spatial treatments. the literature on interference is concerned with spillover, or indirect, effects of treatments assigned to individuals in violation of the stable unit treatment value assumption (rosenbaum, ; hudgens and halloran, ; tchetgen tchetgen and vanderweele, ; aronow and samii, ; vazquez-bare, ; sävje et al., ; sävje, ; basse et al., ) . treatment effects in network settings typically originate from individual-level treatment assignment and propagate through the network (e.g. basse et al., ). in contrast to the interference and networks literatures, the present paper is concerned with a setting where the units of treatment are separate from outcome units. while the effect "spills over" to the outcome units, there is no interference between different treatment units if they are few and far apart, as in the baseline setting of this paper. consequently, the estimands and estimators of interest in spatial treatment settings generally differ from those in interference and network settings. for spatial treatment settings with interference, the spatial relationships between observations allow me to make semiparametric functional form assumptions to limit interference; see section . for details. similar assumptions may sometimes also be plausible if treatments are directly assigned to individuals but have spillover effects on other individuals. the design-based finite sample inference developed in this paper complements samplingbased large sample asymptotic theory developed in the spatial statistics and econometrics literature. conley ( ) proposed standard errors taking into account cross-sectional (spatial) dependence in a gmm framework; see also case ( ) ; lahiri et al. ( ) ; lee ( ) ; andrews ( ) ; kelejian and prucha ( ) ; bester et al. ( ); lahiri and robinson ( ) ; kuersteiner and prucha ( ) and references therein for alternative results. spatial proximity is also commonly used to motivate cross-sectional dependence in the literature on clustered sampling (moulton, (moulton, , moulton and randolph, ; hansen, ; donald and lang, ; barrios et al., ; cameron and miller, ; abadie et al., ) . the spatial statistics and econometrics literature is primarily concerned with descriptive estimands, modeling the spatial correlations existing in outcome data even in the absence of spatial treatments. textbook treatments of such models in spatial statistics and econometrics include cressie ( ) ; cressie and wikle ( ); anselin ( ) ; anselin et al. ( ) ; anselin and rey ( ) ; lesage and pace ( ) ; arbia ( ) . since treatment assignment (or distance from treatment) does not vary within location, "increasing domain asymptotics" (cressie, ) (asymptotics in the number or size of regions or clusters) are likely needed for consistency of causal effect estimates. spatial treatment applications, however, typically feature a large number of individuals near a smaller number of treatment locations, such that alternative "infill asymptotics" (cressie, ) may offer better approximations. the primary contribution of this paper to this literature is a focus on the estimation of causal effects and design-based in-sample inference, rather than descriptive estimands and sampling-based inference. this paper also connects to the literature on estimation of treatment effects under unconfoundedness and doubly-robust estimation. specifically, i propose a formal notion of unconfoundedness (cf. rosenbaum and rubin, ; imbens and rubin, ) that is appropriate for spatial treatments. with individuals and treatment locations distributed across space, a large number of covariates, such as population density or average income at different distances, are predictive of both outcomes and treatment assignment probabilities. doublyrobust estimators are particularly promising in observational settings with spatial treatments: they have attractive consistency and efficiency properties based on the combination of outcome and treatment (propensity score) modeling. recent work has adapted these estimators to high-dimensional settings (belloni et al., (belloni et al., , farrell, ; chernozhukov et al., ; . initial results suggest that such estimators may also perform well in spatial treatment settings. finally, this paper contributes to the recent literature illustrating creative uses of modern machine learning methods for economic analyses (see mullainathan and spiess, ; glaeser et al., ; athey, ; gentzkow et al., ; , for recent reviews). i propose a method for finding unrealized candidate treatment locations based on an adversarial task: finding unrealized locations that are indistinguishable (to the algorithm) from realized treatment locations. most closely related, use generative adversarial networks (goodfellow et al., ) to create samples for simulation studies. kaji et al. ( ) similarly propose "adversarial estimation" to estimate structural models using generative adversarial networks. in each of these applications, the aim is to generate synthetic samples which look indistinguishable from the real data. in the application of this paper, only the unrealized candidate treatment locations are synthetic, while the outcome and covariate data around it are real. in this paper, i argue in favor of convolutional neural networks in particular, based on the similarity between spatial data and image data, which sparked more recent developments in this method (krizhevsky et al., ) . relative spatial positions are similar to relative positions of pixels, and different covariates at each location correspond to the different color channels of images. for economic applications using satellite data (see donaldson and storeygard, , for a review), convolutional neural networks have also shown promise (e.g. jean et al., ; engstrom et al., ) . convolutional neural networks are particularly attractive for spatial settings because they build on relevant economic intuition for regularization: while the geographic space might be large and high-dimensional, the immediate spatial neighborhood often matters the most, and relative distances matter similarly at different absolute locations. through careful design decisions, the methods i propose for the spatial treatment setting retain some interpretability in addition to the good performance commonly associated with "black box" machine learning algorithms. in this section, i propose an extension of the potential outcomes notation (cf. imbens and rubin, ) that treats the level of treatment assignment as conceptually distinct from the level at which we measure outcomes. this distinction separates the intervention that is the cause of the effect from the individuals for whom the effect is measured. it allows me to formally characterize estimands of interest, and to derive estimators and their properties in the following sections. with spatial treatments, potential outcomes of individuals are functions not of an individual-level binary or continuous treatment, but of a set of candidate treatment locations. we are interested in the effects of spatial treatments. let s denote the set of candidate treatment locations, shown as triangles in figure . th set of candidate treatment locations is assumed to be finite; in the example of figure just two locations in the region shown. this reflects an inherent scarcity that is common to most applications: only a small number of locations are ultimately realized, and most locations are infeasible, unsuitable, implausible, or unlikely for the treatment. in spatial settings, the candidate locations are typically given by latitude and longitude or other (relative) coordinates, such that s ⊂ r . throughout this paper, the set s is finite, as virtually any practical application will be based on some discretized, or rounded, locations. one can, however, take s as defining a finely spaced grid over r . this is convenient to figure : illustration of the setup. while typically only relative locations matter, locations are often given by their "gps coordinates" as latitude and longitude. in the figure, the candidate treatment locations at which the treatment may occur are given by triangles. the small circles indicate the locations of individuals. the researcher typically estimates the treatment effects, caused by treatment at one of the candidate locations and experienced by the individuals, conditional on distance from treatment. when the (weighted) euclidean distance function is used, individuals within a narrow distance bin from a candidate location are located on a ring, here displayed as an area shaded gray. if driving time is used instead to measure distance, individuals at a given distance need not be located on a circular ring. the figure shows data from a single region. in the baseline setting of this paper, the researcher has data from multiple such regions, with treatment realized only in some of them. if treatment is realized at multiple (both) candidate locations (triangles) within the same region, there is potential interference between them, complicating estimation and inference. in the baseline setting, the probability of treatment at locations and in regions describes a two-stage process. in the first stage, a fixed number of regions are chosen randomly for treatment somewhere in the region. in the second stage, a single candidate location in each chosen region is chosen randomly to receive treatment. conceptualize situations where treatment could be realized anywhere with some positive probability. the random variable ⊂ s denotes the set of the realized treatment locations. we measure the outcome of interest for units indexed by . for the remainder of this paper, i will refer to these outcome units as individuals, but in some settings may be a business, census tract, or similar, typically small, unit with fixed geographic location. denote the set of all individuals by i. individual has spatial location, or residence, , shown as small circles in figure . throughout this paper, i assume that the locations of individuals are fixed; there is no migration. in some applications, corresponds to, for instance, the workplace of individual rather than their residence. the location of is in the same space as the candidate treatment locations, such that typically ∈ r are latitude and longitude. define potential outcomes for each individual ∈ i potential outcomes: as the outcome for individual if treatment is realized in locations ⊂ s. to simplify notation, and consistent with standard potential outcomes notation, let the potential outcome of individual in the absence of any realized treatment be ( ) ≡ (∅). the treatment effects of primary interest contrast some treatment vector ⊂ s with the absence of realized treatments, ′ = ∅. specifically, i define the effect of on an individual ∈ i as treatment effects: oftentimes, the treatment vector of interest, , is a singleton, = { } for a single candidate location ∈ s. with slight abuse of notation, define treatment effects: i define meaningful average treatment effects in section . these average treatment effects average across both individuals and treatment vectors . distances distances between treatment locations and individuals are central to defining interesting average treatment effects in section . for instance, the researcher may estimate the average effect of a treatment at a distance of mile. in figure , the areas shaded gray highlight all locations approximately mile away from any candidate treatment location. the distance between treatment location ∈ s and individual ∈ i is given by a distance function distance function: ( , ) ≥ importantly, the distance between two locations must be observable (to the researcher) and must not be affected by treatment assignment, ruling out migration in response to the treatment. the distance function is used for two purposes. first, to estimate heterogeneous average treatment effects by distance from treatment. second, to assume distances at which treatments have no effect to limit interference and to thereby aid in estimation and inference. when locations are given as cartesian coordinates, we can use the euclidean distance in r : euclidean distance: when locations are given by latitude and longitude, the great circle distance is more accurate than a euclidean distance with fixed weights on latitude and longitude. for some applications in social sciences, driving distances are arguably more relevant. suppose the spatial treatment corresponds to an employer opening a new location. then an individual's access to the treatment, and hence treatment effect, likely depends on driving time rather than straight line distance. however, computing driving times between many locations may be computationally and financially expensive. when using straight line distances instead, some interpretability, but not validity, is lost. we can also study the effects of state-wide policies and other clustered assignments in this framework. in this setting, each candidate treatment location ∈ s corresponds to one cluster, or state. the appropriate distance function for this setting is in the simplest case of state-wide policies, we use this distance function to estimate the treatment effect at a distance of . this corresponds to estimating the treatment effect of the policy by comparing individuals in treated states to individuals in untreated states. we can generalize the cluster membership function to be smooth in distance to a treated state: for individuals in treated states, this distance is . for individuals in untreated states, the distance is smallest if they are most exposed to treated states. exposure may measure, for instance, distance to the state border, shared media markets, number or cost of flights between airports, or the relevance of the industries of treated state to 's occupation. regions in many applications, it is convenient to group individuals and treatment locations into regions. for instance, in a sample of data from different cities, individuals and treatment locations of each city may form a separate region. when regions are not directly coded in the data, one can sometimes define regions based on geographic proximity such that treatment locations only have effects within their own regions. that is, no individual is close enough to candidate treatment locations from two or more distinct regions to be affected by both of them. figure shows data from one such region. in the baseline setting of this paper, the researcher has access to data from multiple such regions, but this requirement is relaxed in section . . throughout, i denote regions by subscripts = , . . . , . let s ⊂ s be the set of candidate treatment locations within region . the set of realized treatment locations within region is . if treatment is realized within region , ̸ = ∅, let = , and otherwise, = ∅, let = . if = , i say that region "is treated" or "is a treated region." analogously, if = , i say that region "is a control region." let i ⊂ i be the set of individuals with residence in region . the region where individual resides is given by ( ), such that ∈ i ( ) . interference the notation in this paper can be seen as an extension of the notation of the literature on interference (cf. aronow and samii, ) . consider first a setting with individual-level treatments. let be the treatment assigned to an individual = , . . . , , and ∈ { , } be the vector stacking all of the . in the absence of interference, that is, under the stable unit treatment value assumption (cf. imbens and rubin, ) , the observed outcome of individual is = ( ). with interference, the outcome of individual may depend not only on her own treatment assignment, but also on the treatment assignment of other individuals. that is, the potential outcomes of are function a function of the entire rather than only her own , and her observed outcome is = ( ). notationally, spatial treatments generalize this setting by allowing to have a dimension other than , the number of individuals. for the closest analogy, enumerate the candidate treatment locations by = , , . . . , where is the finite number of candidate treatment locations. the random variable of realized treatment locations takes on values ∈ { , } , such that ≡ whenever the kℎ candidate location is treated, and ≡ otherwise. the realized outcome for individual is then = ( ), where is rather than dimensional. consider the example given in figure . some individuals are at a distance of mile from both treatment locations. if the treatment has an effect at that distance, the treatment states of both candidate locations jointly determine the observed outcome. the two candidate locations can interfere because conditional on the treatment state of just one of them, the outcome for some individuals still varies depending on the treatment state of the other candidate location. the literature on interference is typically interested in answering (at least) one of two questions. first, what is the effect of changing 's treatment status, holding the treatment status of 's neighbors fixed? second, what is the effect of changing the treatment status of 's neighbors, holding the treatment status of fixed? with spatial treatments, neither of these questions is of primary interest. if is mile away from a realized treatment location, then a neighbor of , say ′ , is also approximately mile away from the same realized treatment location. a counterfactual where is mile away from a realized treatment location, while her neighbor ′ is not, is typically not feasible or relevant in practice. the treatment does not spill over from to ′ , it affects both of them directly, such that decompositions into direct and indirect effects (cf. hudgens and halloran, ) are not well defined. interference in the spatial treatment setting refers to multiple treatment locations affecting the same individual, rather than the treatment or effect of one individual spilling over to another individual. formally, a treatment location affects an individual if for some set of treatment locations ⊂ s, the outcome of changes when is included or excluded: . two treatment locations , ′ ∈ s interfere with one another if there is an individual affected by treatment at both locations, that is in spatial treatment settings, it is often natural to assume that treatment locations that are far away from an individual do not affect her. formally, assume that whenever ( , ) > max for some sufficiently large distance max , ( ∪ { }) = ( ∖ { }) for all ⊂ s. assumption formally states that there is no interference across regions. assumption (no interference across regions). individuals in region are unaffected by treatment locations in regions ′ ̸ = . that is, for ∈ i and ⊂ s, regions are sufficiently far apart that individuals in one region are unaffected by treatment locations in another region. the results in this paper, however, fundamentally rely on the absence of interference between treatment locations that are far apart, not on separate regions. section . discusses a setting where all data available to the researcher comes from a single large contiguous region. if the region is sufficiently large and realized treatment locations are sufficiently scarce, it is still possible to estimate causal effects without strong additional assumptions. the separate region framework, however, helps clarify key concepts by simplifying estimators, and it is applicable to a large number of empirical studies. the assumption that treatment locations only affect individuals within the same region is similar in spirit to assumptions that interference or spillovers are limited to family members, classrooms, or other subgroups in settings with individual-level treatments (e.g. vazquez-bare, ). the assignment mechanism (imbens and rubin, ) determines the probabilities with which treatment is realized at each of the candidate treatment locations. the marginal probability that treatment is realized at a location ∈ s is given by pr( ∈ ). in the main part of the paper, i consider a two-stage assignment mechanism that imposes structure on pr( ∈ ) as well as on the conditional probabilities pr( ∈ | ′ ∈ ) and pr( ∈ | ′ ̸ ∈ ). in the first stage, either a fixed number of regions is chosen to receive treatment, or assignment is through independent bernoulli trials (coin flips). in the second stage, a single location receives treatment in each treated region. i discuss methods for some observational settings that deviate from this assignment mechanism in sections . . suppose the randomization of treatments across regions takes the form a completely randomized experiment with a fixed number of treated regions. assumption formalizes this design together with an assumption that each region is equally likely to be treated. define ≡ pr( = ) for = , . . . , to be the probability that a region receives treatment. note that the completely randomized design differs from experiments that are paired or stratified at the region-level. results for stratified experiments are generally similar and can be obtained by substituting the appropriate covariances of treatment indicators in the proofs. estimating the variance of estimators under paired designs is often difficult (e.g. bai et al., , for individual-level treatment assignment), but does not contribute conceptually to our understanding of the spatial treatment setting. assumption (completely randomized experiment). regions are chosen for treatment according to a completely randomized design (e.g. imbens and rubin, , ch. . ) where each region has equal marginal probability of receiving treatment somewhere, = for all regions . that is, all assignment vectors ∈ { , } with ∑︀ = ≡ are equally likely, and assignments with ∑︀ ̸ = have zero probability: as an alternative to completely randomized designs with fixed probability of treatment, i also consider designs where treatment is decided by independent coin flip for each region, potentially with different probabilities. assumption below formalizes this assumption. assumption (bernoulli trial). regions are chosen for treatment according to a bernoulli trial (e.g. imbens and rubin, , ch. . ) where region has marginal probability of receiving treatment somewhere and assignment is independent across regions. that is, the probability of assignment ∈ { , } is such that the number of treated regions varies. in the main part of the paper, i consider a setting with exactly one treated location in each treated region. this restriction of the assignment mechanism rules out interference by design under the minimal assumption that treatments have no effects across regions. for each candidate treatment location in a region, ∈ s , define the probability of treatment conditional on the region receiving treatment as ( ) ≡ pr( ∈ | = ). then, by the definition of conditional probabilities, pr( ∈ ) = pr( ∈ | = ) pr( = ) = ( ) . the notational distinction between treatment of regions and treatment of particular locations within regions is motivated by an asymmetry in which potential outcomes are observed: in control regions, the control potential outcomes are observed for all individuals near each (unrealized) candidate treatment location. in treated regions, in contrast, only the treated potential outcomes corresponding to one particular treatment location are observed for all individuals. this asymmetry is apparent in the estimators and variances throughout section . individual-level effects express the average effects of treatment locations on individuals. the most intuitive estimator of the average effect of a spatial treatment on nearby individuals takes the simple average of individuals near realized treatment and subtracts from it the average outcome of properly chosen control individuals. in this section, i first show who the proper control individuals are under the ideal experiment of random variation in treatment locations. then i present properties of this estimator and discuss its interpretation as the average treatment effect on the treated. the average of individuals who are treated at a distance ± ℎ from a treated location is where ( ) = if and only if individual is in a region ( ) that is treated. the indicator function equals if and only if the distance between individual and the realized treatment location in her region, ( ) , is within the distance bin of distances between − ℎ and + ℎ. for instance, to estimate the average outcome for individuals who are between and miles from treatment, calculate¯( . ) with ℎ = . . the choice of control individuals to compare this average of treated individuals to is less obvious. recent empirical studies compare the treated to controls on an outer ring; that is, to individuals ′ in treated regions ( ( ′ ) = ) who are farther away from treatment. effectively, this estimates the treatment effect at distance as¯( ) −¯( ′ ) where ′ ≪ . in analogy to individual-level randomized experiments, one might also consider taking the simple average of individuals in control regions, ∑︀ ( − ( ) ) / ∑︀ ( − ( ) . while either of these strategies is valid under further assumptions or in particular settings, below i argue in favor of a different strategy that is justified by the experimental design. one particular choice of (weighted) control average is, however, justified by the experimental design of the ideal experiment considered in this paper: most importantly, the estimator¯( ) only averages over individuals who are at approximately distance from some candidate location ∈ s ( ) . the remaining weighting is similar to inverse probability weighting estimators of the average effect of the treatment on the treated (att) in settings with individual-level treatments (cf. imbens, ) . to see that the control average¯( ) provides the appropriate counterfactual for the simple average of the treated ( ), consider the expected value of the terms in the numerator of the latter. it is straightforward to show that see appendix a. for the details. the difference between the expression above and the terms of the estimator¯( ) is that the latter can only average over individuals in control regions, with ( ) = , requiring the additional inverse probability weight ( ) in¯( ). the estimator¯( ) therefore aligns, in expectation, the weights placed on each control potential outcome ( ) with those placed on the corresponding treated potential outcome ( ) bȳ ( ). consequently, the estimator^( estimates a weighted average of the differences ( ) − ( ), which are the individual-level treatment effects ( ) defined in section above. the particular inverse probability weights make^( ) an estimate of the average treatment effect on the treated at a distance of ± ℎ. theorem states approximate finite sample properties of this estimator. (i) unbiasedness for the att: is the average potential outcome of individuals at distance from location corresponding to treatment at location ,˜( ) averages the˜( , ) within region , with weights proportional to the probability of treatment at location .˜( ) is the analogous withinregion average potential outcome for the same individuals but in the absence of treatment. ( ) and˜( ) similarly average the within-region averages across regions. the number of individuals at distance from location is ( , ),¯( ) when averaged within region , while¯( ) is the expected number of individuals at distance from realized treatment across regions. the theorem is a special case of theorem below with weight remark . the approximation in theorem arises because the denominators of the estimator ( ) are stochastic. the proof proceeds by deriving the finite sample properties of an infeasible demeaned estimator˜( ) with non-stochastic denominators that satisfies^( )−˜( ) = ( − ), where is the number of regions; details are given in the appendix. even with relatively few regions, the approximation is likely to perform well in practice. similar issues arise with individual-level treatments if treatment is decided by successive coin flips, rather than by fixing the number of treated. in spatial treatment settings, however, it is rarely feasible to hold the number of individuals near treatment fixed when randomizing the assignment of treatment locations. when all candidate locations have equal numbers of individuals in the distance bin, the approximations in the theorem above hold with equality. remark . the expected value given by theorem is also relevant for other estimators usinḡ ( ) as the mean of the treated but relying on a different control comparison group and auxiliary assumptions to justify the comparison. when researchers argue that randomization in the spatial locations for treatments allows them to estimate the treatment effect usinḡ ( ) (or close analogs), they therefore implicitly estimate the average treatment effect on the treated. i believe there is value in making the estimation target explicit: as i argue in section . . below, the att as defined above does not necessarily allow the most meaningful comparisons of the effects at different distances. remark . the control average¯( ) used by the proposed estimator^( ) simplifies to the simple average over all individuals in control regions, if each individual is equally likely to be distance from realized treatment. this typically requires that treatment can be realized at any location within a region with equal probability ( ( ) is constant within ), and the probability that a region is selected for treatment ( ) must be proportional to its area. then the unconditional treatment probability ( ) is constant for all locations , not just for a small, finite, set of candidate locations. figure illustrates and contrasts this with the more common setting where only a small number of candidate locations have positive probability of receiving treatment. remark . the variance given in the theorem is the design-based variance (abadie et al., ) of the estimator. it expresses the variation in the estimate arising from assigning treatment randomly to one candidate location in a fixed number of randomly chosen regions. the individuals whose outcomes are measured are held fixed across these repeated samples; the only difference between samples lies in which potential outcome is observed for each individual. the thought experiment behind the variance above is therefore similar to performing a permutation, or placebo, test. aronow et al. ( ) also suggest permutation tests as an alternative basis for inference in the spatial treatment setting. remark . the first three terms in the variance expression are similar to the variance of the difference in means estimator in a completely randomized experiment with individual-level treatments (cf. imbens and rubin, , ch. ). in the ideal spatial experiment considered in this section, treatment is randomized similar to a completely randomized experiment across regions with outcomes aggregated within regions (and distance bins).˜( ) ( ) is the variance of aggregated treated potential outcomes,˜( ) ( ) is the variance of aggregated control potential outcomes, and ( ) ( ) resembles a variance of treatment effects, such that˜( ) ( ) +˜( ) ( ) − ( ) ( ) resembles the variance of the difference in means under repeated sampling of fixed individuals but varying treatment assignment, the framework of this paper. remark . there is a distinct asymmetry between treated and control outcomes in the expressions for the variance: there are two terms capturing different variances of treated potential outcomes, but only one variance of control potential outcomes. in a treated region, ( ) only averages over potential outcomes corresponding to the realized treatment location, but not those of other, unrealized, candidate treatment locations. the variance of this estimator therefore depends both on how treated potential outcomes vary across regions and within region across candidate locations. if most of the variance is across regions, the final term, −˜( ) is large (negative), reducing the overall variance of the estimator that is due to the variance of treated potential outcomes,˜( ) ( ). since most of the variance is across regions, little is lost by only observing outcomes corresponding to one treatment location in regions with treatment. in a control region, in contrast, we observe the control potential outcomes ( ) that are the counterfactual to all candidate treatment locations s ( ) in the region.¯( ) therefore averages over potential outcomes for all candidate locations within each region, and˜( ) ( ) is the variance of such averages of ( ) within region, across candidate locations. remark . the last two terms in the variance expression arise due to the two-stage randomization in the ideal experiment. after randomizing between regions, the ideal experiment also randomizes between the candidate treatment locations within each treated region. when each region only has a single candidate treatment location, the variance can be simplified to only use the first three terms (scaled), as there is no second stage randomization in that case. estimation of variance without further assumptions, one can only estimate the first two terms of the variance,˜( ) ( ) and˜( ) ( ), to form a conservative estimator of the approximate finite sample variance of^( ). if there is a single candidate treatment location per region, the fifth term can be combined and estimated along with the first (and second) term. the third and fourth term are (approximately) variances of treatment effects, which are unidentified. however, the third term is larger in absolute value than the fourth term (see appendix a. . ), such that − ( ) ( ) + ( ) ≤ . intuitively, ( ) ( ) is approximately the unconditional variance of treatment effects, while ( ) is the variance of the conditional expectation (conditional on region) of treatment effects. by the law of total variance, the difference is expectation of the conditional variance, which is necessarily non-negative. hence, dropping both terms yields a conservative estimate of the variance. if there are multiple candidate treatment locations per region, one can still estimate the fifth term under semiparametric assumption on potential outcomes, such as constant treatment effects. specifically, note that the fifth term consists of the variance of regionaverage potential outcomes, ≈ var( (¯( , )| ∈ s )). one can readily estimate the variance of ≈ var( (¯( , ))), as in the estimation of ≈˜( ) ( ). one can also estimate both types of variances for control potential outcomes because in control regions, the relevant control potential outcome for individuals at distance from any candidate treatment location are observed. if treatment effects are constant, one can estimate¯by scaling^¯( ) by the ratio of the average within region variance to the across region variance of average control potential outcomes. the estimand ( ) is not generally appropriate when the researcher is interested in how the effect of the treatment changes with distance from treatment. as an alternative, i propose the estimand − ( ) with a more attractive interpretation when comparing effects at the figures show regions with individuals (small circles) and candidate treatment locations (triangles), highlighting areas that are distance away from a candidate treatment location in gray. suppose each candidate treatment location is equally likely to be realized. in panel a, all individuals who are distance away from a candidate treatment location receive equal weight in the estimand ( ). in estimation, if the region is in the control group, we take the simple average of outcomes of the highlighted individuals. in panel b, some individuals are distance away from both candidate treatment locations, so these individuals receive greater weight in the estimand ( ). in estimation, if the region is in the control group, we take the average of outcomes of the highlighted individuals, but individuals who are located in both gray rings receive twice the weight. in panel c, candidate treatment locations are everywhere (for illustration, only candidate treatment locations along a grid are displayed). if we assume that candidate treatment locations extend past the boundaries of the region, then all individuals in the region receive equal weight in the estimand ( ). in estimation, if the region is in the control group, we take the simple average of outcomes of all individuals. distance from treatment different distances. additional, one can interpret − ( ) as the expected average effect at distance of a new treatment location. figure illustrates the problem of interpreting the difference between the estimands ( ) and ( ′ ) as the pattern of treatment effects across distance from treatment . suppose the researcher is interested in comparing the average treatment effect at a short distance = short and long distance ′ = long . suppose further that there are two types of candidate treatment locations, each type equally likely to be realized. the first type of candidate treatment locations has many individuals located at the short distance and few individuals at the long distance. these first candidate locations all have relatively small treatment effect at both distances, but decreasing in distance from treatment. the second type of candidate treatment locations has few individuals located at the short distance, and many individuals at the long distance. these second candidate locations all have relatively large treatment effect at both distances, but also decreasing in distance from treatment. in the example in figure , the estimand ( ) is increasing in distance even though the treatment effect of any single treatment location is decreasing in distance from treatment. the estimand ( short ) places most weight on the first type of candidate locations because most individuals at the short distance from treatment are near this type of location. in contrast, the estimand (long) places most weight on the second type of candidate locations. hence, (long) > (short). this inequality states that the average treatment effect at a long distance for the average individual at the long distance from a candidate treatment location is larger than the average effect at a short distance for the average individual at the short distance from candidate treatment locations. it does not imply that the average effect of any single treatment is increasing in distance from treatment. instead, the average individual at a long distance may simply be both a different type of individual (in terms of observables and unobservables) and also be exposed to a different treatment location on average. an alternative estimand, − ( ) defined below and also shown in figure , avoids such issues in interpretation by placing the same aggregate weight on each candidate treatment location irrespective of the distance . the estimand − ( ) first separately averages the potential outcomes of nearby individuals for each candidate treatment location. these averages are then averaged again, with weights proportional only to the probability of treatment at the location. in contrast, the estimand ( ) uses weights proportional to the product of the treatment probability and the number of individuals near the treatment location. formally, where¯( , ) is the average effect of a given candidate location on individuals at distance ± ℎ from it. these average effects are then averaged with weights ( ), which do not depend on distance from treatment. hence, the weight placed on the average effect of a given location does not depend on the distance from treatment. to also non-parametrically control for observable differences in pre-treatment variables , one can estimate − ( ) separately using only individuals with covariate values falling into groups defined by . the comparison of − ( ) and − ( ′ ) then compares individuals with the same average exposure to the different candidate locations and similar individual characteristics . holding the aggregate weight per treatment location constant across distance from treatment is attractive when the treatment effects are expected to be heterogeneous by region or location. such heterogeneity is particularly plausible in many spatial treatment settings: oftentimes, the exact implementation of the treatment differs substantially from location to location. for instance, the million dollar plants in the study of greenstone and moretti ( ) are each operated by distinct companies which may differ in their labor demand and wage setting. hence, heterogeneous treatment effects arise not only due to differences between individuals, but also due to differences in the implementation of the treatments. since spatial treatments are often larger, rarer, and more complex, their implementation tends to vary more than, say, the administration of a drug in medical trials to different patients, or the content of a job training program across training sites or cohorts. additionally, the estimand − ( ) has an attractive interpretation as the expected effect at distance of a new treatment location. consider the following hierarchical model. first, when treatment is realized at location , its average effect at distance is drawn as ( ) ∼ . second, the individual-level effect of location on individual is given by where ( ) is a mean zero individual-specific component. then, as the width of the distance bin, ℎ, goes to , the estimand − ( ) approaches the mean of the distribution . hence, one can interpret − ( ) as the expected average individual-level treatment effect of a new treatment location drawn in the same way as existing realized treatment locations. i propose the following estimator to estimate − ( ): theorem gives the approximate properties of the finite sample distribution of − ( ). under assumptions (no interference across regions) and (completely randomized design), the estimator^− ( ) has an approximate finite sample distribution over the assignment distribution with (ii) and variance as given by theorem with the theorem is a special case of theorem below with weight as specified above. remark . the estimator here is exactly unbiased because under a completely randomized design, the sum of weights is constant across assignment realizations. this is different from theorem above, where the number of treated individuals varies. here, treated individuals are averaged by candidate treatment location, and the number of treated locations is constant across assignment realizations by assumption . more generally, the same ideas allow estimation of any weighted average of individual-level treatment effects that places non-zero weights only on the effects of candidate treatment locations with positive probability of realization. write these estimands of individual-level average effects of the spatial treatment on individuals at a distance from treatment as: where ( ) is the effect of treatment at location on individual , and ( , ) are weights specified by the researcher. the estimand here therefore can be any weighted average of the effect of single treatments on individuals with weights as specified by the researcher. for the average effect of the treatment at distance , weights ( , ) are non-zero only when location and individual are (approximately) distance apart. while i define the att estimands ( ) and − ( ) for distance bins ± ℎ above by using the rectangular, or uniform, kernel function {| ( , ) − | ≤ ℎ}, the weights ( , ) can generally use any kernel function in place of distance bins to estimate the effects at distance . the average effect of the treatment on the treated estimands in equations (i) and are special case of . for att the estimand corresponding to^( ), choose weights for att the estimand corresponding to^− ( ), choose weights i propose an inverse probability weighting estimator (cf. imbens, ) to estimate the weighted average treatment effect in equation above. in short, the estimator is the difference between weighted average outcomes of individuals near realized treatment locations and weighted average outcomes of individuals in regions without treatments. the weights here need to account for two aspects: first, the researcher specifies the desired weights ( , ) in the estimand. second, individuals near locations with high treatment probability are relatively more likely, across samples of repeated treatment assignment, to appear in the sum of "treated" individuals than in the sum of "control" individuals due to the experimental design. the estimator cancels out the probability weighting induced by averaging over individuals (not) near realized treatment for the treated (control) average. to estimate the average effect of the treatment on the treated, the treatment probabilities ( ) ( ) ( ) can be included in the weights ( , ). the proposed estimator for the weighted average treatment effect in iŝ the weights ( , ) are fixed and specified by the researcher. the weights ( ) and , in contrast, are stochastic due to their dependence on the treatment assignment random variables and . specifically, ( ) = unless treatment is realized at location , in which case it is equal to the inverse of the probability of this event. similarly, = unless there is no treatment in the region of individual , in which case it is equal to the inverse of the probability of no treatment in the region. consequently, the stochastic weights are equal to in expectation. the estimator divides each term by the sum of realized weights, ( ) ( , ) and ( , ), such that it is the difference between a convex combination of treated outcomes and a convex combination of control outcomes. theorem gives the approximate finite sample properties of the estimator^( ). under assumption proof: see appendix a. . remark . the variance in theorem can be estimated analogously to that of theorem , also see appendix a. . . remark . the approximate finite sample variance is smaller under bernoulli trials than under a completely randomized design. this is due to the nature of the approximation, which does not penalize the variance as heavily when for instance few treated regions are available under an imbalanced assignment. in practice, the difference between both designs is negligible due to the factor − in the denominator of , such that √ → and there is no difference between the two designs under standard asymptotics in the number of regions. the aggregate effects of a single treatment on all affected individuals is of importance for cost-benefit and welfare analysis. in this section, i propose estimators of aggregate effects that build on estimators of individual-level effects. in experiments with spatial treatments, there are two units of observation: outcome individuals and spatial treatments. the individual-level treatment effects of the previous section are average effects per outcome individual. the aggregate treatment effects of this section are average effects per spatial treatment. suppose the researcher is interested in the aggregate effect that a single treatment location has on all affected individuals. define the estimand where, as before, ( ) = ( ) − ( ) is the effect of treatment location on individual . the aggregate treatment effect sums these effects across individuals and averages them across candidate treatment locations , with weights ( ). in this section, i focus on the average aggregate treatment effect on the treated, , with weights ( ) ≡ pr( = | = ) pr( = ) these weights place larger weight on the effects of treatment locations that are more likely to be realized. the estimand therefore answers the question: what is the expected aggregate effect of a treatment location under the observed policy of assigning treatments to locations? one can estimate the aggregate effect by aggregating outcomes at the region-level: . this is the propensity score weighting estimator of an average treatment effect on the treated, where the outcome variable of interest is the sum over the outcomes of all individuals in a region. when there is a single candidate treatment location per region, standard results from the literature on experiments with individual-level treatments apply (cf. imbens, ) , with regions taking the role of individuals. estimators based on region-aggregate outcomes are likely to have very large variance. each region-aggregate outcome is the sum of outcomes of individuals in the region. if there is substantial variance in the number of individuals per region and outcomes are positive, the aggregate outcome of regions with many individuals can be substantially larger than the aggregate outcome of smaller regions. for instance, suppose that the number of individuals per region is poisson distributed with mean , and individual-level outcomes are i.i.d. within and across regions, with mean and variance . then region-aggregate outcomes have variance · ( + ) by the law of total variance. hence, aggregate potential outcomes have large variance, which leads to large variance of the estimator (cf. imbens, ) . variation in region sizes generates a large variance of the region-aggregate estimator , in two ways. first, if there is variance in the number of individuals per region, then in finite samples, some treatment assignments will be such that there are more individuals in treated regions than in control regions. suppose outcomes are positive and constant, for instance all individuals have the exact same value for the outcome. then the treatment effect estimate^, in such a sample is positive and sensitive to the scale of the outcome value. hence, the estimator^, can have large variance even when there is no variance in potential outcomes. second, variation in region sizes increases the variance in a sampling-ofregions thought experiment. even if the average individual-level treatment effect was known, needing to estimate the number of times the effect is realized on average per region can create substantial variance. the design-based variances considered in this paper condition on the individuals in the sample. with known number of individuals and known individual-level average treatment effect, it is possible to form an estimator of aggregate treatment effects with a design-based variance equal to zero, in contrast to the variance results for the estimator , above. i therefore recommend an estimator of average aggregate effects that reduces the variance by building on the estimator of the average individual-level effect at a distance . let where¯( ) is the average number of individuals at distance from candidate treatment locations: using the same distance bins (uniform kernel and bandwidth equal to bin width) for botĥ ( ) and¯( ). the set of distances d contains the midpoints of the bins that partition the full space into distance bins. for instance, if one uses distance bins [ , ], ( , ], . . . , ( , ] for a treatment that is known not to have effects past a distance of miles, then d = { . , . , . . . , . }. the theoretical properties of the estimator^, follow from those of^( ) in theorem above. theorem . under the ideal experiment, the estimator^, has an approximate finite sample distribution over the assignment distribution with remark . for approximate unbiasedness, the estimator^, must be based on^( ), not^− ( ). intuitively, when "integrating" the effect^( ) against the number of individuals at this distance, one needs to ensure that^( ) is an unbiased estimate of the effect for these particular¯( ) individuals. remark . the variance follows from theorem and theorem . the covariances can be derived analogously. since^, is a sum, its variance is a sum of the covariances of the terms. in the design-based perspective, the analysis is conditional on the individuals in the sample. hence, the number of individuals in each bin,¯( ), is fixed. the estimators^( ) for distances ∈ d are therefore the only stochastic components. remark . the optimal choice of distance bins (and bandwidths) remains an open question. if individuals are spread uniformly across space, equal-width rings with larger radii have larger area and hence contain more individuals. more generally, in densely populated areas, smaller bins may be preferable, and under suitable sequences of populations (infill asymptotics or growing number of regions), it may be possible to allow ℎ → and |d| → ∞. generally, in the formula above, additional distance bins decrease the (squared) weights¯( ) at the cost of increasing variances var i discuss issues in imposing parametric assumptions on the decay of treatment effects over distance from treatment and estimation by least squares regression. first, i show how to impose a parametric model on the individual-level effects at different distances. second, i show how to estimate aggregate effects based on such a model. most simple linear parametric models for the decay of average treatment effects over distance from treatment take the form ( ) = ∑︁˜( ) where˜are known functions of distance, and are coefficients to be estimated. in many settings, one needs to impose a distance after which the treatment has no effect, even within region, to obtain reasonable estimates from parametric models. assumption below formalizes this assumption. assumption . the treatment has no effect after a distance max if, for any individual ∈ i, set of treatment locations ⊂ s, and location ∈ such that ( , ) > max , without such a restriction, any simple functional form for˜will typically offer a poor approximation for at least some distances from treatment. one can improve the approximation to the treatment effect at short distances by using functions that only fit the treatment effect pattern up to the maximum distance max : relatively simple functions may well approximate the average treatment effects at distances ∈ ( , max ). this imposes contextual knowledge that average treatment effects are negligible at large distances from treatment. it also resembles a "bet on sparsity" (hastie et al., ) : if treatment effects really are negligible at distances longer than max , the estimators proposed below will likely perform well. if treatment effects are not negligible even at long distances, then no (parametric) estimator will perform well. for instance, one can impose a linear functional form on the treatment effect decay by choosing = , = . the coefficient then estimates the rate of decay. a quadratic functional form is imposed by = , = , = . in principle, the analysis in this section can be extended also to functional forms that are non-linear in the parameters, such as an exponential decay of treatment effects with unknown rate of decay, ( ) = exp( (− )). to estimate the parameters , suppose initially that there is only a single candidate treatment location in each region. this allows the definition of the distance of individual from the candidate treatment location uniquely as , irrespective of realized treatment. then estimate the weighted linear regression with weights reflecting those in section . . depending on the estimand, such as ( ) or − ( ) for different versions of the average effect of the treatment on the treated. the function ℎ models the average control potential outcomes at each distance from candidate treatment locations. for semiparametric estimation, specify the treatment effect decay ( ) parametrically, and estimate ℎ nonparametrically, as a partially linear model (e.g. robinson, ) . in this paper, i instead focus on parametric linear estimation, which imposes known parametric functions and ℎ and estimates their coefficients: the same caveat about setting a maximum distance applies also to ℎ. since there is no interest in effects at distances larger than max , the constant captures the mean outcome for individuals at such larger distances. in practice, one typically not only want to impose a zero treatment effect after distance max (assumption ), but a treatment effect that tends to zero continuously at max . to this end, estimate the linear regression with transformed covariates figure illustrates what it means to impose this restriction. in panel (a), without the restriction, the estimated treatment effect will jump to discontinuously at max . imposing the restriction in panel (b), the estimated treatment effect is continuous also at max . the restriction generally reduces the variance of the estimator, in particular for estimating aggregate effects, as discussed below. in practice, most functional forms for imply not just a zero effect after distance max , but also a non-zero effect at distances slightly shorter than max . the figure shows a scatter plot of outcomes against distance from treatment. both regression estimators use a quadratic in distance that is set to at a distance of max . the restricted estimator further restricts the regression coefficients such that function is continuous at max . the same parametric functional form can be imposed to estimate the average aggregate effects of the treatment. under the parametric model, the average aggregate treatment effect on the treated is solving for plugging this into the regression specification above, obtain the one-step regression specification where the coefficient on the first (transformed) covariate is the estimate of the average aggregate treatment effect. the transformed covariates are readily computed by realizing they are equal to the original covariates multiplied or shifted by average covariates. the average here is taken across all regions, both treated and untreated, such that this estimates has similarly attractive properties as the nonparametric estimator^, above, in leveraging that the number of individuals near candidate treatment locations are available irrespective of assignment. when there is more than one candidate treatment location per region, augment the regression approach as follows. the variable is not uniquely defined, since there are multiple "distances from candidate treatment locations" for individuals. suppose individual in a control region ( ( ) = ) is mile away from one candidate treatment location and miles away from a different candidate treatment location. then should be used to estimate the control mean ℎ( ) for the two distances = and = . one can therefore duplicate observation . specifically, if individual is in a region with |s ( ) | candidate treatment locations, then include |s ( ) | times in the regression. each version of uses the corresponding to a different candidate treatment location. this ensures ( | = , = ) = and hence results in consistent linear regression estimates. the framework and estimators proposed in the previous sections can readily be adapted to variations in the setting that are of empirical relevance, such as panel data and settings with interference. panel data can serve two distinct purposes in settings with spatial treatments. first, one can use pre-treatment outcomes to reduce the variance of treatment effect estimators. second, with panel data one can base identification of causal effects on a "parallel trends" assumption that is familiar from difference-in-differences methods. i show that existing empirical work relies on a version of this assumption that is not justified by the ideal experiment, discussed in section above, or other (quasi-) random variation in the location of spatial treatments. reducing variance under the ideal experiment, the nonparametric estimators proposed above are (approximately) unbiased, but may have large variance. the variance may be particularly large if potential outcomes of individuals in different regions are on substantially different levels. then, for some treatment assignment realizations, treatment is predominantly realized in the regions with large potential outcomes, such that the estimate ex-post overstates the true average treatment effect. symmetrically, under the inverse of this assignment, treatment is predominantly realized in the regions with small potential outcomes, and the estimate understates the true effect. ex-ante (on average across treatment assignments) the estimator is unbiased. the large differences between estimates for different treatment assignments imply, however, a large design-based variance of the estimator. if the researcher has a pre-treatment outcome for each individual, she can difference out the different levels of the potential outcomes in different regions. to implement this, simply take the difference between post-treatment and pre-treatment outcome for each individual, − pre , and then use the same estimators as before. this does not substantively affect the approximate unbiasedness of the nonparametric estimators. denote, for instance, the estimator^( ) with differenced outcomes as^d iff ( ). it follows immediately that where the pre-treatment outcomes, pre , are fixed across treatment assignments. the treated and control weights, ( ( ) , ( ) , ) and ( ( ) , ) mirror the weights in¯( ) and¯( ), respectively. hence, they are (approximately) equal in expectation by the arguments for unbiasedness of^( ) itself (appendix a. . ). hence, the second term is equal to zero in expectation. subtracting the pre-treatment outcomes from the potential outcomes within the estimand ( ) does not change the estimand at all because the pre-treatment outcomes cancel between the treated potential outcome and the control potential outcome. for the regression estimators, one can alternatively use pre-and post-outcomes as separate observations and include individual fixed effects in the regression for a similar effect. differencing out the levels of the potential outcomes greatly reduces the variance of the estimator if the temporal persistence in potential outcomes is large. this is most easily seen in the case with one candidate treatment location per region. then subtracting the pre-treatment outcomes affects the marginal variances¯( ) ( ) and¯( ) ( ). i recommend using the same formula for the variance estimator as before, but applied to the differenced outcomes, to obtain an estimate of the variance of^d iff ( ). loosely speaking, the variance of^d iff ( ) is smaller if the differenced outcomes have smaller marginal variance: var( ( ) − pre ) < var( ( )) and var( ( ) − pre ) < var( ( )). hence, using the differenced outcomes is likely to reduce the variance if the coefficients in (population) regressions of post-treatment potential outcomes on pre-treatment outcomes is at least . . one can also incorporate multiple pre-periods into this approach for variance reduction. relying on randomized treatment assignment for identification, additional pre-periods can be useful for differencing out the levels of the potential outcomes more precisely. specifically, if there are period specific unobservable components affecting outcomes, averaging over outcomes from multiple pre-periods may provide a more precise estimate of the level of control potential outcomes in the post-period. since the target of estimation is the postperiod effect, however, it is attractive to give greater weight to pre-periods that are closer in time to the post-period. intuitively, the goal is to use the pre-period outcomes to make a one-step-ahead forecast of post ( ). small adjustments have to be made if the pre-period data is for different individuals than those observed in the post-period. since the individuals are distinct, there is no single pre for a post-period individual . instead, the goal is to deterministically construct an estimate^p re based on pre-period outcomes of individuals with locations near the location of , . one can then use the same estimators as before with the transformed outcomes −^p re . if the construction of^p re does not depend on treatment assignment and post-period outcomes, formal results, such as theorem , continue to hold for the differenced outcomes. averaging over pre-period outcomes for different individuals estimates the expected outcome conditional on location. however, it fails to remove individual-specific fixed effects that are not correlated with the location of the individual. intuitively, the loss due to only having pre-period outcomes for different individuals is greater if individual-specific components are large and individual-time specific "noise" is small. in practice, pre-period outcomes for different individuals remain useful as long as neighbors' outcomes are sufficiently predictive of own outcomes, and neighborhood-level outcomes are sufficiently stable across time. identification based on parallel trends one can alternatively use the panel structure of the data to rely on a "parallel trends" assumption for identification of causal effects in a difference-in-differences approach. in practice, such an approach uses the same estimators as proposed for variance reduction. under the ideal experiment, treatment assignment is independent both of the post-period potential outcomes and of trends between the pre-period and the post-period, conditional on the known randomization probabilities. hence, the experimental setting allows the use of the pre-period data but does not require it, as discussed before. in observational settings, discussed in section , using pre-period data augments the assumption underlying identification. whether treatment assignment is more plausibly conditionally independent of levels or of trends depends on the setting. existing empirical work oftentimes uses panel data without control regions in which no treatment occurred (for instance linden and rockoff, ; currie et al., ; diamond and mcquade, ) . instead, these papers compare individuals near a treated location to individuals farther away from the same treated locations. these farther-away individuals are the control group in a difference-in-difference setup. figure illustrates which individuals these estimators are based on. when estimating the treatment effect ( ) at distance , individuals in an "inner ring" at radius from realized treatment constitute the treatment group. individuals who are substantially farther away in an "outer ring" around the same realized treatment location constitute the control group. typically, the same outer ring individuals serve as control units irrespective of the distance at which the treatment effect is estimated. in a difference-in-differences setup, estimators used in much existing empirical work hence rely on a different parallel trends assumption. specifically, individuals on the inner ring need to be on the same trend as individuals on the outer ring. for each distance for which the researcher estimates an effect, she obtains a different set of inner ring individuals. when the effect at each distance is estimated using the same outer ring individuals, she therefore needs to assume that individuals at any distance from treatment (up to the farther distance) are on parallel trends. effectively, this is the semi-parametric functional form assumption that control potential outcomes in all neighborhoods within a region share the same additively separable time-specific component. for these existing estimator, one additionally needs to assume that the farther-way individuals are unaffected by the treatment. if individuals on the outer ring were directly affected, their outcomes in the post-period would not generally reflect the control potential outcomes of individuals on inner rings even when the parallel trend assumption holds. researchers therefore typically restrict the control group to individuals who are substantially farther away from treatment than the treated individuals. however, this assumption is partly incongruent with the parallel trends assumption: the farther the control individuals are figure : existing estimators focus only on regions that received treatment. in this figure, the realized treatment location is shown as filled-in triangle. the treatment group consists of individuals in an "inner ring" at a given distance of interest from treatment, here displayed as small filled-in circles. the control group consists of individuals in an "outer ring" who are farther away from realized treatment, here displayed as hollow squares. existing estimators use pre-and post-treatment data for both groups in a difference-in-differences setup. typically, when researchers estimate the effect at multiple distances, the same control group is used for all distances. panel a shows the estimator^( short ) for a short distance short . panel b shows the estimator^( med ) for a medium distance med . away from treatment, the less likely the parallel trends assumption is to hold. the choice of distance for the outer ring needs to carefully balance these two competing assumptions. as with other difference-in-differences estimators, demonstrating an absence of pre-trends can strengthen the credibility of the parallel trends assumption. for inner vs. outer ring estimators, researchers need to argue that the absence of pre-trends suggests parallel trends even into the post-treatment period based on randomness of timing, not randomness of treatment locations. when treatment effects at multiple distances are estimated, control potential outcomes at each distance from treatment must be on parallel trends with one another and with the outer ring control individuals. for instance, (diamond and mcquade, , figures , , ) illustrate the absence of pre-trends in plots of three-dimensional data (time since treatment, geographic distance from treatment, outcome). in contrast to the more familiar two-dimensional plots from non-spatial settings, it is unfortunately challenging to include standard errors in such figures. it is therefore oftentimes difficult to accurately assess the magnitude and sometimes even direction of possible pre-trends visually. i therefore recommend formal sensitivity analysis and estimation of the partially identified set of treatment effects under small violations of the parallel trends assumption. recent theoretical work has proposed promising approaches to this problem for non-spatial settings that likely extend to the setting of spatial treatments (for instance manski and pepper, ; freyaldenhoven et al., ; rambachan and roth, ) . in settings with panel data, existing estimators and the estimators proposed in this paper both compare individuals near realized treatment to individuals farther away. for existing estimators, far-away individuals are in an outer ring around the realized treatment locations. for the estimators proposed in this paper, far-away individuals are in other, untreated, regions, near candidate treatment locations that appear similar to real treatment locations. however, the assumption for estimators using individuals on an outer ring as a control group is not generally justified by an ideal experiment of randomizing treatment locations. suppose the researcher is interested in the effect of the treatment at some distance . if individuals on the outer ring were the proper control individuals under an ideal experiment, then for each individual on the outer ring, there must be at least one candidate treatment location at distance from the individual. similarly, there must be candidate treatment locations such that individuals who are at distance from the realized treatment would be in the outer ring relative to these locations. this suggests that candidate treatment locations are everywhere and realized with equal probability, as in panel (c) of figure . this assumption is, in general, testable and typically violated in treatments that are of interest to social scientist; an example is given below. hence, these estimators are generally based on functional form assumptions such as additive separability of time-specific effects, rather than on an ideal experiment that involves randomized treatment locations. a first example illustrates when existing estimators based on an outer ring are relatively more attractive. suppose the researcher is interested in the effect of a spatial treatment at a distance of . miles, and knows that individuals at a distance of . miles are unaffected by it. in this setting, individuals at either distance from treatment are likely similar. they live in the same neighborhood and experience the same conditions except for exposure to treatment. the parallel trends assumptions between inner and outer ring individuals is plausible. instead, one should primarily focus on supporting the argument that the treatment has no effect after a distance of . miles. a second example illustrates when the estimators proposed in this paper based on untreated regions are relatively more attractive. suppose the researcher is interested in the effect of a spatial treatment that is typically realized in the city center. she is only willing to assume that the treatment has no effect after a distance of more than miles. then a comparison of individuals close to the treatment to individuals farther than miles from treatment may compare individuals who live close to the city center to individuals living in suburban neighborhoods. the parallel trends assumption between these individuals is less plausible. since treatment is typically realized in city centers, simple tests are likely to reject pr(treatment at | in rural area). instead, it may be more attractive to compare the individuals near treatment to individuals who live close to the city center of other, untreated, cities. with panel data, one can then assume that the inner city neighborhoods of treated and untreated cities are on parallel trends. if one can argue that the location of the treatment was chosen (quasi-) randomly from a set of candidate treatment locations across multiple cities, the assumption is satisfied by design. the estimators proposed in this paper allow this information to be used directly for identification and estimation of causal effects. in this section, i discuss two assumptions on how realized treatment locations that are close to one another interfere. under either of these assumptions, average treatment effects very similar to those in section are identified and readily estimated. the two assumptions i focus on in this section are: (i) treatment locations have additively separable effects; and (ii) only the nearest realized treatment location matters. additively separable treatment effects are an appropriate specification if the effect of each treatment is independent of the realization of other treatments. for instance, the effects of toxic waste plants (cf. currie et al., ) or air-polluting power plants (cf. zigler and papadogeorgou, ) on exposure to pollution are likely approximately additive. typically, only the nearest realized treatment location matters if individuals only access, or visit, a single realized treatment location. for instance, if a developing country quasi-randomly chooses locations to construct new schools (cf. duflo, ) , it may be plausible to assume that only the nearest school matters to an individual. for the effects of infrastructure projects, such as additional bus or subway stops, on commute times and real estate prices (cf. gupta et al., ) , the appropriate assumption may depend on the type of stops that are added. an additive effects specification for bus or subway stops may be a good approximation if each stop gives access to a different transit line. a specification where only the nearest stop matters may be more appropriate for stops of the same line. in contrast, if the treatments interact in some way leading to diminishing or increasing returns in the number of nearby treatment locations, different parametric assumptions on the functional form of these returns may be necessary. this section serves as an example for how to incorporate such assumptions on interference into the analysis of causal effects. i focus one two settings: a first setting where if a region is treated, a fixed number of candidate locations in the region are realized (completely randomized design within region), and data from untreated regions are available. a second setting where treatment assignment to candidate locations is independent (bernoulli trials), but all data come from a single (contiguous) region. suppose that if region receives treatment, exactly˜of the |s | candidate treatment locations are realized, each with equal marginal probability. assuming a completely randomized experiment between the candidate treatment locations within a region greatly simplifies the formulas in this section without mechanically resolving key conceptual issues. in practice, it is sometimes more plausible to assume that the assignment mechanism guarantees some minimum distance between realized treatment locations. it may be possible to obtain analogous results for such more complicated assignment mechanisms. continue to consider a setting with some regions with no realized treatment location. the presence of regions without realized treatment locations is a crucial simplification because it allows identification of control potential outcomes. within this setting, one can see how the assumptions on treatment effects limit interference and allow estimation average treatment effects similar to those in section . to give an example, suppose a company operating chain stores (quasi-) randomly chooses which cities to enter, and opens multiple stores in chosen cities. then there are multiple realized treatment locations close to one another (in the same city), but also control regions with (unrealized) candidate treatment locations. i discuss a settings without untreated regions further below. even in settings with control regions, one needs to make an assumption on interference to identify and estimate the treatment effects as defined in section . . . suppose one makes no such assumption. if some treated regions have multiple, for instance two, realized treatment figure : an example of a region with three candidate treatment locations (panel a): (blue), (red), (yellow). suppose exactly two of these treatment locations are realized whenever the region is treated, such that there is interference. under the assumption that only the nearest realized treatment location matters, panel b illustrates the locations for which we can estimate effects for individuals in each area. for individuals in the orange area, we can estimate the effects of the red and yellow locations. for individuals in the green area, we can estimate the effects of the blue and yellow locations. for individuals in the purple area, we can estimate the effects of the blue and read locations. locations, then it is impossible to identify the average (across all candidate locations) causal effect of implementing one treatment location. but even the effect of implementing multiple treatment locations at once is difficult to estimate in the detail of interest. presumably, one would be interested in the average effect of implementing two treatment locations at distance and , respectively. a non-parametric estimate of this effect is likely based on very few individuals, since few treated individuals are at distance from one treatment and at distance from another treatment. for a given pair of realized treatment locations, there are at most two locations where circles around them with radii and intersect. limiting estimation to only individuals residing close to such intersection points is therefore oftentimes impractical. it implies a dramatic reduction in sample size relative to estimating the effect of a single treatment at a given distance, based on all individuals around this distance ring. if there are more than two realized treatment locations, or treated regions vary in the number of realized treatment locations, this estimation issue worsens. a simple example, illustrated by figure a, helps to build intuition for the estimators proposed below. suppose the researcher has data from multiple regions . each region has three candidate treatment locations; , , , , and , . if region receives treatment, the assignment mechanism randomly chooses exactly two of the three candidate locations to be realized. hence, each candidate location has marginal conditional probability of / of being realized. the set of realized treatment locations in region , , satisfies ∈ i present and discuss two assumptions on interference and how to estimate effects under them in turn. assumption (additive separability of treatment effects). let ⊂ s be an arbitrary subset of the candidate treatment locations, and let ∈ be an arbitrary location in this subset. the effects of spatial treatments are additively separable if, for all individuals ∈ i, ( ) = ( ∖ ) + ( ). assumption formally states that the effects of all treatment locations are additively separable. intuitively, the assumption requires that there are no diminishing (or increasing) returns to having additional treatment locations nearby. under assumption , one can still identify the average treatment effects defined in section . these estimands are weighted averages of individual-level treatment effects ( ) of individual and candidate treatment location which are distance apart. for exposition, i focus on the example with three candidate treatment locations, two of which are realized in treated regions. under the additive separability, assumption , the potential outcomes satisfy hence the treatment effect of interest is where each of the potential outcomes has positive probability of realization. one can therefore estimate ( ) aŝ additive ( , ) = each term in the sum is an unbiased estimator of the the corresponding potential outcome, such that (^a dditive ( , )) = ( , ). one can then average such estimators to estimate, for instance, the att estimand, ( ). see appendix a. for a generalization. assumption (only nearest realized treatment location matters). let ⊂ s be an arbitrary subset of the candidate treatment locations, and ∈ i an arbitrary individual. only the nearest realized treatment location matters if whenever ∈ satisfies ( , ) ≤ ( ′ , ) for all ′ ∈ , we have, for ′ ∈ ∖ { }, assumption states that if ′ ∈ is not the nearest realized location to individual , it does not affect her. the assumption also implies that if individual is at equal distance to two treatment locations and , then both have the same effect on her: under assumption , only some of the average treatment effects of section are nonparametrically identified in general. specifically, it is impossible to identify the effect of a candidate treatment location on an individual if the treatment location is never the nearest realized location for the individual. consider the example of three candidate locations with two realized locations. the effect of location , is unidentified for individuals nearer to both locations , and , . panel b of figure highlights areas in which each candidate treatment location is nearest with positive probability before realization of treatment assignment. generally, the estimand ( ) from section is identified nonparametrically under assumption if it only places weight on individual level effects ( ) if is the nearest realized location to individual with positive probability. formally, write this as where the probability is taken over draws from the assignment distribution of for fixed , , , and . in the example illustrated in figure , one can estimate ( , ) for individuals in the purple and green shaded areas. under assumption , the potential outcomes satisfy an unbiased estimator of ( , ) iŝ one can then average estimates^n earest ( ) across individuals and locations to estimate average treatment effects similar to those in section . however, the estimator^n earest ( , ) is undefined for individuals in the orange shaded area (last line of the definition). since location , is never the nearest realized treatment location for these individuals, it is impossible to estimate its effect on individuals in that area. that is, only average treatment effects that place weight ( , , ) = on individuals in the orange area are identified nonparametrically. see appendix a. for examples of identified estimands and the general setting. suppose the researcher has data on a single contiguous region with individuals , outcomes and candidate treatment locations s. the realized treatment locations are ⊆ s, with assignment to locations , ′ ∈ s independent when ̸ = ′ . assumption formalizes this assumption, which is a straightforward extension of assumption above. assumption (independent treatment assignment -single region). assignment of treatment to locations is independent: for ∈ s,˜⊆ s with ̸ ∈˜⊆ s, as before, the researcher is interested in the weighted average treatment effect with known weights ( , ), for instance for a distance-bin estimator of the average effect of the treatment on the treated. to estimate the average this average treatment effect, consider the estimator which is the difference in average outcomes for individuals near realized candidate locations, remark . while all treatment probabilities are known to the experimenter in experimental analyses, they typically need to be estimated in observational studies. to this end, first note that one can generally write, for any potential assignment ∈ s , second, pr( ⊂ ) pr( = ) cancels between numerator and denominator. hence, to estimate pr( ∈ | ⊂ ) in practice, it is convenient to parameterize this conditional probability and estimate where ( ) are other (spatial) covariates specific to treatment location (and its neighborhood). the framework, estimators, and analysis of this paper are applicable more generally to settings where treatment assignment is separate from the units of observation, and the effect of treatment is moderated by some observable, not necessarily geographic, distance from treatment. i give two examples in this section: firm entry in markets with differentiated products, and shift-share designs based on randomness of the shifts. for the first example, suppose the researcher is interested in the effects of firm entry on competition in markets with differentiated products. she has data for several markets on prices charged by firms ∈ i for products with horizontal or vertical locations in characteristics space. in some markets, a new firm enters with a product with characteristics . here, the estimand ( ) measures the average effect an entrant has on the price of a product at distance in characteristics space. for short distances , it captures competitive effects or deterrence behavior by firms selling products very similar to the product of the entrant. for longer distances , it captures ripple effects that arise if in equilibrium firms with more different products react to the price changes of firms with products similar to the entrant's. these estimands are therefore informative about the nature of competition. firm entry, however, is not generally random. theoretical models of competition and profits may therefore help to determine the probability of firm entry at any given point in characteristics space, conditional on the locations of existing competitors in characteristic space. for instance, expected profits of the entrant may come from a structural model based on distance to competitors in characteristics space (cf. hotelling, ) , perhaps calibrated to pre-treatment data. intuitively, validity of the estimator then requires that firm entry is random conditional on the expected profitability in the model. the structural model provides a baseline to enhance the credibility of the quasi-experimental analysis, but does not directly restrict the estimated pattern of competition. for a second example, suppose the researcher is interested in the causal effects of exogenous shocks to individual industries on employment outcomes in cities based on their industry mixes (cf. autor et al., ) . the framework of this paper is useful in this setting if the claims of causal identification are based on randomness in which industries are shocked, rather than on randomness in industry composition. importantly, the analysis in this paper reflects that cities with similar industry mixes are shocked similarly, in a way that is difficult to capture accurately with existing clustered standard errors. adao et al. ( ) and borusyak et al. ( ) develop alternative approaches based on the same idea, and show how it relates to bartik ( ) and shift-share instruments more generally. a benefit of the framework of this paper is that its results are not specific to linear (or other) functional form and that it allows for very transparent estimation of aggregate effects. the setting fits into the framework of this paper as follows. data are available for time periods = , . . . , . in some time periods, a single industry ∈ s = { , . . . , } receives an exogenous shock, potentially with different industries shocked in different time periods. assume that the time periods are chosen such that the shock only affects outcomes within the same time period. define the indicator = if an industry in period is shocked, and = otherwise. the researcher observes employment outcomes for cities ∈ i in time period . city has industry shares ∈ r , satisfying , ∈ [ , ] and ∑︀ = , = . here, the distance function captures exposure to the shock. city is heavily exposed to shocks of sector if industry has large share , , such that the "distance" ( , ) = − , is small between industry and city . the estimands ( ) and measure the effects of the exogenous industry shocks. for = , the estimand ( ) measures the average effect of shocking an industry on employment in cities with employment only in the shocked industry. for = . , the estimand measures the average effect of the exogenous shock on cities with % of their employment in the shocked industry. the estimand measures the aggregate effect of the exogenous shock across all cities, averaged across shocks to different sectors. the estimators and inference procedures of section are valid if it is random in which time periods and sectors an exogenous shock occurs. in principle, one can augment the variance calculations to allow, for instance, dependence structure in the shocked industry across time periods. the results in section . are relevant for settings where shocks occur to multiple industries in the same time period. while the previous sections presumed that the researcher designed the experiment for assignment of the spatial treatment, much empirical work relies on observational data. the primary challenge to observational studies in this setting is that researchers typically do not observe the exact locations of unrealized candidate treatment locations. to emulate the analysis of the ideal experiment with observational data, researchers need to estimate candidate treatment locations and their treatment probabilities. estimation is then based on an unconfoundedness assumption stating that among individuals near candidate treatment locations, whether their treatment location is realized is as good as random, conditional on characteristics of the individuals and the neighborhood of the candidate treatment location. suppose that there are multiple regions = , . . . , , defined such that any treatment location only affects individuals within the same region. define the location-specific treatment indicator ( ) to equal if location in region is treated, and − if the location is no treated: where = if treatment occurs somewhere in region , and is the realized treatment location in region as in section . in treatment effect settings with individual-level randomized experiments, unconfoundedness is often written as ⊥ ⊥ ( ), ( ) | = which is equivalent to an assumption on densities i similarly define unconfoundedness of spatial treatments at distance from location as here, = means that the sets of individual covariates are the same up to permutation. in practice, it is rarely feasible to find two candidate locations with equal number of individuals and equal covariates. instead, one can assume that treatment is unconfounded conditional on, for instance, average characteristics of individuals in the neighborhoods of candidate locations. such an assumption greatly simplifies estimation in practice. alternatively, one can make an individual-level unconfoundedness assumption for spatial treatments as a conditional mean equality, where, for the control potential outcome, there is no conditioning on distance from candidate treatment locations. in other words, individuals with the same covariates , potentially including neighborhood characteristics of , in control regions offer a valid comparison for the individuals treated at distance . such an assumption simplifies estimation, but is not justified by experimental design or arguments that the location of the treatment is as good as random. in this section, i outline a general strategy for finding unrealized candidate treatment locations with observational data. these counterfactual locations for the treatment are necessary for the quasi-experimental methods i propose in this paper. consider first the example of linden and rockoff ( ) given in the introduction, where the choice of candidate locations is relatively straightforward. they argue that the exact houses where sex offenders move in are as good as random due to random availability of houses within neighborhoods. here, the candidate treatment locations are houses in these neighborhoods. hence, the candidate locations are known, but their probabilities of treatment need to be estimated. see section . for propensity score estimation. when there are no (or insufficiently many) known unrealized candidate locations, however, the problem of choosing candidate locations from continuous space is hard. in principle, one could imagine estimating the probability of treatment at any location in a region conditional on all the features of the region. this is akin to estimating the spatial distribution of treatment locations ∼ ( ), where are the characteristics of region , potentially relative locations of all individuals in the region as well as moments of their covariates. one could then use the estimated^to inform the treatment probabilities at each point in the region as inputs in the estimators proposed in this paper. in practice, it is typically sufficient to find a finite number of candidate treatment locations that offer a plausible counterfactual to the realized treatment locations. computationally, it is often infeasible to use a continuous distribution , since the weight of each individual when estimating effects at distance would depend on the integral of^along a ring with radius around her location, . instead, i recommend finding a finite number of candidate locations. the average across these finitely many candidate locations approximates the strategy based on the complete distribution . i propose taking draws ∼^( ) to obtain candidate treatment locations. perhaps surprisingly, recent machine learning methods achieve good results at this task, despite the difficulty of estimating itself. specifically, i recommend a formulation similar to generative adversarial networks (goodfellow et al., ) ; see liang ( ) and singh et al. ( ) on the relationship between generative adversarial networks and density estimation. most closely related to this paper, use generative adversarial networks to draw artificial observations from the distribution that generated the (real) sample, for use in monte carlo simulations. generative adversarial methods for drawing ∼ ( ) are based on iteration between two steps. first, a generator generates draws˜∼˜( ), where˜is an implicit estimate of the density maintained by the generator in the current iteration. second, a discriminator receives as input either counterfactual locations proposed by the generator,˜| , or real treatment locations, | , and guesses whether its input is real. both the generator and the discriminator are highly flexible parametric models for their given tasks. the discriminator is trained by taking (stochastic) gradient descent steps in the direction that improves discrimination between real and counterfactual locations. the generator is trained by taking (stochastic) gradient descent steps in the direction that leads to fooling the discriminator into classifying counterfactual locations as real. effectively, the output of such models are counterfactual candidate treatment locations | that are indistinguishable (to the discriminator) from real treatment locations | . with a sufficiently flexible discriminator, the process is therefore similar to matching. if a proposed candidate location˜is noticeably different from all real treatment locations , a flexible discriminator will learn to reject˜. in contrast, synthetic control-type methods (abadie et al., ) would average multiple candidate locations, for instance˜and˜, to create a synthetic counterfactual for a real treatment location . if˜and˜individually differ from all real treatment locations , the discriminator will reject them despite their average resembling . the goal therefore is to find "false positives:" occasions when the classifier suspects a missing realized location even though there is no such missing realized location. typical classifier networks do not directly make binary predictions, but give a continuous activation score that indicates how likely each location (or the "no missing location" category, see below) is. in practice, i recommend looking for high activation scores for a particular location and low activation score for "no missing location." alternatively, one can look directly for activation scores resembling the activation scores of real treatment locations. such locations are likely to be decent matches for the real treatment locations, since they must share features of realized locations in order to achieve high activation scores. in the remainder of this section, i discuss how to tune generic machine learning methods to find suitable candidate treatment locations in social science applications. i recommend four high-level implementation decisions in adapting these methods. first, discretization of geographic space into a fine grid for tractability. second, convolutional neural networks capture the idea that spatial neighborhoods matter in a parsimonious way. third, incorporating the adversarial task of the discriminator into a classification task for the generator greatly simplifies training. fourth, data augmentation (rotation, mirroring, shifting) for settings where absolute locations and orientation are irrelevant. discretization to tractably summarize the relative spatial locations of individuals and treatment locations, i recommend discretizing geographic space into a fine grid. discretization provides an approximation that is particularly tractable for the convolutional neural networks recommended below. in principle, future improvements to, for instance, capsule neural networks (hinton et al., ) or other novel methods, may replace this as the preferred architecture and eliminate the need for discretization. for each grid cell, one can include a count of individuals with residence in the cell, potentially separately for individuals with different values of covariates, as well as average covariate values of the individuals in the cell or other moments of their covariates. if the grid is very fine, this discretization retains almost all meaningful information about relative locations. for instance, in the application of this paper, each grid cell has size . mi × . mi (approximately m × m). the discretized grid creates a three-dimensional array: the first two dimensions determine spatial location, and the third dimension enumerates the different covariates that are summarized. rather than taking the spatial dimensions to be entire regions, i recommend using square cutouts of regions such that the probability of treatment in the center of the cutout is only affected by individuals and covariates within the cutout. convolutional neural networks convolutional neural networks (cf. krizhevsky et al., ) have been particularly successful at image recognition tasks. in image recognition tasks, the input is a d array: a d grid of pixels, with multiple layers corresponding to the rgb color channels. for spatial treatments, the input also is a d array: the d spatial grid with layers corresponding to different covariates as described above. convolutional steps in neural networks generally retain the shape of the d grid, but the value of each neuron is a function of the covariates (or neurons) of the previous step not just at the same grid cell, but also the covariates (or neurons) at neighboring grid cells. figure illustrates this aspect of the convolution operation. however, the particular way in which the neighborhood of a grid cell is averaged is the same for any point in the grid. this makes convolutional layers substantially more parsimonious than fully connected layers, and allows the neural network to capture neighborhood patterns appearing in different parts of a region in a unified way. in particular, i recommend using at least two convolutions with reasonably large spatial reach. consider the application in this paper, where grocery stores are spatial treatments and restaurants are individuals with foot-traffic to the restaurants as the outcome. the first convolution allows each grid cell to see what other cells are around it. in the example, the output of the first convolution for a particular grid cell may be: "there are grocery stores nearby, competing restaurants very close, and restaurants within walking distance." the second convolution then uses the information on such neighborhoods to determine whether treatment is likely in a grid cell: "if there are many grid cells nearby (in all directions) containing restaurants or grocery stores facing much competition, this location is probably in center of a shopping area and reasonably likely to contain another grocery store." intuitively, the first convolution may measure what is important to the restaurants, while the second figure : convolutions in a neural network allow the prediction of a candidate location in a grid cell to depend on the characteristics of neighboring grid cells (up to a user-specified distance). these models remain parsimonious by requiring the same "neighborhood scan" to be performed for each grid cell. convolution translates how that is important for the treatment location choice, mirroring the unconfoundedness assumption (equation ) of the previous section. adversarial classification generative adversarial networks are oftentimes difficult to train despite recent advances such as networks with wasserstein-type criterion function . the difficulty arises because the training of generator and discriminator needs to be sufficiently balanced such that both improve. in contrast, convolutional neural networks for image classification are much easier to train. i therefore recommend to set up the problem of finding candidate treatment locations as a classification task. specifically, the convolutional neural network takes a given input array and "classifies" it into, say, categories, where each category corresponds to a grid cell and signifies that there should be an additional treatment location at that point in the grid. to retain the adversarial nature of the task, train the classification on three sets of data: first, regions with at least one real treatment location, but with one treatment location removed. the correct classification of such region data is into the category corresponding to the grid cell from which the treatment location was removed. second, regions with at least one real treatment location, but without any treatment location removed. the correct classification of such region data is into a specially added category signifying no missing treatment location. third, regions without treatment locations. these are also classified as not missing any treatment location. the neural network then balances two tasks: a generative task of picking the correct location if a treatment location is missing, and a discriminatory task of deciding whether a treatment location is missing at all. this structure retains the attractive interpretation of generative adversarial networks, but is substantially easier to train. technically, it resembles denoising autoencoders (cf. vincent et al., ) . data augmentation data augmentation serves two closely related purposes. first, rotating, mirroring, and shifting regions, while maintaining relative distances, produces additional, albeit dependent, observations. this is helpful since training neural networks requires large numbers of training samples. second, these transformations effectively regularize the parameters of the estimated model. one can choose transformation that induce equivariance to rotation, mirroring, and shifts as appropriate for the particular setting. for instance, in many applications in the social sciences, north-south and east-west orientation is irrelevant on a small scale; only the relative distances matter. in particular, suppose an individual who visits a business to the north of her home because it is on the way to work in the north. if the whole space was rotated, the individual equally visits the same business now to the west as it is still on the way to work, now also rotated to be to the west of her home. in image classification, the use of similar data augmentation is common and often associated with greater generalizability of the learned models. shifting the entire grid has two further desirable effects: first, if one imposes a continuous shift of relative coordinates in combination with a fixed grid, the exact discretization becomes less relevant. the average (across draws from the shift distribution) distance in grid cells between two observations becomes directly proportional to their actual distance. second, the location of an observation within a grid cell is no longer fixed. this is attractive because the classification is not actually informative of whether the candidate treatment location is at the center or towards the edge of a grid cell. with a continuous shift of the observations, the center of the grid cell points to different absolute locations depending on the shift. one can then average over several realizations of the shift to reduce the influence of the particular translation of grid cell to absolute location. there are at least two notable alternatives or complements to data augmentation in the machine learning literature. first, spatial transformer networks (jaderberg et al., ) attempt to estimate a rotation or other transformation that makes the subsequent classification task as easy as possible. second, some recent work considers imposing the desired in-and equivariance properties on the convolution kernel. similarly, penalization of deviations from in-or equivariance serves as a less strict regularization of the model parameters. ultimately, current implementations of these methods are less computationally efficient than data augmentation and standard convolutional neural networks. furthermore, simulation evidence suggests that data augmentation achieves the first order gains implied by these properties. one can also inspect the models to assess the implied degree of invariance, and consider averaging parameters as implied by invariance. suppose candidate treatment locations s are known (in all regions), for instance as output of the convolutional neural network classification tast described in the previous section. the remaining challenge in implementing the methods proposed in this paper is the estimation of the "propensity score" pr( ∈ ). i briefly sketch propensity score estimation in two canonical settings: a fixed number of realized treatment locations per treated region (often just one realized location), and independent bernoulli trials determining realization of treatment at candidate locations. fixed number of realized treatment locations suppose there are a fixed number of realized treatment locations per treated region. then the problem of propensity score estimation resembles discrete choice modeling: there are |s | discrete alternatives in region , a fixed number of which is realized. see, for instance, greene ( ) for an overview of estimation methods. when treatment assignment is independent across locations, propensity score estimation for spatial treatments is similar to propensity score estimation for individual-level treatments. logistic regression is a simple option. each candidate treatment location ∈ s is a separate observation. with logistic regression, regress the indicator { ∈ } on covariates ( ) that describe the neighborhood of candidate location as well as (moments of) the characteristics of individuals near location , ( ) : ( , )= for all distances of interest . adjusting for the true propensity score is likely sufficient for unconfoundedness in equation , similar to the setting with individual-level treatments (cf. rosenbaum and rubin, ) . using estimated propensity scores in observational studies, the propensity score is typically estimated by the methods above rather than known. even when the propensity score is known, there may be benefits from using estimated propensity scores for parts of the analysis as in experiments with individual-level treatments (cf. hahn, ; hirano et al., ; frölich, b) . when estimated propensity scores are close to or , the inverse propensity score weighting estimators proposed in this paper may perform poorly (cf. frölich, a; busso et al., ) because small estimation errors in the propensity scores have large effects on the weights when denominators are close to zero. to reduce the effect of estimation error from this first-stage estimation, i also use cross-fitting and a doubly-robust moment condition (e.g. chernozhukov et al., ) in the application of this paper. while existing results assuming i.i.d. data are not directly applicable to the spatial treatment setting, doubly-robust moments likely still substantively reduce the effect of error due to propensity score (and outcome model) estimation. treatments, restaurants are the (outcome) individuals, and foot-traffic (the number of customers) is the outcome of interest. i argue that the inner ring vs. outer ring comparison used in many recent empirical studies is unattractive in this setting: its identifying assumption is not credible, and it requires discarding the majority of the sample for practical reasons. i show how to implement the methods proposed in this paper, and argue that the control groups these methods are based on are preferable to outer ring control groups. the average treatment effect of interest is identified by an ideal experiment where some grocery store locations are randomly closed during covid- lockdowns. specifically, take a restaurant near a grocery store at location . what is the difference between the number of customers of restaurant during the covid- lockdown when there is a grocery store at location , and the number of customers of restaurant if there was no grocery store at location , holding fixed the locations of all other businesses and grocery stores. in the notation of this paper, if are the locations of other grocery stores, the treatment effect of interest is ( ) = ( ∪ { }) − ( ). this effect is distinct from fixing a spatial location near a grocery store, and considering the difference in the outcome (during covid- ) of the business that exists at this point in space when there is a grocery store nearby, and the outcome (also during covid- ) of the, possibly different, business that would have been at the same location, had there never been a grocery store nearby. grocery stores may have causal effects on the number of customers to nearby restaurants if they draw customers into the shopping and business area. in particular during the first few weeks of the covid- lockdowns, when individual mobility was greatly reduced, getting groceries may have been one of the few trips still made. if grocery store customers are more likely to stop by coffee shops or restaurants for pick-up orders right before or after getting groceries, restaurants and similar businesses may receive more foot-traffic if there is a grocery store nearby. large department stores serving as "anchor stores" of shopping malls may play a similar role in normal times. relatedly, jia ( ) studies the effects of new wal-mart stores on existing businesses. study the effect of restaurant closings on nearby restaurants. the effects of grocery stores on nearby restaurants are informative about several questions. do grocery stores have (positive) externalities on other businesses? if so, should mall operators subsidize grocery stores through lower rent such that they internalize these externalities, to support other businesses in the mall? in the context of pandemics, are grocery stores likely choke points leading to bunching of customers at nearby restaurants instead of spreading out across all restaurants, increasing the risk of infections? alternatively, grocery stores may resolve a coordination problem: suppose that the overall reduced number of restaurant customers is insufficient to operate restaurants profitably or with reduced loss when spread across all restaurants. grocery stores may then help to resolve a coordination problem between restaurants, by focusing potential restaurant customers on the nearby restaurants. i use safegraph data on the number of customers of each business in the week starting april , . i restrict the sample to businesses in the area between san francisco and san jose in the san francisco bay area, as highlighted in figure . restricting to businesses with the outcome of interest is the inverse hyperbolic sine of visits to restaurants, with visits as measured by safegraph. to interpret the percentage point effect on the number of safegraphtracked customers as the overall effect, assume that safegraph's sample selection is orthogonal to the presence and absence of grocery stores. otherwise, the estimates retain internal validity as the effects on the number of safegraph-tracked customers to these restaurants. the inverse hyperbolic sine allows for zero visits, and effects on it can be transformed into elasticity estimates similar to log( ) or log( + ) specifications (see bellemare and wichman, , for a discussion). businesses with fewer customers may also be open. however, grocery stores with few if any customers tracked by safegraph are unlikely to have effects on the number of safegraph-tracked customers to nearby restaurants. safegraph ( ) describes the algorithm used for attributing visits to businesses. generally, pick-up orders as well as outside dining are likely picked up by the algorithm as long as a customer's smartphone sends location data at the point of interest for more than one minute. for errors in attribution to matter in the application of this paper, they need to correlate with the presence or absence of nearby grocery stores. the inverse hyperbolic sine is defined as arcsinh( ) ≡ ln( + √︀ + ). hence arcsinh( ) = , arcsinh( ) ≈ . , arcsinh( ) = . , and arcsinh( ) ≈ ln( ) + . if ≥ . figure : the comparison of businesses on an inner vs. outer ring around a particular grocery. the grocery store is marked by an orange triangle in the center of the figure. other businesses are small blue circles. businesses on the gray inner ring, at a distance of . ± . miles, are primarily in strip malls, while businesses on the gray outer ring, at a distance of . ± . miles, are away from these main shopping areas. figure illustrates why comparisons between observations on an inner ring and observations on an outer ring around a strategically chosen location are often not attractive. here, businesses (blue circles) on the inner ring are at a distance of . ± . miles from the grocery store (orange triangle), while businesses on the outer ring are at a distance of . ± . miles from the same grocery store. while inner ring businesses are part of the same strip mall, outer ring businesses are outside of the primary shopping areas. interpreting differences in outcomes for these two groups of businesses as causal effects requires assuming that outer ring businesses are unaffected by treatment and have similar outcomes as inner ring businesses in the absence of treatment. generally, distance from treatment often correlates with many other variables (kelly, ) . with small numbers of grocery stores (see below), the mode of average treatment effect estimates may not be close to the true average effect, even if the locations of grocery stores were random. this arises due to spatial correlations in outcomes even in the absence of treatments (cf. lee and ogburn, , in a network setting). while panel data can in principle relax one of the underlying assumptions, the common (visual) test for the absence of pre-trends carries little information about the validity of the identifying assumption in this setting. with panel data, the assumption of comparability of inner and outer ring businesses is relaxed slightly to an assumption of parallel trends. businesses on inner and outer rings are allowed to have different average levels of customers, but trends in the inverse hyperbolic sine of the number of customers must be parallel. however, even if panel data suggested that trends between inner and outer ring businesses were indeed parallel pre covid- , one may question whether this is informative about changes in (potential) outcomes during covid- lockdowns. given the dramatic decrease in customers for all businesses, it is questionable that this decrease would have occurred in parallel with only an additive shift (in the inverse hyperbolic sine) for inner and outer ring businesses in the absence of treatment. additionally, the estimand of a difference in differences estimator in this setting is the additional effect of grocery stores on nearby businesses during covid- on top of any effects that may have already existed pre covid- . even if the parallel trends assumption was credible, this estimand differs from the estimand of interest described above. the difference in differences estimand can be negative even though the effect of grocery stores on nearby businesses is positive during covid- if the effect of grocery stores pre covid- was also positive but larger in magnitude, for instance due to overall difference in the scale of the number of customers. finally, in most instances, businesses on the outer ring around a grocery store are not actually far away from grocery stores ("untreated"), as illustrated by panel (a) of figure . here, some of the businesses on the outer ring centered around the grocery store in the center of the figure are very close to a second grocery store to the north. applying the inner vs. outer ring estimator in this setting therefore requires restricting the sample to the neighborhoods of the few grocery stores that are sufficiently far away from other grocery stores. specifically, to guarantee the absence of interfering grocery stores for an outer ring "no effect" distance of . miles, only grocery stores with no other grocery store within × . miles can be used. panel (b) of figure shows the locations of the remaining grocery stores. compared to figure , these grocery stores are in more remote, less (sub-) urban neighborhoods. while the average treatment effect of grocery stores in such locations may continue to be of interest, it is plausibly distinct from the treatment effect in areas with higher population or business density. figure shows the comparison of means resulting from the inner vs. outer ring estimation. the average outcome of any distance to treatment (blue curve) is differenced with the average outcome of the outer ring (horizontal gray line), here chosen to be businesses between . and . miles from real grocery store locations. using grocery store fixed effects improves upon these estimates slightly by allowing the weights on the outer ring of each grocery store to vary by distance from treatment. intuitively, if % of all inner ring businesses are at distance from grocery store a, then the outer ring businesses around grocery store a should receive % of the aggregate weight of all outer ring businesses for estimating the effect at distance . if the fraction of inner ring businesses that are near grocery store a is different at distance , then also the businesses on the outer ring of grocery store a should on aggregate receive the different weight. estimates from this fixed effect specification are shown in row of table . for row , the aggregate weight for businesses near each grocery store are constant at / (weighting each of the grocery store locations equally), irrespective of the number of businesses near each grocery store, resembling the weighting of the estimand att-eq ( ) and facilitating a comparison of the effect at different distances from treatment. note that, for the inner ring vs. outer ring estimation, i cannot estimate the effect at a distance of larger than . miles because i have to assume that there was no treatment effect at that distance to be able to define an outer ring that is not near any grocery store. the spatial experiment estimator based on the ideas proposed in this paper, also shown in table , suggests that there indeed likely is no treatment effect past that distance. however, : panel (a) shows an example of a grocery store (triangle in the center) with a second "interfering" grocery store (triangle towards the top) nearby. some businesses on the outer ring are close to (treated by) this second grocery store and therefore not a valid control group. panel (b) shows that restricting the sample to the (out of ) grocery stores without interference leads to a sample selected heavily towards less business-dense areas compared to the overall sample shown in figure . the inner ring vs. outer ring estimator additionally requires that the average outcome at those longer distances is informative about the average outcome at shorter distances. as argued above, figure suggests this assumption is not a particularly good approximation. this application is covered by the framework of section . for a single contiguous region with independent treatment assignment. the key idea behind identification for the proposed methods is that the location of a grocery store is as good as random between candidate locations with similar numbers and industries of nearby businesses. figure shows an example of an ideal comparison where the only difference between the (parts of the) regions is the absence of the bottom-most grocery store, and all other relative distances are the same. the approach i propose for observational data proceeds in two steps: first, it finds good "matches" for each grocery store; that is, locations without a grocery store that are similar in terms of the number, types, and relative locations of other businesses and grocery stores. second, assume the matched data resemble the ideal experiment of randomizing grocery stores between the real and counterfactual candidate treatment locations. i recommend inverse propensity score weighting estimators based on the results of sections and . . conceptually similar combinations of matching or stratification and propensity score weighting or regression adjustments have been advocated for by abadie and imbens ( ) , (imbens and rubin, , ch. ) , and kellogg et al. ( ) , among others. the grocery store location prediction following section . discretizes the south bay region into a fine grid and aggregates characteristics of businesses in each grid cell. figure illustrates the discretization for the surroundings of an example grocery store, see panel (a). for each grid cell, record the number of grocery stores as in panel (b) . other characteristics of each grid cell, for instance the number of businesses by industry are recorded in similar grids as in panel (c). figure : the propensity score model can still distinguish between some of the false positives / counterfactual locations and real grocery store location, resulting in many candidate locations with low propensity score. after a propensity score matching step and re-estimation of the propensity score, overlap is better. real and counterfactual grocery store locations have similar (estimated) propensity score. based on this discretization, i use the method as described in section . to find counterfactual candidate grocery store locations that are indistinguishable from the real grocery store locations. since the method can find a very large number of counterfactual grocery store locations, i use propensity score matching to narrow the sample down to a smaller but more balanced sample of real and counterfactual grocery store locations. panel (a) of figure shows the limited overlap in propensity scores before this second matching step, while panel (b) shows good overlap for the final set of candidate locations. to estimate propensity scores in this setting, i assume that grocery store openings are independent decisions at each location, assumption . in practice, this assumption is primarily relevant at the margin of opening (or closing) additional grocery stores relative to the existing grocery stores. since there are neighborhoods similar in other businesses but differing in the number of grocery stores, this assumption may offer a reasonable approximation. the inverse probability weighted real and counterfactual grocery store locations are similar in everything except their exposure to real grocery stores, which differs by one additional grocery store. figure shows that the exposure to treatment is as intended: the number of grocery stores at distance between . and . miles from a business is the same between businesses at any distance from real and counterfactual grocery store locations, except businesses at that distance from a candidate grocery store location. businesses at distance from a real grocery store have exactly one additional real grocery store at distance on average, compared to businesses at distance from counterfactual grocery store locations. furthermore, the composition of nearby businesses is similar between real and counterfactual grocery store locations at any distance. figure shows that the fraction of restaurants among businesses at distance from counterfactual grocery store locations is comparable to the fraction of restaurants among businesses at distance from real grocery store locations. this lends credibility to the treatment effect estimates below. treated and control businesses are alike, except for a single additional grocery at the intended distance. distance from potential grocery store location in miles share of businesses that are restaurants realized false true figure : the composition of businesses near real and counterfactual grocery store locations is similar. it is encouraging that counterfactual grocery store locations mimic the business composition pattern across distance of real grocery store locations. since the fraction of restaurants decreases meaningfully from short distances to longer distances, inner vs. outer ring comparisons of all businesses would compare businesses in different industries. inner ring vs. outer ring comparisons of restaurants would compare restaurants in different (business) neighborhoods. figure : weighted mean of inverse hyperbolic sine of visits for businesses near real grocery store locations (blue line) and for businesses near counterfactual grocery store locations (red line). the difference between the two lines at a given distance is the estimate of the average treatment effect at that distance. panel (a) includes all businesses, while panel (b) restricts the sample to restaurants. there is a substantial estimated treatment effect at very short distances of up to . miles, and no meaningful difference between treated and control businesses at larger distances. given candidate treatment locations and propensity scores, i estimate treatment effects with the estimators of section . . to interpret the estimated effect as the average effect of opening single grocery stores, rather than the marginal of adding a grocery store to existing exposure, one can make the additivity assumption . additivity may be plausible if each additional grocery store brings new customers into an area. during covid- , customers may reduce the number of different grocery stores they shop at to limit their exposure. furthermore, there is differentiation in the grocery store market: the customers at discount grocery outlets may be distinct from the customers at whole foods. figure shows the average outcome of all businesses (panel a) and restricted to restaurants (panel b) by distance from candidate treatment location, contrasting real grocery store locations (blue line) and counterfactual grocery store locations (red line). at very short distances, businesses (including restaurants) on average have more customers if a (real) grocery store is nearby. if the grocery store is . or more miles away, it has no more effect on the businesses. table shows the spatial experiment estimator, which is the same as the difference between the curves at each distance for restaurants (corresponding to panel b of figure ). i also report estimates for the alternative estimator^a tt-eq ( ), which holds the aggregate weight placed on each grocery store constant across distances. i recommend this estimator for comparisons of effects across distances. since the grocery stores causing the effects are heterogeneous in their numbers of customers, their effects on foot-traffic to nearby restaurants is likely to be heterogeneous as well. i also estimate the att using a doubly-robust moment (e.g. chernozhukov et al., ) . the natural extension of the att-moment to the spatial treatment setting with interference table : estimated effects on the inverse hyperbolic sine of number of visits to restaurants using different estimators. the first panel uses the inner vs. outer ring comparison. the second panel uses the inverse probability weighting estimators for spatial experiments proposed in this paper. the third and final panel uses a doubly-robust version of the spatial experiment estimator. for each method, i implement to estimators: the average effect of the treatment on the treated (^( )), and the equal weighted att estimator (^a tt-eq ( )) that has a more attractive interpretation for comparing the effect at different distances. standard errors for the inner vs. outer ring estimators are clustered by grocery store. standard errors for the spatial experiment estimators will be reported in future version. note that the inner ring vs. outer ring comparison uses substantially fewer treatment locations because it requires restricting the sample to isolated grocery stores. where ( ( ) ) averages over all combinations of candidate grocery store locations and individuals satisfying ( , ) ≈ . { ∈ } plays the role of the "treatment indicator." the function ( , ) gives the expected outcome (inverse hyperbolic sine of number of visits) for a business with covariates , including neighborhood characteristics, when there are grocery stores at locations . for a business near a real grocery store, the conditional mean function is evaluated in the absence of the nearby grocery store , ∖ { }, with the parameter of interest, ( ), capturing the difference between actual outcome and expected outcome in the absence of the nearby grocery store. for businesses near an unrealized candidate location , the conditional mean function is evaluated at the background treatment exposure level . the propensity score ( ) gives the probability that there is a real grocery store at candidate location , conditional on characteristics of the neighborhood of . this moment function satisfies the neyman orthogonality condition of chernozhukov et al. ( ) . relative to the spatial experiment estimator, which treats the propensity score as known, this estimator has the advantage of reducing the impact of small errors in the estimated propensity score through orthogonalization. overall, the inverse propensity score weighting estimator and the doubly-robust estimator yield similar results as shown in table above. grocery stores have an economically large positive effect during covid- lockdowns only at short distances of less than . miles. intuitively, grocery store customers do visit nearby restaurants and coffee shops, but are unlikely to walk for more than a couple of minutes from the grocery store location. for instance, at the (control) average inverse hyperbolic sine of visits of approximately . , an increase of . points implies a % increase in the number of customers. the aim of this paper is to argue that leveraging quasi-random variation in the location of spatial treatments is both conceptually attractive and feasible in many settings in practice. i propose a framework and experimental approach for estimating the effects of spatial treatments. this approach uses random variation in the realized locations of the spatial treatments for causal identification. i argue that an alternative estimator commonly used in practice is not justified by the same random variation, but instead identifies causal effects only under sometimes questionable functional form assumptions. to operationalize the (quasi-) experimental approach with observational data, i propose a machine learning method to find counterfactual locations where the treatment could have occurred but did not. the proposed method specifically leverages that neighborhood characteristics are predictive of both the location of treatments and the outcomes of individuals. convolutional neural networks learn this rich spatial dependence structure encoding relevant institutional features from the data. i incorporate the appealing properties of generative adversarial networks in a classification problem that leads to much simpler training in practice, similar to denoising autoencoders. i illustrate the proposed methods in an application studying the causal effects of grocery stores on foot-traffic to nearby restaurants during covid- lockdowns. several key questions remain for future research. in some settings, the spatial treatment is endogenous, but geographic characteristics which are continuous in space are available as plausibly exogenous instruments (cf. feyrer et al., feyrer et al., , james and smith, ) . it is unclear how to construct powerful instruments from such geographic characteristics and incorporate them in the causal framework of this paper. in this paper, i also assume that there is no migration response to the treatment. to allow for migration, one could either focus on outcomes at fixed geographic locations instead of outcomes of fixed individuals or embrace a local average treatment effect (angrist et al., ) with a large number of compliance types if individuals move to different distances from treatment. the analysis in this paper is focused on estimating (potentially weighted) average treatment effects. in practice, decision makers may often be more interested in the optimal location for the spatial treatment. here, consider the expectation of the term in the numerator corresponding to individual , the first step uses that the realized outcome is the potential outcome corresponding to the realized treatment. the second step rewrites the potential outcome and distance bin indicator function in terms of non-stochastic candidate locations by summing over all possible treatment locations in the region, ∑︀ ∈s ( ) { = ( ) }. the third step moves the expectation into the summation, and the non-stochastic distance bin indicator function and potential outcome out. the final step resolves the expectation in terms of the probabilities determined by the experimental design, defined in section . the general estimator of interest in the setting without interference can be written aŝ where index denotes regions, = if region is treated at some location, and is the single treatment location chosen in region (if any). the weight function ( , ) is chosen by the user to weight individuals and treatment locations as desired and primarily place weight on pairs that are distance apart. for instance, for the att estimator with distance bin, choose ( , ) = ( ) { ( , ) ≤ ℎ}. the probabilities of treatment in regions and locations are given by ≡ pr( = ) and ( ) ≡ pr( = { }| = ). the first term averages over individuals at distance from a realized treatment location. the second term averages over individuals at distance from unrealized candidate treatment locations. the estimator estimates the weighted average treatment effect: with user-specified weights . the experiment considered here is a completely randomized experiment at the region level, where a fixed number of regions receive treatment at exactly one location each, and treatment in a region is assumed to have no effect on outcomes in other regions -regions are "far apart." the estimator^( ) is hard to analyze (in finite samples) because the denominators are random. this arises because, depending on treatment assignment, there may be more or fewer individuals near realized / unrealized locations. the same problem exists in standard randomized experiments when the treatment is randomized by an independent coin flip for each individual, such that the number of treated varies from assignment to assignment. in that setting, we can instead analyze the experiment with number of treated fixed at the value observed in the realized sample. conditioning on the number of realized treatment locations is not sufficient in the spatial setting because the number of individuals would still vary since some locations have more individuals near them than other locations. conditioning on the number of individuals restricts the assignment distribution asymmetrically -inverting an assignment generally changes the number of individuals near treatment -such that standard estimators are no longer unbiased by design. the theoretical analysis of^( ) therefore relies on an approximate estimator that fixes the denominators (at their expected values), and centers the numerators in a way that minimizes the difference between^( ) and its approximation. the approximate estimator is where ( ) and ( ) are average potential outcomes: here, i show that the estimators^( ) and˜( ) are very close in large enough samples. this motivates the use of exact finite sample results for the mean and variance of the infeasible estimator˜( ) for inference with the feasible estimator^( ). the analysis uses the mean value theorem to derive the difference^( ) −˜( ) and argues that this difference is small in large enough samples. as a practical matter, a sample is large enough if the number of individuals near treatment and control are close to their expected values. the approximation of^( ) by˜( ) is particular close when also the average outcomes are close to their expected values. to simplify notation, define the following shorthands: where˜, ( ) and˜, ( ) replicate^, ( ) and^, ( ) but with expected values rather than sample averages in the denominators. the sample average denominators are^, ( ) and , ( ) (scaled such that they converge under suitable conditions when grows), and the expected value of the denominators is ( ) (similarly scaled). without loss of generality, i fix the distance and weighting of interest and suppress the dependence on and in the following derivations for ease of presentation. the feasible estimator written in terms of the shorthand notation iŝ where˙is some convex combination of^and . it is straightforward to see thatΔ( , , , ) = . hence the left-hand-side of the equality above is justΔ(^,^,˜,˜), such that the right-hand-side is an expression for^−˜. hencê each of the four terms is a product with each factor close to zero under appropriate asymptotics. for instance, with independent regions and bounded outcomes and number of individuals per region, one can get √ (^− ) → . that is, the difference between the estimators^( ) and˜( ) is negligible under standard asymptotic frameworks. since the difference between estimators is very small for large samples, exact finite sample results for ( ) likely provide decent approximations for^( ) in smaller samples. consider the expected value of the estimator˜( ). to show: (˜( )) = ( ). since ( ) is the first term of˜( ), i proceed by showing that (˜( ) − ( )) = . since the denominators are non-stochastic, it suffices to show that the expectations of the numerators are equal to zero. the "first term" and "second term" designations below therefore refer to the first and second term of˜( ) − ( ). the expectation of the numerator of the first term is: the first equality rewrites the observed outcome = ( ( ) ) in terms of potential outcome ( ) = ( ) for = . the second equality moves all non-stochastic terms out of the expectation. the third equality rewrites the expectation of indicators as probabilities. the fourth equality distributes the difference ( ) − , ( ) and replaces , ( ) by its definition. for the second term, the factor multiplying the ratio cancels with the denominator, and the numerator is equal to the first term, such that the difference is equal to zero. analogously, the expectation of the numerator of the second term is: hence (˜( )) = ( ). the approximate estimator˜( ) in equation is the sum of three terms. since the first term, ( ) is fixed, the variance only depends on the last two terms. for the third equality, distribute out the − term of −( − ( ∑︀ ( ))) . . ., which is non-stochastic and hence does not contribute to the variance, such that only +( ∑︀ ( )) . . . remains of the second term. the fourth and final equality above distributes out the ( ) of the second term and then combines the first and second term by factoring out ( ). for ease of notation, definē the only stochastic terms left are the ( ); they represent the design-based variation that is due to random treatment assignment. the average¯+ , ( , ) consists only of a sum of potential outcomes, which are non-stochastic in the design-based perspective, in the numerator and the expected number of individuals near treatment, which is also non-stochastic, in the denominator. the where pr( ′ = | = ) is determined by the completely randomized design. let be the (fixed) number of treated regions in a completely randomized design. then pr( ′ = | = ) = − − since, under assumption , if region receives treatment, − of the remaining − regions receive treatment, each with equal probability. so )︂ the first equality combines the added term with the first summation and the subtracted term with the second summation. the second equality simplifies the factor of the first term, factors the second term into and ′ , and notices that both summations are the same, yielding the square in the second term. here, the third summation is "missing" the terms where = ′ . adding and subtracting by combining the added = ′ term into the second term and the subtracted = ′ term into the third term. note that dropping the (unidentified) variances of treatment effects (terms four and five) unambiguously leads to a conservative estimator of the variance. the absolute value of the factor in the fourth term, , is larger than the factor in the fifth term, − , and the numerator of the ratio in the fourth term is larger than the numerator of the ratio in the fifth term by jensen's inequality (while the denominators are identical). hence the absolute value of the fourth term is larger than the fifth terms, such that dropping both terms increases the expression, leading to a conservative estimator of the variance. to estimate the first term, takê to estimate the second term, takê { ̸ ∈ } pr( = ) pr( ̸ ∈ | = ) the estimator^a dditive ( ) here 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when, why, and how generative adversarial nets discrete choice modeling identifying agglomeration spillovers: evidence from winners and losers of large plant openings bidding for industrial plants: does winning a 'million dollar plant' increase welfare? take the q train: value capture of public infrastructure projects on the role of the propensity score in efficient semiparametric estimation of average treatment effects generalized least squares inference in panel and multilevel models with serial correlation and fixed effects the elements of statistical learning: data mining, inference and prediction transforming auto-encoders efficient estimation of average treatment effects using the estimated propensity score latent space approaches to social network analysis stability in competition toward causal inference with interference estimating spatial treatment effects: an application to base closures and aid delivery in afghanistan nonparametric estimation of average treatment effects under exogeneity: a review causal inference for statistics, social, and biomedical sciences: an introduction spatial transformer networks. advances in neural information processing systems geographic dispersion of economic shocks: evidence from the fracking revolution: comment combining satellite imagery and machine learning to predict poverty what happens when wal-mart comes to town: an empirical analysis of the discount retailing industry an adversarial approach to structural estimation consequences of the clean water act and the demand for water quality hac estimation in a spatial framework combining matching and synthetic controls to trade off biases from extrapolation and interpolation the standard errors of persistence imagenet classification with deep convolutional neural networks dynamic spatial panel models: networks, common shocks, and sequential exogeneity on asymptotic distribution and asymptotic efficiency of least squares estimators of spatial variogram parameters central 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treatment effects in the presence of unknown interference nonparametric density estimation under adversarial losses nonparametric policy analysis nonparametric policy analysis: an application to estimating hazardous waste cleanup benefits on causal inference in the presence of interference identification and estimation of spillover effects in randomized experiments extracting and composing robust features with denoising autoencoders bipartite causal inference with interference the average of treated individuals at distance ± ℎ from realized treatment locations isthe term inside the square equals zero:the first equality substitutes the definition of¯+ , ( , ). the second equality splits the ratio into two separate sums, one of treated, the other of control potential outcomes. for the first term, the third equality factors out = , which is constant across regions by assumption , and cancels ( ) ( ) . for the second term, the third equality factors out − = − , which is constant across regions by assumption , and notes that the sum of conditional probabilities is equal to in each region, ∑︀ ( ) = . both terms are equal to zero by the definitions of , ( ) and , ( ).hence, under assumption (completely randomized experiment), equation becomes var (︂˜()︂ where = = by assumption .bernoulli trial under assumption (bernoulli trial), equation becomesto treat the variances under assumptions and jointly, define both under assumption and under assumption , the variance of˜( ) depends on squares of (sums of) the potential outcome sums¯+ , ( , ).consider the first square of potential outcomes above. by applying the binomial theorem twice, rewrite the squared sum of potential outcomes as the difference between estimable marginal variances and an inestimable (approximate) treatment effect variance. by dropping the inestimable variance of treatment effects, one obtains a conservative estimate of the variance.since ( + ) = + + and ( − ) = − + , ( + ) = + − ( − ) . similarly for the second square of potential outcomes above:substituting these expressions into equation , the variance in equation consists of five terms. the first and third terms resemble a variance of outcomes of treated individuals. the second term resembles a variance of outcomes of control individuals. the fourth and fifth terms resemble variances of treatment effects. it is only possible to identify the effect of a candidate treatment location on individual , ( ), if is the closest realized treatment location to with positive probability. one can take^,the estimator^n earest ( ) is equal to if the region of individual is treated but location is not the closest realized treatment location to . this happens both when is not realized itself, and when another realized treatment location ′ is closer to . if is the closest realized location to ,^n earest ( ) is equal to the outcome of scaled by the inverse of the probability of this event. if the region is not treated,^n earest ( ) is equal to the outcome of scaled by the inverse of the probability of region not being treated. clearly,^n earest ( ) is an unbiased inverse probability weighting estimator of ( ) ≡ ( ) − ( ) under the assumption that only the nearest realized treatment matters. key: cord- -a prku k authors: mao, liang; yang, yan title: coupling infectious diseases, human preventive behavior, and networks – a conceptual framework for epidemic modeling date: - - journal: soc sci med doi: . /j.socscimed. . . sha: doc_id: cord_uid: a prku k human-disease interactions involve the transmission of infectious diseases among individuals and the practice of preventive behavior by individuals. both infectious diseases and preventive behavior diffuse simultaneously through human networks and interact with one another, but few existing models have coupled them together. this article proposes a conceptual framework to fill this knowledge gap and illustrates the model establishment. the conceptual model consists of two networks and two diffusion processes. the two networks include: an infection network that transmits diseases and a communication network that channels inter-personal influence regarding preventive behavior. both networks are composed of same individuals but different types of interactions. this article further introduces modeling approaches to formulize such a framework, including the individual-based modeling approach, network theory, disease transmission models and behavioral models. an illustrative model was implemented to simulate a coupled-diffusion process during an influenza epidemic. the simulation outcomes suggest that the transmission probability of a disease and the structure of infection network have profound effects on the dynamics of coupled-diffusion. the results imply that current models may underestimate disease transmissibility parameters, because human preventive behavior has not been considered. this issue calls for a new interdisciplinary study that incorporates theories from epidemiology, social science, behavioral science, and health psychology. despite outstanding advance in medical sciences, infectious diseases remain a major cause of death in the world, claiming millions of lives every year (who, ) . particularly in the past decade, emerging infectious diseases have obtained remarkable attention due to worldwide pandemics of severe acute respiratory syndrome (sars), bird flu and new h n flu. although vaccination is a principal strategy to protect individuals from infection, new vaccines often need a long time to develop, test, and manufacture (stohr & esveld, ) . before sufficient vaccines are available, the best protection for individuals is to adopt preventive behavior, such as wearing facemasks, washing hands frequently, taking pharmaceutical drugs, and avoiding contact with sick people, etc. (centers for disease control and prevention, ) . it has been widely recognized that both infectious diseases and human behaviors can diffuse through human networks (keeling & eames, ; valente, ) . infectious diseases often spread through direct or indirect human contacts, which form infection networks. for example, influenza spreads through droplet/physical contacts among individuals, and malaria transmits via mosquitoes between human hosts. human behavior also propagates through inter-personal influence that fashions communication networks. this is commonly known as the 'social learning' or 'social contagion' effect in behavioral science, i.e., people can learn by observing behaviors of others and the outcomes of those behaviors (hill, rand, nowak, christakis, & bergstrom, ; rosenstock, strecher, & becker, ). in the current literature, models of disease transmission and behavioral diffusion have been developed separately for decades, both based on human networks (deffuant, huet, & amblard, ; keeling & eames, ; valente, ; watts & strogatz, ) . few efforts, however, have been devoted to integrating infectious diseases and human behaviors together. in reality, when a disease breaks out in a population, it is natural that individuals may voluntarily adopt some preventive behavior to respond, which in turn limits the spread of disease. failing to consider these two interactive processes, current epidemic models may under-represent human-disease interactions and bias policy making in public health. this article aims to propose a conceptual framework that integrates infectious diseases, human preventive behavior, and networks together. the focus of this article is on issues that arise in establishing a conceptual framework, including basic principles, assumptions, and approaches for model formulization. the following section (section ) describes the conceptual framework and basic assumptions, which abstract essential aspects of a disease epidemic. the third section discusses approaches to formulize the model framework into a design. the fourth illustrates a computing model upon various human network structures and compares the simulation results. the last section concludes the article with implications. the conceptual model consists of two networks and two diffusion processes (fig. ) . the two networks include an infection network that transmits disease agents (dark dash lines), and a communication network that channels inter-personal influence regarding preventive behavior (gray dash lines). both networks are composed of same individuals but different types of interactions. these two networks could be non-overlapping, partially or completely overlapping with one another. the two diffusion processes refer to the diffusion of infectious diseases (dark arrows) and that of preventive behavior (gray arrows) through the respective network. as illustrated in fig. , if individual # is initially infected, the disease can be transmitted to individual # and # , and then to individual # , following the routes of infection network. meanwhile, individual # may perceive the risk of being infected from individual # , and then voluntarily adopt preventive behavior for protection, known as the effects of 'perceived risks' (becker, ) . further, the preventive behavior of individual # may be perceived as a 'social standard' by individual # and motivate him/her toward adoption, i.e., the 'social contagion'. in such a manner, the preventive behavior diffuses on the communication network through inter-personal influence. during an epidemic, these two diffusion processes take place simultaneously and interact in opposite directions. the diffusion of diseases motivates individuals to adopt preventive behavior, which, in turn, limits the diffusion of diseases. this two-network two diffusion framework is dubbed as a 'coupled diffusion' in the subsequent discussion. the conceptual framework entails five assumptions. first, individuals differ in their characteristics and behaviors, such as their infection status, adoption status, and individualized interactions. second, both infection and communication networks are formed by interactions among individuals. third, the development of infectious diseases follows disease natural history, such as the incubation, latent, and infectious periods. fourth, individuals voluntarily adopt preventive behavior, dependent on their own personality, experiences, and inter-personal influence from family members, colleagues, as well as friends (glanz, rimer, & lewis, ) . fifth and lastly, the infection status of surrounding people or their behavior may motivate individuals to adopt preventive behavior, which then reduces the likelihood of infection. of the five assumptions, the first two provide networks as a basis for modeling. the third and fourth assumptions are relevant to the two diffusion processes, respectively. the last assumption represents the interactions between the two processes. corresponding to the five assumptions, this article introduces a number of approaches to represent individuals, networks, infectious diseases, and preventive behavior, as four model components, and depicts the relationships between the four. the first model assumption requires a representation of discrete individuals, their unique characteristics and behaviors. this requirement can be well addressed by an individual-based modeling approach. in the last decade, this modeling approach has gained momentum in the research community of both epidemiology and behavioral science (judson, ; koopman & lynch, ) . specifically, the individual-based approach views a population as discrete individuals, i.e., every individual is a basic modeling unit and has a number of characteristics and behaviors. the characteristics indicate states of individuals, e.g., the infection status, adoption status, and the number of contacts, while the behaviors change these states, e.g., receiving infection and adopting preventive behavior. by simulating at an individual level, this approach allows to understand how the population characteristics, such as the total number of infections and adopters, emerge from collective behaviors of individuals (grimm & railsback, ) . from an implementation perspective, the characteristics and behaviors of individuals can be easily accommodated by object-oriented languages, a mainstream paradigm of programming technologies. various tools are also available to facilitate the design and implementation of individual-based approach, such as the netlog and repast (robertson, ) . with regard to the second assumption, both the infection and communication networks can be abstracted as a finite number of nodes and links. nodes represent individuals and links represent interactions among individuals. the network structure is compatible with the aforementioned individual-based approach, in that the individual nodes directly correspond to the basic modeling units, while links can be treated as a characteristic of individuals. interactions between individuals (through links) can be represented as behaviors of individuals. to be realistic in modeling, both networks can be generated to fit observed characteristics and structures of real-world networks. important characteristics of networks include: the number of links attached to a node (the node degree), the minimum number of links between any pair of nodes (the path length), the ratio between the existing number of links and the maximum possible number of links among certain nodes (the level of clustering), and so on (scott, ) . particularly for human networks of social contacts, empirical studies showed that the average node degree often varies from to , dependent on occupation, race, geography, etc (edmunds, kafatos, wallinga, & mossong, ; fu, ) . the average path length was estimated to be around , popularly known as the 'six degrees of separation' (milgram, ) . the level of clustering has typical values in the range of . e . (girvan & newman, ) . besides these characteristics, studies on human networks have also disclosed two generic structures: "small-world" and "scale-free" structures. the "small-world" structure is named after the 'small-world' phenomena, arguing that people are all connected by short chains of acquaintances (travers & milgram, ) . theoretically, the small-world structure is a transition state between regular networks and random networks (watts & strogatz, ) . the regular networks represent one extreme that all nodes are linked to their nearest neighbors, resulting in highly clustered networks. the random networks are the other extreme that all nodes are randomly linked with each other regardless of their closeness, resulting in short path lengths. a typical small-world structure has characteristics from both extremes, i.e., most nodes are directly linked to others nearby (highly clustered), but can be indirectly connected to any distant node through a few links (short path lengths). the "scale-free" structure has also been commonly observed in social, biological, disease, and computer networks, etc. (cohen, erez, ben-avraham, & havlin, ; jeong, tombor, albert, oltvai, & barabási, ; liljeros, edling, amaral, stanley, & aaberg, ) . it depicts a network with highly heterogeneous degrees of nodes, whose distribution follows a power-law decay function, p < k > wk Àg (k denotes the node degree and empirically < g < ). in other words, a few individuals have a significantly large number of links, while the rest of individuals only have a few (albert, jeong, & barabasi, ) . all of these observed characteristics and structures can be used to calibrate the modeled networks, which then serve as a reliable basis to simulate the coupled-diffusion process. in epidemiology, the development of infectious diseases has been characterized by a series of infection statuses, events, and periods, often referred to as the natural history of diseases (gordis, ) . the progress of an infectious disease often starts with a susceptible individual. after having contact with an infectious individual, this susceptible individual may receive disease agents and develop infection based on a transmission probability. the receipt of infection triggers a latent period, during which the disease agents develop internally in the body and are not emitted. the end of the latent period initiates an infectious period, in which this individual is able to infect other susceptible contacts and may manifest disease symptoms. after the infectious period, this individual either recovers or dies from the disease. among these disease characteristics, the transmission probability is critical for bridging infectious diseases to the other model components: individuals, networks, and preventive behavior. this probability controls the chance that the disease agents can be transmitted between individuals through network links. meanwhile, the reduction of transmission probability reflects the efficacy of preventive behavior. the individual-based modeling approach enables the representation of disease progress for each individual. the infection statuses, periods, and transmission probability per contact can be associated with individuals as their characteristics, while infection events (e.g., receipt of infection and emission of agents) can be modeled as behaviors of individuals. each individual has one of four infection statuses at a time point, either susceptible, latent, infectious, or recovered (kermack & mckendrick, ) . the infection status changes when infection events are triggered by behaviors of this individual or surrounding individuals. the simulation of disease transmission often starts with an introduction of a few infectious individuals (infectious seeds) into a susceptible population. then, the first generation of infections can be identified by searching susceptible contacts of these seeds. stochastic methods, such as the monte carlo method, could be used to determine who will be infected or not. subsequently, the first generation of infections may further infect their contacts, and over time leads to a cascade diffusion of disease over the network. to parameterize the simulation, the transmission probability of a disease, the lengths of latent period and infectious period can be derived from the established literature or from observational disease records. like other human behaviors, the adoption of preventive behavior depends on the individual's own characteristics (e.g., knowledge, experience, and personal traits) and inter-personal influence from surrounding individuals (e.g., family supports and role model effects) (glanz et al., ) . because individuals vary in their willingness to adopt, human behaviors often diffuse from a few early adopters to the early majority, and then over time throughout the social networks (rogers, ) . a number of individual-based models have been developed by sociologists and geographers to represent such behavioral diffusion processes, e.g., the mean-information-field (mif) model (hägerstrand, ) , the threshold model (granovetter, ) , the relative agreement model (deffuant et al., ) , etc. the mif model populates individuals on a regular network (or a grid), and assumes that a behavior diffuses through the 'word-of-mouth' communication between an adopter and his/ her neighbors. the mif is a moving window that defines the size of neighborhood and the likelihood of human communications to every adopter. the simulation centers the mif on every adopter and uses the monte carlo method to identify a new generation of adopters (hägerstrand, ) . the threshold model assumes that individuals observe their surroundings and adopt a behavior based on a threshold effect (granovetter, ; valente, ) . the threshold is the proportion of adopters in an individual's social contacts necessary to convince this individual to adopt. the behavioral diffusion begins with a small number of adopters, and spreads from the low-threshold population to the high-threshold population. the recently proposed relative agreement model assumes that every individual holds an initial attitude, which is a value range specified by a mean value, maximum and minimum. based on the value ranges, individuals' attitudes are categorized as positive, neutral, and negative. individuals communicate through a social network, and influence their attitudes (value ranges) reciprocally according to mathematical rules of relative agreement. if individuals can hold positive attitudes for a certain time period, they will decide to adopt a behavior (deffuant et al., ) . due to the individual-based nature of all these models, they can be easily incorporated under the proposed conceptual framework. to further discuss the individual-based design of behavioral models, this research chose the threshold model for illustrations. in terms of complexity, the threshold model lies midway between the mif model and the relative agreement model, and its parameters can be feasibly estimated through social surveys. the mif model has been criticized for its simplicity in that it assumes an immediate adoption after a communication and oversimplifies the decision process of individuals (shannon, bashshur, & metzner, ) . by contrast, the relative agreement model is too sophisticated: many parameters are difficult to estimate, for example, the ranges of individual attitudes. the threshold model can be formulized as follows so as to become an integral part of the coupled-diffusion framework. first, individuals are assumed to spontaneously evaluate the proportion of adopters among their contacts, and perceive the pressure of adoption. once the perceived pressure reaches a threshold (hereinafter called the threshold of adoption pressure), an individual will decide to adopt preventive behavior. second, in order to relate the preventive behavior to infectious diseases, individuals also evaluate the proportion of infected individuals (with disease symptoms) among their contacts, and perceive the risks of infection. once the perceived risk reaches another threshold (hereinafter called the threshold of infection risk), an individual will also adopt preventive behavior. these two threshold effects can be further formulized as three characteristics and two behaviors of individuals. the three characteristics include an adoption status (adopter or non-adopter) and two individualized thresholds toward adoption. the two behaviors represent the individual's evaluation of adoption pressure and infection risk from surrounding contacts, which in turn determines their adoption status. the individualized thresholds toward adoption reflect personal characteristics of individuals, while the behaviors of evaluation represent the inter-personal influence between individuals. to build a working model, the individualized thresholds toward adoption can be best estimated by health behavior surveys as illustrated below. based on the discussion above, the conceptual framework ( fig. ) can be transformed into a formative design with four model components and their relationships (fig. ) . individuals are building blocks of the proposed model, and their interactions compose networks as a core of the model. through the infection network, individuals may receive infection from others and have their infection status changed, propelling the diffusion of diseases. meanwhile, individuals may perceive risks and pressure from the communication network, and gradually adopt preventive behavior, resulting in the behavioral diffusion. the adoption of preventive behavior reduces the disease transmission probability, thus controlling and preventing the disease transmission. in this manner, the diffusion of diseases and preventive behavior in a population are coupled together. to illustrate the proposed coupled-diffusion model, an influenza epidemic was simulated in a hypothetic population of individuals (n ¼ ), each with characteristics and behaviors as described in fig. . influenza was chosen because it is common and readily transmissible between individuals. the simulation simply assumes that the population is closed, i.e., no births, deaths, or migrations. with regard to the network component, the average number of links per individuals was set to , reasonably assuming that an individual on average has contact with family members and colleagues. for the purpose of sensitivity analysis, the illustrative model allowed the disease and communication networks to take either a small-world (sw) structure or a scale-free (sf) structure. the generation of sw structures started with a regular network where all individuals were linked to their nearest neighbors. then, each individual's existing links were rewired with a probability to randomly selected individuals (watts & strogatz, ) . the rewiring probability p ranged from to , and governed the clustering level and average path lengths of resultant networks (fig. a) . the sf structures were created by a preferential attachment algorithm, which linked each new individual preferentially to those who already have a large number of contacts (pastor-satorras & vespignani, ) . this algorithm produces a power-law degree distribution, p < k > wk Àg (k is the node degree), with various exponents g (fig. b) . based on fig. a and b, the rewiring probabilities p were set to . , . , and . to typically represent the regular, small-world, and random networks, respectively (fig. cee) . the exponent g were set to , , and to represent three scale-free networks with high, medium, and low levels of node heterogeneity (fig. feh) . a sensitivity analysis was performed to examine every possible pair of <p, p>, <g, g>, <p, g> and <g, p> as a network combination ( p-values  g-values  ¼ combinations in total), where the first parameter indicates the structure of infection network and the second specifies the structure of communication network. to simulate the diffusion of influenza, the latent period and infectious period were specified as day and days, respectively, based on published estimates (heymann, ) . the transmission probability per contact was varied from . to . (with a . increment) to test its effects on the coupled-diffusion processes. % of infected individuals was assumed to manifest symptoms, following the assumption made by ferguson et al. ( ) . only these symptomatic individuals could be perceived by their surrounding individuals as infection risks. recovered individuals were deemed to be immune to further infection during the rest of the epidemic. with respect to the diffusion of preventive behavior, the use of flu antiviral drugs (e.g., tami flu and relenza) was taken as a typical example because its efficacy is more conclusive than other preventive behavior, such as hand washing and facemask wearing. for symptomatic individuals, the probability of taking antiviral drugs was set to % (mcisaac, levine, & goel, ; stoller, forster, & portugal, ) , and the consequent probability of infecting others was set to be reduced by % (longini, halloran, nizam, & yang, ) . susceptible individuals may also take antiviral drugs due to the perceived infection risk or adoption pressure. if they use antiviral drugs, the probability of being infected was set to be reduced by % (hayden, ) . the key to simulate the diffusion of preventive behavior was to estimate thresholds of infection risk and that of adoption pressure for individuals. a health behavior survey was conducted online for one month (march eapril , ) to recruit participants. voluntary participants were invited to answer two questions: ) "suppose you have close contacts, including household members, colleagues, and close friends, after how many of them get influenza would you consider using flu drugs?", and ) "suppose you have close contacts, including household members, colleagues, and close friends, after how many of them start to use flu drugs would you consider using flu drugs, too?". the first question was designed to estimate the threshold of infection risks, while the second was for the threshold of adoption pressure. the survey ended up with respondents out of participants (a % response rate), and their answers were summarized into two threshold-frequency distributions (fig. ) . the monte carlo method was then performed to assign threshold values to the modeled individuals based on the two distributions. this survey was approved by the irb in university at buffalo. to initialize the simulation, all individuals were set to be non-adopters and susceptible to influenza. one individual was randomly chosen to be infectious on the first day. the model took a daily time step and simulated the two diffusion processes simultaneously over days. the simulation results were presented as disease attack rates (total percent of symptomatic individuals in the population), and adoption rates (total percent of adopters in the population). another two characteristics were derived to indicate the speed of coupled-diffusion: the epidemic slope and the adoption slope. the former is defined as the total number of symptomatic individuals divided by the duration of an epidemic (in day). similarly, the latter is defined as the total number of adopters divided by the duration of behavioral diffusion (in day). they are called slopes because graphically they approximate the slopes of cumulative diffusion curves. a higher slope implies a faster diffusion because of more infections/adoptions (the numerator) in a shorter time period (the denominator). all simulation results were averaged by model realizations to average out the randomness. simulation results were presented in two parts. first, the coupled-diffusion process under various transmission probabilities was analyzed, and compared to an influenza-only process that is fig. . (a) standardized network properties (average path length and clustering coefficient) as a function of rewiring probability p from to , given n ¼ ; (b) the power-law degree distributions given g ¼ , and , given n ¼ ; (cee) an illustration of generated sw networks for three p values, given n ¼ for figure clarity; (feh) an illustration of sf networks for three g values, given n ¼ . widely seen in the literature. the influenza-only process was simulated with the same parameters in the coupled-diffusion process except that individual preventive behavior was not considered. for the ease of comparison, a typical "small-world" network (p ¼ . ), was chosen for both infection and communication networks, assuming the two are overlapping. the second part examined the dynamics of coupled-diffusion under various structures of infection and communication networks, i.e., the pairs of network parameters <p, p>, <g, g>, <p, g> and <g, p> while fixing the influenza transmission probability to . (resultant basic reproductive number r ¼ e . ). fig. a indicates that the diffusion of influenza with and without the preventive behavior differs significantly, particularly for medium transmission probabilities ( . e . ). for the influenzaonly process (the black curve with triangles), the disease attack rate rises dramatically as the transmission probability exceeds . , and reaches a plateau of % when the probability increases to . . the coupled-diffusion process (the black curve with squares) produces lower attack rates, which slowly incline to the maximum of %. this is because individuals gradually adopt preventive behavior, thereby inhibiting disease transmission from infectious individuals to the susceptible. meanwhile, the adoption rate (the gray curve with squares) also increases with the transmission probability, and can achieve a % of the population as the maximum. this is not surprising because the more individuals get infected, the greater risks and pressure other individuals may perceive, motivating them to adopt preventive behavior. individuals who have not adopted eventually may have extremely high-threshold of adoption (see fig. ), and thus resist adopting preventive behavior. fig. b displays an example of the coupled-diffusion process (transmission probability ¼ . ), ending up with nearly symptomatic cases and approximately adopters of flu antiviral drugs. despite differences in magnitude, the two diffusion curves exhibit a similar trend that follows the -phase s-shaped curve of innovation diffusion (rogers, ) . the 'innovation' phase occurs from the beginning to day , followed by the 'early acceptance' phase (day e ), 'early majority' (day e ), 'late majority' (day e ) and 'laggards' (after day ). this simulated similarity in temporal trend is consistent with many empirical studies regarding flu infection and flu drug usage. for example, das et al. ( ) and magruder ( ) had compared the temporal variation of both influenza incidence and over-the-counter flu drug sales in the new york city and the washington dc metropolitan area, respectively. both studies reported a high correlation between over-the-counter drug sales and cases of diagnosed influenza, and thus suggested that over-the-counter drug sales could be a possible early detector of disease outbreaks. the consistency with the observed facts, to some extent, reflects the validity of the proposed model. in addition to the transmission probability, the coupled-diffusion process is also sensitive to various combinations of network structures, i.e., pairs of network parameters <p, p>, <g, g>, <p, g> and <g, p> (fig. ) . the z axis represents either the epidemic or adoption slope, and a greater value indicates a faster diffusion process. in general, both epidemic and adoption slopes change dramatically with the structure of infection network, while they are less sensitive to the variation of communication networks. given the small-world infection network ( fig. aeb and e-f), the epidemic and adoption slopes increase quickly as the rewiring probability p rises from . to . . when p ¼ . (a regular network), almost all individuals are linked to their nearest neighbors, and influenza transmission between two distant individuals needs to go through a large number of intermediate individuals. the slow spread of influenza induces a low perception of infection risks among individuals, thereby decelerating the dissemination of preventive fig. . the sensitivity of coupled-diffusion processes to various network structures, including sw infection Àsw communication as <p infection , p communication >, sf infection Àsf communication as <g infection ,g communication > sw infection Àsf communication as <p infection , g communication > and sf infection Àsw communication as <g infection , p communication >. each combination is displayed in one row from top to bottom. the sw and sf denote the network structure, while the subscripts indicate the network function. parameter p is the rewiring probability of a sw network, taking values ( . , . , . ), while parameter g is the exponent of a sf network, taking values ( , , ). the z axis denotes epidemic slopes (the left column) and adoption slopes (the right column) as a result of a network structure. a greater z value indicates a faster diffusion process. behavior. as p increases to . (a random network), a large number of shortcuts exist in the network, and the transmission of influenza is greatly speeded by shortcuts. as a result, the diffusion of preventive behavior is also accelerated, because individuals may perceive more risks of infection and take actions quickly. likewise, given a scale-free infection network ( fig. ced and g-h) , both influenza and preventive behavior diffuse much faster in a highly heterogeneous network (g ¼ ) than in a relatively homogeneous network (g ¼ ) . this is because a highly heterogeneous network has a few super-spreaders who have numerous direct contacts. super-spreaders act as hubs directly distributing the influenza virus to a large number of susceptible individuals, thus speeding the disease diffusion. as individuals perceived more risks of infection in their surroundings, they will adopt preventive behavior faster. human networks, infectious diseases, and human preventive behavior are intrinsically inter-related, but little attention has been paid to simulating the three together. this article proposes a conceptual framework to fill this knowledge gap and offer a more comprehensive representation of the disease system. this twonetwork two diffusion framework is composed of four components, including individuals, networks, infectious diseases, and preventive behavior of individuals. the individual-based modeling approach can be employed to represent discrete individuals, while network structures support the formulization of individual interactions, including infection and communication. disease transmission models and behavioral models can be embedded into the network structures, and simulate disease infection and adoptive behavior, respectively. the collective changes in individuals' infection and adoption status represent the coupled-diffusion process at the population level. compared to the widely used influenza-only models, the proposed model produces a lower percent of infection, because preventive behavior protects certain individuals from being infected. sensitivity analysis identifies that the structure of infection network is a dominant factor in the coupled-diffusion, while the variation of communication network produces fewer effects. this research implies that current predictions about disease impacts might be under-estimating the transmissibility of the disease, e.g., the transmission probability per contact. modelers fit to observed data in which populations are presumably performing preventive behavior, while the models they create do not account for the preventive behavior. when they match their modeled infection levels to those in these populations, the disease transmissibility needs to be lower than its true value so as to compensate for the effects of preventive behavior. this issue has been mentioned in a number of recent research, such as ferguson et al. ( ) , but the literature contains few in-depth studies. this article moves the issue towards its solution, and stresses the importance of understanding human preventive behavior before policy making. the study raises an additional research question concerning social-distancing interventions for disease control, such as the household quarantine and workplace/school closure. admittedly, these interventions decompose the infection network for disease transmission, but they may also break down the communication network and limit the propagation of preventive behavior. the costs and benefits of these interventions remain unclear and a comprehensive evaluation is needed. the proposed framework also suggests several directions for future research. first, although the illustrative model is based on a hypothetical population, the representation principles outlined in this article can be applied to a real population. more realistic models can be established based on the census data, workplace data, and health survey data. second, the proposed framework focuses on inter-personal influence on human behavior, but has not included the effects of mass media, another channel of behavioral diffusion. the reason is that the effects of mass media remain inconclusive and difficult to quantify, while the effects of interpersonal influence have been extensively studied before. third, the proposed framework has not considered the 'risk compensation' effect, i.e., individuals will behave less cautiously in situations where they feel safer or more protected (cassell, halperin, shelton, & stanton, ) . in the context of infectious diseases, the risk compensation can be interpreted as individuals being less cautious of the disease if they have taken antiviral drugs, which may facilitate the disease transmission. this health psychological effect could also be incorporated to refine the framework. to summarize, this article proposes a synergy between epidemiology, social sciences, and human behavioral sciences. for a broader view, the conceptual framework could be easily expanded to include more theories, for instance, from communications, psychology, and public health, thus forming a new interdisciplinary area. further exploration in this area would offer a better understanding of complex human-disease systems. the knowledge acquired would be of a great significance given that vaccines and manpower may be insufficient to combat emerging infectious diseases. error and attack tolerance of complex networks the health belief model and personal health behavior hiv and risk behaviour: risk compensation: the achilles' heel of innovations in hiv prevention? breakdown of the internet under intentional attack monitoring over-the-counter medication sales for early detection of disease outbreakse new york city an individual-based model of innovation diffusion mixing social value and individual benefit mixing patterns and the spread of close-contact infectious diseases strategies for mitigating an influenza pandemic measuring personal networks with daily contacts: a single-item survey question and the contact diary community structure in social and biological networks health behavior and health education: theory, research, and practice epidemiology. philadelphia: wb saunders threshold models of collective behavior individual-based modeling and ecology on monte carlo simulation of diffusion perspectives on antiviral use during pandemic influenza control of communicable diseases manual infectious disease modeling of social contagion in networks the large-scale organization of metabolic networks the rise of the individual-based model in ecology networks and epidemic models a contribution to the mathematical theory of epidemics individual causal models and population system models in epidemiology the web of human sexual contacts containing pandemic influenza with antiviral agents evaluation of over-the-counter pharmaceutical sales as a possible early warning indicator of human disease visits by adults to family physicians for the common cold epidemic spreading in scale-free networks agent-based modeling toolkits netlogo, repast, and swarm diffusion of innovations social learning theory and the health belief model social network analysis: a handbook the spatial diffusion of an innovative health care plan will vaccines be available for the next influenza pandemic? self-care responses to symptoms by older people. a health diary study of illness behavior an experimental study of the small world problem social network thresholds in the diffusion of innovations collective dynamics of small-world networks world health organization report on infectious diseases. world health organization the authors are thankful for insightful comments from the editor and two reviewers. key: cord- -jibmg ch authors: dunbar, r. i. m. title: structure and function in human and primate social networks: implications for diffusion, network stability and health date: - - journal: proc math phys eng sci doi: . /rspa. . sha: doc_id: cord_uid: jibmg ch the human social world is orders of magnitude smaller than our highly urbanized world might lead us to suppose. in addition, human social networks have a very distinct fractal structure similar to that observed in other primates. in part, this reflects a cognitive constraint, and in part a time constraint, on the capacity for interaction. structured networks of this kind have a significant effect on the rates of transmission of both disease and information. because the cognitive mechanism underpinning network structure is based on trust, internal and external threats that undermine trust or constrain interaction inevitably result in the fragmentation and restructuring of networks. in contexts where network sizes are smaller, this is likely to have significant impacts on psychological and physical health risks. the processes whereby contagious diseases or information propagate through communities are directly affected by the way these communities are structured. this has been shown to be the case in primates [ ] [ ] [ ] and has been well studied in humans in the form of epidemiological [ ] and information diffusion (opinion dynamics or voter) models [ ] . the ising phase state model (originally developed to describe the magnetic dipole moments of atomic spin in ferromagnetism) has been the workhorse of most of these models and of many of the models currently used to calculate the value of the r-number (or reproduction rate) used to drive current covid- management strategies. most early models were mean field models that assumed panmixia. however, human social networks are highly structured and small world: most people interact with only a very small number of individuals whose identities remain relatively stable over time. when it became apparent that the structure of networks could dramatically affect the flow of information (or infections) through networks [ , ] , structure began to be incorporated into epidemiological models [ ] [ ] [ ] [ ] [ ] . many of the best current models are 'compartmental models' which represent structure by the fact that a community consists of households or other small population units [ , ] . in effect, these use spatial structure as a proxy for social structure, which has the advantage of ensuring that the models compute easily. in reality, of course, it is people's interactions with each other that give rise to the spatial structure represented by households. while it is true that most (but not all) individuals see and interact with household or family members more often than with anyone else, in fact this dichotomizes what is in reality a continuum of interaction that flows out in ripples from each individual. these ripples create social layers of gradually declining amplitude that spread through the local community well beyond the household. my aim in this paper is to examine the social and psychological processes that underpin natural human sociality in order to better understand how these affect both network structure and the way information or diseases propagate through them. like all monkeys and apes, humans live in stable social groups characterized by small, highly structured networks. individuals do not interact with, let alone meet, everyone else in their social group on a regular basis: a very high proportion of their interactions are confined to a very small subset of individuals. these relationships are sometimes described as having a 'bonded' quality: regular social partners appear to be fixated on each other [ , ] . the mechanisms that underpin these relationships have important consequences for the dynamics of these networks. i will first briefly review evidence on the size and structure of the human social world. i will then explain how the cognitive and behavioural mechanisms that underpin friendships in all primates give rise to the particular form that human networks have. finally, i explore some of the consequences of this for information and disease propagation in networks, and how networks respond to external threats. humans have lived in settlements only for the past years or so, with mega-cities and nation states being at all common only within the last few hundred years. prior to that, our entire evolutionary history was dominated by very small-scale societies of the kind still found in contemporary hunter-gatherers. our personal social worlds still reflect that long evolutionary history, even when they are embedded in connurbations numbering tens of millions of people. table summarizes the sizes of egocentric personal social networks estimated in a wide variety of contexts ranging from xmas card distribution lists (identifying all household members) to the number of friends on facebook, with sample sizes varying between and a million individuals. the mean network size varies across the range - , with an overall mean of approximately . table also lists a number of studies that have estimated community size in a variety of pre-industrial societies as well as some contemporary contexts where it is possible to define a personalized community within which most people know each other on a personal level. these include the size of hunter-gatherer communities, historical european villages from the eleventh to the eighteenth centuries, self-contained historical communes, academic subdisciplines (defined as all those who pay attention to each other's publications) and internet communities. the average community sizes range between and , many with very large sample sizes, with an overall mean of approximately . christmas card distribution list . [ ] . [ ] . the value of approximately as a natural grouping size for humans was, in fact, originally predicted from an equation relating social group size to relative neocortex size in primates before this empirical evidence became available [ ] . this prediction had a % confidence interval of - , very close to the observed variance in the data. in primates as a whole (but not other birds and mammals), social group size is a function of neocortex volume, and especially the more frontal neocortex regions (the social brain hypothesis [ ] ). in the last decade, neuroimaging studies of both humans [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] and monkeys [ , ] indicate that the relationship between personal social networks (indexed in many different ways) and brain size also applies within species at the level of the individual as well as between species. the social brain relationship arises because primates are unusual in that they live in relatively large, stable, bonded social groups [ ] . in contrast with the more casual groups (i.e. herds, flocks) of most mammals and birds, the problem with bonded groups is that they are, in effect, a version of the coupled oscillator problem. if animals' foraging and resting schedules get out of synchrony, . . some individuals will drift away when others go to rest, resulting in the fragmentation of the group [ , ] . individuals have to be willing to accept short-term costs (mainly in relation to the scheduling of foraging) in order to gain greater long-term benefits (protection from predators by staying together). maintaining spatial coherence through time is cognitively difficult. it depends on two key psychological competences that appear to be unique to the anthropoid primates: the ability to inhibit prepotent actions (a prepotent response is the tendency to take a small immediate reward in preference to waiting for a larger future reward) and the capacity to mentalize. inhibition depends on the volume of the brain's frontal pole [ ] , while mentalizing depends on a dedicated neural circuit known as the theory of mind network (also known as the default mode neural network) that integrates processing units in the brain's prefrontal, parietal and temporal lobes [ ] , supplemented by connections with the limbic system [ , ] . the frontal pole is unique to the anthropoid primates [ ] ; the default mode network that underpins mentalizing is also common to both humans and monkeys [ ] . maintaining group cohesion is not simply a memory problem (though it is commonly misunderstood as such). rather, it is one of predicting others' future behaviour under different conditions (e.g. knowing how others will respond to one's own actions) and being able to gauge the future reliability (trustworthiness) of other individuals [ , ] . this is much more costly in terms of both neural activity and neural recruitment than simple factual recall [ ] . in humans, the number of friends is directly correlated with mentalizing skills [ , ] , and mentalizing skills are, in turn, correlated with the volumetric size of the brain's default mode neural network [ , ] . the latter relationship has recently been shown to extend to primates as a whole [ ] . social networks have generally been viewed from two different perspectives. network analysts with a statistical physics background have tended to view them top-down as macroscopic phenomena (i.e. from above looking down on the spatial distribution of a population of nodes), whereas sociologists have tended to view them from below as egocentric networks (the individual's experience of that population). on the whole, the first group have tended to focus on large-scale patterns in very large networks, often with an emphasis on triadic closure (heider's structural balance theory [ ] ) as the glue that gives structure to a network; the second have focused on the micro-structure of individual's personal social networks, often focusing on the inner core of intimate friendships immediately beyond the simple triad. an important finding from the second approach has been that networks actually consist of a series of layers that correspond to relationships of different quality [ , , ] . seen from an egocentric point of view, the frequency with which an individual contacts the members of their network does not follow a conventional power law distribution but, on closer inspection, contains a series of plateaux. cluster analyses of very large datasets invariably reveal that these personal networks contain four layers within them (figure ). this gives the network a layered structure, where individual alters in a given layer are contacted with more or less similar frequency and there is a sharp drop-off in contact frequencies to the next layer. it turns out that, while there is some individual variation, these layers have quite characteristic sizes. moreover, when counted cumulatively, they have a very distinct scaling ratio: each layer is approximately three times the size of the layer immediately inside it (figure ). this layered structure in figure (referred to as a dunbar graph [ ] ) has been identified, with virtually the same numerical layer values, in surveys of network size, the calling patterns in national cellphone databases, science co-author networks and the frequencies of reciprocated postings in both facebook and twitter (table ). each layer seems to correspond to a very specific frequency of interaction (figure ), and these frequencies are remarkably consistent across media [ ] , suggesting both that they are hardwired and that communication media are substitutable. one way this structure might arise would be if the basal layer of five people represented, for example, a family or household, such that the next layer of consists of three families with an especially close relationship, and the -layer beyond that consisted of three of these trios. this [ ] . (b) optimal number of clusters identified by k-means clustering algorithm in three online datasets. reproduced from [ ] . pattern, however, is likely to reflect small-scale traditional communities; in more mobile, postindustrial societies, figure can arise simply a consequence of the patterns of interaction between individuals and need have no family-based (or spatial) underpinning to it at all. it is notable, nonetheless, that the same patterns emerge in either case, suggesting that there is an underlying universal constraint on how networks are constructed. this same pattern, with the same layer sizes, has also been identified in a number of topdown analyses of the social (or spatial) organization of human populations (table ), including hunter-gatherers, the size distribution of irish bronze age stone circles (as estimates of local population distribution), the sizes of residential trailer parks, the structure of modern armies, the size of communities of practice in the business world and even the patterns of alliance formation in massive online multiplayer games (moms). this pattern, with the same scaling ratio, has also been noted in the political organization of a large sample of historical city states [ ] . in fact, this layered structure with a consistent scaling ratio was first noted in an analysis of huntergatherer societies in the early s by johnson [ ] , who suggested that it was a 'span on control' management solution in response to internal stresses created as grouping size increases. more surprisingly, perhaps, these same numbers reappear in both the distribution of primate social group sizes [ ] and in the layered structure of groups for those mammals that live in multilevel social systems (mainly baboons, chimpanzees, elephants and dolphins) [ , ] (table ) . animal societies with stable groups do not extend beyond the -layer, but all the internal layers are present. the fact that these numbers are so consistent across so wide a range of species perhaps suggests that they may be the outcome of natural scaling effects due to the structural stresses that social groups incur as they grow in size in response to ecological demands. as a result, social evolution in primates [ ] occurs as a result of a stepwise increase in group size [ ] achieved by bolting together several basal subgroups to create successive layers rather than through a continuous adjustment of group sizes as in most birds and mammals. primate species achieve larger groups by delaying group fission that would normally act as a nonlinear oscillator to keep group size within a defined range around the local mean [ ] [ ] [ ] . the process thus seems to behave more like a series of phase transitions triggered by a natural fractionation process. although, in humans, there is remarkably little variation in both overall network size and layer sizes across samples, irrespective of sample size, sample origin and cluster detection algorithm, nonetheless within populations, there is considerable variation between individuals (figure a). some of this variation is due to sex (women tend to have larger inner layers than men [ but smaller outer layers [ ] ), some due to age (network and layer sizes are an inverted-jshaped function of age, peaking in the s- s [ , , ] ) and personality (extroverts have larger networks at all layer levels than introverts [ ] [ ] [ ] [ ] ). in addition, all human social networks are divided into two components, family and friends. although in small-scale societies, virtually everyone in your network is a member of your extended family, in the post-industrial world with our lower birth rates, the typical network is split roughly : between family and friends [ , , ] . however, it still seems that preference is given to family: those who come from large extended families have fewer friends [ , ] . in effect, family and friends form two largely separate subnetworks that are interleaved through the layers of the network, with a roughly even split in the two innermost -and -layers, friends predominating in the middle -layer and family predominating in the outer -layer [ ] . the latter seems to reflect the fact that friends are more costly to maintain in terms of time investment than family members [ ] , and hence survive less well in the outermost layer (see below). conventional top-down networks tend to focus on the degree of individual ego's, usually with some kind of cut-off to define how many primary contacts an individual has. irrespective of where the cut-off is taken to be, these relationships tend to be viewed as one-of-a-kind. dunbar graphs, by contrast, recognize that individuals have relationships of different quality with many individuals, which might be viewed as primary, secondary, tertiary, etc. relationships. the first will usually be a subset of the second. in this section, i provide a brief explanation of how the primate bonding process works. the main purpose is to stress that it is both complex and time-consuming. this will help explain some of the patterns we will meet in the following two sections where i discuss network dynamics and their consequences. primate social groups are implicit social contracts designed to ensure protection from predators and, secondarily, rival conspecifics through group augmentation selection effects [ ] . group-living is often mistaken for a cooperation problem, but it is in fact a coordination problem. cooperation problems invariably involve a public goods dilemma (cooperators pay an upfront cost), whereas a coordination problem does not (you are either in the group or not, and everyone pays the same simultaneous cost) [ ] . the problem animals have to solve is how to maintain group stability (i.e. coordination) in the face of the stresses that derive from living in close proximity [ , , ] which would otherwise cause the members to disperse (as happens in herd-and flock-forming species [ , ] . the primate solution to this problem is bonded relationships, since this ensures that individuals will maintain behavioural synchrony and stay together as a group. in primates, relationships are built up by social grooming [ ] . grooming is an exceptionally time-costly activity, with some species devoting as much as one-fifth of their entire day to this seemingly trivial activity [ ] . grooming creates a sense of reciprocity, obligation and trust (operationally, a form of bayesian belief in the honesty and reliability of an alter's future behaviour [ ] ). the layered structure of human social networks is a consequence of how we choose to distribute our social time around the members (figures and ). in both monkeys [ ] and humans [ , ] , the quality of a relationship (indexed by its likelihood of producing prosocial support when it is needed) depends directly on the time invested in it. however, the time available for social interaction is severely limited [ , , ] , and this forces individuals to make trade-offs between the benefits offered by relationships of different strength and the costs of maintaining those relationships. the process involved is a dual process mechanism that involves two separate mechanisms acting in parallel. one is a psychopharmacological mechanism acting at the emotional (raw feels) level that is mediated by the way social grooming triggers the brain's endorphin system (part of the pain management system); the other is the cognitive element that forms the core of the social brain itself [ ] . social grooming is often assumed to have a purely hygienic function. while it certainly has this effect, in primates it has been coopted to form a far more important function in social bonding. the action of leafing through the fur during grooming triggers the endorphin system in the brain [ , ] via a specialized neural system, the afferent c-tactile (or ct) fibres [ ] . these are highly specialized nerves that respond only to light, slow stroking at approximately . cm s − (the speed of hand movements in grooming), and nothing else [ ] . endorphin activation and uptake in the brain creates an opioid-like sense of relaxation, contentment and warmth [ , ] that seems to provide a psychopharmacological platform for bondedness [ , [ ] [ ] [ ] off which the second process, a cognitive sense of trust and obligation, is built. endorphins have a relatively short half-life (around . h), and so the system needs constant activation via grooming to maintain the requisite bonding levels, thereby making the system very time-costly. physical touch in the form of stroking and casual touch continues to form an important part of human social interaction and yields exactly the same endorphin effect [ ] as it does in primate grooming. however, physical contact has an intimacy that limits it mainly to the inner layers of our networks [ , ] . moreover, it is physically impossible to groom with more than one individual at a time with the same focused attention that seems to be important in its execution. this, combined with the constraints on time and the minimum time required to maintain a working relationship, ultimately places a limit on the number of relationships an animal can bond with using only this mechanism. in primates, this limits group size to about individuals (the upper limit on average species group size in primates [ ] ). groups larger than this are prone to fragmentation and ultimately to fission [ ] . in order to be able to increase group size, humans discovered how to exploit other behaviours that also trigger the endorphin system in a way that is, in effect, a form of grooming-at-adistance. these include laughter [ ] , singing [ ] , dancing [ ] , emotional storytelling [ ] , and communal eating [ , ] and drinking (of alcohol) [ ] , all of which trigger the endorphin system and do so incrementally when done in synchrony [ , ] . because they do not involve direct physical contact, more individuals can be 'groomed' simultaneously, thereby allowing a form of time-sharing that makes it possible to reach more individuals and so increase group size. the second component of this system is a cognitive mechanism. it centres around the knowledge of other individuals that can be built up by being in close contact. evolutionary studies of cooperation tend to view relationships as a form of debt-logging. such knowledge would not necessarily require frequent interaction since that can be done by third-party observation. rather, interacting closely with others allows an individual to get to know them well enough to predict their behaviour-to know that they really will come to your aid when you really need them, not because they owe you a favour but because they have a sense of obligation and commitment to you. in effect, it creates a sense of trust that acts as a rapid, intuitive (albeit imperfect) cue of reliability. in humans, this has been augmented by a capacity to build a more detailed 'picture' of another individual through conversation in a way that short circuits the need to invest excessive amounts of time in getting to know them. in other words, we can form a near-instantaneous impression of a stranger and use that as the basis for decisions about whether or not to engage with them. we do this by evaluating an individual's status on a set of largely exogenous cultural dimensions known as the seven pillars of friendship [ ] . the seven pillars are: language (or, better still, dialect), place of origin, educational trajectory, hobbies and interests, worldview (religious/moral/political views), musical tastes and sense of humour. the more of these we share in common with someone, the stronger the relationship between us will be and the more altruistic we will be to each other [ ] . this 'birds of a feather flock together' phenomenon is termed homophily [ ] . the seven pillars are cues of membership of the same community. in small-scale societies, they would identify an extended kinship group, where kin selection (the 'kinship premium' [ ] ) provides an additional guarantee of trustworthiness [ ] . in effect, they function as a cultural totem pole at the centre of the metaphorical village green on which the community can hang its hats-an emotional consensus of who we are as a community and how we came to be that way, a way of building up mutual trust. in the contemporary context, it still identifies your (now reduced) kin group, but it also seems to identify the small community where you spent your formative years-the period when you acquired your sense of who you are and what community you belong to. this is the community whose mores and behaviour you understand in a very intuitive way, and it is this understanding that determines your sense of how well you can trust its members. homophily in friendships has also been documented in respect of a number of endogenous traits, including gender [ , , , ] , ethnicity [ ] and personality [ , ] . gender has a particularly strong effect: approximately % of men's social networks consist of men, and approximately % of women's networks consist of women, with most of the opposite sex alters in both cases being extended family members. one reason for this is that the two sexes' style of social interaction is very different. women's relationships are more dyadic, serviced mainly by conversation and involve significantly more physical touch, whereas men's relationships are more group-based, typically involve some form of activity (sports, hobbies, social drinking) rather than conversation, and make much less use of haptic contact [ , , ] . men's friendships are also typically less intense, more casual and more substitutable than women's: women will often try to keep core friendships going long after one of them has moved away (e.g. through e-mail or facebook), whereas men simply tend to find someone else to replace the absent individual(s) in a rather out-of-sight-out-of-mind fashion. homophily enables interactions (and hence relationships) to 'flow', both because those involved 'understand' each other better and because they share strategic interests. between them, these emotional and cognitive components create the intensity of bonds that act as the glue to bind individuals together. human, and primate, friendships are often described in terms of two core dimensions: being close (desire for spatial proximity) and feeling close (emotional proximity) [ ] . between them, these ensure that bonded individuals stay together so that they are on hand when support is needed, thereby ensuring group cohesion through a drag effect on other dyads created by the ties in the network. since bonding, and the time investment this is based on, is in principle a continuum, this will not, of itself, give rise to the layered structure of a dunbar graph. to produce this, two more key components are needed: a constraint on time and the fact that friendships provide different kinds of benefits. the next section explains how this comes about. two approaches have been used to understand why social networks might have the layered structures they do. one has been to use agent-based models to reverse engineer the conditions under which the intersection between the time costs of relationships and the benefits that these provide give rise to structured networks. the other has been to solve the problem analytically as an optimal investment decision problem. in many ways, these represent top-down and bottom-up approaches, with the first focusing on the macro-level exogenous conditions that produce layered networks, and the second focusing on the micro-decisions that individuals have to make within these environments when deciding whom to interact with. building on the time budget models of dunbar et al. [ ] , sutcliffe et al. [ ] conceived the problem as the outcome of trying to satisfy two competing goals (foraging and socializing, where socializing provides a key non-foraging ecological benefit such as protection against internal or external threats) in a time-constrained environment. the aim was to identify which combination of strategies and cost/benefit regimes reproduced the exact layer structure of human social networks (for these purposes, taken as the , and layers) when agents try to maximize fitness (with fitness being the additive sum of five proximate components that reward social strategies differentially). in the model, agents armed with different strategic preferences for investing in close versus distant ties interacted with each other to form alliances that provided access to different resources. in each run, the population initially consisted of equal numbers of agents pursuing each of three investment preference strategies. following the conventional design for models of this kind, at the end of each round (generation) the % of agents with the lowest fitness were removed (died) and were replaced by offspring produced by the top % (duplicating the parent's strategy), thereby allowing the size of the population to remain constant but its composition to evolve. the model was allowed to run until the distribution of strategy types reached an equilibrium (typically cycles). the outcomes from greater than runs (in which weightings on the fitness functions were systematically varied) were sorted into clusters using k-mean cluster analysis with quantitative fit to the dunbar numbers as the criterion. numerically, strategies that favour having just a few strong ties dominate the fitness landscape, yielding the kinds of small monogamous or harem-based societies that are widely common in mammals. the second most common strategy was the one where agents have no preferences for forming close ties of any kind and instead form large, anonymous herds with no internal structure similar to those characteristic of herd-forming mammals. by contrast, multilevel social structures of the kind found in many primates, and especially those with the specific layer sizes of human social networks, were extremely rare (accounting for less than % of runs). they occurred only under a very limited set of circumstances, namely when a capacity for high investment in social time (i.e. sufficient spare time over that needed for foraging), preferential social interaction strategies, high mortality risk and steep reproductive differentials between individuals coincided. these are all traits characteristic of primates. the alternative approach considers the investment decisions themselves. tamarit et al. [ ] developed a one-parameter bayesian statistical urn model in which individuals choose to invest their limited social capital in relationships that provide different benefits (identified here as network layers). the model seeks to optimize the distribution of effort across relationship types where s k is the cost of a relationship in layer k∈ , . . . r, k is the number of alters assigned to layer k (with l = Σl k ), s is the total amount of resource (time) available, n is the total population size and µ is the lagrange multiplier associated with the constraint imposed by total resources. when the cost (i.e. the time investment that has to be made in a relationship) is a monotonic negative function of layer (as in figure ), this yields layered structures of exactly the kind found in human social networks-few close ties and many weak ones (the lower curve in figure ). however, it turned out that the structure of the network inverts (more close ties and few distant ties) when the lagrange multiplier falls below µ = (upper curve in figure ). one context in which this might happen is when the available community of alters to choose from is small, and so there is spare resource capacity per available alter. a comparison of migrant versus host communities in spain revealed that there is indeed a phase transition between conventionally structured networks (layers with a concave structure, i.e. a few close friends, more intermediate friends and many casual friends) to inverted networks (convex structures, in which ego has more close friends, some intermediate friends and only a few casual friends) at µ ≈ [ ] . this had not been noted previously because in the normal population, most individuals fall in the µ > region; the very small number falling in the µ < region had simply been viewed as statistical error. however, most migrants, who typically have fewer social opportunities, fall in the µ < region and so have inverted (convex) networks as a result, with only a small number having standard (i.e. concave) networks. this seems to suggest that, when surplus time is available, people prefer to invest more heavily in their closest ties rather than distributing their effort more evenly because the emotional and practical support offered by these inner layer ties is more valuable to them. this may explain the structure of primate groups where the inner core of strong ties typically represents a larger proportion of group size in species that live in smaller groups. the fact that the scaling ratio is consistently approximately in human (and primate) social networks raises the possibility that heider's structural balance triads might explain the layered structuring. this possibility was considered by klimek et al. [ ] who studied an ising-type coevolutionary voter model in a context where there are several social functions (say, friendship and business alliances) such that there are separate linked networks where most individuals occupy positions in each network. they showed that when the networks (i.e. functions) vary in rewiring probability (slow versus fast turnover in relationships), the single large network will eventually undergo a phase transition known as shattered fragmentation in which the community fractures into a large number of small subnetworks (or cliques). this happens only when one of the rewiring frequencies reaches a critically high level. when klimek et al. examined data from the pardus online mom game world, they found that the slow rewiring network (friendship) produced a weakly multimodal right-skewed, fattailed distribution with modal group sizes at - and approximately players with a few very large super-communities centred around or members. by contrast, the two fast rewiring networks (in this context, trading and communication functions) both underwent fragmentation into a large number of smaller subnetworks, with a single peak in group size at approximately in both cases, just as the model predicts. when the three networks were projected onto a single multidimensional mapping, very distinct peaks emerged in the distribution of group sizes in both model and data at approximately , and , much as we find in table . this seems to suggest that when triadic closure is a criterion for relationship stability and there is more than one criterion by which individuals can form ties, layering emerges naturally in networks through self-organizing fragmentation effects. so far, we have considered hierarchically inclusive layer structures. in these, the whole population is contained in the lowest layer, and the higher layers are created by successively bolting together, layer by layer, the groupings that make up each lower layer rather in the way military units are structured [ ] . most social networks seem to work like this. however, layers can also arise when some individuals are allocated positions of status, so that the members of the community are distributed across different layers with most individuals in the base layer and a few individuals in one or more higher layers. networks of this kind are characteristic of management structures and the kinds of social hierarchies found in feudal societies. layered structures of this kind seem to emerge rather easily when individuals differ in their willingness to compromise. dávid-barrett & dunbar [ ] used an agent-based model to investigate the processes of group coordination when a community has to converge on an agreed compass direction (a proxy for any communal action or opinion that has the advantage of allowing up to different values to be held rather than just two as in more conventional ising models), but one group member is so convinced they have the right answer that they refuse to compromise. if agents can assign weightings to each other on the basis of some preference criterion, however arbitrary, a layered structure emerges with an 'elite' subgroup that acts, in effect, as a management clique. multilevel structures of this kind have the advantage that they increase the speed with which decisions are adopted. multilayer networks are optimal when the costs associated with maintaining relationships, combined with the costs of information flow, are high. in such cases, a social hierarchy can be adaptive: when the hierarchy is steep, information needs to traverse fewer relationships (shorter path lengths), either because the elite effectively act as bridges between lower level groups (distributed management) or because the elite imposes its decisions on the individuals in the lower strata (dictatorial management). falling communication costs lead to a less steep hierarchy when socially useful information is evenly distributed, but to a steeper hierarchy when socially useful information is unevenly distributed. in human social networks, the layers have very characteristic interaction frequencies with ego ( figure ) . approximately % of all social effort (whether indexed as the frequency or duration of interaction) is directed to the five individuals in the closest layer, with another % devoted to the remaining members of the second layer. thus, % of social time is devoted to just people. comparable results have been reported from large-scale surveys in the uk [ ] and in china [ ] . this will inevitably affect the rate with which information, innovations or disease propagate through a network. however, network structure can speed up or slow down the rate of propagation, depending on the precise nature of the social processes involved. in a very early ( ) analysis of this, we used boyd & richerson's [ ] mean field ising model of cultural transmission to study what happens when these kinds of models are applied to structured networks [ ] . in the model, individuals acquire their information from n cultural parents, each of whom can differ in their cultural state. the model was run with a population of agents mapped as nodes on a * lattice wrapped on a torus so as to prevent edge effects. structure was imposed by allowing nodes to interact only with their eight closest neighbours on the lattice. on a regular lattice, these consist of two distinct sets: direct contacts (the four adjacent nodes on the main diagonals) and indirect contacts (the four corner nodes that can only be reached indirectly through the four adjacent nodes). in effect, these are equivalent to friends and friends-of-friends. at each generation, a node can change its cultural variant either by mutation or by imitation from one of its neighbouring nodes, with transition probabilities determined by a three-element vector specifying node-specific values of the boyd-richerson cultural inheritance bias functions (one reflecting the self-mutation rate, the other two the transmission, or copying, rates from the four 'friends' and the four 'friends-of-friends', with the proviso that all three sum to ). when the spatial constraint is dropped and everyone is allowed to interact with everyone else, the model replicates exactly the findings of the boyd-richerson [ ] cultural inheritance model. the population evolves to full penetrance by a mutant cultural variant initially seeded at just one node (i.e. with a probability of occurrence of just . ) in - generations. with spatial (or social) constraints in place, however, two important effects emerge. first, depending on the steepness of the inheritance bias functions, - % of mutant seedings went extinct before achieving full penetrance, apparently because they often became trapped in eddies at particular locations and could not break out before going extinct. in those runs where the mutant achieved full penetrance (i.e. all nodes became mutants), the time to penetrance was - generations for the same set of transmission biases. in other words, the mutant trait took far longer to spread through the population. once again, the time taken to break out of local eddies was the main reason for the much slower penetrance. the difference between these runs and those where the mutant went extinct depended on the balance between the stochastic rates at which new 'infected' clusters were created and died out. if a local extinction occurred early in the system's evolution when few mutant clusters had become established, global extinction was more likely (the classic small population extinction risk phenomenon in conservation biology [ ] ). changing population size or the number of cultural 'parents' had a quantitative effect, but did not change the basic pattern. the cumulative probability asymptotes at a network size of approximately , but the optimum number of alters is (identified by the point at which the curve begins to decelerate, defined by e − of the way down from the asymptote) since after this, the benefits of increasing network size diminish exponentially. reproduced from [ ] . (b) effect on reachability of removing nodes in different layers of egocentric twitter graphs: the larger the effect, the greater the disruption on information flow. the horizontal dotted lines demarcate /eth from the asymptote, and the vertical dotted line the optimal group size for information diffusion. data from [ ] . penetrance was slower if there were fewer cultural 'parents', for example, or if the population size was larger. to explore the rate at which information flows through a community, dunbar [ ] modelled the likelihood that ego (at the centre of the network) would hear about a novel innovation via direct face-to-face contact for communities of different size ( , , , , , and individuals), given the layer-specific rates of contact shown in figure (extrapolated out to the layer). the probability, p i , of hearing about an innovation seeded somewhere in a network with i layers is the conjoint probability of encountering any given individual in a network layer of size n i and the likelihood that any one of these individuals would have the trait in question (i.e. be infected), summed across all layers where n i is the number of individuals in the ith annulus (network layer), r k is the likelihood that any one of them will have the trait (here taken to be constant, and equivalent to r k = . ), c i [f f] is the likelihood of contacting any given individual face-to-face. figure a plots the results. the probability of acquiring information reaches an asymptotic value at a community size of approximately , with no further gain in the likelihood of hearing about an innovation as community size increases beyond this. the optimal community size for information transmission can be identified by the inflection point (the point at which the marginal gain begins to diminish). with a graph of this form, this occurs at the value on the x-axis when the asymptotic value on the y-axis is reduced by /e. this is at a community size of exactly . the gains to be had by increasing community size beyond approximately diminish exponentially and become trivial beyond a community size of approximately individuals. this was later confirmed by arnaboldi et al. [ ] who modelled information diffusion in actual twitter networks. figure importantly, and contrary to granovetter's [ ] well-known claim, it seems that it is the inner layers (stronger ties) that may have most impact on the likelihood of acquiring information by diffusion, not the outermost layer (weak ties). the outermost -layer (which is disproportionately populated by distant kin [ , ] ) presumably serves some other function such as a mutual support network [ ] . this finding appears to conflict with earlier analyses [ , ] that have emphasized the importance of weak links (long-range connections) in the rate at which infections or information are propagated in networks. the issue, however, hinges on which layers are counted as strong (short-range) and which weak (long-range). previous analyses, including granovetter himself, have tended to be unspecific on this point. if what he had in mind as weak ties was the -layer, then his claim holds; if he was thinking of the -or even layer, then it seems he was wrong. even so, it seems that the information value of -layer ties is considerably less than that of alters in the -and -layers, who are also likely to be considered more trustworthy sources of information. nonetheless, granovetter might still be right if either of two conditions hold. one is that the analyses considered only ego acquiring information by direct personal contact; the models did not consider the impact of upward information flow through the network from the source of the information towards ego. the other is that granovetter might have been right for the wrong reason: the function of networks is not information flow (or acquisition) but the provision of direct functional support such as protection against external threats or sources of economic support (a view which would accord better with the view of primate social systems elaborated in § ). in other words, as is the case in primate social systems, information flow is a consequence of network structure, not its driving force in terms of evolutionary selection [ ] . it may, nonetheless, be that the -layer provides the principal access channels to the global network beyond the individual's primary personal social sphere. this is suggested by an analysis that used m-polynomials derived from chemical graph theory to integrate dunbar graphs into the milgram small world 'six degrees of separation' phenomenon. the capacity to reach an unknown remote individual in - links is only possible if, at each step in the chain, the message-holder can access a large number of alters in their personal network [ ] . however, this analysis only considered versus network contacts, and significantly over-engineers the solution. further work is needed to explore the optimal network size and structure for transmission in more detail. a moot point, of course, is whether the capacity to send letters to a remote stranger is ever of any real functional value to us, or simply an amusing but unimportant by-product of the way personal networks interface with each other in global networks. one complicating aspect of real social networks not usually considered in these models is the fact that social subnetworks are characterized by a high level of homophily, especially in the inner layers. in other words, people's friends tend to resemble them on an array of social and cultural dimensions [ , , ] . analysing a large ( million users) cellphone dataset, miritello et al. [ ] differentiated, on the basis of calling patterns, two distinct phenotypes: 'social keepers' who focused their calls on a small, stable cohort of contacts (introverts?) and 'social explorers' who had a larger number of contacts with high churn (social butterflies, or extraverts?). each tended to exhibit a strong preference for its own phenotype. assuming that phone contact rates mirror face-to-face contact rates (as, in fact, seems to be the case [ , , ] ), explorers were more likely to contact an infected individual because they were more wide-ranging in their social contacts. keepers remained buffered by their small social radius for longer. this reinforces the suggestion made earlier that innovations frequently go extinct in structured networks because they get trapped in eddies created by network structuring and risk going extinct before they can escape into the wider world. the role of extraverts in facilitating information flow was also noted by lu et al. [ , ] in a study of networks parametrized by personality-specific contact rates from the community studied by [ ] . they found that information flow was more efficient if the network consisted of two distinct phenotypes (in this case, actual introvert and extravert personality types) than if all community members were of the same phenotype. in large part, this was because extraverts (those who opted to prioritize quantity over quality of relationships) acted as bridges between subnetworks, thereby allowing information to flow more easily through the network as a whole. much of the focus in network dynamics has been on disease propagation. in most models, networks are assumed to remain essentially static in structure over time. this may not always be the case, since network structure may itself respond to both internal threats (stress or deception) and external threats (such as disease or exploitation or attack by outsiders). this is because threats such as disease or exploitation cause a breakdown in trust and trust is, as we saw, central to the structure of social networks. other factors that might cause networks to restructure themselves include a reduction in the time available for social interaction, access to a sufficiently large population to allow choice [ ] or a change in the proportion of phenotypes (sex, personality or family size) when these behave differently. methods for studying networks that change dynamically through time have been developed [ ] , although in practice these typically reflect past change rather than how networks are likely to respond to future challenges. here, my concern is with how networks might change as a consequence of the internal and external forces acting on them. because of the way relationships are serviced in social networks ( § ), a reduction in time devoted to a tie results in an inexorable decline in the emotional strength of a tie, at least for friendships ( figure ) . note, however, that family ties appear to be quite robust in the face of lack of opportunity to interact. figure suggests that this effect happens within a matter of a few months (see also [ , ] ). saramäki et al. [ ] reported a turnover of approximately % in the network membership of young adults over an -month period after they had moved away from their home town, most of which occurred in the first nine months. a similar effect will occur when there is a terminal breakdown in a relationship. these seem to occur with a frequency of about % of relationships per year, though it is clear that some people are more prone to relationship breakdown than others [ ] . most such breakdowns occur because of a breakdown in trust [ , ] . although almost never considered in models of network dynamics, the division between family and friends can have significant consequences for the dynamics of networks, especially when comparing natural fertility (no contraception) with demographic transition fertility regimes (those that actively practise contraception). friendships require significantly more time investment than family relationships to maintain at a constant emotional intensity, especially so in the outer layers [ , ] , and because of this are more likely to fade (and to do so rather quickly) if contact is reduced [ ] ( figure ). family relationships, on the other hand, are more forgiving of breaches of trust and underinvestment. in addition, when family relationships breakdown, they are apt to fracture catastrophically and irreparably [ ] , creating structural holes. by contrast, most friendships die quietly as a result of reduced contact, in many cases because they are simply replaced by alternatives. this probably means that, when a network is under threat, friendship ties are more likely to be lost than family ties. this would seem to be born out by casual observation of the response to the covid- lockdown: virtual zoom-based family gatherings seem to be much more common than friendship-based meetings. under normal circumstances, the gaps left by the loss of a tie following a relationship breakdown are filled by moving someone up from a lower layer or by adding an entirely new person into the network from outside. saramäki et al. [ ] noted that, when this happens, the new occupant of the vacated slot is contacted with exactly the same frequency as the previous occupant, irrespective of who they are. it seems that individuals have a distinctive social fingerprint, and this fingerprint is very stable across time [ ] . however, if the opportunity for social interaction is restricted, or there is widespread breakdown in the level of trust (as when many people cease to adhere to social rules, or a culture of deception or antisocial behaviour evolves), then the inevitable response is for networks to fragment as individuals increasingly withdraw from casual contacts and focus their attention on those whom they trust most (normally the alters in the innermost layers of their network). iñiguez et al. [ ] and barrio et al. [ ] modelled the effect of two kinds of deception (selfish lies versus white lies) on network structure. selfish lies are those that benefit the liar, while white lies are those that benefit either the addressee or the relationship between the liar and the addressee (e.g. 'likes' on digital media). these two phenotypes differ radically in the effect they have on the relationship between the individuals concerned: the first will cause a reduction in the frequency of contact resulting in a fragmentation of the network, whereas the second often reinforces network cohesion. if networks shrink sufficiently under stress, they may invert (figure ). there is indirect evidence for this in the effect that parasite load has on the size of communities in tribal societies: these decline in size the closer they are to the equator (the tropics being the main hotspot for the evolution of new diseases), and this correlates in turn with a corresponding increase in the number of languages and religions, both of which restrict community size [ , ] . at high latitudes, where parasite loads tend to be low and less stable climates make long-range cooperation an advantage, community sizes are large, people speak fewer languages and religions tend to have wider geographical coverage, which, between them, will result in more extensive global networks [ , ] . similar effects have been noted in financial networks, where network structure between institutions that trade with each other also depends on trust. there has been considerable interest in how network structure might influence the consequences of contagion effects when financial institutions collapse. network structure can affect how shocks spread through networks of banks, giving rise to default cascades in ways not dissimilar to the way diseases propagate through human social networks. although well-connected banks may be buffered against shocks because of the way the effects are diluted [ ] [ ] [ ] much as a well-connected individuals may be buffered against social stresses, a loss of trust between institutions invariably results in the contraction of networks, associated with more conservative trading decisions and a greater reluctance to lend [ ] in ways reminiscent of social networks fragmenting in the face of a loss of trust. if effective network size (i.e. the number of ties an individual has) is reduced as a result of such effects, more serious consequences may follow at the level of the individual for health, wellbeing and even longevity. smaller social networks are correlated with increasing social isolation and loneliness, and loneliness in turn has a dramatic effect on morbidity and mortality rates. there is now considerable evidence that the number and quality of close friendships that an individual has directly affects their health, wellbeing, happiness, capacity to recover from surgery and major illness, and their even longevity (reviewed in [ , ] ), as well as their engagement with, and trust in, the wider community within which they live [ , ] . indeed, the effects of social interaction can even outweigh more conventional medical concerns (obesity, diet, exercise, medication, alcohol consumption, local air quality, etc.) as a predictor of mortality [ ] . most epidemiological studies have focused on close friends, but there is evidence that the size of the extended family can have an important beneficial effect, especially on children's morbidity and mortality risks [ ] . these findings are mirrored by evidence from primates: the size of an individual's intimate social circle has a direct impact on its fertility, survival, how quickly it recovers from injury, and ultimately its biological fitness [ ] [ ] [ ] [ ] [ ] [ ] [ ] . it is worth noting that dunbar graphs, with their basis in trust, have been used to develop online 'secret handshake' security algorithms for use in pervasive technology (e.g. safebook [ , ] ). pervasive technology aims to replace cellphone masts by using the phones themselves as waystations for transmitting a call between sender and addressee. the principal problem this gives rise to is trust: a phone needs to be able to trust that the incoming phone is not intent on accessing its information for malicious purposes. safebook stores the phone owner's seven pillars as a vector which can then be compared with the equivalent vector from the incoming phone. a criterion can be set as to how many 'pillars' must match for another phone to be considered trustworthy. the dunbar graph has also been used to develop a bot-detection algorithm by comparing a node's network size and shape with that of a real human (i.e. a dunbar graph): this algorithm out-performs all other currently available bot-detection algorithms [ ] . we might ask what effects we might expect in the light of this from the lockdowns imposed by most countries in in response to covid- . i anticipate four likely effects. one is that if lockdown continues for more than about three months, we may expect to see a weakening of existing friendships, especially in groups like the elderly whose network sizes are already in age-dependent decline. since older people find it more difficult to make new friends, an increased level of social isolation and loneliness is likely to result, with consequent increases in the diseases of old age, including dementia and alzheimer. second, we may expect to see an increased effort to recontact old friends, in particular, immediately after lockdown is lifted. we already see evidence for this in telephone call patterns: if there is a longer than normal gap before an alter is called again, the next call is significantly longer than average as though attempting to repair the damage to relationship quality [ ] . third, the weakening of friendship quality can be expected (i) to make subsequent meetings a little awkward because both parties will be a little unsure of how they now stand when meeting up again and (ii) to result in some churn in networks where new friendships developed through street-based covid community groups are seen as more valuable (and more accessible) than some previous lower rank friendships. finally, we may expect the fear of coronavirus contagion (an external threat) to result in a reduction in the frequency with which some individuals (notably introverts and the psychologically more cautious) visit locations where they would come into casual contact with people they do not know. they may also reduce frequencies of contact with low-rank friends, and perhaps even distant family members, whose behaviour (and hence infection risk) they cannot monitor easily. this is likely to result in more inverted networks, as well as networks focused mainly on people who are more accessible. although this effect will weaken gradually with time, and network patterns are likely to return to pre-covid patterns within - months, some friendship ties may have been sufficiently weakened to slip over the threshold into the (acquaintances) layer. my aim in this paper has been to introduce a rather different perspective on the social structure of communities than that normally considered in disease propagation models, and to explain the forces that underpin real-world social networks. i have presented evidence to suggest that human social networks are very much smaller and more highly structured than we usually assume. in addition, network size and composition can vary considerably across individuals as a function of sex, age, personality, local reproductive patterns and the size of the accessible population. while casual contacts might be important for the spread of highly infectious diseases [ social time is actually devoted to no more than individuals and this will slow down rates of transmission if physical contact or repeated exposure to the same individual is required for successful infection. both external and internal threats can destabilize network ties by affecting the level of trust, 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hamilton's rule predicts anticipated social support in humans the costs of family and friends: an -month longitudinal study of relationship maintenance and decay effects of deception in social networks dynamics of deceptive interactions in social networks pathogen prevalence predicts human cross-cultural variability in individualism/collectivism assortative sociality, limited dispersal, infectious disease and the genesis of the global pattern of religion diversity contagion in financial networks contagion in financial networks where the risks lie: a survey on systemic risk fire sales in a model of complexity . the neurobiology of social distance social relationships and mortality risk: a metaanalytic review one thousand families in strong and consistent social bonds enhance the longevity of female baboons social bonds of female baboons enhance infant survival the benefits of social capital: close social bonds among female baboons enhance offspring survival responses to social and environmental stress are attenuated by strong male bonds in wild macaques network connections, dyadic bonds and fitness in wild female baboons social support reduces stress hormone levels in wild chimpanzees across stressful events and everyday affiliations family network size and survival across the lifespan of female macaques safebook: a privacy-preserving online social network leveraging on real-life trust a provably secure secret handshake with dynamic controlled matching making social networks more human: a topological approach absence makes the heart grow fonder: social compensation when failure to interact risks weakening a relationship academy centenary research project (lucy to language), the erc relnet advanced research fellowship, the eu fp socialnets grant and the eu horizon ibsen research grant.acknowledgements. i thank the reviewers for drawing my attention to some useful additional material. key: cord- -nqn qzcu authors: chapman, lloyd a. c.; spencer, simon e. f.; pollington, timothy m.; jewell, chris p.; mondal, dinesh; alvar, jorge; hollingsworth, t. deirdre; cameron, mary m.; bern, caryn; medley, graham f. title: inferring transmission trees to guide targeting of interventions against visceral leishmaniasis and post-kala-azar dermal leishmaniasis date: - - journal: nan doi: . / . . . sha: doc_id: cord_uid: nqn qzcu understanding of spatiotemporal transmission of infectious diseases has improved significantly in recent years. advances in bayesian inference methods for individual-level geo-located epidemiological data have enabled reconstruction of transmission trees and quantification of disease spread in space and time, while accounting for uncertainty in missing data. however, these methods have rarely been applied to endemic diseases or ones in which asymptomatic infection plays a role, for which novel estimation methods are required. here, we develop such methods to analyse longitudinal incidence data on visceral leishmaniasis (vl), and its sequela, post-kala-azar dermal leishmaniasis (pkdl), in a highly endemic community in bangladesh. incorporating recent data on infectiousness of vl and pkdl, we show that while vl cases drive transmission when incidence is high, the contribution of pkdl increases significantly as vl incidence declines (reaching % in this setting). transmission is highly focal: > % of mean distances from inferred infectors to their secondary vl cases were < m, and estimated average times from infector onset to secondary case infection were < months for % of vl infectors, but up to . yrs for pkdl infectors. estimated numbers of secondary vl cases per vl and pkdl case varied from - and were strongly correlated with the infector's duration of symptoms. counterfactual simulations suggest that prevention of pkdl could have reduced vl incidence by up to a quarter. these results highlight the need for prompt detection and treatment of pkdl to achieve vl elimination in the indian subcontinent and provide quantitative estimates to guide spatiotemporally-targeted interventions against vl. . pkdl has therefore been recognised as a major potential threat to the vl elimination programme in the isc ( ), which has led to increased active pkdl case detection. nevertheless, the contribution of pkdl to transmission in field settings still urgently needs to be quantified. although the incidence of asymptomatic infection is to times higher than that of symptomatic infection in the isc ( ), the extent to which asymptomatic individuals con- (fig. a) . the data from this study are fully de- scribed elsewhere ( , ) . briefly, month of onset of symptoms, treatment, relapse, and relapse treatment were recorded for vl cases and pkdl cases with onset between and (retrospectively for cases with onset before ), and year of onset was recorded for vl cases with onset before . there were vl cases and pkdl cases with onset between january and december in the study area, and vl cases with onset prior to january . over the whole study area, vl incidence followed an epi- demic wave, increasing from approximately cases/ , /yr in to ≥ cases/ , /yr in before declining to < cases/ , /yr in (fig. b) . pkdl incidence fol- lowed a similar pattern but lagging vl incidence by roughly yrs, peaking at cases/ , /yr in . however, vl and pkdl incidence varied considerably across paras (aver- age para-level incidences: vl - cases/ , /yr, pkdl - cases/ , /yr, table s ) and time (range of annual para-level incidences: vl - cases/ , /yr, pkdl - cases/ , /yr, fig. s ). ú ci = credible interval, calculated as the % highest posterior density interval † risk of subsequent vl/asymptomatic infection if susceptible ‡ based on assumed infectiousness § in the absence of background transmission and relative to living directly outside the case household. based on the relative infectiousness of vl and the di erent types of pkdl from the xenodiagnostic data, in the absence of any other sources of transmission, the estimated probability of being infected and developing vl if living in the same household as a single symptomatic individual for month following their onset was . ( % ci: . , . ) for vl and ranged from . to . ( % cis: ( . , . )-( . , . )) for macular/papular pkdl to nodular pkdl. living in the same household as a single asymptomatic individual, the monthly risk of vl was only . ( % ci: . , . ), if asymptomatic individuals are % as infectious as vl cases. the risk of infection if living in the same household as an infectious individual was estimated to be more than times higher than that if living directly outside the household of an infectious individual (hazard ratio = . ), with a % ci well above ( . , . ). the estimated spatial kernel (fig. s ) around each infectious individual shows a relatively rapid decay in risk with distance outside their household, the risk of infection halving over a distance of m ( % ci: , m). mission. we assess the contribution of di erent infectious groups to transmission in terms of their relative contribu- tion to the transmission experienced by susceptible individuals ( fig. a and fig. s ). the contribution of vl cases was fairly stable at around % from to the end of before decreasing steadily to at the end of the epidemic, while the contribution of pkdl cases increased from in to ≥ % in ( % ci: , %) (fig. s ) . only a small proportion of the total infection pressure on susceptible individuals, varying between % and % over the course of the epidemic, was estimated to have come from asymptomatic and pre-symptomatic individuals. reconstructing the transmission tree. by sampling , transmission trees from the joint posterior distribution of the transmission parameters and the unobserved data (as de- scribed in materials and methods), we can build a picture of the most likely source of infection for each case and how infec- tion spread in space and time. fig. shows the transmission tree at di erent points in time in part of the south-east cluster of villages. early in the epidemic and at its peak (figures a and b), most new infections were due to vl cases. towards the end of the epidemic, some infections were most likely due to pkdl cases and there was some saturation of infection around vl cases (fig. c) . the inferred patterns of trans- mission suggest that disease did not spread radially outward from index cases over time, but instead made a combination of short and long jumps around cases with long durations of symptoms and households with multiple cases. . arrows show the most likely source of infection for each case infected up to that point in time over , sampled transmission trees, and are coloured by the type of infection source and shaded according to the proportion of trees in which that individual was the most likely infector (darker shading indicating a higher proportion). asymptomatic infections are not shown for clarity. s/a = susceptible or asymptomatic, e = pre-symptomatic, i = vl, r = recovered, d = dormantly infected, p = pkdl (see si text). gps locations of individuals are jittered slightly so that individuals from the same household are more visible. an animated version showing all months is provided in si movie . there is considerable heterogeneity in the estimated contri- by each vl/pkdl case is typically less than (fig. s a ). the times after onset of symptoms in the infector at which secondary vl cases become infected are typically longer for pkdl infectors than for vl infectors (fig. b) detected after a longer delay than subsequent cases and there will be some delay in mounting a reactive intervention, such as active case detection and/or targeted irs around the index case(s), interventions will need to be applied in a large radius (up to m) around index cases to be confident of capturing all secondary cases and limiting transmission. our results demonstrate the importance of accounting for spatial clustering of infection and disease when modelling vl transmission. previous vl transmission dynamic models ( , - ) have significantly overestimated the relative con- tribution of asymptomatic infection to transmission (as up to %), despite assuming asymptomatic individuals are only - % as infectious as vl cases, by treating the population as homogeneously mixing, such that all asymptomatic indi- viduals can infect all susceptible individuals via sandflies. in reality, asymptomatic individuals do not mix homogeneously with susceptible individuals as they are generally clustered together around or near to vl cases ( , ), who are much more infectious and therefore more likely to infect suscepti- ble individuals around them, even if they are outnumbered by asymptomatic individuals. asymptomatic infection also leads to immunity, and therefore local depletion of suscep- tible individuals around infectious individuals. hence, for the same relative infectiousness, the contribution of asymp- tomatic individuals to transmission is much lower when spatial heterogeneity is taken into account. nonetheless, our results suggest that asymptomatic indi- viduals do contribute a small amount to transmission and that they can "bridge" gaps between vl cases in transmission chains, as the best-fitting model has non-zero asymptomatic relative infectiousness. superficially, this appears to conflict with preliminary results of xenodiagnosis studies in which asymptomatic individuals have failed to infect sandflies ac- cording to microscopy ( ). however, historical ( , ) and experimental ( ) data show that provision of a second blood meal and optimal timing of sand fly examination are criti- cal to maximizing sensitivity of xenodiagnosis. these data suggest that recent xenodiagnosis studies ( , ), in which dissection occurred within days of a single blood meal, may underestimate the potential infectiousness of symptomatic and asymptomatic infected individuals. occurrence of vl in isolated regions where there are asymptomatically infected individuals, but virtually no reported vl cases ( , ), also seems to suggest that asymptomatic individuals can generate vl cases. however, it is possible that some individuals who de- veloped vl during the study went undiagnosed and untreated, and that we have inferred transmissions from asymptomatic individuals in locations where cases were missed. we will in- vestigate the potential role of under-reporting in future work. the analysis presented here is not without limitations. as can be seen from the model simulations (fig. s ) , the model is not able to capture the full spatiotemporal heterogeneity in the observed vl incidence when fitted to the data from the whole study area, as it underestimates the number of cases in higher- incidence paras (e.g. paras , and ). there are various possible reasons why the incidence in these paras might have been higher, including higher sandfly density, lower initial lev- els of immunity, variation in infectiousness between cases and within individuals over time, dose-dependence in transmission (whereby flies infected by vl cases are more likely to create vl cases than flies infected by asymptomatic individuals ( )), where k(d) = e ≠d/is the spatial kernel function that determines . cc-by . international license it is made available under a author/funder, who has granted medrxiv a license to display the preprint in perpetuity. is the (which was not peer-reviewed) the copyright holder for this preprint . bangladesh (protocol # - ) and the centers for disease con- • recovered (i.e. treated for primary vl, vl relapse or pkdl, or self-resolved from pkdl, or recovered from asymptomatic upon infection, individuals either develop pre-symptomatic infection with probability pi or asymptomatic infection with probability ≠ pi (see table s for values of fixed parameters used in the model of . cc-by . international license it is made available under a author/funder, who has granted medrxiv a license to display the preprint in perpetuity. whereis the rate constant for spatial transmission between infected and susceptible individuals; k(dij) is the spatial kernel function that scales the transmission rate by the distance dij between individuals i and j; " (Ø ) is a rate constant for additional within-household transmission; ij is an indicator function for individuals living in the same household, i.e. between an exponentially decaying spatial kernel and a cauchy-type kernel in our previous study ( ) (the exponential kernel gave a marginally better fit), we use the exponential kernel here: and asymptomatic individuals, we take the relative infectiousness of pre-symptomatic individuals, h , to be the same as that of asymptomatic individuals (i.e. h = h ). one-hundred and thirty-eight of the pkdl cases underwent one or more examinations by a trained physician to determine the type and extent of their lesions (table s ). data from a recent xenodiagnosis study in bangladesh ( ) pre-symptomatic -- thus, individual j's infectiousness at time t is given by [ ] incubation period. following previous work ( ), we model the incubation period as negative binomially distributed nb(r, p) with fixed shape parameter r = and 'success' probability parameter p, and support starting at (such that the minimum incubation period is month): we estimate p in the mcmc algorithm for inferring the model parameters and missing data (see below). vl onset-to-treatment time distribution. several vl cases with onset before have missing symptom onset and/or treatment times (only their onset year is recorded), and may therefore have been infectious at the start of the study period. in order to be able to infer the onset-to-treatment times of these cases, ot Õ j = min(r Õ j , d Õ j ) ≠ i Õ j (j = , . . . , ni ), in the mcmc algorithm (see below) we model the onset-to-treatment time distribution as a negative binomial distribution nb(r , p ) and fit to the onset-to-treatment times of all vl cases for whom both onset and treatment times were recorded ( figure s a ): to obtain r = . and p = . (corresponding to a mean onset-to-treatment time of . months). assume that all cases not recorded as having immediate recurrence of symptoms su ered treatment relapse and that the time to relapse follows a geometric distribution geom(p ) with pmf: where fitting to the recorded gaps gives p = . (corresponding to a mean time to relapse of . months). relapse cases are assumed to be uninfectious from their treatment month to their relapse time and their duration of symptoms upon relapse is assumed to follow the same distribution as the onset-to-treatment time for a first vl episode (eq. ( )). we assume all relapse cases were treated for relapse before the end of the study, since the latest treatment time for primary vl in a case that while the probabilities of pre-symptomatic or asymptomatic infection in month t given susceptibility up to month t ≠ are, respectively: [ ] model for initial status of non-symptomatic individuals. as there was transmission and vl in the population before the start the probabilities of each non-symptomatic individual initially present (i.e. with vj = ) being susceptible, asymptomatically infected, or recovered from asymptomatic infection at time t = can then be found by calculating the probability of avoiding infection in every month from their birth to the start of the study, summing over the probabilities of being infected in one of the months between their birth and the start of the study and recovering after the start of the study, and summing over the of probabilities of being infected in a month before the start of the study and recovering before the start of the study, respectively: ps (aj) := p(aj > , rj > ) = e ≠⁄ a j [ ] pa (aj) := p(aj ae , where aj is the age of individual j in months at t = . since we assume that non-symptomatic individuals who are born, or who immigrate into the study area, after the start of the study (with vj > ) are susceptible, for notational convenience we define the probabilities for these individuals as ps (aj) = , pa (aj) = pr (aj) = . we estimate the historical asymptomatic infection rate, ⁄ , by fitting the model to age-prevalence data on leishmanin skin test (lst) positivity amongst non-symptomatic individuals from a cross-sectional survey of three of the study paras conducted in ( ) (see figure s ). we assume that entering state r corresponds to becoming lst-positive, as lst positivity is a marker for durable, protective cell-mediated immunity against vl ( , ), and estimate ⁄ by maximising the binomial with these definitions, the complete data likelihood for the augmented data z = (y, x) given the model parameters ◊ = (-, -, ', ", p) is composed of the products of the probabilities of all the di erent individual-level events over all months: the joint posterior distribution of the model parameters ◊ = (-, -, ', ", p) and the missing data x given the observed data y [ ] we do this using a metropolis-within-gibbs mcmc data augmentation algorithm in which we iterate between sampling from the conditional posterior distribution of the parameters given the observed data and the current value of the missing data, t=v j qj(t) + qj(t + ) is a normalising constant to account for the fact that we know that j was not pre- and ", which are non-negative, since there is little information available with which to construct informative priors (table s ) . the mean of the prior distribution foris chosen as m based on our previous findings ( ) . a beta distribution, beta(a, b) , is chosen as a conjugate prior for the incubation period parameter p, since it is a probability (p oe where -= (-, -, ', "), so p can be updated e ciently in the mcmc by drawing from this full conditional distribution rather than using a random walk metropolis-hastings update. ≠ aj, ) for rj, = t + . by repeating the following steps. note that throughout the following we suppress notation of conditional dependencies in the likelihood terms where they are obvious to maintain legibility. the algorithm also accounts for the fact that some individuals were born or migrated or died during the study when updating the unknown pre-symptomatic infection times and asymptomatic infection and recovery times (using the birth/migration/death times as bounds on the proposed unobserved times), but we omit these details from the following description for simplicity. (b) accept the infection time move with probability where (c) i. if aj = : if rj = , if rj > . ii. if aj = t + : a. if a Õ j = t + , then r Õ j = t + , so accept immediately as the likelihood does not change. step (c)ic, except with . iii. if aj oe [ , t ]: a. if a Õ j = , follow step (c)ia, but with q replaced by step (c)ib except with step (c)ic but with . update missing treatment times of vl cases during the study: update the treatment time of the vl case whose treatment time is missing but whose onset time is known, conditional on the treatment time being before their pkdl onset: (a) propose a new treatment time as update the onset and treatment times of all cases who potentially had active vl at the start of the study (t = ) who n( , ) ) " = p ) . update the treatment times of cases who potentially had active vl at the start of the study whose treatment times were not recorded but whose onset times are known, one by one. for each case j: p ) . . update whole relapse period of cases missing both relapse and relapse treatment times: update the relapse and relapse treatment times of all vl cases who su ered relapse during the study who are missing step in the above algorithm may appear complicated, but essentially consists of proposing a new asymptomatic infection is the empirical covariance of the last k ≠ f (k) + samples offrom the chain, with the mean of the last k ≠ f (k) + samples; is the initial guess for the covariance matrix, and k determines the rate at which the influence of on k+ decreases (the weight of halves after the first k iterations). we use k = here. if f (k) = f (k ≠ ) (i.e. if k is odd with f (k) chosen as above), an additional observation is added to the estimate of the covariance matrix if k is even), the new observation replaces the oldest it has been shown that n (k , . /n -), where is the covariance matrix of the posterior distribution, is the optimal proposal distribution for rapid convergence and e cient mixing of the mcmc chain for symmetric product-form posterior distributions as nae oe, and leads to an acceptance rate of . % ( , ) . this corresponds to a scaling of c k = in eq. ( ). however, we are in a context with a large amount of missing data, which is strongly correlated with some of the transmission parameters (see parameter estimates below), so the posterior distribution is not symmetric, and this scaling is not optimal. we therefore follow ( ) and scale c k adaptively as the algorithm progresses to target an acceptance rate of approximately . % for updates to -. we do this by rescaling c k by a factor of x k > every time an acceptance occurs and by a factor of x ‹/(‹≠ ) k < every time a rejection occurs such that the acceptance rate ‹ approaches . % in the long run, if proposal is rejected. in order to satisfy the 'diminishing adaptation' condition ( ), which is necessary to ensure the markov chain is ergodic and converges to the correct posterior distribution, it is required that c k tends to a constant as k ae oe. so that the adaptation diminishes as k increases, we use the sequence where m is the number of iterations over which the scaling factor x k decreases from to . . here, we use m = . model comparison we compare the goodness of fit of models with di erent asymptomatic and pre-symptomatic relative infectiousness (between % and % of that of vl cases), with and without additional within-household transmission, to test di erent assumptions about how infectious asymptomatic and pre-symptomatic individuals are, using dic ( ). dic measures the trade-o between model fit and complexity and lower values indicate better fit. since some variables were not observed, we use a version of dic appropriate for missing data from ( ), which is based on the complete data likelihood l(◊; z) = p(y, x|◊). this is equivalent to the standard version of dic for fully observed data except that it is averaged over the missing data: where d(◊) is the deviance (the measure of model fit), given (up to an additive constant dependent only on the data) by . [ ] the relative contribution of state x to the infection pressure on the ith vl case at their infection time, i.e. the probability that i's infection source is x (fig. b in the main text), is: , x oe {a, e, i, p}. [ ] the probability that the ith vl case is infected from the background transmission is ' ⁄i(ei ≠ ) . reconstructing the epidemic reconstructing the transmission tree. we reconstruct the transmission tree following the 'sequential approach' described in ( ). we draw n samples (◊ k , x k ) (k = , . . . , n) from the joint posterior distribution from the mcmc, calculate the probability that infectee i was infected by individual j conditional on their infection time ei and uncertainty in the parameter values and missing data (over the posterior distribution). we use n = here. calculating transmission distances and times. the mean infector-to-vl-infectee distance and mean infector-onset-to-vlinfectee-infection time for each vl and pkdl infector ( figures a and b in the main text) are calculated from the sample of n transmission trees by averaging the distances and times from each infector to their vl infectees within each tree, and then averaging these quantities over all the trees in which that vl/pkdl case is an infector: where · [ ] the absolute contribution of each infectious state to the e ective reproduction number at time t is: where x oe {a, i} denotes the infectious state, and, as described above, in the main text we split the numbers of secondary infections (rj) arising from vl and pkdl for cases that had both. to assess the fit of the model and simulate hypothetical interventions against pkdl, we create a stochastic simulation version of the individual-level spatiotemporal transmission model described above. we follow standard stochastic simulation methodology for discrete-time individual-level transmission models ( ), converting infection event rates into probabilities in order to determine who gets infected in each month. we assume that an individual's progression through di erent infection states following infection occurs independently of the rest of the epidemic (i.e. is either governed by internal biological processes or random external processes of detection), which enables the simulation of an individual's full infection history from the point of infection. so that we can simulate durations of pkdl infectiousness, we fit a negative binomial distribution nb(r , p ) to the observed pkdl onset-to-treatment times and onset-to-resolution times for self-resolving pkdl cases in the data: given these pieces of information, the simulation algorithm proceeds as follows: negative binomially distributed ( ). the pmf of a size-biased negative binomial random variable x ú corresponding to x ≥ nb is: and assign a pkdl infectious by drawing from cat({h , h , h , hu}, p) . ii. else the individual recovers without developing pkdl, so draw a recovery time: figure s and table s respectively. based on the deviance distributions and dic values, the best-fitting model is the model with additional within-household transmission and the highest level of relative pre-symptomatic and asymptomatic infectiousness (both % as infectious as vl). hence, we focus on the output of this model in the main text and below. and ") and incubation period distribution parameter p for the di erent models are shown in table s . the parameter estimates are very similar across the di erent models and vary in the way expected -the spatial transmission rate constantand background transmission rate ' are lower for models with additional within-household transmission (" > ) and decrease with increasing relative asymptomatic infectiousness h , and the mode foris slightly larger for models with " > (since a flatter kernel shape compensates for the extra within-household transmission). the posterior distributions for the incubation period distribution parameter p correspond to a mean incubation period of . - . months ( % hpdis ( . , . )-( . , . ) months). the log-likelihood trace and posterior distributions for the parameters for the best-fitting model are shown in figure s . the parameters are clearly well defined by the data, as the posterior distributions di er significantly from the weak prior distributions. the corresponding autocorrelation plots are shown in figure s . the high degree of autocorrelation evident for all the parameters is due to strong correlation between the transmission parameters and the missing data, in particular between the spatial transmission rate constantand the asymptomatic infection times. figure s shows thatis strongly negatively correlated with the mean asymptomatic infection timeĀ. this is expected since a higher overall transmission rate leads to show that there is some negative correlation betweenand ', -and ', and " and p. these correlations are not surprising: the more transmission that is explained by proximity to infectious individuals (the higher -), the less needs to be explained by the background transmission (the lower '); the flatter the spatial kernel (the larger -), the fewer infections need to be explained by the background transmission; and the more infections are accounted for by transmission within the same household (the higher "), the longer the incubation period (the lower p) needs to be (due to long times between onsets of cases in the same household). the acceptance rate for the transmission parameter updates (step in the mcmc algorithm) was . demonstrate that the data augmentation algorithm works as expected. figure s shows the incidence curve of vl and pkdl cases for the whole study area and the inferred incidence curve of asymptomatic infections (averaged over the mcmc chain). the number of asymptomatic infections increases and decreases with the number of vl cases as expected given the assumption that the incidence ratio of asymptomatic to symptomatic infection is fixed. the posterior probabilities that individuals were asymptomatically infected during the study (shown in figure s , with is higher). this is as expected given the structure of the model (the decrease in the risk of infection with distance from an infectious individual encoded in the spatial kernel) and the estimates of the transmission parameters. the examples shown in figure s demonstrate that non-symptomatic individuals' asymptomatic "infection" time posterior distributions (red). note that asymptomatic "infection" in months and t + = , represent asymptomatic infection before the study and no asymptomatic infection before the end of the study, respectively. (a) individual who migrated into a house with an active vl case from outside the study area in month and therefore had a high initial probability of asymptomatic infection, followed by further peaks in asymptomatic infection risk in months and with the pkdl and vl onsets of two other household members in months and respectively. (b) individual born in month with a high probability of having avoided asymptomatic infection for the duration of the study. 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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- - st mvh authors: overton, christophere.; stage, helenab.; ahmad, shazaad; curran-sebastian, jacob; dark, paul; das, rajenki; fearon, elizabeth; felton, timothy; fyles, martyn; gent, nick; hall, ian; house, thomas; lewkowicz, hugo; pang, xiaoxi; pellis, lorenzo; sawko, robert; ustianowski, andrew; vekaria, bindu; webb, luke title: using statistics and mathematical modelling to understand infectious disease outbreaks: covid- as an example date: - - journal: infect dis model doi: . /j.idm. . . sha: doc_id: cord_uid: st mvh during an infectious disease outbreak, biases in the data and complexities of the underlying dynamics pose significant challenges in mathematically modelling the outbreak and designing policy. motivated by the ongoing response to covid- , we provide a toolkit of statistical and mathematical models beyond the simple sir-type differential equation models for analysing the early stages of an outbreak and assessing interventions. in particular, we focus on parameter estimation in the presence of known biases in the data, and the effect of non-pharmaceutical interventions in enclosed subpopulations, such as households and care homes. we illustrate these methods by applying them to the covid- pandemic. mathematical epidemiology is a well-developed field. since the pioneering work of ross in malaria modelling [ ] and kermack and mckendrick's general epidemic models [ ] , there has been gathering interest in using mathematical tools to investigate infectious diseases. the allure is clear, since mathematical models can provide powerful insight into how these complex systems behave, which in turn can enable these problems to be better controlled/prevented. not only is the power of the mathematical tools increasing, but the availability of data on infectious diseases, whether this be a rapid release of data during an outbreak or detailed collection of data for endemic pathogens, is increasing. rapid interpretation of epidemiological data is critical for the development of effective containment, suppression and mitigation interventions, but there are many difficulties to interpreting case data in real-time. these include interpreting symptom progression and fatality ratios with delay distributions and right-censoring, exacerbated by exponential growth in cases leading to the majority of case data being on recently infected individuals; lack of clarity and consistency in denominators; inconsistency of case definitions over time and the eventual impact of interventions and changes to behaviour on transmission dynamics. mathematical and statistical techniques can help overcome some of these challenges to interpretation, aiding in the development of intervention strategies and management of care. examining key epidemiological quantities alongside each other in a transmission model can provide quantitative insights into the outbreak, testing the potential impact of intervention strategies and predicting the risk posed to the human (or animal) host population and healthcare preparedness. mathematical modelling has been used as part of the planning process during outbreak response by governments worldwide for many recent outbreaks. for example the uk department of health has a long established committee scientific pandemic influenza group on modelling, or spi-m to advise on new and emerging respiratory infections [ ] . one of the largest instances of such an outbreak in recent history was the h n pandemic. the world health organisation developed a network of modelling groups and public health experts to work on exploring various characteristic of the outbreak [ , ] . these ranged from characterising the dynamics of the outbreak to investigating the effectiveness of different intervention strategies. this integration of mathematics into policy design indicates the important insights that modelling and statistics can provide. this paper is a collection of work-streams addressing various technical questions faced by the group as part of the ongoing response to covid- , and as such is written to be reflective of the experience we have gone and are currently going through. therefore, to aid the reader each section includes results and a short discussion. many of the questions and techniques presented here can be further developed as the availability of data and research interests evolves, but are compiled into this manuscript as an overview of methodology and scientific approaches beyond the standard sir textbook model that benefit the ongoing efforts in tackling this and other outbreaks. first documented in december , an outbreak of community-acquired pneumonia began in wuhan, hubei province, china. in january, this outbreak was attributed to a novel coronavirus, sars-cov- . the initial spread of the pathogen in wuhan was fast, and after a period of case-finding and contact tracing, china moved to implement a 'shutdown' of wuhan on january , and other cities in china the following days, to try to suppress the growth of the epidemic. these measures may have succeeded at slowing down the rate at which cases have been seeded elsewhere, but in many countries initial importation of cases and transmission has not been contained. countries around the world are now seeing outbreaks that are overwhelming, or have the potential to overwhelm, healthcare systems and cause a high number of deaths even in high-income countries [ ] . while the majority of documented symptomatic cases are mild, characterised in many reports by a persistent cough and fever, a significant proportion of these individuals go on to develop pneumonia, with some then developing acute respiratory failure and a small proportion of overall cases becoming fatal. severity of symptoms has been observed to increase with age and with the presence of underlying health conditions such as diabetes [ ] and cardiac conditions, with some evidence that severity of symptoms might depend on gender and ethnicity [ , , , , ] . sars-cov- has a fast doubling time (the time it takes for the number of cases in the region to double, estimated at approximately days [ ] ) and, potentially, a very large r (the average number of infections caused by each infected individual, with estimates ranging from . to . [ , , , ] ). it is possible that there is a significant degree of asymptomatic and/or pre-symptomatic transmission [ , , ] , though without robust serosurveys, this is difficult to quantify with certainty. these characteristics result in the pathogen being able to spread widely, rapidly and undetected, presenting a significant risk to public health. typically, the aim of an intervention strategy would be to push and keep the reproduction number t r , defined as the average number of cases generated by a typical infective at time t, below . at this point each infected individual subsequently infects, on average, less than one individual, such that the number of cases should decline. the basic reproduction number, r , represents the initial value of t r , before any intervention is put in place and the population can be assumed to be fully susceptible. high r , fast growth, and possible pre-or asymptomatic infection make the design of potential interventions, and the modelling that would inform them, particularly challenging. large values of r mean a substantial amount of transmission needs to be halted; fast growth causes the number of cases in the absence of interventions to rise rapidly, so that the time scale of interventions to reduce r must also be fast in order to effect substantive early changes on a population level; finally, the resulting interventions must encompass possible pre-and asymptomatic cases, a challenging prospect when in many instances these individuals are indistinguishable from healthy individuals. consequently, we must consider the possibility of interventions that are massively disruptive to society and may have to be sustained for a long period of time in order to cause the number of infections to decline towards zero [ ] . if infections remain, and the susceptible proportion of the population remains above the herd immunity threshold, these interventions must be upheld to prevent a second wave of the epidemic. there is not yet conclusive evidence as to the degree and duration of immunity conferred by infection with sars-cov- nor the feasibility of a vaccine, the timeline for which is unlikely to be any time shorter than months away at the time of writing [ ] . therefore, short term extreme interventions are not as effective as they might be in other circumstances, since after their removal there remains a long period of time in which cases can rise again. the longer these significantly suppressive and disruptive interventions are in effect, the more severe the effect on the economy, and broader societal health and well-being. furthermore, adherence to interventions will likely vary with their duration and severity. we are further challenged by the lack of transferable intuition. early work looked at intuition gained from sars and mers outbreaks, also caused by coronaviruses. some parameters do appear to be similar to these pathogens, such as the average length of the incubation period [ , , ] . however, there are also clear differences, with both sars and mers being more fatal, but seemingly less efficient at spreading since they did not seed major global pandemics. another complication is the spread of the infection during the chinese spring festival, a time period during which movement, social, and contact patterns vary significantly. this presents significant challenges as experience and intuition from other studies regarding population mixing and spatial patterns must either be modified or are invalid. furthermore, the pandemic has received a proportionately larger level of public attention than e.g. the h n pandemic [ , ] , largely boosted by social media. this greater level of public awareness, and the successive, staggered interventions placed to prevent disease spread are responsible for significant variations in behaviour [ , ] and adherence to public guidance both in china and abroad. the structure of this paper follows two main themes. in section , we discuss various biases that are present in outbreak data and techniques for estimating epidemiological parameters. accounting for biases and producing robust parameter estimates is important throughout the duration of an epidemic, both for increasing our understanding of the underlying dynamics, and for feeding into models. firstly, we discuss a bias-corrected method for estimating the incubation period, which can also be applied to serial intervals, onset-to-death time, and other delay distributions. we then present a method for estimating the true growth rate of the epidemic, accounting for the bias encountered since infected individuals may be exported from the region. our next method is a tool for estimating the expected size of the next generation of infectives based on the rate of observed cases. this tool provides insight into the size of small outbreaks, which can inform decision making when trying to prevent a major outbreak taking off. in section , we propose a variety of mathematical models looking at disease impact and intervention strategies, with particular focus on non-pharmaceutical interventions due to the current lack of widely deployable, targeted pharmaceutical treatments. these models focus on enclosed populations, since this is the level at which most interventions are implemented. since the disease is particularly fatal in the elderly and other at-risk groups, we develop a care home model to investigate how the pathogen may spread through care homes. we also develop household models to investigate the impact of different intervention/control strategies. these models can inform policy design for mitigating or controlling epidemic spread. finally, in the context of relaxing strong social distancing policies, we investigate the extinction probability of the pathogen. we first consider the extinction probability after lifting restrictions. we then develop a household-based contact tracing model, with which we investigate the extinction probability under weaker isolation policies paired with contact tracing, thus shedding light on possible combinations of interventions that allow us to feasibly manage the infection while minimising the social impact of control policies. . biases and estimation during outbreaks . . potential biases in the outbreak data techniques are constantly developing that enable higher volumes of more accurate data to be collected real-time during an epidemic. these data present a large opportunity for analysis to gain insight into the pathogen and the dynamics of the outbreak. however, although the quality of the data is constantly increasing, there are still many biases present. some of these are due to the data collection methods, and in an ideal world we would be able to eliminate them, and some are simply due to the nature of the outbreak, and will be present regardless of data collection methods. during an outbreak, many parameters depend on delay distributions (the length of time between two events), such as the time from infection to symptom onset (the incubation period). if an individual can be followed indefinitely, it is easy to determine the length of these events. however, in reality only events that occur before a given date are observed. therefore, the data is subject to censoring and truncation issues. in the incubation period, for example, censoring comes into play since, if we have observed an infection but the individual has not yet developed symptoms, we only have a lower bound on how long it will take them to develop symptoms. to account for this, we can instead condition on observing symptom onset before the cut-off date. however, this leads to a truncation issue, since individuals who were infected close to the cut-off date will only be observed if they have a short incubation period, which leads to an overexpression of short delays. the number of cases tends to grow exponentially during the early stages of an outbreak, causing the force of infection and the number of reported cases to increase with time. this further complicates the truncation issue since not only are recent cases truncated but they also account for the majority of cases. the growing force of infection also needs to be accounted for, since if the potential time of infection is interval-censored rather than observed directly, the probability that the case was infected in each day of that interval is not constant. in theory, both of these biases are relatively straightforward to account for. in practice however, there are other biases in the data. one of the major biases is the reporting rate. although the total number of cases may be reasonably described as growing exponentially with a constant rate in the early stages of an outbreak, high-resolution data may exhibit more complex behaviour. this can be due to a variety of reasons, such as the workload becoming overwhelming, the availability of individual-level data decreasing, the laboratories or offices slowing down activity over the weekend, the case definition changing, the testing capabilities increasing, and so on. another uncertainty arises since generally only the date of each event is recorded rather than the time. this presents a large window of uncertainty in the length of the delay, since the time of each event can vary up to hours, and for a delay distribution, which depend on two events, it could vary by up to hours. travel rate is another bias present in the data. for example, this changes the density of observed cases in a region, which can change the apparent growth rate. intervention strategies present a further bias because this can change the growth rate of the epidemic and the reporting rate. additionally, estimates of certain parameters may vary depending on the interventions that are implemented, so these need to be considered carefully. to model the incubation period, we require information regarding when an individual was infected and when they expressed symptoms. observing exact time of infection is unlikely, but it can be possible to find potential exposure windows. we consider three different data sets. the first two consist of individuals who travelled from wuhan before expressing symptoms. we can assume these individuals were infected in wuhan, since at the time of this data, the force of infection was significantly higher in wuhan than elsewhere. the length of time spent in wuhan therefore provides a window during which each individual became infected, and for many of these individuals we also have the date of symptom onset. in the early stages, the growth rate in reported cases was constant, and dependent on the epidemic growth rate in wuhan and the rate at which people left wuhan. by using travel to estimate the true number of cases, we estimate the exponential growth rate in wuhan as . r = (see section . ). therefore, the force of infection on day i, ( ) g i , is proportional to . e i . after january when significant travel bans were introduced, the rate at which individuals left wuhan diminished significantly, causing the reporting rate for our sample dataset to suddenly drop. this occurs since cases are only included if we have a fixed window of time spent in wuhan prior to developing symptoms. therefore, if the data is truncated after january, the reporting rate must be appropriately adjusted. this is illustrated in figure a . the difference between these two datasets is the truncation date, with the first truncated at january and the second at february. the third dataset contains cases that were infected through a discrete infection event, such as spending time with a known infected case. in this ''non-wuhan" dataset, the reporting rate is constant and the force of infection can be assumed constant over each exposure window. the source we use for these three data sets is a publicly available line-list [ ] . incubation periods, and many other delay distributions, are generally observed to have right skewed distributions. we therefore choose to use a gamma distribution, though other distributions can also be applied using the proposed methods, such as weibull and log-normal. to fit the data, we use maximum likelihood estimation. to adjust for the biases we use a ''forwards'' approach [ , , , ] , where we condition on the time of the first event, time of exposure, and find the distribution looking forward to the second event, time of symptom onset. for a data point { } , , infection occurs between i a and i b , and i y is the symptom onset date, the likelihood function is given by where ( ) g ⋅ is the density function of the infection date and ( ) f θ ⋅ is the density function of the incubation period parameterised by θ. from this, the likelihood function for our dataset x is given by this approach is independent of the reporting rate bias, since the reporting rate depends on the date an individual leaves wuhan ( i b ), which is conditioned against (see appendix ) . we use the mean and standard deviation to characterise the mle. since the tail of the incubation period is important when designing quarantine strategies, we then calculate the probability that the incubation period is longer than days and find the minimum day by which % of cases will have expressed symptoms (excluding true asymptomatic cases). we also investigate the reporting date uncertainty mentioned in section . by considering the different extremes that the data could represent. this is achieved through adding or subtracting a day to all recorded data. methods accounting for truncation and growth biases in epidemic data have been discussed widely in the literature [ , , , ] , however there are fewer applications to outbreaks [ ] . in the context of covid- , estimates have considered growing force of infection, for example [ ] , and some approaches have considered truncation, for example [ ] . however, these attempts do not adjust for the reporting rate in the data or use the correct force of infection, causing the incubation period to be overestimated. although the method presented here is independent of the reporting rate, other approaches for estimating the incubation period are not. here we demonstrate the importance of truncation (table ) . we use the data truncated at january, which has exposure windows between december and january. this data set is chosen since it is most sensitive to truncation due to the exponentially growing force of infection and high reporting rate. without accounting for truncation, the length of the incubation period is significantly underestimated, which could have a large impact on the success of intervention strategies. to demonstrate the effectiveness of the bias correction method, we compare three different data sets ( table ) . the similar distributions predicted across these datasets suggests a robust method. figure b compares the full distributions for these three estimates. here we investigate the effect that uncertainty in the reporting date can have on the results, using the data truncated at february (table ) . the standard interval is the recorded data, wide intervals are obtained by removing a day from the exposure window lower bound and adding a day to the upper bound, and the narrow interval vice versa. the uncertainty in the reporting date can impact the estimated incubation period, showing that it is important to consider this risk when designing interventions. when constructing intervention strategies for an epidemic, the incubation period is an important parameter. for example, consider the quarantine strategy deployed in many countries during the early stages of the epidemic, aimed at preventing cases being imported from wuhan. this strategy quarantined individuals upon their return from wuhan for days. for such a strategy to be effective, we require most incubation periods to be less than days, so that the majority of infected people would develop symptoms before quarantine ended, enabling them to be further isolated. in this analysis, we show that in the worst-case scenario we would expect in cases to slip through this quarantine, with the best fit predicting in cases. therefore, the day quarantine period would capture the majority of cases. throughout the epidemic, this seems to have been reasonably successful and prevented early seeding of cases in many countries. however, potentially due to complicated travel patterns or asymptomatic transmission, cases have slipped through detection and not been quarantined, which unfortunately has led to the situation observed today. in addition to the incubation period, there are many other delay distributions that must be estimated while an epidemic is growing, which can be estimated using the same technique. these include the generation time, the time between two infection events in a transmission chain; the serial interval, the time between symptom onset of an infector to their infectee; and the onset-to-death delay, the time from symptom onset to death. transportation modelling plays a crucial role in the early stages of an outbreak; an infected individual may travel outside of the region in which they were originally infected and seed further infections across geographical scales which are impossible to contain. furthermore, as the rate of travelling increases, the number of observed cases within the known ''origin" region decreases, and if exportation is not taken into account this results in an underestimation of the number of cases. these underestimates can be improved by looking at the total number of cases across all known affected regions, but doing so introduces further complications. for example, if an individual has less severe symptoms they may not seek medical assistance, thereby not being recorded as a case at their destination. this underestimation of cases can have significant effects if the traveller is able to infect more people. a new transmission chain can thus be started which remains undetected for some time due to a lacking known connection to the ''origin" region. in the ''origin" region an individual with mild symptoms may still be tested for an infection due to a higher level of alertness in the local health care system. however, this level of active case-finding may not be present elsewhere, or may not have been allocated a comparable level of resources. further complications to this model arise from the incubation period of individuals wherein detection is unlikely, and the variations in movement and mixing between people when preventative measures are put in place. we consider a metapopulation model seeded with an infection in one of the regions, o, and investigate how exportation from this region combined with variability in case-finding can alter estimates for the doubling time and the expected portion of the population we expect to identify. this accordingly bounds the proportion of the infected population one would be able to target for personal intervention (e.g. quarantine or treatment). note that the proportion of identified cases need not necessarily correlate with the proportion of the infected population who exhibit symptoms. let us assume that movement from o begins at time where ω is the mean case-finding ability across all destinations. in the presence of real-time transition probabilities ij p of moving between two regions, these estimates can be further elaborated. we assume that detection occurs immediately following the end of the incubation period, i.e. . similarly, we assume a gamma-distributed incubation period with shape and scale parameters k and θ, respectively. we can parametrise this distribution using the ''non-wuhan" estimate of the incubation period in table , which yields a gamma-distribution with mean . and standard deviation . . in contrast to other values in the table, this estimate is obtained from discrete infection events, e.g. contact with a known infected case, and therefore has a constant reporting rate, and a constant force of infection over each exposure window. therefore, this estimate of the incubation period does not rely on the exponential growth rate unlike other estimates from section . when accounting for ρ. this difference may seem small, but it reduces the doubling time by approximately hours. the expected value of r grows linearly with the exportation rate, which has also been observed with real-time travel models [ ] . further models have also been developed which consider travel and exportation of cases in greater detail [ , ] . the relationship between the observed cases in our origin and destinations can be used to determine the case-finding ability, though it should be noted that ω likely varies with time as burdens are increased on public services and the number of cases grow. early estimates using data from [ ] indicate at most an % case-finding ability, suggesting thousands of undetected cases exported to other regions of china, a sufficient quantity to sustain further transmission post-exportation independently of the number of asymptomatic cases present. the intention of these estimates is not to provide specific values for the doubling time of the spread of covid- in china (as the estimates above use historic travel data and are limited by the availability of data), but to bring attention to the unusual circumstances surrounding changes in contact patterns, and mobility during the chinese spring festival, the largest human migration on earth [ ] . failing to account for the significant level of dispersion or exportation of cases during these circumstances will significantly skew our estimates. in a scenario where a single individual exposes a group to infection, it can be unclear how many people have been infected since they do not immediately develop symptoms. however, knowing the true prevalence in the population is essential to determine the most effective interventions to put in place, and to estimate future burdens on public services. using the probability density function of the incubation period, we consider the efficacy of using the time it takes for people to present with symptoms as a predictor for the size of the infected group. this analysis is an effective ready reckoner at early stages of a novel infection, or in close contact environments, and is useful for predicting generation size when a complete data set is not yet available. in this analysis we focus on a scenario where infection time is known. in reality, we may only know an exposure window. for short exposure windows this method can still be valid, but for longer exposure windows it will need extending to account for this added uncertainty. we assume that the number of individuals who have been exposed to potential infection is known, in which case the number of people who are infected can be assumed to be binomially distributed with an unknown probability p that each individual has been infected. to determine the distribution of infected individuals, we use the available information regarding the number of individuals who have expressed symptoms. this yields two cases. in the first case, we assume that the true number of symptomatic individuals are observed. in the second case, we take the number of observed symptomatic individuals as a lower bound on the true value. we wish to determine the probability that the first generation has e individuals, e e = , given that i τ symptomatic individuals are observed on day τ, i i τ τ = . this is given by (see appendix ) this gives a distribution of the generation-size based on the number of observed symptomatic individuals by time τ. we can extend it to investigate a scenario where no symptomatic individuals have been observed by time τ by using a value of for i τ : this can be used to illustrate worst and best case scenarios given τ time has passed without symptomatic individuals. additionally, if we consider the probability that e = , we can find the value of τ where we can have a % confidence that there will not be a second generation: this analysis considers the case when the number of observed symptomatic individuals to date is the true number. in practice however, we do not generally observe every symptomatic individual, so the number of observations is only a lower bound on the true number. to address this, rather than considering i τ as the total number of people who have developed symptoms by time τ, we can define i τ as the minimum number of people who have developed symptoms by time τ. we assume that the probability that i τ is equal to i τ for a given value of i τ is uniform at i τ + . we can then use the same methods as above to infer a distribution for p. details are provided in appendix . e , in an infection event in which people were exposed. a, b and c show the density when the number of observed symptomatics is taken to be the true number of symptomatics, d, e and f consider the case where the observed symptomatics is a lower bound on the true symptomatics. a and d consider the case when zero symptomatics are observed after days, b and e when are observed after days, and c and f when are observed after days. the incubation period for the disease has been modelled as a gamma distribution with a mean of . and standard deviation of . ( table ) . as we can see from figure , this method can be used to predict the number of infected individuals in the original exposed group. however, we have also demonstrated the importance of caution when interpreting this data. if there is uncertainty surrounding the presentation of symptomatic patients, using i τ as a lower bound is a robust method to ensure the size of the generation is not underestimated. . modelling intervention strategies when designing intervention strategies, we need to consider how adherence may alter their effectiveness. this is important, since highly effective interventions may not be adhered to if they present great individual cost to a population. in this case, a theoretically less effective intervention may perform better, if it has sufficient reduction in individual-level cost. in this section, we illustrate the potential impacts of adherence on the effectiveness of interventions using a toy model. consider a standard sir model, and denote by ( ) s t and ( ) r t , respectively, the susceptible and recovered/immune fractions of the population at time t. we can write s in terms of r such that if an intervention is put in place that reduces (with full adherence) r < then the outbreak will be controlled. indeed, let us assume that r is reduced to zero by the intervention: for example, assume that social distancing is perfect and the number of contacts of a fully-adherent individual is zero. if only % of people adhere to the intervention then the average number of contacts is effectively reduced by a half and logically † / . r r = = (the † representing quantities post intervention) and ( ) † . r ∞ = in this case. however, this assumes that adherence is an independent random process at each contact. this suggests that for each contact an individual would ordinarily make, they ''toss a coin" to decide whether to isolate or not. in reality, individuals are more likely to show polarity, where some individuals reduce all their contacts and follow the measures and a proportion of individuals choose to not adhere to the intervention. if there was distinct polarity in the population such that % adhered perfectly and % ignored policy, then a toy model can be created with two infectious groups, a i and b i , that behave differently. in this case where a dot over a variable represents its time derivative. such an epidemic model, where the two groups have the same susceptibility but different infectivity, has the same final size as an epidemic in a single-type model with the same r (e.g. see [ ] ). however, they have different durations as can be seen in figure , where this shows that the assumptions about the nature of adherence predict the same growth rate and final size, but that the more polarised adherence has faster early growth and therefore an earlier peak. more complicated model structures could be constructed by incorporating adherence with intervention by susceptible states, which would lead to core group dynamics (see for example [ ] ). this issue of independent versus polarised adherence is related to the idea of all-or-nothing versus leaky vaccination [ , ] , where you either vaccinate a fraction of the population with % efficacy or vaccinate % of the population with reduced efficacy [ ] . note however that vaccination reduces your susceptibility (whether only or also), rather than only your infectivity as in the model discussed above, and variation in susceptibility does reduce the final size, with imperfect coverage with a perfect vaccine (all-or-nothing) leading to a lower final size than full coverage with a leaky vaccine (all individuals having the same mean susceptibility). the ongoing covid- outbreak is known to have higher mortality rates amongst the elderly, the immunocompromised and those with respiratory and health complications [ , , , , ] . in this section, we model the introduction of an infectious disease into care homes, in order to obtain estimates of the final size of the epidemic in the vulnerable population as well as predictions for the number of hospitalisations and fatalities. modelling of care homes in the uk is conducted against the backdrop of a wider epidemic in the general population, which we here assume to be following seir dynamics with a basic reproduction number r that might be different from the within-care home reproduction number c r . care homes are assumed to be closed populations, with the infection entering each of them independently with a certain probability. infection is seeded only once, and within-care home outbreaks then evolve independently from, and do not contribute to, other care home outbreaks and the epidemic in the background population. to keep track of hospitalisations, we model the withincare home infection dynamics using a compartmental model that, in addition to seir model, has compartments for mildly symptomatic prodromal cases (p), who show no symptoms but are capable of transmitting the virus, those who recover from the disease after mild symptoms that did not require hospitalisation (m), those who have severe symptoms and are admitted to hospital (h), those who recover after hospitalisation (r), and those that die (d). this is illustrated in figure . the infection pressure up to time t for a median sized care home is the integral from to t of the force-of-infection (foi) applied to the care home coming from all infectious sources, multiplied by a probability p. this probability represents the probability of the infection being introduced to a median-sized care home. for other care homes, we allow this probability to be proportional to its size, under the assumption that larger care homes employ more staff and are therefore at higher risk of introduction. when the infection pressure becomes higher than an individual care home's resilience threshold, that care home begins its own deterministic infection dynamics with a single initial infected case. the equations describing the background epidemic and the within-care home epidemic are given in appendix . figure : compartmental model for disease dynamics within a care-home. we extend a deterministic seir model to include compartments for prodromal (infectious) cases (p), mildly symptomatic cases that recover without requiring hospitalisation (m), cases that do require hospitalisation and are removed from the care home (h), cases that die in hospital (d) and cases that recover in hospital (r). we run this model on data for the entire care home population in the uk, so that there are approximately , care homes with a total population of approximately , residents [ ] . care home sizes range from to , with a mean size of . . in this model we only consider the vulnerable population within care homes. we assume . r = in the background epidemic, a relatively low value that somehow accounts for a certain degree of control, and an c r = to allow relatively explosive epidemics in care homes due to potentially more frail individuals, difficulty in isolation and staff inadvertently passing the infection from one case to the next. the other parameters in the baseline scenario are reported in table . apart from the reproductive number, the background epidemic uses the same parameters as the care home epidemic. however, in the background model there are only rates from e to i and i to r, which are taken to be the rates from e to p and i to m, respectively. there are a variety of assumptions underpinning this model. firstly, the background epidemic ignores structure and assumes homogeneous mixing. this is likely to make the peak more pronounced, so presents a worst case scenario for the demand on hospital beds. the assumption of r for the background epidemic only affects the shape and duration of the background epidemic, since the tuneable parameter p controls the risk of introduction to the care home. that is, if r is small, a large p still presents a high force of infection into the care homes. therefore, for a fixed p, we expect that changing r does not affect the total number of deaths, but it changes the peak hospitalisation incidence because a faster and more explosive background epidemic makes epidemics in care homes more synchronised. in fact, when testing the impact of a longer, flatter background epidemic, for example obtained by simulating three slightly desynchronised background seir epidemics, results have lower peaks and a much more variable timing (not shown). assuming each care home is independent might not be realistic, since it is likely that staff are shared between multiple homes, in which case they can act as vectors of transmission between homes. however, in the model current outbreaks are already quite synchronised (the within care home outbreaks occur at similar times), so the effect of this assumption is likely to be minimal. the final major assumption is that the epidemic within the care homes is deterministic. this removes the probability of random extinction and random delays, and should obviously be relaxed with a stochastic model, given half of care homes have size smaller than . however, the extinction probability is very low with c r = , so this stochastic effect is unlikely to have a large impact. random delays, instead, may change the shape and timing of the epidemic, which could potentially reduce the peak burden. therefore, this model represents a worst case scenario. in the absence of cure or vaccine for covid- , governments worldwide must rely on nonpharmaceutical interventions (npis) to control the outbreak [ ] . a natural such intervention is to ask individuals who express symptoms similar to covid- to isolate themselves, but variants to such individual isolation might include policies sometimes referred to as household isolation, household quarantine and mixed isolation. in this section, we investigate how such strategies affect the spread of the epidemic when bearing in mind that adherence to each intervention may differ. individual isolation relies on individuals staying in isolation when they express symptoms, thereby stopping transmission. however, there is potential asymptomatic or prodromal transmission before they go into isolation. additionally, isolation strategies generally ask infected individuals to remain at home, which presents an infection risk to the other members of their household, who may go on to spread the infection. the term 'household isolation' refers to a policy where, upon first detection of symptoms within a household, all individuals within the household go into isolation for a fixed duration of time. this strategy reduces the risk that other household members, if they are infected within the household, transmit in the community when pre-symptomatic (and hence before they self-isolate themselves) or if asymptomatic but still infectious. a blanket policy invoking a fixed duration of household isolation might cover the full epidemic in a small household. however, a larger household might present multiple generations of infection, potentially extending the within-household outbreak beyond the fixed duration of the household isolation policy. to address this issue, 'household quarantine' is another potential strategy. upon detection of symptoms, the entire household is isolated until a fixed duration of time after the last symptomatic case within the household expresses symptoms. this ensures that there are no symptomatic cases evading intervention but applies quite drastic measures to the household. a fourth strategy, that reduces the cost relative to household quarantine, is mixed isolation. here, upon detection of symptoms the entire household is isolated for a fixed length of time. any subsequent cases within the household then undergo individual isolation as described above. this reduces the risk of cases not being isolated whilst allowing recovered individuals to return to work. there is however still some remaining risk that infected individuals may not yet express symptoms after the end of the isolation period, but this risk can be controlled through the duration of each isolation. although there is now a rich theoretical literature on households models [ , , ] , the mainstream methodological tools in this research area present important limitations that make them not directly applicable to studying these control policies. first, exact theoretical or asymptotic results in these models are mostly restricted to time-integrated quantities, i.e. those quantities that do not depend on the detailed temporal shape at which the infectivity is spread by an individual: these are r (or any other reproduction number [ , ] , e.g. the household reproduction number * r ), the probability of a large epidemic, and the epidemic final size [ ] . for this reason, the vast majority of the literature relies on the standard stochastic sir model [ ] , despite its unrealistic infectivity profile. even if more recent work has expanded beyond time integrated quantities, for example considering the real-time growth rate [ , ] , if the interest is on tracking the dynamics of infection spread, a model based on full temporal representation of between-and within-household dynamics [ ] appears necessary. a second limitation of standard household models is the key assumption of constant parameter values. this appears essential for any form of analytical progress. however, in the context of the interventions discussed above, a reduction in transmission between households, as well as a potential increase in within the household, require parameters to change over time. to overcome these limitations, we consider two approaches. the first approach fully captures both within and between-household dynamics with a master-equation formalism, i.e. by relying on a markovian within-household dynamics and keeping track of the expected number of households in each possible state of their internal dynamics. the second approach has a greater emphasis on withinhousehold dynamics, and is fundamentally an independent-households, individual-based, stochastic simulation. the more limited mathematical tractability is the price to pay for an increased flexibility, as the within-household markov assumption is relaxed and exact distributions for delays between events, typically informed by the data, can be explicitly inputted. although both approaches can account for increased within-household transmission as isolation and quarantine are imposed, we only consider this for the second method here. this aspect allows us to study the increased risk of infection a vulnerable individual in the household would experience following the implementation of a control policy. to model the households in the uk, we construct a realistic distribution of household sizes (which is given in the supplied code). we take this demographic data from the census [ ] . more recent information, though less specific on large household sizes, shows that sizes of smaller households are largely unchanged over time [ ] . . in this section, we investigate the above intervention strategies under the assumption that a fraction of households adhere % with an intervention and the remaining households ignore the intervention. to model the interventions, we implement a dynamical household model that explicitly represents the small sizes of households. the dynamics of the outbreak are simulated using an sepir model. this model assumes that there are five possible states in which an individual can be. these are, susceptible, latent, mildly symptomatic prodrome, symptomatic infectious and removed. individuals are infectious during the mildly symptomatic prodrome state and the symptomatic infectious state. following [ ] , we assume that within-household transmission scales with the inverse of the household size to a specified power η. such a model can be used to investigate how the pathogen spreads through and between households. the methodology involved is the use of self-consistent differential equations, first written down by ball [ ] . more recent developments, including numerical methods for these equations, include [ , , , ] . important features of this approach include allowing for a small, finite size of each household in which random effects are important and each pair can only participate in one infection event. here Λ represents infections imported from outside the population of households, and the other terms represent between-household transmissions. in our code, we assume Λ is a step function. results are largely insensitive to the precise choice of Λ , but compared to, for example, random seeding of infections in households, starting the whole population susceptible and exposing to a small amount of external infection for a fixed time period has less room for the precise initial condition chosen to influence results, and is more realistic for the situation observed in countries apart from china. we take a 'global' intervention as part of the baseline, in particular, we can model phenomena such a school closures that hold during a set of times t as we call ε the global reduction. we will generally drop this t-indexing for simplicity, and will also consider only a household isolation strategy (though the other strategies can be considered similarly, with an example of how other strategies could be captured in this model framework given in appendix ). instead of isolating for a fixed duration, we assume that a fraction w α of households isolates when there is at least one symptomatic case in the household, and isolating households leave isolation when no symptomatic cases remain. we make this assumption since it may potentially capture the behaviour of real households, who are more likely to remain isolated based on presence of symptoms rather than for a fixed duration. in the non-markovian household model in section . using the methods in [ , ] , it is possible to fit household models of this kind to the overall growth rate, r, which we take to correspond to a doubling time of three days. natural history parameters can then be set directly based on reasonable estimates: e p r → to the inverse of the latent period; p i r → to the inverse of the prodromal period; i r ∅ → to the inverse of the symptomatic period. shaw [ ] analyses various household datasets for respiratory pathogens and estimates values for η close to , so this is taken to be . . the remaining degrees of freedom are relative infectiousness of the prodrome (taken as a third) and the probability of transmitting within a pair, which we can take as a typical value given by shaw [ ] . for the numerical results in figures and using the given parameter values for our baseline scenario (table ) , we consider a combination of household isolation (which follows all-or-nothing adherence) with global reduction in transmission (which follows leaky adherence) for three weeks and show the results in figure . the distribution of infectious individuals varies with household size, which is shown in figure for different durations of global intervention. applying household isolation at % adherence ( . w α = ) manages to reduce the spread of infection, but appears insufficient in this model and with baseline parameters for controlling the outbreak in the long-term, unless other intervention strategies that reduce the global transmission (increasing ε) are adopted at the same time. alternatively, different levels of adherence can be considered to determine if and when control may be achieved purely through household-based interventions. for the model proposed in the next section, we look into the effectiveness of increasing adherence. parameters are in the main text. the model described above has the advantage of being able to track the dynamics within the household as well as the overall epidemic in the population in a relatively efficient manner. we now discuss a different framework that loses part of the capability in keeping track of the overall epidemic, but offers further flexibility both in the impact of policies on the within-household dynamics and in the distributions between events in the infectious life of an individual. we use this model to investigate the relative effectiveness of the different control policies. we also consider allowing recovered individuals to leave the household, even in the context of household isolation or household quarantine. this has no impact on the transmission dynamics, but reduces the individuals' life disruption and potential economic cost of any policy implemented. this model assumes that there is no reintroduction within households so each household can only be isolated or quarantined once. the assumption that only one household member is infected from outside is approximately satisfied if we assume homogeneous mixing between households and a large number of households, which are all fully susceptible at the start of the epidemic. however, the reality of heterogeneous mixing makes reintroduction a likely possibility even early on in the epidemic. this model, therefore, lacks an explicit description of the social network structure beyond the household. for simplicity, we assume that within households all individuals are identical in terms of their disease dynamics, although the method might be extended to allow for different age/risk groups with different disease dynamics. we assume that the level of within-household transmission in a household of size n scales proportionally to ( ) / n − , though we acknowledge that true transmission is slightly more complex [ ] . we consider independent households of size each individual is given an indicator function of whether they are symptomatic or not (individuals show symptoms independently of each other with probability s p ) and a resilience threshold. this last quantity is drawn from an exponential distribution with mean , and represents the overall infection pressure this individual is able to withstand before they get infected. the infection pressure up to time τ is the integral from to τ of the force-of-infection (foi) applied to this individual coming from all infectious sources. at the beginning of the within-household epidemic, a single initial case is assumed. time is discretised with a predefined time step d . t = days. at any time step, the current infectivity of all infectives in that time step is summed over, keeping track differently of the infectivity spread outside and inside the household. an overall measure of the accumulated infectivity within the household is updated at each time step and when this crosses the resilience threshold of a susceptible individual, they acquire the infection. we assume an individual spends half of their time outside and half inside the household. when selfisolation starts, the assumed adherence i a represents the fraction of the time spent outside that is shifted from outside to within the household. therefore, for perfect adherence, from the moment symptoms occur, the individual stops transmitting outside but their infectivity within the household grows by %. we also explore variations in this compensatory behaviour, so that the time of an individual is split in a more flexible proportion than : . the same argument applies to other control policies, with adherence levels h a for household isolation and q a for household quarantine. when multiple control policies are in place at the same time, their effect is assumed to be multiplicative: if an individual has symptoms and the household isolates, the outside transmission rate from that individual is reduced from baseline by a multiplicative factor ( ) ( ) ( ) and the area under this curve is known in the literature as the household reproduction number, and is typically denoted by * r . if enough transmission is prevented, so that * r < , the epidemic is controlled. the basic reproduction number r and * r share the same threshold at one, so they are simultaneously larger, equal or smaller than unity. however, in a growing epidemic * r r < [ , ] . the real-time growth rate r is related to * r by the lotka-euler equation asymptomatic cases, which are assumed to be half as infectious as symptomatic ones. the total number of cases under isolation (possibly compounded, e.g. both household and individual isolation) is shown in red (right axis). all random numbers involved in the realisation of the stochastic epidemic are drawn at the start, before the impact of each control policy is implemented. row shows no isolation and individual and isolation. rows , and show, respectively, household isolation, mixed isolation and household quarantine. the difference between the columns is that the basic policy on the left is ''upgraded'' to the more cost-effective version on the right that allows recovered individuals to leave the house as they cannot transmit outside anymore. when no control is implemented, the primary case (individual a, infected at time ) infects another individual (b) around time . after a long latent period (i.e. incubation minus prodromal), b becomes infectious and infects a further individual (c). the last individual (d) escapes infection. when different intervention strategies are in place, within-household infectivity is increased. this can result in individual c becoming infected earlier in the outbreak and individual d no longer escaping infection, both due to the increased force of infection. in this simulation, the dynamics for individual b do not change since they are infected before a becomes symptomatic. individual d is infected earliest under mixed isolation, because within-household transmission is higher than household isolation alone, due to increased adherence from individual isolation also being in place. adherence levels to household quarantine are lower than those of household isolation, due to the higher demand of full quarantine, thus leading to less enhanced within-household transmission. we assume that adherence to individual isolation is %, household isolation is % and household quarantine is %. the more severe the intervention, the better it captures the infectious periods of infected individuals within the household. the lower x-axis gives the adherence to household quarantine, and the upper x-axis adherence to household isolation. we assume that household isolation is less demanding, and therefore adherence is assumed to be ''twice as high'', meaning it is at the midpoint between that of household quarantine and (e.g. . for an x value of . , . for an x value of . , etc.). the black dash-dotted line in (a) gives the amount needed to control the spread by achieving * r = . notice how: the effect of individual isolation is independent of adherence to household quarantine (dotted lines); the effect of household isolation is independent of adherence to individual isolation (overlapping dash-dotted lines); mixed isolation is always superior to household isolation; household quarantine is only optimal at really high levels of adherence (for these baseline parameters, generally, beyond the level needed to achieve control), but quickly becomes suboptimal to mixed isolation as adherence is reduced. when a sufficiently large reduction in * ); similarly, in all households, individual isolation would total exactly days if all cases were symptomatic and all individuals in the household were ultimately infected. in (d), we assume that adherence is % to each intervention. under the baseline parameter values (table ) , control can in principle be achieved via certain interventions, but only for high levels of adherence, which might be difficult to enforce for a prolonged length of time (figure a ). more importantly, the model's conclusions are highly sensitive to variations in parameter choices, which are uncertain. parameters that present problems here are the delay from symptom onset to isolation (with control failing for day detection delay unless adherence is essentially perfect), proportion of asymptomatic infections (any chance of control lost at %) and the strength of asymptomatic transmission. the short delay before symptomatic individuals isolate may be unrealistic unless the susceptible population is very well-informed about symptoms that call for isolation, and so likely does not apply in very early stages of an outbreak. overall, in the face of the many uncertainties, household-based interventions triggered purely by symptoms appear useful to slow the spread but need to be complemented by other policies. comparing the different strategies (figure b , household quarantine can be optimal (as one might expect), but this requires high adherence levels. as adherence drops, this strategy becomes suboptimal to mixed isolation. mixed isolation is significantly better than household isolation on its own and requires little extra social cost, so should not cause adherence to drop (relative to household isolation adherence levels). the difference between the two strategies comes down to the transmission slipping through after the day household isolation. the cheapest strategy, when considering working age adults, is individual isolation (figure d ), but the effect is limited compared to the other models and cannot achieve control in the baseline scenario even with % adherence. overall, the mixed isolation strategy appears to be most cost-effective. however, this is dependent on the assumption that adherence is better for day isolation rather than a very long quarantine. it can be observed that household-based interventions are more effective than individual isolations, demonstrating the importance of these strategies in designing intervention policy. figure shows how the different isolation strategies contain the infectious periods of individuals within the household and also indicates the number of individuals being isolated within the household. to study the impact such an increased within-household transmission has on the chance that a vulnerable individual is infected in the household, we randomly choose one non-primary case in the household as the vulnerable one and count how many of the e n epidemics result in this individual being infected under the different control policies (figure c ). under these interventions, the risk of a vulnerable individual getting infected within-household, conditional on the infection entering it in the first place, is in the range % − . since this model relies on the sellke construction, we calculate the infection pressure that accumulates (within a household) during the outbreak. in relation to figure , we report in figure the infection pressure that accumulates for the different control policies, showing the different impact each intervention can have on the within household dynamics. figure : accumulated infection pressure in the simulation presented in figure for different control policies. horizontal dotted lines represent individuals' resilience thresholds. as time progresses, the accumulated infection pressures (coloured lines) increase and when they cross the resilience thresholds, the corresponding individual acquires infection. notice that: in the absence of control, one individual escapes infection; with household isolation only, the infection pressure reaches a relatively low endpoint because of the last symptomatic individual slipping through and not transmitting much in the household; with mixed isolation, infection pressure is higher due to combined adherence; and with household quarantine, the infection pressure builds up more slowly at the beginning due to lower adherence. we assume that adherence to individual isolation is %, household isolation is % and household quarantine is %. social distancing, isolation and lockdowns act to mitigate the spread of an infectious disease and reduce the number of cases. however, such interventions, particularly widespread lockdowns, cannot be maintained indefinitely and must be lifted at some point. for the disease to be controlled, these interventions can be implemented until pharmaceutical interventions are developed, such as a vaccine, or until the case numbers are low enough that the disease may go extinct. here, we consider the situation where interventions are lifted just before extinction, when the number of cases has reached a low but non-zero initial value n : at this point, the number of cases might rebound or might go extinct by random chance despite an r > . we use a time-inhomogeneous birth-death chain model [ ] to , q t s satisfies the differential equation subject to the initial condition ( ) , . q s s = solving for q and setting s = gives the probability that, at time t, the number of cases has reached zero and the disease has become extinct. we denote this probability by ( ) q t [ ] , which is given by the corresponding generating function, ( ) , r t s , for this random variable satisfies again, solving for ( ) we simulate data based on one initial case n = , though this may easily be extended to any number of initial cases. we run simulations both with and without immigration, choosing w is the initial (constant) rate of importation of cases before any controls on immigration are put into effect. we set w = imported cases per day. with these choices of parameters, the resulting extinction probabilities are given in figure . note that we are assuming the immigration rate is decreasing to , so if the infection is controlled internally for long enough, an overall ultimate extinction is possible in this model. for these parameter choices, the final probability of extinction, defined as n q t . these probabilities suggest that, without widespread immunity, stochastic extinction might be aided by social distancing but is heavily compromised by immigration. border controls, therefore, if of limited use when transmission is self-sustaining, become key when the number of cases is low. note that we have assumed an importation function ( ) t η that goes to for large t, in line with a pandemic that goes extinct in other geographical regions. however, the presence of an animal reservoir might lead to an importation function that is non-zero over longer time scales, thus effectively making ultimate extinction impossible unless the effective reproduction number is kept below one by a systematic and permanent intervention (e.g. technology-based change in behaviour) or herd immunity. contact tracing is a complementary control policy to isolation or quarantine. when a case is discovered, attempts are made to identify and isolate individuals who may have been infected. in doing so, some of the secondary cases will be discovered and isolated early in their infection, decreasing their effective infectious period. if contact tracing is successful, it can greatly reduce the effective reproduction number of the infection, and in combination with other interventions may drive an epidemic extinct, as was seen in the case of sars [ ] . contact tracing in itself presents numerous challenges, which are exacerbated by its success relying not only on the effectiveness of the tracing process but also the underlying transmission characteristics. for covid- , some of these challenges include mild symptoms which cause infections not to be reported, pre-symptomatic transmission which occurs before a case is reported, and short generation times [ ] which can cause the epidemic to outrun contact tracing. additionally, contact tracing is only feasible for smaller case numbers, because each case generates multiple contacts to follow up, so the tracing workload expands dramatically, and an increasing number of chains remain unobserved. this makes it a viable strategy in the early days of an outbreak, or, if containment has failed, following a period of severe interventions, such as a lockdown. combining contact tracing with isolation is being considered by many countries as part of a test, trace and isolate strategy to be implemented once lockdowns or comparable measures are lifted, provided these lockdowns succeed at driving case numbers sufficiently low. in this section, we develop a householdlevel contact tracing model for an emerging outbreak, since we do not wish to make assumptions about immunity or depletion of susceptibles. these assumptions can be added to the model as the availability of data into immunity improves. we are interested in the likelihood that the contact tracing process is overwhelmed by large case numbers and the likelihood that, combined with isolation, it can drive the disease to extinction. the early days of an outbreak can be modelled using a branching process, where generations of infections produce infectious offspring. contact tracing processes can be incorporated as a superinfection along the tree generated by the branching process [ ] . when a node is 'superinfected' by the contact tracing process, it is isolated. we model the infection spreading through a fully susceptible population of individuals, segmented into households of different sizes according to the ons survey [ ] , and progress through discrete time steps of day. as such, our branching process is at the household level, coupled with localised within-household epidemics. this allows us to model contact tracing strategies that isolate whole households, which may contain several undetected infections. it also enables a wider range of contact tracing strategies to be modelled, each with different intervention scope and costs. each day, individuals (or nodes) make contacts to a random set of individuals; divided into local contacts to members of the same household, and global contacts to members of other households. the number of individuals contacted in a day is distributed using an overdispersed negative binomial distribution and parameterised using estimates from the polymod social contact survey [ ] , stratified by household size. since the probability that a contact causes infection cannot be directly observed, we use improper hazard rates that give rise to the day covid- generation time [ ] and r = . for contact tracing to begin, an infection must be diagnosed, which we assume occurs % of the time among infected individuals due to flaws in reporting or very mild symptoms in those infected. we assume a gamma distributed incubation period with mean . (table ) and a geometric reporting delay from symptom onset with mean . days [ ] . intuition suggests that if r = then tracing two thirds of contacts will control the epidemic. however, in practice transmission may occur before tracing, so this will not reduce the number of infectious contacts by two thirds. to demonstrate this, we assume that contact tracing successfully traces two thirds of contacts. trained professionals have to trace all reported contacts from the last days, so we assume that the contact tracing delay follows a geometric distribution with a mean of days. individuals are considered recovered days after infection, as the chances that they are still transmitting then are negligible. though our general framework can be modified extensively, we assume the following contact tracing strategy. when an individual reports infection, their household is immediately isolated. contact tracing attempts are then made for all households connected to one of the individuals in this household, whether symptomatic or not. when a connected household is identified (after the contact tracing delay), all individuals within the household are immediately placed under observation. if any of the individuals in the observed households develop symptoms, then the household becomes isolated and the contact tracing process continues to connected households. when a household is isolated, we assume all individuals are isolated with % adherence, and cannot transmit the virus within or outside the household. the assumption that isolation prevents local infections is unrealistic, but does not change the overall behaviour of the process as there are no more global infections. this strategy imposes high individual-level cost, since by isolating all individuals within a household, it isolates individuals who have not had direct contact with an infected individual. in practice, such a strategy may have poor adherence. figure a shows an example contact tracing network. . when choosing contact tracing strategies, a balance must be struck between the effectiveness of a strategy and the resources that it requires. some strategies are only feasible when there are few infections, since the resources required can grow rapidly depending on the dynamics of the outbreak and the contact tracing process. to define the capacity of the contact tracing process, we consider the ability of a public health agency to observe the condition of those asked to self-isolate, due to their recent exposure to an infected individual. the health agency must remain in contact for the duration of the day self-isolation period, so that if any individual under isolation develops symptoms and then tests positive, the contact tracing process can be initiated on this node. we will define the capacity of the contact tracing process to be the number of people that can be placed under observation and assume two possible capacities: and . we assume that when a node is contact traced, they are asked to report their global contacts for the last days. all global contacts are assumed to be to a new person since we are in the early stages of an outbreak. parameters are given in table . hitting probability ( ) . % we carried out simulations of the contact tracing process for days. contact tracing capacity was reached in simulations, and in the epidemic neither went extinct nor was the capacity reached. in the remaining simulations, the epidemic went extinct. figure a and table show that increasing the contact tracing capacity tenfold less than doubles the time until that capacity is reached. however, it does increase the odds of driving the epidemic to extinction without hitting the capacity by about % (table ) . different contact tracing strategies will strain different aspects of the health agency. a strategy that generates large amounts of work is only feasible if there are few active infections. the optimal strategy will need to compromise and may need to change depending on the number of active infections, which cannot be directly observed. figure : capacity hitting times for the contact tracing model. when there is a small number of cases in a single country, it may be possible to drive the pathogen to extinction. this small case number could correspond to the start of an outbreak or removing of severe interventions. we consider the latter case, but conservatively assume a fully susceptible population. we assume that social distancing is enforced on day and reduces global contacts by %. full parameters are given in table . since we are interested in extinction, we will no longer consider the contact tracing capacity. under these baseline parameter assumptions and simulations, the combined force of this contact tracing strategy and isolation is enough to drive the epidemic extinct ( figure b ), but measures will need to be in place for months in some cases. if the infection is ever re-imported, then the process would begin again, since herd immunity is not achieved. note that the minimum extinction time is days due to this being the time after which an infected individual is labelled recovered. additionally, this model only considers extinction under the assumption that no cases are imported. in section . , we have shown that importation of cases significantly reduces the extinction probability. this suggests that extinction may no longer be guaranteed, and the time to extinction will be significantly increased. this analysis has focused on a single contact tracing strategy using indicative parameters for covid- . the proposed model can be extended to more strategies and region specific parameters to inform the design of control policies. also, as is shown in table , contact tracing capacity is likely to be reached, which may prevent extinction from being achieved. this complication is compounded by the issues of loss of immunity or the presence of an animal reservoir discussed in section . . figure : example of the contact tracing process (a) and the extinction times distribution (b) for the contact tracing model. . discussion in this manuscript we have presented a range of mathematical tools to tackle infectious disease outbreaks. in particular, these tools address various technical questions posed by the authors to support the ongoing public health response to covid- . this toolkit considers both estimation efforts for key parameters, and investigative efforts (often numerical simulations) in gauging the effectiveness of various intervention or control measures. joint consideration of estimation and simulation efforts is critical. parameter estimates are obtained using a certain set of assumptions regarding the data, and investigations or simulations utilising these estimates should ensure that their underlying assumptions are consistent. these challenges in model construction and applicability of statistical methods are compounded by the limitations of the data with which decisions must be made. some of the biases present in the data can be addressed with an improved data collection methodology -often challenging in the context of a fast-moving outbreak -but many are also inherent to the nature of early outbreak data [ , ] . the consequent lack of intuitive insight from this data underscores the need for careful parametric estimates, especially considering the large variability in predicted outcomes resulting from small differences in parameters. even with robust estimates for some parameters, many other parameters are challenging to estimate using the available data. therefore, models need to address this variability and uncertainty in order to inform public health policy. we have presented methods to address biases arising from a growing force of infection, changes in the reporting rate, truncated data samples and a varying travel rate. we use these methods to account for these biases when estimating delay distributions, such as the incubation period, and the growth rate/doubling time. these biases can have significant impact when estimating key parameters: the mean incubation period estimates for covid- range from . days without correcting for truncation to . days with the correction, and the doubling time in hubei province decreases from . days without correcting for travel to . days. these differences can significantly alter our understanding of the outbreak, and could have a large impact on policy and public health. for instance, underestimating the incubation period may lead to quarantine strategies failing to identify infected individuals if the quarantine length is too short. overestimating the doubling time (or underestimating the growth rate) will underestimate the risk posed to the host population -both in terms of final size of the epidemic and the rate at which it spreads, which can have significant public health impacts as discussed in [ ] . it is important to note that the above-mentioned biases, and consequent impact of implementing the methods correcting for their presence, may vary across different settings. as an example, the potential underestimation of the covid- growth rate is exacerbated by an overlap in early outbreaks with a period of significant travel and movement in china, and would be less detrimental if first observed in other populations such as italy. also, for the incubation period, we have shown two different types of data; one from wuhan and one from discrete infection events. in the wuhan data set, truncation and force of infection biases are very important, whereas in the other data set, there is no force of infection bias since the infection events are observed. when an outbreak occurs in an enclosed group, such as a large gathering, we may wish to know how many individuals are likely to be infected. we developed a statistical method to estimate the first generation size based on the number of symptomatic individuals, taking care to account for the uncertainty in this quantity. this ready reckoner can inform testing of large groups to help control the disease spread, but does not apply to later generations or the possible interventions enacted on the population. building on these enclosed population scenarios, we have developed a set of models that investigate public control measures or interventions on enclosed populations, such as households and care homes. these structured descriptions improve the population risk profiles relative to assumptions of homogeneous mixing. a complementary aspect to a structured population when modelling interventions is adherence. motivated by vaccination modelling, we consider leaky adherence, where every household chooses to adhere or not whenever an event occurs, and all-or-nothing adherence, where some households adhere every time and some never adhere. we observed that in a homogeneous population, although the two types of adherence predict the same growth rate and final size, the timing of the peak and the early growth can be faster under all-or-nothing adherence. this insight, combined with lessons from the vaccination literature, suggests that efforts should focus on ensuring complete adherence in individuals or households with some level of pre-existing adherence, rather than pushing non-adherent individuals or households to change behaviour. dedicated modelling of disease spread in care homes is essential due to the documented history of comorbidity of their residents during pandemics [ , , , , ] . we do so by regarding care homes as closed populations that are subjected to a force of infection from an external epidemic. we develop a tool for analysing the risk posed to this population by determining the peak size of the epidemic within the care homes and the number of deaths. applying this model to covid- , we find that by ''cocooning" the care homes, i.e. shielding them to reduce the chance of introduction from the external outbreak, we can significantly reduce the size of the peak and therefore reduce the number of deaths. however, assessing the necessary level of shielding requires accurate characterisation of the external force of infection, and underestimating this may invalidate shielding efforts. a limitation to the proposed model is the deterministic within care home epidemic. however, since the average size of care homes is relatively large and we assume a high r within care homes, the deterministic assumption is unlikely to significantly alter the conclusions. when modelling households however, we are concerned with much smaller population sizes. therefore, it is important to consider stochastic effects within each household, combined with between-household dynamics. we consider two different household models: one which contains features of both within-and between-household transmission, where small-scale transmission can be linked to the epidemic on a population level, and another which facilitates more detail in the withinhousehold transmission and delay distributions, but with reduced correspondence to the populationwide transmission. with the first model, a % adherence to household isolation appears insufficient to control the epidemic without severe global reductions in transmission. coupled with a short term global reduction, the epidemic can be controlled, but upon lifting the global intervention, which could take the form of a lockdown, household isolation is insufficient to maintain control. for the second model, we look into changing the strength of adherence, and the impact this can have on achieving control. indicative but reasonable parameter values suggest that the covid- outbreak can potentially be controlled using household isolation strategies, provided the level of adherence is sufficiently high. however, such a high level of adherence may be difficult to maintain in the long-term and this modicum of control is anyway highly sensitive to the chosen parameters. we further investigated the efficacy of various isolation or quarantine measures. a policy of individual isolation struggles to curtail the epidemic for any adherence. instead, mixed isolation, whereby first the whole household isolates and any individual infected during isolation goes on to self isolate after household isolation is lifted, appears to be the most cost-effective strategy. countries have put into place strict social distancing and lockdown intervention to suppress or regain control of epidemics that threaten to overwhelm the health system and cause massive mortality, but they cannot be sustained in the long term without growing social and economic costs. we have shown however, that the probability of the epidemic becoming extinct once these policies are lifted, even when very few cases remain, is very small. we therefore consider a contact tracing intervention as a potential strategy for managing the covid- outbreak, once severe lockdown interventions are lifted. we developed a household-level contact tracing model to explore the feasibility of combining these strategies to control the epidemic. firstly, we noted that by using knowledge of household structure, we can reduce the burden on the contact tracing process by isolating household and removing them from the contact tracing process once an infected member has been identified. secondly, we investigated how contact tracing combined with household isolation may drive the disease to extinction, finding that aggressive contact tracing coupled with household isolation can drive the epidemic to extinction under the indicative parameters assumed, when starting with a single infection. however, the time until extinction can be impractically long, which risks the contact tracing capacity being overwhelmed, suggesting such a strategy may be infeasible in practice. a less aggressive strategy could be implemented that would be less likely to overwhelm local health agencies. whilst it may not lead to extinction, this can still be beneficial at mitigating and controlling the spread of an outbreak as part of a test, trace and isolate strategy. there are many complexities when modelling an outbreak of a novel infectious disease. to address some of these, we have described a variety of techniques to serve as part of a generally applicable toolkit. however, our proposed models, and many other models, are subject to important limitations which must be considered prior to their application. key among these is the lack of heterogeneous population mixing, such as through age-stratification [ ] and different risk-groups [ ] , and spatiotemporal variations [ ] , all of which influence modelling estimates and predictions. nevertheless, the relative simplicity of the presented models allows for the development of qualitative intuition regarding the efficacy of various intervention methods, whilst providing tractable theoretical frameworks which can be further developed and better inform policy-makers. . independence of the incubation period likelihood function and the reporting rate to estimate the incubation period distribution, we need to find the distribution that maximises the probability of observing the sampled data. however, the sampled data does not directly record incubation period, and instead contains infection exposure window and the symptom onset date. additionally, the sample does not contain all individuals, and therefore there is a reporting rate that must be incorporated into the likelihood function. if the reporting rate is constant, it can be ignored. however, in the data coming out the wuhan, the reporting rate varies significantly, since individuals are no longer exported from wuhan after travel restrictions. since the reporting rate depends on individuals leaving wuhan, the main factor effecting the probability that a case is included in the data set is the date an individual leaves wuhan. therefore, the reporting rate depends on the days an individual spends in wuhan and is independent of their symptom onset date. we need the likelihood function that an individual was infected between days a and b, had symptom onset on day y, and was included in the data set. we will condition against the infection window, a i b < < , the case being included in the data set, x d ∈ , and symptom onset occurring before the truncation date, y t < , and determine the probability that for such an individual we observe the given symptom onset date, y y = . where f θ is the probability density function of the incubation period distribution. therefore, the likelihood function ( | , ) p y y a i b y t = < < ≤ is independent of the reporting rate for the data coming out of wuhan in the early days of the outbreak. . generation-size derivation to solve this, we need to determine the distribution of the infection probability p given the number of observed symptomatics. assuming that p is uniformly distributed, we have f represents the hypergeometric function [ ] . substituting this into equation ( ) gives ( ) ( . estimating the generation size using a lower bound on the number of symptomatic individuals in the analysis in section . , it is assumed that every person who has developed symptoms by time τ is known to the observer. however, depending on the disease, symptoms can be subjective. one person may not notice something another person may visit hospital for. additionally, one person may not want to come forward with symptoms if they are worried about the repercussions of coming forward (for example being isolated against their own will). to address this, rather than considering i τ as the total number of people who have developed symptoms by time τ, we can consider i τ as the number of people who have presented with symptoms by time τ. we do no know the true value of i τ , but we know that it cannot be below i τ . we assume that the probability of i τ being i τ for a given value of i τ is uniform at i τ + , di e i dt ρ γ = − ( ) . dr i dt γ = ( ) this provides a force of infection that is used to model seeding within 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in the novel wuhan coronavirus (covid- ) infection: a systematic review and meta-analysis clinical course and risk factors for mortality of adult inpatients with covid- in wuhan author contributions co and hs compiled the manuscript. all authors were involved in the research and revising of the manuscript. the authors declare no competing interests. all data and code used in this analysis is provided in the github repository https://github.com/thomasallanh ouse/covid -stochastics and https://github.com/thomasallanhouse/covid -growth, with the exception of uk specific data. this data is provided by public health england under a data sharing agreement and we are unable to share this data. where c is a normalising constant such that we add further compartments to the within care home model since we are interested in the different pathways that these individuals may take. for the background epidemic this is not important, since all we need is a force of infection provided by individuals in the infectious class. . population and household transmission: individual isolation and household quarantine individual isolation does not intimately involve the household and so we assume that a fraction i α of symptomatic cases self-isolates and ceases transmission outside the household, meaning that we take the baseline but with to capture the essential features of household quarantine, we need to add states to the dynamical variables. let we now suppose that a fraction s in this model, we assume that the duration of isolation after the absence of symptoms is exponentially distributed with mean equal to the fixed isolation period, given by / σ . this assumption aids the modelling and is justifiable because, in reality, although a household may choose to isolate, they may not strictly follow the fixed period. it is likely that within-household isolation will increase transmission to other members of the household. we do not incorporate this property into the model, but this limitation is worth bearing in mind when drawing conclusions about the effectiveness of different strategies. key: cord- -hxlebas authors: broekhuis, femke; madsen, emily k.; keiwua, kosiom; macdonald, david w. title: using gps collars to investigate the frequency and behavioural outcomes of intraspecific interactions among carnivores: a case study of male cheetahs in the maasai mara, kenya date: - - journal: plos one doi: . /journal.pone. sha: doc_id: cord_uid: hxlebas intraspecific interactions between individuals or groups of individuals of the same species are an important component of population dynamics. interactions can be static, such as spatial overlap, or dynamic based on the interactions of movements, and can be mediated through communication, such as the deployment of scent marks. interactions and their behavioural outcomes can be difficult to determine, especially for species that live at low densities. with the use of gps collars we quantify both static and dynamic interactions between male cheetahs (acinonyx jubatus) and the behavioural outcomes. the % home-ranges of males overlapped significantly while there was little overlap of the % home-ranges. despite this overlap, male cheetahs rarely came into close proximity of one another, possibly because presence was communicated through frequent visits to marking posts. the minimum distance between individuals in a dyad ranged from m to m but the average proximity between individuals ranged from , ± , m to , ± , m. possible interactions took place more frequently at night than by day and occurred mostly in the % home-range of one individual of a dyad or where cores of both individuals overlapped. after a possible encounter male cheetahs stayed in close proximity to each other for up to hours, which could be the result of a territory defence strategy or the presence of a receptive female. we believe that one of the encounters between a singleton and a -male coalition resulted in the death of the singleton. our results give new insights into cheetah interactions, which could help our understanding of ecological processes such as disease transmission. intraspecific interactions, or interactions between members of the same species, are an important component of population dynamics as they play a role in sociality [ ] , mating events [ ] , of movement behaviour and mortalities. based on previous research we predict that males will overlap spatially but that there will be little overlap of the core areas [ ] . we also predict that marking posts are frequently visited by both individuals in a dyad, i.e. pair of cheetahs, and that occasions where individuals of the dyad are in close proximity to each other are infrequent. because encounters between males can be aggressive [ ] we predict that the movement behaviour after a possible encounter would indicate avoidance behaviour (moving away from the encounter location, moving away from one another, increased distance travelled and decreased path tortuosity). the study was conducted in the maasai mara, in the southwest of kenya (centred at ˚s and ˚e), which is part of the larger serengeti-mara ecosystem. the study area (~ , km ) included the maasai mara national reserve and the surrounding wildlife conservancies. the area experiences one wet season spanning from november to june and one dry season spanning from july to october [ ] . after the wet season, the long grass attracts large numbers of migratory ungulates, including the white-bearded wildebeest (connochaetes taurinus) and the common zebra (equus quagga), from the serengeti in tanzania. throughout the year there is an abundance of cheetah prey including resident white-bearded wildebeest, thomson's gazelle (eudorcas thomsonii), grant's gazelle (nanger granti) and impala (aepyceros melampus) [ ] . the habitat in the maasai mara varies, ranging from open grasslands and shrubland, to riverine forests found along the major rivers and their tributaries [ ] . the open grassland plains, which are dominated by red oat grass (themeda triandra), are mostly found toward the south and west of the study area, while the north and north-east consist mostly of croton thickets (croton dichogamous) and vachellia woodlands (vachellia drepanolobium and v. gerrardii). global positioning system (gps) satellite collars (african wildlife tracking -www.awt.co.za) were fitted on four adult male cheetahs between th october and th february . in compliance with kenyan law, all immobilizations for deployment/removal of collars were performed by a kenya wildlife service veterinarian. cheetahs were free-darted and immobilized using a combination of ketamine ( - . mg/kg) and medetomidine ( . mg/kg), remotely administered by a dan-inject co rifle (dan-inject, denmark), and reversed with atipamezole ( . mg/ml; following [ ] ). sedation time was kept to a minimum, typically less than hour. after immobilization all cheetahs recovered fully, showing no signs of distress and no apparent side effects were observed in the short-and long-term. collars, which were only fitted on adults, weighed grams which is the recommended weight for cheetah collars [ ] . all collars were removed if they malfunctioned or if the batteries were low. the animal handling protocols used conformed to the standards of the american society of mammalogists [ ] and permissions to deploy collars were provided by the kenya wildlife service (permit no.: kws/ brm/ ) and the national commission for science, technology and innovation (permit no.: nacosti/p/ / / ). the collared males were all singletons, except for one male (m ), who was part of a fivemale coalition. over an month period, the five-male coalition were sighted on occasions and only on one occasion did the coalition separate for a period of < hours. we therefore collected data on a total of eight individuals in four social groups. while this is a relatively small sample size, it is a quarter of the entire population as there are approximately adults within the study area [ ] . the collars collected gps coordinates every three hours ( h, h, h, h, h, h, h and h) and when there was satellite communication, data were uploaded on a daily basis at h. on average, the collars were deployed for days ranging from to days (table ) . for each pair of cheetahs (hereafter referred to as a dyad), we only used simultaneously collected data for the analyses. static interactions. to determine the static interactions between male cheetahs we calculated their space use and the amount of overlap for each dyad to determine the possibility that individuals could encounter each other either directly or indirectly. space use for each individual per dyad was based on their utilisation distributions, which is the distribution of an individual's locations over time [ ] , using the adehabitat package [ ] in r [ ] . to calculate the utilisation distributions we used a fixed kernel density estimate using a bivariate normal kernel. we used the reference bandwidth parameter (h ref ) as the smoothing factor unless h ref > then we used % of the h ref to minimise over-smoothing of the data. using the resulting utilisation distribution, we determined both the % and % kernels which respectively represent an individual's total space use and their core areas. for each dyad we then calculated the amount of overlap of the % kernels and the % kernels. marking posts are used by male cheetahs to communicate their presence to conspecifics. using the methods described by [ ] , we located marking posts based on a cluster analysis using data from the gps collars and opportunistically when conducting fieldwork. for each dyad, we determined how many marking posts were found within the % kernel overlap. we used the recurse package [ ] to calculate ) how many marking posts were visited by each individual and ) how many marking posts were visited by both individuals in a dyad (hereafter referred to as mutual marking posts). we classified a visit when a cheetah came within m (half the average step-length, see dynamic interaction for details) of a marking post. for the mutual marking posts we calculated ) the time between individual visits and ) the time spent within m of a mutual marking post by each individual and tested whether there were differences between individuals. in addition, we calculated the time between visits from two different individuals i.e. we calculated how long it took for individual x to visit a mutual marking post once individual y had visited and vice versa. we then tested whether the time it took for an individual to visit a marking post once the other individual had been there differed between the individuals. we tested the data for normality using the shapiro-wilk test and used a t-test if the data were normally distributed and a wilcoxon test if they were not. if the data were not normally distributed then we provided the median ± median absolute deviation in addition to the mean ± standard deviation. dynamic interaction. we first explored the movement of the different individuals using the movevis package [ ] . then, to determine whether interactions between two individuals in a dyad were likely to occur, we calculated the proximity between simultaneous locations using the wildlifedi package [ ] . the hr resolution of the data is quite coarse so we used different proximity thresholds to group possible encounters based on the average -hour step-length which was , m ± , m (mean ± standard deviation). we used four proximity thresholds: < m, < m, < m and < m which correspond to . , , . and times the average step-length. we then determined whether these possible encounters took place at night (fixes at hr, hr, hr or hr) or during the day (fixes at hr, hr, hr or hr), whether they occurred within % kernels and the distance to the nearest known marking post. the half-way points between the two individuals were used as the estimated location where a possible encounter occurred. encounter outcomes. the gps data were examined once every few days. if any unusual behaviour was detected, such as no movement after a possible encounter, the field team would investigate to establish whether any injuries or deaths occurred as a result. in addition, for each possible encounter we compared the behaviour before to the behaviour after at four different time lags; hrs, hrs, hrs and hrs. first, we calculated the distance between two individuals before and after a possible encounter to determine whether males moved away from one another after an encounter. then, per dyad, we calculated ) the distance to the encounter location for each individual, ) the distance travelled per individual and ) the path tortuosity, or straightness. path tortuosity was calculated by dividing the net displacement by the total distance travelled. a value of around would indicate that the individual travelled in a straight line whereas a value < would be indicative of a tortuous path. we compared the proximity of the two individuals within a dyad, distance to encounter location, distance travelled and tortuosity before and after a possible encounter. we tested the data for normality using the shapiro-wilk test and used a t-test if the data were normally distributed and a wilcoxon test if they were not. in total, we secured simultaneous data on four male cheetah dyads ranging from to days per dyad. one individual (m ) was part of three of the four dyads, two individuals (m and m ) were part of two dyads and one individual (m ) was part of one dyad ( table ). across the four dyads the % kernels ranged from km to , km and the % kernels ranged from km to km ( table ) . for all the dyads, the % kernels overlapped but the amount of overlap ranged from % to % where in dyad the % kernel of individual m fell completely within the % kernel of individual m (fig ) . only the core areas ( % kernel) of dyad had an extensive area of overlap ( % and %), whereas the cores of the other dyads did not overlap or the area of overlap was minimal (< %). we found marking posts in the study area and the number of mutual marking posts per dyad ranged from to with the average number of visits to these marking posts ranging from to . (table ) . for the three dyads that had the most extensive spatial overlap and the largest number of mutual marking posts (dyads , and ) the average time that an individual was within m of a mutual marking post did not vary significantly between individuals in the same dyad, ranging from . ± . hours to . ± . hours (mean ± standard deviation; table ). the data were not normally distributed and the median for the same three dyads ranged from . ± . hours to . ± . hours (median ± median absolute deviation). for all the dyads, the average time between visits of a mutual marking post varied significantly between the individuals (table ). in the case of dyad and , individual m , who we classified as territorial, visited mutual marking posts more frequently compared to individuals m and m , neither of which were strictly territorial ( table ) . the time between different individuals visiting the same mutual marking post ranged from . ± . days to . ± . days and did not differ significantly across the dyads (table ) . for three of the four dyads (dyads , and ) the possibility of individuals within each dyad encountering each other was high as they overlapped extensively in space and had a large number of mutual marking posts. for these three dyads we explored their simultaneous movements and calculated the proximity between each individual within a dyad. the individuals within the three dyads did on occasions come into close proximity to one another as can be seen in the animation provided in the s movie. the minimum distance between individuals in a dyad ranged from m to m but the average proximity between individuals ranged from , ± , m to , ± , m (fig ) . possible encounters were classified according to four different thresholds and we detected four possible encounters with a proximity threshold of < m, with a proximity threshold of < m, with a proximity threshold of < m and with a proximity threshold of < m (table ). possible encounters were more likely to occur at night than during the day (χ = , df = , p = . ) and occurred most frequently at hr and midnight. of the possible encounters, % (n = ) occurred within the core area of one individual, % (n = ) occurred where the % kernels overlapped and two possible encounters in dyad did not occur in any of the core areas. eleven ( %) of the possible encounters occurred within m of a known marking post. for possible encounters with proximity thresholds of < m, < m and < m the distance between males was overall significantly less during the period to hours after a possible encounter, compared to the and hours before a possible encounter (table ). in other words, rather than moving away from each other, male cheetahs stayed in close proximity to each other for up to hours after a possible encounter. for the distance to the encounter location, distance travelled and tortuosity we wanted to determine whether there was individual variation within each dyad. however, because of the paucity in the number of possible encounters that were detected per dyad we were only able to carry out the analysis for possible encounters with a proximity threshold < m. in general, cheetahs were closer to the encounter location after a possible encounter compared to before for all four time lags, apart from individual m in dyad where the opposite trend was intraspecific interactions among carnivores: a case study of male cheetahs observed, however none of the results were significant (s table) . similarly, cheetahs travelled less after a potential encounter compared to before, apart from individual m in dyad where the opposite trend was observed. some of the results, especially at the hr and hr lag were significant for dyad and (s table) . on the th february the collar on m stopped transmitting but when the team visited the last location sent by the collar, neither cheetah nor collar could be found and the individual has not been seen since. on the st october the collar on m stopped transmitting data after the collar data showed that individuals m and m had come within m of each other. the team went to the last gps coordinate that was transmitted by the collar and found the remains of m m from the last gps fix sent by the collar. upon inspecting the carcass, a puncture wound was found on the left side of the skull. based on the circumstantial evidence, we believe that the death of m was either a direct or an indirect result of an aggressive interaction between him and the -male coalition (m ). interestingly, three months prior to this encounter m and his coalition mates started establishing a territory approximately km southwest from m 's territory. two days before the encounter the coalition travelled km to the encounter location, spent hours within m of m and then travelled km straight back to the core of their territory. m did not return to the vicinity of the encounter between the st october , when the encounter took place, and rd february , when m 's collar was removed. the closest they came to m 's territory during that time was approximately km (fig and the animation in s movie). using gps collar data we documented static and dynamic interactions between male cheetahs in kenya's maasai mara and investigated the outcomes of these interactions in terms of movement behaviour and mortalities. as we predicted, male cheetahs showed extensive spatial overlap of the % kernels. this high degree of overlap observed in the maasai mara could be related to the pattern of prey availability [ ] , although we do not have the data to test this. however, apart from one dyad, there was little overlap of core areas ( % kernels) and it could be that core areas are defended more intensively than the peripheral areas [ ] . similar to observations in other areas, marking posts were frequently visited by males [ , ] and this could indicate the mechanism that results, despite the extensive spatial overlap, in the rarity of occasions when members of a dyad were in close proximity [ ] . interestingly, our results show that possible encounters were most likely to take place in the core area of one individual of a dyad or where cores of both individuals overlapped. we also found that, similar to african wild dogs (lycaon pictus), possible encounters occurred more at night than during the day [ ] . while cheetahs, like african wild dogs, are predominantly diurnal they can be active at [ ] and nocturnal activity for males has been found to be considerably higher than for females [ ] . data from camera traps set at marking posts found that visits occurred more at night than during the day ( [ ] ; kk unpublished data) suggesting that male nocturnal activity is partly driven by patrolling behaviour which is probably why encounters predominantly took place at night. in some species, including african wild dogs and white-faced capuchins (cebus capucinus), avoidance behaviours, characterised by an increase in distance and speed travelled postencounter, were observed as a result of interactions between different groups [ , ] . however our results, in contrast to our predictions, did not show avoidance behaviour postencounter as males stayed in close proximity to each other - hours after a potential encounter. it is possible that males stayed in close proximity to each other, as part of a territorial defense strategy, if a recent scent of a conspecific was detected. this behaviour has been observed in dwarf mongoose (helogale parvula) groups, who moved slower and covered shorter distances in the hour following the encounter of rival faeces at a latrine site within their territory [ ] and red fox (vulpes vulpes) males who spent more time in scent-marked areas [ ] . alternatively, males could come into close proximity to one another if they are attracted to a resource, such as a female in oestrus [ , ] . cheetahs exhibit a high rate of multiple paternity [ ] so it is possible that multiple males stay in the vicinity of a receptive female with the hope of getting a chance to mate. these encounters could however result in fatalities if the removal of competition increases future mating opportunities [ ] . if encounters occur as a result of access to a receptive female rather than to a static, long-term resource such as a territory then this could explain why the five-male coalition did not take-over the territory of individual m after he died. aggressive interactions with fatal consequences are not uncommon in cheetahs. caro [ ] reported three cases in serengeti where singletons were killed by coalitions (all three-male coalitions). similarly, mills and mills [ ] found that % of male-male encounters recorded in the kgalagadi transfrontier park in botswana/south africa resulted in death. to our knowledge, fatal interactions have not been observed between female cheetahs. this could explain why male mortality is higher and life expectancy lower for males compared to females [ , ] resulting in a female biased sex ratio [ ] . for some species, such as voles (microtus oeconomus), lions and grizzly bear (ursus arctos), the removal of males, through either displacement or mortality, has a negative effect on population growth as a result of increased infanticide [ ] [ ] [ ] . infanticide has however not been observed amongst cheetahs [ ] possibly because it rarely occurs in predominantly solitary species [ ] . the removal of males could however have other population-level consequences [ ] but the impact of male mortality on population dynamics in cheetahs is unclear. static and dynamic interactions can play a role in disease transmission [ , ] . in the mara-serengeti ecosystem there is a relatively high prevalence of mange [ , ] and in southern africa cheetahs have been positively tested for feline coronavirus (fcov) and feline panleukopenia virus (fpv), which can be highly contagious and fatal [ , ] . pathogens such as these can easily spread through faeces and other bodily fluids, which are deposited and investigated by male cheetahs at marking posts. this could explain why in several males in the maasai mara, who overlapped spatially, died of a yet unknown disease within a short space of time [ ] . we suggest that future epidemiological research should investigate the role of scent marking posts and movement in disease transmission [ ] . here we give a descriptive analysis of the static and dynamic interactions between male cheetahs and the outcomes of these encounters. despite the clear patterns that were observed, there are several caveats that warrant discussion. firstly, we were only able to use data from four collared males, one of which was part of a -male coalition. it is therefore possible that other uncollared individuals, including the other members of the -male coalition, could have influenced the results. secondly, because of the resolution of the collar data we might have missed visits to marking posts and we inferred when interactions took place rather than being able to detect actual interaction (apart from one occasion). our results are therefore likely to be on the conservative side and we suggest that future studies use higher resolution data and/ or proximity loggers to investigate actual interactions between individuals (e.g. [ , ] ). however, even with a relatively coarse resolution of data and only a small number of individuals we managed to investigate interactions and subsequent outcomes between males giving a first detailed insight into intraspecific interactions in cheetah. table. summaries for each dyad of the distance to the encounter location, distance travelled and tortuosity before and after a possible encounters with proximity threshold of < m. 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free-ranging namibian cheetahs (acinonyx jubatus) disease outbreak thresholds emerge from interactions between movement behavior, landscape structure, and epidemiology wildlife contact analysis: emerging methods, questions, and challenges we would like to thank the mara cheetah project and mara lion project teams for assisting with fieldwork. key: cord- -iac fak authors: mao, liang title: evaluating the combined effectiveness of influenza control strategies and human preventive behavior date: - - journal: plos one doi: . /journal.pone. sha: doc_id: cord_uid: iac fak control strategies enforced by health agencies are a major type of practice to contain influenza outbreaks. another type of practice is the voluntary preventive behavior of individuals, such as receiving vaccination, taking antiviral drugs, and wearing face masks. these two types of practices take effects concurrently in influenza containment, but little attention has been paid to their combined effectiveness. this article estimates this combined effectiveness using established simulation models in the urbanized area of buffalo, ny, usa. three control strategies are investigated, including: targeted antiviral prophylaxis (tap), workplace/school closure, community travel restriction, as well as the combination of the three. all control strategies are simulated with and without regard to individual preventive behavior, and the resulting effectiveness are compared. the simulation outcomes suggest that weaker control strategies could suffice to contain influenza epidemics, because individuals voluntarily adopt preventive behavior, rendering these weaker strategies more effective than would otherwise have been expected. the preventive behavior of individuals could save medical resources for control strategies and avoid unnecessary socio-economic interruptions. this research adds a human behavioral dimension into the simulation of control strategies and offers new insights into disease containment. health policy makers are recommended to review current control strategies and comprehend preventive behavior patterns of local populations before making decisions on influenza containment. during the past decade, influenza has obtained unprecedented attention due to widespread occurrence of novel viruses, such as the bird flu in and the swine flu in [ , ] . recent estimates by the center of disease control and prevention (cdc) indicated that the swine flu is responsible for , hospitalizations and , deaths in the united states [ ] . these staggering health burdens call for effective measures to control and prevent future outbreaks. the control of influenza primarily involves applying health resources to affected people, known as control strategies, for example, medical treatment for infected individuals, closure of affected workplaces/schools, and travel restriction to affected communities [ ] . the prevention of influenza emphasizes healthy people and depends on their voluntary behavior against the disease, referred to as the preventive behavior. as recommended by cdc, the preventive behavior against influenza include receiving vaccination, wearing facemasks, washing hands frequently, taking antiviral drugs, and others [ ] . while devising various control strategies and evaluating their effectiveness, few studies have incorporated the preventive behavior of individuals [ , ] . in most cases, individuals are often assumed to passively comply with control strategies, but their active prevention against the disease has been overlooked. in reality, the preventive behavior of individuals also reduces infections and takes effect concurrently with typical control strategies. for instance, individuals may voluntarily protect themselves from infection, once they realize some control strategies being applied to their family members, colleagues, or communities [ , , ] . by far, the combined effectiveness of control strategies and individuals' preventive behavior remains unclear, and little attention has been paid to this issue. lack of such knowledge may bias estimation of health resources needed to suppress an outbreak, and mislead the real practice of influenza containment. the purpose of this article is to evaluate the combined effectiveness of control strategies and individual preventive behavior. agent-based stochastic simulations are used to investigate three control strategies, including the targeted antiviral prophylaxis (tap), workplace/school closure, and travel restriction, as well as combinations of all three. the urbanized area of buffalo, new york, usa, is taken as a study area. the control effectiveness with and without considering individual preventive behavior is compared to indicate if there exists a significant difference. cost-effective strategies are suggested based on the comparison analysis. the remainder of this article is organized as follows. the method section that follows reviews two established influenza models for simulation and describes the design of control strategies being simulated. the result section presents and compares the simulation results. the discussion section concludes this article with implications. epidemic models, including mathematical and computer models, have been extensively used to investigate disease control strategies, because of their ease and flexibility to deal with different scenarios. the classic mathematical model, the sir model, and its variants employ differential equations to describe continuous variations between three subpopulations, i.e., the susceptible, infectious and recovered [ , ] . various control strategies are often expressed as different initial conditions (e.g., the size of susceptible population) or parameter settings (e.g., the infection rate) of differential equations. the computer-based simulation models have recently gained their impetus in epidemiology [ , , , ] . these models study population-level health outcomes through the simulation of individuals and their microinteractions. control strategies can be represented by altering individuals' health status and their behavior, such as endowing them immunity against infection and prohibiting their out-ofhome activities. all of these epidemic models provide solid platforms to evaluate and compare alternative strategies, thus informing health policy making [ , ] . epidemic models without considering individual preventive behavior are widely seen in the literature and hereinafter referred to as 'influenza-only' models, because they primarily focus on influenza transmission. in this research, an influenza-only model is implemented in the study area, which includes a total number of , individuals. these individuals live in census block groups and , households according to us census [ ] , and carry out daily activities in , business locations [ ] . the model involves an agent-based stochastic simulation, discrete time steps, and spatially explicit representation of individuals. each individual is a modeling unit with a set of characteristics (e.g., age, occupation, infection status, location and time of daily activities) and behaviors (e.g., traveling between locations for activities and having contact with other individuals) [ , ] . individuals and households are simulated under the constraints of census data so that the modeled population matches the age and household structure of the real study area. individuals are also assigned to business locations to represent their daily activities, such as working, shopping, eating out, etc. ( figure s ). the contacts between individuals take place when individuals meet at the same time and location, such as homes, workplaces, shops, and restaurants. because individuals travel over time and location, their mobility weaves a spatio-temporally varying contact network (see text s section . ). through such a network, influenza viruses diffuse from one individual to another. each individual is allowed to take one of four infection status during a time period, i.e. susceptible, latent, infectious, and recovered. the progress of infection status follows the natural history of influenza, including the latent, incubation, and infectious periods (table s ). during the infectious period, individuals may manifest symptoms and become symptomatic. to initiate the disease transmission, five infectious individuals are randomly seeded into the study area at the first day of simulation, which then lasts for days. in each day, the model traces susceptible contacts of infectious individuals, and stochastically identifies the next generation of infections using the monte-carlo method (see text s section . ). in order to further consider individual preventive behavior, this research employs an agent-based 'dual-diffusion' stochastic model that simulates the concurrent diffusion of both influenza and individual preventive behavior [ ] . the preventive behavior is considered as a practice or information that also diffuses over contact networks through inter-personal influence. these two diffusion processes interact with one another, i.e., the diffusion of influenza motivates the propagation of preventive behavior, which in turn limits the influenza diffusion [ , , ]. in the model, the diffusion of influenza is simulated similarly to the influenza-only model aforementioned. the diffusion of individual preventive behavior is propelled by two types of inter-personal influence through the contact network: one is the perceived infection risk and the other is the perceived social standard. the former is represented as the proportion of influenza cases among an individual's contacts, while the latter is expressed as the proportion of behavioral adopters among the contacts [ ] . individuals are simulated to evaluate these two proportions every day through the contact network. once either proportion exceeds a corresponding threshold, an individual will be convinced to adopt and practice preventive behavior [ , ] . the estimation of individualized thresholds toward adoption is based on a health behavioral survey approved by the social and behavioral sciences institutional review board, university at buffalo, state university of new york. the waiver of informed consent was obtained from the university review board for this research (see text s section and figures s -s ). compared to the influenza-only model, individuals in the dual-diffusion model have additional characteristics, such as their adoption status of preventive behavior and thresholds toward adoption. individuals also have more behaviors, for example, evaluating infection risks and social standards from their contacts, making decision to adopt, and carrying out preventive behavior against influenza. for illustrative purposes, the use of flu antiviral drugs (e.g., tamiflu) is taken as an example of preventive behavior in the simulation, because its clinical efficacy is more conclusive than other behaviors, for instance, washing hand and wearing facemasks. specifically, if an individual uses antiviral drugs, the chance of being infected and infecting others can be reduced by % and %, respectively [ , ] . implementation details of these two models are not the focus of this article, and readers could refer to text s section . and table s . influenza control strategies are mostly applied at three levels: the individual level, group level, and community level. for each level, one strategy is selected for subsequent investigation, namely, a targeted antiviral prophylaxis (tap) strategy at the individual level, a workplace closure strategy at the group level, and a travel restriction strategy at the community level, as shown in table . detailed descriptions of the three strategies are provided below. first, the tap strategy identifies symptomatic individuals (influenza cases), searches their household members, and then targets antiviral drugs to all these individuals [ , ] . this strategy has been recommended to be quite effective if stockpiles of antiviral drugs are sufficient and infections can be quickly detected [ ] . to account for limited health personnel, this research assumes that only a proportion of influenza cases, % ( %tap) and % ( %tap), can be identified during a day, following the design by germann et al. [ ] . second, the workplace closure strategy shuts down a proportion of workplaces/schools where influenza cases are identified [ ] . this strategy has been suggested to be useful to socially distance individuals, delay the disease spread, and win time for developing vaccines and antiviral drugs [ ] . following the work by ferguson et al. [ ] , a low-level scenario ( %wc) closes % affected workplaces and % affected schools during a day, while a high-level scenario ( %wc) closes % affected workplaces and % affected schools. third, the travel restriction strategy aims to reduce the trips into and out of affected communities [ , ] . each of the census block groups in the study area is treated as a community. following the project by germann et al. [ ] , a low-level scenario ( % tr) restricts % trips into and out of all affected communities, while a high-level scenario prohibits % trips ( % tr). in addition to testing the three control strategies individually, the combinations of all three are also evaluated. a low-level combination scenario (referred to as the combined-low) includes all three strategies at their respective low levels. likewise, a high-level combination (referred to as combined-high) contains all three single strategies at high levels. the three control strategies and their combinations in table are simulated by the influenza-only model and the dual-diffusion model, respectively. results from the influenza-only model indicate the effectiveness of control strategies without individual preventive behavior. meanwhile, outcomes from the dual-diffusion model show the combined effectiveness of both control strategies and individual preventive behavior. these two modeled effectiveness are compared to a baseline epidemic scenario, which represents a worst situation of no control strategies and no preventive behavior. all strategies are assumed to be implemented at the time when the cumulative number of influenza cases exceeds , ( % of the population), and last until the end of the epidemic. individuals having or having not adopted preventive behavior are treated the same by all control strategies, so that the control effectiveness from two models are comparable. for each model and each strategy scenario in table , the simulation is performed realizations to reduce randomness, resulting in a total of , realizations ( strategies scenarios models realizations). each simulation records the time and location of every infection event during a -day period. for each strategy scenario, the control effectiveness is measured by an epidemic curve that depicts the number of daily new influenza cases from day to day . the number of daily new cases is averaged from model realizations, and then plotted against time to form an averaged epidemic curve (figure ). associated characteristics of this epidemic curve are also derived, including an overall attack rate (the percentage of influenza cases in the population) and epidemic peak time (table ). for the ease of comparison, a relative effectiveness of a control strategy is also calculated as an index ranging from to . the relative effectiveness is defined as a ratio of the attack rate reduced by a strategy from the baseline to the baseline attack rate, i.e., (baseline attack rate attack rate under a strategy)/baseline attack rate. a zero value represents the baseline scenario without any control strategy (the attack rate under non-strategy = the baseline rate), while a higher value close to indicates that a control strategy produces a smaller attack rate. an effective strategy is expected to produce a low epidemic curve, small attack rate, and high relative effectiveness. in this research, an epidemic is assumed to be successfully contained, if the overall attack rate is below %. this is because reported influenza epidemics often have a % or higher attack rate [ , ] . the spatial effectiveness of control strategies is also of interest, and thus a series of infection intensity maps are displayed in figure . the infection intensity represents the density of total infections as points occurring within every geographic unit ( m m) during the entire -day epidemic. the intensity value at each cell location is also the average from model realizations and is converted to a unit of infections per sq km for the ease of comparison. an effective strategy is expected to reduce infection intensity at every location, and meanwhile confine the spatial extent of affected areas. on average, the baseline epidemic scenario (red curves in figure ) causes an . % of the population developing influenza symptoms ( table ). the epidemic peaks at day with approximately , new cases occurring at the peak time. the application of % tap and % tap scenario (blue curves in figure a -b) significantly reduces the overall attack rate to . % and . %, respectively. these two tap scenarios also postpone the peak time by - days. without considering preventive behavior, the % tap scenario seems effective to contain the epidemic, because it manages to lessen the overall attack rate under the % epidemic criterion. by further adding the preventive behavior (hereinafter abbreviated as pb), both %tap+pb and %tap+pb scenarios (green curves in figure a -b) result in even lower attack rates around . % ( table ). the epidemic peaks can be limited around , daily new cases, while the peak time remains similar to the baseline scenario. this is because the diffusion of preventive behavior quickly exhausts the pool of susceptible individuals, and need to prepare a smaller stockpile of antiviral drugs than would otherwise being expected. turning to the workplace closure strategies (blue curve in figure c ), the % wc scenario slightly reduces the overall attack rates to . %, and delays the peak time only a little ( table ). in contrast, the % wc scenario ((blue curve in figure d ) lessens the attack rate to a much lower level of . %, and advances the peak time by approximately week. for the purpose of containing the epidemic, the % wc scenario, i.e., the closure of % affected workplaces, is needed to achieve an attack rate under %. by further including the individual preventive behavior (green curves in figure c -d), the % wc+pb and %wc+pb scenarios produce a much smaller attack rate of . % and . %, respectively ( table ) . the time to reach epidemic peaks is shortened to - days, roughly weeks earlier than the baseline scenario. the relative effectiveness of % wc scenario is doubled by considering preventive behavior. a primary reason is that a number of susceptible individuals voluntary protect themselves from infection. these individuals, therefore, cannot be infected or infect others at workplaces and schools, largely limiting the disease transmission. the comparison suggests that given the preventive behavior of individuals is counted, a % workplace closure strategy, instead of the % one, would be adequate to contain an influenza epidemic. surprisingly, the % tr scenario ( figure e ) alone causes an even worse situation than the baseline scenario. the overall attack rate reaches %, and is . % higher than the baseline rate, leading to a negative effectiveness ( = . in table ). a possible reason is that the travel restriction strategy extends the time of individuals spent at home, thereby intensifying the within-home transmission. since only % of trips into and out of affected communities are restricted, the disease can still be easily transported from one affected community to another through the % unrestricted trips. the epidemic thus develops faster and affects more individuals. as the travel restriction level elevates to % (the % tr in figure f ), much more trips into and out of affected communities are restricted. although the infections at homes are intensified, most infections can only take place within communities, instead of between communities. as a result, the overall attack rate drops to . % and the epidemic peak is greatly mitigated. nevertheless, the % tr does not suffice to contain the epidemic, because the attack rate remains above %. the simulation results are distinctly different if adding individual preventive behavior (green curves in figure e -f). the %tr+pb scenario produces a much better outcome than that from the % tr alone, because the relative effectiveness jumps from . to . . the overall attack rate and epidemic peak size are remarkably reduced, although the attack rate remains above % ( table ). the %tr+pb scenario turns out to be effective for influenza containment, because the overall attack rate can be lowered to . %, much less than the % epidemic criterion. the combined strategies (the blue curves in figure g -h) outperform each of the three single strategies. the total infections can be contained far below % of the population, with a small peak size under , cases. particularly, the combined-high scenario is capable of preventing the epidemic, given only . % of the population being infected (table ) . among the three single strategies, the tap strategy reduces infections within households, the workplace closure strategy tends to prevent infections at workplaces, and the travel restriction limits the disease transmission between communities. these three single strategies work together as complements, leading to a significant improvement in control effectiveness (relative effectiveness. . ). without considering preventive behavior, the combined-high scenario seems necessary to contain the epidemic, while the combined-low scenario is insufficient. this argument, however, may be changed by incorporating individual preventive behavior (green curves in figure g -h). the combined-low+pb scenario now is adequate to reduce the overall attack rate below % and thus contain the epidemic, while the high-level scenario is no longer a necessity. based on the comparison analysis above, the tap %+pb, % wc+pb, % tr+pb, and the combined-low+pb scenarios are suggested to be cost-effective in controlling influenza epidemics. therefore, their spatial effectiveness is further examined and compared through infection intensity maps (figure ). for description purposes, the mapped infection intensity is further categorized into levels, i.e., very low ( - infections/km ), low ( - ), moderate ( - ), high ( - ), very high ( - , ), and extremely high (. , ) . the baseline scenario (figure a ) induces an extremely high intensity of infections in the central business district of the study area. the infection intensity decreases in an outward direction to suburbs. this is because the central business district has the densest residential population and highly concentrated business locations. compared to the baseline map, the % tap+pb scenario ( figure b ) greatly reduces the infection intensities all around the study area, although the central business district retains a high-level intensity. the spatial effectiveness of %wc+pb ( figure c ) is similar to the % tap+pb, but moderate infections are more scattered in the suburban areas. the % tr+pb is capable of confining the wide spread of influenza over the study area ( figure d ), leaving only a small number of separated areas with high infection intensity. these hotspots are most located within cbd, university campuses, and large industrial plants, where a large number of people work and live. this is probably because the city-wide travels of individuals are partially prohibited, and hence disease can only develop locally. finally, the combined low+pb scenario not only reduces the intensity of the infections at all locations, but also confines spatial extent of disease spread ( figure e ). the infections in the central business district are reduced to a moderate level, while a vast proportion of the study area has only a small number of infections. in summary, previous studies on influenza containment have only considered the effectiveness of applying control strategies, while overlooking the effectiveness from individuals' preventive behavior. this research estimates the combined effectiveness of both control strategies and individual preventive behavior. the results imply that previous studies on control strategies are incomplete, and the control effectiveness might be under-estimated. the comparison between two model results indicates that preventive behavior of individuals has an extra effectiveness, in addition to the effectiveness from typical control strategies alone. this extra effectiveness produces an even smaller attack rate of influenza, lower epidemic peak, and earlier peak time. by considering the combined effectiveness, the control of influenza epidemics may not require as much health resources as estimated in previous studies. for example, the % tap strategy could be replaced by the % one, reducing the burden of local agencies to prepare health resources. likewise, the % workplace closure strategy, rather than the % strategy, would be sufficient to control the seasonal influenza epidemic in the study area. enormous socio-economic disruptions could be possibly avoided. a low-level combination of the three strategies is recommended to suppress influenza epidemic in the study area, while a high-level combination is no longer a must. particularly, with the help of individual preventive behavior, the % travel restriction strategy and the lowlevel combined strategy can successfully confines the spatial dispersion of influenza in the study area. similar to any modeling analysis, this research has a number of limitations. first, the simulation models focus on one us metropolitan area, one influenza virus strain, and one preventive behavior. it is possible that the model outcomes vary in different cities and different disease parameters, such as a pandemic influenza virus. the interpretation of model outcomes should be limited to seasonal influenza and in the study area. although the use of antiviral drugs is taken as an example in this research, the methodology can be easily extended to other preventive behavior, such as washing hands and wearing facemasks, once their preventive efficacy is conclusively quantified. second, the mass media also influences people's decision to adopt preventive behavior, especially for diseases that are highly infectious or pose severe health risks, such as the severe acute respiratory syndrome (sars). this research has not modeled the mass media because its effects on flu-related preventive behavior remain inconclusive. in addition, the seasonal influenza simulated in this research has a relatively mild infectivity and limited risks, thus is usually not a focus of mass media attention. third, the model assumes that individuals adopt preventive behavior immediately after the threshold effects happen. in reality, individuals' adoption of a behavior may take a relatively longer period as it may involve a number of psychological steps [ ] . a more sophisticated behavioral approach may improve the modeling reality, but also increase the complexity of model structure. a trade-off between model performance and detail levels is always a challenge for modelers [ ] . ongoing research is intended to address these limitations and challenges. control strategies enforced by health agencies and preventive behavior voluntarily practiced by the public are two intertwined components of disease containment. ignoring either component may prevent us from effectively mitigating burdens of influenza on public health. it is hard to resist citing and rephrasing the argument by funk et al. [ ] that ''individual self-initiated behavior can change the fate of an outbreak, and its combined effectiveness with control strategies requires proper understanding if we are to fully comprehend how these control measures work''. this research attempts to fuse the human behavioral dimension into the study of control strategies, and thus offers more comprehensive understandings on disease containment. health agencies are recommended to gain prior knowledge about behavioral patterns of local people before choosing influenza control strategies. the findings of this research call for a review of current control strategies and re-estimate the health resources that are necessary to contain epidemics. it is believed that such a review would shed new insights on improving control effectiveness for looming influenza pandemics. figure s the simulation of contact network. the assignment of individuals to households, workplaces, service places and neighbor households based on the attribute and spatial information of individuals. text s (doc) conceived and designed the experiments: lm. performed the experiments: lm. analyzed the data: lm. wrote the paper: lm. emergence and pandemic potential of swine-origin h n influenza virus public health risk from the avian h n influenza epidemic updated cdc estimates of h n influenza cases, hospitalizations and deaths in the united states planning for smallpox outbreaks preventing seasonal flu capturing human behaviour can influenza epidemics be prevented by voluntary vaccination the spread of awareness and its impact on epidemic outbreaks the health belief model and personal health behavior endemic disease, awareness, and local behavioural response a contribution to the mathematical theory of epidemics a structured epidemic model incorporating geographic mobility among regions mitigation strategies for pandemic influenza in the united states containing pandemic influenza with antiviral agents modeling targeted layered containment of an influenza pandemic in the united states flute, a publicly available stochastic influenza epidemic simulation model modeling influenza epidemics and pandemics: insights into the future of swine flu (h n ) the effectiveness of policies to control a human influenza pandemic: a literature review data releases spatial-temporal transmission of influenza and its health risks in an urbanized area a conceptual framework for an individual-based spatially explicit epidemiological model agent-based simulation for a dual-diffusion process of influenza and human preventive behavior the impact of information transmission on epidemic outbreaks multiple sources and routes of information transmission: implications for epidemic dynamics modelling the influence of human behaviour on the spread of infectious diseases: a review threshold models of collective behavior social network thresholds in the diffusion of innovations perspectives on antiviral use during pandemic influenza containing pandemic influenza at the source individual-based computational modeling of smallpox epidemic control strategies simulation suggests that rapid activation of social distancing can arrest epidemic development due to a novel strain of influenza strategies for mitigating an influenza pandemic the effect of travel restrictions on the spread of a moderately contagious disease key facts about seasonal influenza (flu) global epidemiology of influenza: past and present a model of the precaution adoption process: evidence from home radon testing choosing the best model: level of detail, complexity, and model performance key: cord- -j r nq authors: hernando-amado, sara; coque, teresa m.; baquero, fernando; martínez, josé l. title: antibiotic resistance: moving from individual health norms to social norms in one health and global health date: - - journal: front microbiol doi: . /fmicb. . sha: doc_id: cord_uid: j r nq antibiotic resistance is a problem for human health, and consequently, its study had been traditionally focused toward its impact for the success of treating human infections in individual patients (individual health). nevertheless, antibiotic-resistant bacteria and antibiotic resistance genes are not confined only to the infected patients. it is now generally accepted that the problem goes beyond humans, hospitals, or long-term facility settings and that it should be considered simultaneously in human-connected animals, farms, food, water, and natural ecosystems. in this regard, the health of humans, animals, and local antibiotic-resistance–polluted environments should influence the health of the whole interconnected local ecosystem (one health). in addition, antibiotic resistance is also a global problem; any resistant microorganism (and its antibiotic resistance genes) could be distributed worldwide. consequently, antibiotic resistance is a pandemic that requires global health solutions. social norms, imposing individual and group behavior that favor global human health and in accordance with the increasingly collective awareness of the lack of human alienation from nature, will positively influence these solutions. in this regard, the problem of antibiotic resistance should be understood within the framework of socioeconomic and ecological efforts to ensure the sustainability of human development and the associated human–natural ecosystem interactions. the problem of antibiotic resistance (ar) has been traditionally addressed by focusing on humanlinked environments, typically health care facilities. nevertheless, it is now generally accepted that most ecosystems may contribute to the selection and spread of ar (aminov, ; martinez et al., ; davies and davies, ; martinez, ; berendonk et al., ; larsson et al., ) . a key conceptual point is that, based on cultural, humanitarian, and economic reasons, we have historically preserved the health of individual humans and farming animals. to that purpose, the same families of antimicrobial agents have been used. as a consequence, their positive (healing) and negative (selection of ar, therapeutic failure) effects have influenced the common health of humans and animals in particular locations (one health). the concept one health, first used in early twentieth century, expands the integrative thinking about human and animal medicine, including for the first time ecology, public health, and societal aspects (zinsstag et al., ) . in the case of ar, the one health perspective focuses on the risk assessment of emergence, transmission, and maintenance of ar at the interface between humans, animals, and any other linked (local) environment (robinson et al., ; jean, ) . consequently, the application of one health approaches demands integrative surveillance tools and interventions based on multidisciplinary approaches that include ecological and sociodemographic factors, besides more classic epidemiological models. global health is based on a broad collaborative and transnational approach to establish "health for all humans." in this case, it focuses ar at a general (global) scale, considering that the selection and global spread of antibiotic-resistant bacteria (arbs) and antibiotic resistance genes (args) are a problem that influences the health of human societies with disparate social and economic structures and is linked to many societal and ecological factors (chokshi et al., ) . interventions to reduce ar burden in a global world certainly require common and integrated policy responses of countries, international organizations, and other actors (stakeholders included). its goal is the equitable access to health and minimizing health risks all over the globe. besides its objective aspects (i.e., how travelers, migrating birds, or international commerce may contribute to ar spread), it has important international political aspects. it focuses in how countries and international organizations address the elements connecting and potentially spreading ar among humans, animals, and natural ecosystems at the earth scale (wernli et al., ) . in summary, the problems and the potential solutions concerning ar are not confined to particular regions, but have a global dimension: a problem for all humans, animals, and natural ecosystems, which should be solved with interventions aiming to improve health for all of them koplan et al., ; laxminarayan et al., ) . in the context of ar, a healthy environment would be an environment where ar is low or can be controlled by human interventions (hernando-amado et al., ; andersson et al., ) . of course, the global health concept of "health of an environment" (iavarone and pasetto, ; pérez and pierce wise, ; bind, ; van bruggen et al., ) or, in general, planetary health (lerner and berg, ) , has an unavoidable anthropogenic flavor. in practice, we consider "healthy environments" or "healthy ecosystems" those that minimize their current or their potential harm for the human individual or the society, in our case for ar. in other words, we adopt a selfish strategy, which should be necessarily implemented by the international (global) institutions. selfishness (kangas, ) applies mainly to individuals, but also to societal groups. however, these groups have not enough possibilities to act alone in the case of infectious diseases in general and ar in particular, which may expand worldwide. therefore, individual selfishness for health should be integrated in local one health and also in global health actions. the goal of controlling ar is a highly complex one, and its dimension has been compared to climate change or biodiversity loss, problems where individual actions are not enough for providing a solution, and consequently, individual freedom is confronted with collective responsibility (looker and hallett, ) . the construction of human societies reflects the tension between individual freedom and social rules/laws. the implementation of different social rules/laws for regulating human activities within a society is mainly based on moral (as kant's categorical imperative (kant, ) or religious-based brotherhood (matthew : - ) statements), social stability (as anticrime laws; schiavone, ) , organizative (type of government and how it is formed, group identity), and efficacy (as antitrust laws; ricardo, ) arguments. however, these arguments mainly apply for establishing the socioeconomic organization as well as the individual welfare within a society. the situation concerning human health is somehow different. there are individual diseases, such as cancer or stroke, and social diseases, such as transmissible infections. for the firsts, social norms (as consciousness of the importance of the control of cholesterol, excess sugar uptake, or hypertension levels) are well established, and even laws (non-smoking regulations) had been implemented in occasions. however, the main impact of these regulations is at the individual health level (wikler, ) , because the associated diseases are not physically transmissible. a different situation happens in the case of infectious diseases in general and of ar in particular. for these diseases, everything that happens in a single person affects any one around. further, the fact that an arg emerging in a given geographic area can spread worldwide implies that neither individual norms nor country-based norms have been sufficient until now to counteract the worldwide spread of ar. one important aspect of laws in democratic societies is that they must be well accepted by the community, so that the acceptation of social norms usually comes first than their implementations as rules/laws. actually, the efficiency of democracy for responding to social crisis (as current ar or covid- crises), in opposition to other more autocratic regimens where decisions are implemented top-down, had been the subject of debate from the early beginning of democratic revolutions (tocqueville, ; hobbes, ; rousseau, ; spinoza, ) . in this regard, it is important to remark that one health aspects of ar can be tackled in the basis of countrylevel regulations that are linked to the socioeconomic and cultural aspects of each country (chandler, ; chokshi et al., ) . however, because global earth governance does not exist, global health control of ar is based on recommendations, rather than in rules/laws. consequently, the acceptance of social norms, starting within individuals or small organizations and expanding throughout the whole society (figure ) , is fundamental to provide global solutions to the ar problem (nyborg et al., ; chandler, ) . the acceptance by the community of these social norms, considering that the way of promoting these norms might differ in different parts of the world (cislaghi and heise, ; cislaghi and heise, ) , largely depends on the transfer to the society of the knowledge required to understand the mechanisms and the impact for human health of the emergence and transmission of ar, an information that is discussed below. figure | how the interactions among individual health, one health, global health, and social norms influences antibiotic resistance. the right panel shows the different levels of dissemination of antibiotic resistance. in the left panel, the different types of norms (from individual to global norms) that can impact antibiotic resistance at each level are shown. these norms influence all levels of transmission: the individual promotes (red arrows) his own individual health, but doing it also promotes the health of the group, and the health of the group promotes global health of the human society at large. at each level, there is a positive action (red broken lines) on antibiotic resistance. such dynamics largely depends on social norms (blue arrows) rewarding the individual or the groups whose behavior promotes health. below the left panel, the basic social norm, progress and development, has consequences on the whole ecobiology of the planet (lower panel with bullet points), influencing the undesirable open circulation of antimicrobial resistant bacteria (with their mobile genetic elements) and antibiotic resistance genes. the classic definition of ar is based only on the clinical outcome of the infected patient. an organism is considered resistant when the chances for the successful treatment of the infection it produces are low . this definition, which is the most relevant in clinical settings, presents some limitations for studies based on one health approaches that include the analysis of non-infective organisms, which lack a clinical definition of resistance, as well as analysis of the distribution of args, in several occasions, using non-culture-based methods . even in the case of animal medicine, antibiotic concentration breakpoints defining resistance are still absent for some veterinary-specific antimicrobials and poorly defined for different types of animals with disparate weights, which would influence the availability of the drug inside animal body (toutain et al., ; sweeney et al., ) . to analyze ar beyond clinical settings, the term resistome, understood as the set of genetic elements that can confer ar, irrespectively of the level of resistance achieved, in a given organism/microbiome was coined (d'costa et al., ; wright, ; perry et al., ) . ar acquisition is the consequence of either mutation (or recombination) or recruitment of args through horizontal gene transfer (hgt), transformation included. ar mutations are generally confined to their original genomes, propagating vertically and not spreading among bacterial populations, although some few exceptions of horizontal transfer of chromosomal regions containing ar mutations have been described (coffey et al., ; ferrandiz et al., ; novais et al., ; nichol et al., ) . the set of mutations that confer ar can be dubbed as the mutational resistome. current wholegenome-sequencing methods of analysis can allow defining the mutational resistome in an isolated microorganism (cabot et al., ; lopez-causape et al., ) . however, they are not robust enough yet for determining the mutational resistome in metagenomes. consequently, the impact of these analyses in one health studies is still limited and will not be further discussed in the present review. concerning their relevance for acquiring ar, args can be divided in two categories. the first one comprises the genes forming the intrinsic resistome (fajardo et al., ) , which includes those that are naturally present in the chromosomes of all (or most) members of a given bacterial species and have not been acquired recently as the consequence of antibiotic selective pressure. despite that these genes contribute to ar of bacterial pathogens, they are responsible just for the basal level of ar, which is taken into consideration when antibiotics are developed. in this regard, unless these genes, or the elements regulating their expression mutate, they are not a risk for acquiring resistance and have been considered as phylogenetic markers . further, it has been discussed that these genes may contribute to the resilience of microbiomes to antibiotic injury (ruppe et al., b) , hence constituting stabilizing element of microbial populations when confronted with antibiotics more than a risk for ar acquisition by pathogens. the second category, dubbed as the mobilome, is formed by args located in mobile genetic elements (mges) that can be transferred both vertically and horizontally, hence allowing ar dissemination among different bacteria (frost et al., ; siefert, ; jorgensen et al., ; lange et al., ; martinez et al., ) . while the analysis of the resistome of microbiota from different ecosystems has shown that args are ubiquitously present in any studied habitat (d'costa et al., ; walsh, ; jana et al., ; lanza et al., ; chen et al., b) , the impact of each one of these args for human health is different. indeed, it has been stated that the general resistome of a microbiome is linked to phylogeny and to biogeography, indicating that most args are intrinsic and do not move among bacteria (pehrsson et al., ) . however, some args escape to this rule and are shared by different ecosystems and organisms (forsberg et al., ; fondi et al., ) . these mobile args, frequently present in plasmids (tamminen et al., ; pehrsson et al., ) , are the ones that are of special concern for human health. although not belonging to the antibiotic resistome, genes frequently associated with resistance to other antimicrobials, such as heavy metals or biocides, as well as the genes of the mges backbones, eventually involved in the transmission and selection of args among microbial populations, the mobilome at large, are also relevant to track the emergence and dissemination of ar among different habitats martinez et al., ; baquero et al., ) . hgt processes are recognized as the main mechanisms for transmission of genetic information (baquero, ) . from the ecological point of view, hgt should be understood as a cooperative mechanism that allows the exploitation of common goods as args by different members within bacterial communities. in fact, some studies suggest that the ecological consequences of hgt events in ar evolution are contingent on the cooperation of complex bacterial communities, besides the acquisition of individual adaptive traits (smillie et al., ) . however, the understanding of the ecological causes and consequences of args transmission among organisms and microbiomes is still limited from the one health and global health perspectives. hgt-mediated ar is a hierarchical process (figure ) in which args are recruited by gene-capture systems as integrons and afterward integrated in mges as plasmids, insertion conjugative elements, or bacteriophages (frost et al., ; garcia-aljaro et al., ; gillings et al., ; botelho and schulenburg, ) , which afterward are acquired by specific bacterial clones. selection at each of these levels will also select for all the elements involved in ar spread. for instance, the acquisition of an arg by a clone may promote the expansion of the latter (and of all the genetic elements it contains, other args included) in antibiotic-rich environments, such as hospitals or farms schaufler et al., ) , and vice versa, the introduction of an arg in an already successful clone may increase the chances of this resistance gene for its dissemination even in environments without antibiotics, unless the associated fitness costs are high. in this sense, if arg acquisition reduces the fitness, and this implies a decreased capability for infecting humans (see below), the burden for human health might eventually be lower. nevertheless, it is relevant to highlight that ar transmission cannot be understood just by analyzing the genetic mechanisms involved and the consequences of such acquisition for the bacterial physiology. indeed, as discussed below, there are ecological and socioeconomic elements that strongly influence ar dissemination. the evolution of ar comprises the emergence, the transmission, and the persistence of arbs (martinez et al., ; baquero et al., ) . concerning human health, selection of arbs/args is particularly relevant at the individual health level, whereas transmission is a main element to be taken into consideration at the one health and global health levels (figure ) . indeed, unless ar is transmitted, it will be just an individual problem that would not affect the community at large. it is generally accepted that non-clinical ecosystems are often primary sources of args (davies, ) . as above stated, after their capture and integration in mges (figure ), args and their bacterial hosts can contaminate different ecosystems, which might then be involved in their global spread (martinez, ; fondi et al., ; gillings, ; gillings et al., ) . this means that nearly any ecosystem on earth, along with the humandriven changes produced in it, may modulate evolution of ar. importantly, the huge escalation and worldwide expansion of a limited set of animals, plants, and their derived products, including foods, due to the anthropogenic selection of a few breeds and cultivars for mass production in livestock and agricultural industries (okeke and edelman, ; zhu et al., ) of economic interest have collapsed the variability and biodiversity of animals and plants (seddon et al., ) . because these organisms harbor particular host-adapted bacteria, which are frequently under antibiotic challenge, this situation, together with the ecological similarities of human habitats, might favor ar spread (martiny et al., ; manyi-loh et al., ) . indeed, while in underdeveloped areas of the world food animals are very diverse, intensive farming, common in developed countries, ensures a "shared-stable" environment where only the most productive types prevail (kim et al., ) . the common genetic origin of these types and the process of microbiota acquisition from nearby animals in intensive farming should homogenize also their microbiomes with consequences for ar dissemination. actually, it has been shown that the loss of microbial diversity figure | genetic, ecological, and socioeconomic elements mediating the transmission of antibiotic resistance. args are ubiquitously present in any studied microbiome (a). however, only a few of them are transferred to human/animal pathogens, hence constituting a health problem. the genetics events implied include the acquisition of args by gene-recruiting genetic elements such as integrons (b); the integration of these elements in mges as plasmids, bacteriophages, or frontiers in microbiology | www.frontiersin.org figure | continued insertion conjugative elements (c); and the acquisition of these elements by specific bacterial clones (d). these arbs can share these elements among the members of gene-sharing communities (e) and also move among different ecosystems, including humans, animals (particularly relevant farm animals), and natural ecosystems (with a particular relevance for water bodies). the connection of these ecosystems, as well as the reduced diversity of animals, plants, and in general habitats as the consequence of human activities, allows the different microbiomes to be in contact, favoring args transmission among the microorganism they encompass (f). this transmission is facilitated at the global scale by travel, animal migration, trade of goods, and eventually by meteorological phenomena, climate change included (g), hence producing a global health problem (h). while most studies on the dissemination of args focus on mges (davies, ; muniesa et al., ; lanza et al., ; garcia-aljaro et al., ) , recent works suggest that the contribution of natural transformation (orange arrow), allowing the direct uptake of args by natural competent microorganisms, may have been underestimated (domingues et al., ; blokesch, ) . further, competence can occur due to interbacterial predation (veening and blokesch, ) , a biological interaction that may facilitate the acquisition of beneficial adaptive traits by predator bacterial species (cooper et al., ; veening and blokesch, ) . other hgt mechanisms, such as dna packing in extracellular vesicles (ecv) or transference of dna through intercellular nanotubes, also seem to be relevant in nature (dubey and ben-yehuda, ; fulsundar et al., ) . while the biotic conditions that may enhance hgt have been studied in detail, less is known concerning abiotic modulation of args transfer. under contemporary conditions, at least microorganisms are affected by a freeze-and-thaw cycle, at least are agitated by sand, and at least are subjected to conditions suitable for electrotransformation every year (kotnik and weaver, ) . may favor ar spread (chen et al., a) . note that, beyond the transmission of particular ar spreading clones, ar is expected to spread in farms by the modification (eventually homogenization) of animals' microbiota. notwithstanding, even farm workers are subject to microbiome acquisition from animals, leading to microbiome coalescence sun et al., ) . it is to be noticed, and the recent covid- crisis exemplifies it, that besides economic development, cultural habits are relevant in the use of animals for food, a feature that has not been analyzed in detail, particularly with respect to their role as vectors potentially involved in ar dissemination. despite that the homogenization of hosts may help in ar transmission, the spread of arbs has some constraints, because the differential capability of each bacterial clone for colonizing different hosts may modulate their dissemination. indeed, while some species and clones are able to colonize/infect different animal species, humankind included, several others present some degree of host specificity (price et al., ; sheppard et al., ) . further, it has been shown that the capacity to colonize a new host is frequently associated with a reduction in the capacity for colonizing the former one. the same happens for mobile args; they are encoded in mges that present different degrees of host specificity, which defines the formation of gene-exchange communities, where the interchange of genetic material among members is facilitated (skippington and ragan, ) . conversely, the incorporation of different replicons and modules within plasmid backbones, a feature increasingly reported (douarre et al., ) , would enable arg replication in different clonal/species background and thus modify the community network of args. actually, the risk for humans of animal-based ar seems to be linked in most cases to shuttle, generalist clones able to colonize humans and particular animals (price et al., ; sheppard et al., ) . the understanding of the elements driving the transfer of ar among animals, humans included (figure ) , requires the comprehensive survey of the clones and args that are moving among them (european food safety authority et al., ). tools to track the global epidemiology of antimicrobial-resistant microorganisms such as bigsdb (jolley et al., ) or comprehensive databases of args, ideally providing information of their mobility (zankari et al., ; alcock et al., ) , are fundamental for studying ar transmission at a global level. it is worth mentioning that, because humans constitute a single biological species, the human-associated organisms spread easily among all individuals. in fact, more prominent differences in humans' microbiome composition can be observed between individuals than among ethnic groups, even though, as expected, the resemblance in microbiotas is higher among those groups that are geographically clustered (deschasaux et al., ; gaulke and sharpton, ) . some groups of human population are, however, more prone to acquire arbs, due either to socioeconomic or to cultural factors. in lmics (low-to medium-income countries) and brics (brazil, russia, india, china, and south africa) countries, the combination of wide access to antibiotics, weak health care structures, and poor sanitation defines certainly a dangerous landscape. moreover, the progressive aging of the western population might favor the establishment and further expansion of an elderly reservoir of arbs and args, an issue that deserves further studies. the hypothesis that the microbiome of elder people might be a reservoir of ar is based not only on their cumulative history of antibiotic exposure and contacts with health care centers, but also on the rampant use of antibiotics of this population more prone to suffer from acute, chronic, or recurrent infections. significant worldwide advances in the organization of medical care of the elderly people lead to frequent hospitalizations, but health care centers may also facilitate the selection and further amplification of ar in the community. in addition, this may subsequently favor the entry of high-risk clones and of args in the hospital setting (hujer et al., ) . as stated above, there is a global increasing permeability of the natural biological barriers that have historically prevented bacterial dissemination through different ecosystems. besides local spread of ar in environments shared by animals and humans, which has to be addressed under a one health approach, ar can disseminate worldwide (figure ) by economic corridors that promote the global interchange of goods and trade or human travelers or by natural bridges, such as animal migration paths or natural phenomena such as air and water movements (okeke and edelman, ; baquero et al., ; allen et al., ; overdevest et al., ; kluytmans et al., ; fondi et al., ) . the result is the appearance of similar arbs and args in different geographic areas. as the consequence, ar is a global health problem in the sense that an arb that emerges in a given place can rapidly spread worldwide. indeed, multidrugresistant bacteria, similar to those encountered in clinical settings, have been detected in human isolated populations that were not previously in contact with antibiotic, as well as in wildlife (clemente et al., ) . this indicates that pollution with args is present even in places where antibiotic concentrations are low (kümmerer, ) and might involve mechanisms of transmission that do not require selection. for instance, migrating birds can carry enteropathogenic bacteria resistant to different antibiotics (middleton and ambrose, ; poeta et al., ) , and international travelers, even those not receiving antibiotic treatments, also contribute to ar transfer among different geographic regions (murray et al., ; reuland et al., ) . in the group of long travelers are refugee people, in which dissemination of multidrug-resistant strains is favored by the poor sanitary conditions and overcrowding camps that refugees confront (maltezou, ) . a final issue concerning ar is its stability in the absence of selection. it has been proposed that the acquisition of ar reduces bacterial competitiveness in the absence of antibiotics (fitness costs) (andersson and hughes, ; martinez et al., ) ; certainly, a wishful proposition such as, if true, the reduction in the use of drugs or eventually antibiotic-cycling strategies should decrease ar (beardmore et al., ) . nevertheless, eliminating the use of an antibiotic does not produce a full decline of ar (sundqvist et al., ) . in fact, different studies have shown that ar not always reduces fitness but also can even increase bacterial competitiveness (andersson and hughes, ; schaufler et al., ) . in addition, compensatory mutations or physiological changes that restore fitness can be selected in resistant bacteria (andersson, ; schulz zur wiesch et al., ; olivares et al., ) . it is a fact, however, that although arbs are found nearly everywhere, including wild animals, natural ecosystems, or people from isolated populations without contact with antibiotics, among others (durso et al., ; clemente et al., ; alonso et al., ; fitzpatrick and walsh, ; power et al., ) , ar prevalence is consistently lower when antibiotics are absent, which suggests that pollution may impact ar, a feature that is discussed below. pollution of natural ecosystems is associated with activities that have driven relevant economic transition, in principle favoring human welfare, such as mining, industry, intensive land use, or intensive farming, among others. notwithstanding, globalization of health services, as well as the shift toward intensive farming, besides their positive contribution to human wellbeing, has rendered an increasing pollution by compounds with pharmacological properties of natural ecosystems, particularly water bodies, which may disrupt the stability of these ecosystems (oldenkamp et al., ) . among them, antibiotics are considered the most relevant cause of ar selection. despite regulations for reducing their use (van boeckel et al., ) , a substantial increase in global antibiotic consumption has occurred in the last years, and an even greater increase is forecasted in the next years (klein et al., ) . however, antibiotics are not the unique pollutants that can prime the selection and spread of ar. in this regard, it is important to highlight that heavy metals are one of the most abundant pollutants worldwide (panagos et al., ) . their abundance results from anthropogenic-related activities, such as mining, industry, agriculture, farming, or aquaculture and even for therapeutic use in ancient times. importantly, they may persist in nature for long periods of time. further, likely because metal pollution occurred before the use of antibiotics, heavy metal resistance genes were incorporated to mge backbones before args (mindlin et al., ; staehlin et al., ) . this means that heavy metals may coselect for mges and the args they harbor (partridge and hall, ; staehlin et al., ; zhao et al., a) . even more, the presence of heavy metals, as well as of biocides or sublethal antibiotic concentrations (jutkina et al., ; zhang et al., ) , may stimulate hgt, as well as modify the dynamics of antibiotics, such as tetracyclines, in natural ecosystems (hsu et al., ) . coselection may also occur when a single resistance mechanism, such as an efflux pump, confers resistance to both heavy metals and antibiotics (cross-resistance) (pal et al., ) . although most published works analyze the effect of different pollutants on their capacity to select arbs or args, it is important to highlight that args should also be considered pollutants themselves. actually, a recent work indicates a close relationship between the abundance of args and fecal pollution (karkman et al., ) . in this respect, it is worth mentioning that, differing to classic pollutants, args/arbs are not expected to disappear along time and space, but rather, their abundance may even increase as the consequence of selection and transmission (martinez, ) . while the direct selection of ar by antibiotics or the coselection mediated by other pollutants, as the aforementioned heavy metals, has been discussed (wales and davies, ) , the effect of other types of human interventions on the dissemination of args and arbs through natural ecosystems has been analyzed in less detail. as an example, it has been proposed that wastewater treatment plants, where commensals, arbs, args, and antibiotics coexist, could act as bioreactors favoring the selection and transmission of args between different organisms (rizzo et al., ; su et al., ; manaia et al., ) , although evidences supporting this statement are scarce (munck et al., ; azuma et al., ) . in addition to the aforementioned pollutants with a direct effect in ar selection, it is worth noting that there are other abundant contaminants, such as sepiolite (present in cat litters or used as a dietary coadjuvant in animal feed) or microplastics, present in almost all aquatic ecosystems, which can favor the transmission of args or mges between bacterial species (rodriguez-beltran et al., ; kotnik and weaver, ; arias-andres et al., ) , hence amplifying the ar problem at a global scale. finally, the possible effect of climate change on the spread of ar is worth mentioning. indeed, it modifies the biogeography of vectors (such as flies, fleas or birds) involved in the spread of infectious diseases (fuller et al., ; beugnet and chalvet-monfray, ) . in addition, the increase of local temperatures seems to correlate with an increased ar abundance in common pathogens (macfadden et al., ) . besides, climate change is affecting ocean currents (martinez-urtaza et al., ) , which may allow the intercontinental distribution of arbs and args (martinez, a,b) . although this phenomenon might contribute to the globalization of ar, further research is needed to clearly demonstrate a cause-effect relationship. it is relevant to mention that increased pollution and climate change are the unwanted consequences of human development. it would then be worth discussing how human development in general may impact (positively and negatively) ar, a feature that is analyzed below. human development is a necessity of our human behavior, although different models of development have been and are proposed, each one producing different impacts in the structure of human societies and on the preservation and stability of natural ecosystems (fenech et al., ; farley and voinov, ; seddon et al., ) . nevertheless, even for different socioeconomic models, there are some social norms that tend to be widely accepted, in particular those aiming to improve individual well-being. this implies the establishment of a society of welfare, understood as a right of any human on earth, a feature that depends on the economic development, and can be particularly relevant in the case of transmissible infectious diseases in general and of ar in particular. a continuously repeated mantra in worldwide ar policies is that the abusive consumption of antibiotics for the treatment or prevention of infections in humans and animals constitutes the major driver of ar. however, we should keep in mind that antibiotics constitute an important example of human progress supporting individual and global human health. in fact, the origin of the massive production of antimicrobials was a consequence of the needs resulting from world war ii in the s. this was followed by many decades of human progress, most importantly by the common understanding of equal human rights, which was followed by the economic and social development (including medicine and food industry) of densely populated regions in the planet, including india and china. these countries are currently among the leaders in the production and consumption of antimicrobial agents. notwithstanding, as in any area of economy, progress bears a cost that, in this case, is antibiotic pollution of the environment, globally accelerating the process of the emergence, the transmission, and the persistence of arbs (martinez et al., ; baquero et al., ) . the non-controlled use of antibiotics is facilitated in lmics with disparate economic growth by different factors. heterogeneous regulation of antibiotic sales and prescriptions (often weak or missing) and the increase of online on-bulk sales in recent years contribute to their overuse (mainous et al., ). most of live-saving medicines represent out-of-pocket costs in most lmics, which led to an exacerbated use of cheap (usually old and less effective) antibiotics, phasing out their efficacy and increasing the demands and prices for the most expensive ones, eventually resulting in treatment unavailability (newton et al., ) . further, the cost of treating ar infections is much higher than that of treating susceptible ones, which is increasing the cost of health services (wozniak et al., ) . conversely, the growing economic capability of lmics in the brics category triggers the access of the population to health services and last-resort antibiotics. these countries also face a sudden high demand for meat and thus a prompt industrialization of animal production that has favored the misuse of antibiotics for growth promotion facilitated by their online availability (mainous et al., ). in addition, counterfeit or substandard antibiotics recently become a serious global problem (gostin et al., ) , which is exacerbated in lmics, where they represent up to a third of the available drugs. noteworthy, % of all reports received by the who global surveillance and monitoring system on substandard and falsified medicines worldwide come from africa, and most of them correspond to antimalarials and antibiotics (newton et al., ; gostin et al., ; hamilton et al., ; petersen et al., ) . despite this situation, it is important to highlight that human consumption of antibiotics is an unavoidable need to preserve human health. in fact, most health problems dealing with infections in lmics are still caused by a poor access to antibiotics, not by an excessive use of them. proof of this is the fact that the distribution of antibiotics has reduced endemic illnesses and children mortality in sub-saharan africa (keenan et al., ) . this means that, while a global decline in the use of antibiotics would be desirable to diminish the problem of ar, there are still several parts in the globe where antibiotic use should still increase to correctly fight infections. in fact, our primary goal should not be to reduce the use of antibiotics, but to ensure the effective therapy of infectious diseases for the long term. this does not mean that ar is not a relevant problem in lmics; it means that reducing antibiotic use is not enough to solve the problem. indeed, the current high morbidity and mortality due to infectious diseases (malaria, tuberculosis, low respiratory infections, sepsis, and diarrhea) in lmics will be worsened in the absence or low efficiency of therapeutic treatments. further, ar has economic consequences. according to world bank, . million people could fall into extreme poverty by because of ar, most of them from lmics (jonas and world bank group team, ) . consequently, besides a global health problem, ar has an important economic impact (rudholm, ) , hence constituting a global development problem, endangering not only the achievements toward the millennium development goals but also the sustainable development goals (van der heijden et al., ). world bank estimates that ar could impact the gross domestic product from to . %, which is even higher than what is estimated for the climate change (jonas and world bank group team, ) . these economic foresights are linked to the threads of increased poverty, food sustainability, global health deterioration (associated with both food safety and affordability to health care), and environment protection. all these issues are also impacted by the overuse and misuse of antibiotics, its lack of effectiveness, and the affordability to medicines and health care (van der heijden et al., ) . when talking about reducing antibiotic consumption, it is important to remind that up to two-thirds of overall antibiotic usage is for animal husbandry (done et al., ) . further, recent work states that the use of antibiotics in crops, particularly in lmics, might have been largely underestimated (taylor and reeder, ) . despite that evidences on the presence of common args distributed among animals and humans were published decades ago wegener et al., ; aarestrup, ; aarestrup et al., ) , and although the use of antibiotics as growth promoters has been banned in different countries (cox and ricci, ) , they are still allowed in many others (mathew et al., ) . of relevance is the fast increase of antibiotic consumption for animal food production in china ( % in ) and other brics countries . as stated previously, in these countries, increased income has produced a fast increase in meat products demand, due to changes in diet of their population. in addition, the increasing international competitiveness in meat production of these countries has fostered the rampant development of their industrial farming. together with the fact that legislation on antibiotics use remains weak, this situation increases the risk of emergence of ar linked to animal production. nevertheless, the problem is not restricted only to lmics, because antibiotics consumption rose as well in the highincome countries as the united states ( %) , where approximately % of the antimicrobials purchased in were applied in livestock production as non-therapeutic administration (done et al., ) . the development of intensive methods of fish production has also contributed to the rise in the use of antimicrobials and the selection of resistance determinants that can be shared among fish and human bacterial pathogens (cabello et al., ) . economic development has facilitated as well more global transport, waste disposal, and tourism, favoring ar spread within and between different geographical areas (ruppe et al., a; ruppe and chappuis, ) . however, economic growth can also reduce the ar burden, especially when it enables the development of regulations and infrastructures that might reduce the risks of infection and ar spread. this is particularly relevant in the case of public health interventions on food, water, and sewage. because ar pathogens are mainly introduced in natural ecosystems through the release of human/animal stools (karkman et al., ) , the best way of reducing this impact is through the use of wastewater treatment plants, which are still absent in several places worldwide. indeed, it has been described that drinking water is a relevant vehicle for the spread of arbs in different countries (walsh et al., ; fernando et al., ) and that raw wastewater irrigation used for urban agriculture may increase the abundance of mobile args in the irrigated soil (bougnom et al., ) . notably, the analysis of args in wastewaters has shown that the prevalence of args in the environment in each country might be linked to socioeconomic aspects mainly related to economic development, as general sanitation, particularly the availability of drinking and wastewater treatments, malnutrition, number of physicians and health workers, human overcrowding, or external debt grace period (hendriksen et al., ) . the field of ar has mainly focused in the mechanisms of selection; the main driver for the increased burden of ar would be then the use of antibiotics itself. however, these results indicate that transmission, even in the absence of direct human-to-human contact, might be, at least, equally relevant. in this situation, an important element to reduce the ar burden will be to break the transmission bridges among different ecosystems that could be reservoirs of args. even when wastewater-treatment plants are available, the presence of arbs in drinking, fresh, and coastal waters, as well as in sediments nearby industrial and urban discharges, has been described in several countries (ma et al., ; leonard et al., ) . as in the case of fecal contamination markers, a reduction in the amount of args to non-detectable levels would be extremely difficult even when advanced water treatment procedures are applied. a standard definition of polluting arb/arg markers, as well as their acceptable levels, is then needed. this would be required not only for potable water, but also for water reutilization, as well as for land application and release of sewage effluents, because in all cases the reused water/sewage may carry arbs and args, together with pollutants, such as antibiotics, metals, biocides, or microplastics, which, as above stated, may select for ar (baquero et al., ; moura et al., ; yang et al., ; zhu et al., ; larsson et al., ; imran et al., ; wang et al., ) and may even induce hgt. the examples discussed above justify that human health in general and ar in particular are closely interlinked with economic development (sharma, ) . economic differences are also found at individual level, because there is a positive relationship between economic status and health (tipper, ) . in addition, social behavior might also impact ar, a feature discussed in the following section. different socioeconomic factors can modulate the spread of infective bacteria in general and of ar in particular. among them, the increasing crowding of humans and foodborne animal populations favors transmission at the local level (one health), whereas trade of goods and human travel (figure ) favor worldwide transmission (global health) (laxminarayan et al., ; hernando-amado et al., ) . besides these global changes in social behavior, linked to economic development, more specific socioeconomic factors (income, education, life expectancy at birth, health care structure, governance quality), sociocultural aspects (inequalities, uncertainty avoidance, integration of individuals into primary groups, gender biases, cultural long-term orientation), and personality dimension highly influence antibiotic use and ar transmission (gaygısız et al., ) . for instance, although the governance quality seems to be the most important factor associated with a proper antibiotic use, western countries with distinct national culture patterns show different levels of antibiotics consumption (kenyon and manoharan-basil, ) . a better understanding of human social responses facing ailments, especially epidemics and antibiotic use, requires then a more detailed analysis of the differences between collectivistic (individuals living integrated into primary groups) and individually long-term oriented societies (oriented to future individual rewards) (hofstede, ; gaygısız et al., ; kenyon and manoharan-basil, ) . consistent with the sociological elements of ar, many of the aspects influencing ar reviewed above depend on social norms (figure ) . in the classic view of the psychoanalyst erich fromm presented in his book "escape from freedom" (fromm, ) , human individual behavior is oriented to avoid being excluded from a higher social group. indeed, not following social common rules can be eventually considered as a mental disorder; a sociopathology. a social norm is defined as a predominant behavioral pattern within a group, supported by a shared understanding of acceptable actions and sustained through social interactions within that group (nyborg et al., ) . in democratic societies, laws usually derive from already accepted social norms; otherwise, they would be changed, and in that sense, the establishment of accepted social norms for fighting ar is a prerequisite to implement the global approaches, based on worldwide rules, which are required for tackling this relevant problem. interestingly, the ar problem is a bottom-up process, where small emergent changes (in some type of individual patients, in some groups, in some locations) cumulatively escalate to gain a global dimension. frequently, that occurs by crossing tipping points, that is, points where the local ar incidence becomes significant enough to cause a larger, eventually global, health problem. because of that, the implementation of solutions should be adapted to the control of critical tipping points in the small groups of individuals to disrupt the bottom-up processes. however, as ar spread can occur everywhere and at any time, global surveillance and mechanisms of control should be implemented to prevent a top-down process of global ar expansion. individual selfishness for ar is the cornerstone of social norms. this concept was coined and developed by one of us over a decade ago (baquero, ) . let us imagine that each individual is aware that each consumption of an antibiotic increases the personal risk of himself/herself or for his/her closer relatives (frequently exchanging microorganisms) of dying because of an antibiotic-resistant infection. the situation is analogous to the consumption of cholesterol-rich or highly salted food, or drinks with excess of sugar, concerning individual health. however, in the case of ar, it requires the understanding of the impact of individual actions at the global level. in this respect, anti-ar social actions should resemble more antitobacco and even general pollution/ecological campaigns. at the individual level, there is inertia that precludes changing habits, until a tipping point is crossed and health is compromised. the conclusions of studies mainly based on long-term cohort analysis, such as the framingham program for the influence of diet or smoking on personal cardiovascular disease (mahmood et al., ) , have become social norms that are naturally imposed by the ensemble of individuals. this creates a kind of societal culture, leading to appropriate individual behaviors, in occasions without the need of specific laws (diet), in occasion favoring the implementation of such laws (antismoking). however, we lack similar studies on issues such as these dealing with personalfamiliar risks that have successfully shifted social norms, driven by groups of individuals and based on the promotion of individual behaviors in the case of ar. despite that quantitative models on how individual antibiotic use may impact ar at the population level are still absent, it is worth mentioning that a reduced antibiotic consumption has also begun to occur in a number of countries just as a result of a change in individual behavior (edgar et al., ) , and some tools and indicators to address these changes have been suggested (ploy et al., ) . the "tragedy of the commons" metaphor, first proposed in the xix century (lloyd, ) and later on discussed in (hardin, ) , has been used for addressing the sociology of ar, by showing how individual selfishness promotes antibiotic use, increases resistance, and influences the health of the community by impairing antibiotic efficacy (baquero and campos, ; foster and grundmann, ) . ensuring the prestige of individuals that follow the social rules is needed to counteract the tragedy of the commons. nevertheless, it is important noticing that the tension between individual freedom and social rules that is inherent to the construction of democratic societies (tocqueville, ; hobbes, ; rousseau, ; spinoza, ) also applies here. one example of this situation is vaccination, considered in the last century as one of the most important advances to fight infectious diseases and now being the focus of antivaccination campaigns (megget, ) , a movement that has been considered by the who as one of the top global health threats of . it is commonly accepted that social norms are mainly created by learning and education, a rational path that promotes health (chen and fu, ) . also, the increasing activities of "personalized medicine, " including antibiotic stewardship, follow the same trend (gould and lawes, ) . however, the antivaccination movement is an example of how the narrative, as well as the use of decentralized, social information channels such as the internet search, blogs, and applications to facilitate communication such as twitter, facebook or whatsapp, is of particular relevance in the construction of social norms, not necessarily based on scientific and rational grounds (jacobson et al., ; scott and mars, ) . the impact of social norms goes beyond human societies as human activities alter natural ecosystems; consequently, humans cannot be aliens of nature. we should then shape a socioecological system, linking the individuals, the groups, and the entire society, as well as natural ecosystems, also potentially damaged by ar, in a common multilevel adaptive system based on social norms and policies at the individual, local (one health), and global (global health) scale (levin et al., ) . the recent crisis of covid- illustrates the influence of social norms in the individual behavior. each one of the individuals, protecting himself/herself, also protects the others. a person not wearing on face mask is frowned upon, and on the contrary, somebody attaching to the rules increases reputation. the individual adopts the right behavior being influenced by the judgment. of others. in addition, different political regimes (democracy or autocracy), as well as their organization (centralized, federal), together with the capacity of the health services to support the norms and their efficacy to communicate the chosen policy to the citizenry, may shape the individual responses to social norms (greer et al., ; häyry, ; kavanagh and singh, ) . notwithstanding, two reasons that have been proposed to explain the low prevalence of covid- in japan were related with social norms more than with biological issues. these reasons, which are not common to other countries, were the socially accepted use of face masks and the mandatory vaccination of all the population against tuberculosis, which might protect from sars-cov- infection (iwasaki and grubaugh, ) , a feature that is still to be confirmed. the loss of social prestige of individuals taking antibiotics without prescription, as well as the pharmacies delivering these drugs or do not respect environmental protection, or the overconsumption of antibiotics in hospitals or in farms, or even in certain countries, is progressively constituting a "social norm, " converted in rules able to reduce ar emergence and spread. of course, family and school education, as well as governmental campaigns, including the use of social media (grajales et al., ) reinforces such social norms, which could allow the support of the society for the implementation of different interventions, some of them described below. controlling resistance not only requires establishing local interventions, which could be relatively easily implemented, but would also require global interventions that every country should follow, despite their disparate regulatory systems. local and global interventions are necessarily intertwined; for example, the use of a new drug to treat a single individual depends on regulations at the county level (one health approach), but the worldwide prevalence and transmission of resistance to this drug, as well as the regulations of its use, should be established internationally (global health approach). three main interventions to tackle ar have been historically considered: first, reduction of the antibiotic selective pressure by decreasing antimicrobials use; second, reduction of transmission of arbs using improved hygienic procedures that prevent spread; third, development of novel antimicrobials with limited capacity to select arbs or the design of new treatment strategies based on use of non-antibiotic-based approaches or, more recently, on the exploitation of trade-offs associated with ar evolution (imamovic and sommer, ; gonzales et al., ; barbosa et al., ; imamovic et al., ) . these interventions have been basically limited to local initiatives, applied mainly to hospitals and, more recently, to farms. however, ar has emerged and spread globally, in bacteria from different environments, so the health and dynamics of the global microbiosphere could be affected by antibiotics. in a sense, ar is affecting the planetary health (lerner and berg, ) , and the needed interventions for tackling this problem cannot be restricted to hospital settings (figure ) . the proposed reduction in the use of antibiotics (blaskovich, ) must be compensated with alternative approaches for fighting infectious diseases. in this regard, strategies based on improving the capability of the immune system for counteracting infections (levin et al., ; traven and naderer, ) or the use of non-antibiotic approaches to prevent them, such as vaccines (jansen and anderson, ) , may help to reduce the burden of ar infections. indeed, vaccination against haemophilus influenzae and streptococcus pneumoniae has been demonstrated to be an effective intervention for reducing ar (jansen and anderson, ) . however, while vaccination has been extremely useful to prevent viral infections, it has been less promising in the case of bacterial ones. recent approaches, including reverse vaccinology, may help in filling this gap (delany et al., ; ni et al., ) . moreover, vaccination should not be restricted to humans, because veterinary vaccination can also contribute to animal wealth and farm productivity (francis, ) . besides, the use of vaccines in animal production reduces the use of antibiotics at farms/fisheries, hence reducing the selection pressure toward ar. other strategies to reduce antibiotic selective pressure include the use of bacteriophages (a revitalized strategy in recent years) (viertel et al., ; forti et al., ) , not only in clinical settings, but also in natural ecosystems (zhao et al., b) , as well as the use of biodegradable antibiotics (chin et al., ) or adsorbents, able to reduce selective pressure on commensal microbiome (de gunzburg et al., . besides reducing the chances of selecting arbs, the use of antibiotics adsorbents may preserve the microbiomes, reducing the risks of infections (chapman et al., ) . importantly, the procedures for removing antibiotics should not be limited to clinical settings, but their implementation in wastewater treatment plants would reduce selection of ar in non-clinical ecosystems (tian et al., ) . concerning the development of new antimicrobials (hunter, ) , while there is a basic economic issue related to the incentives to pharmaceutical companies (sciarretta et al., ; theuretzbacher et al., ) , the focus is on the possibility of developing novel compounds with low capacity for selecting ar (ling et al., ; chin et al., ) . for this purpose, multitarget (li et al., ) or antiresistance drugs, such as membrane microdomain disassemblers (garcia-fernandez et al., ) , are also promising. furthermore, antimicrobial peptides, with a dual role as immunomodulators and antimicrobials, may also help fight infections (hancock et al., ) . in fact, some works figure | local and global intervention strategies to tackle ar and knowledge gaps that could help improve existing ones. most interventions for reducing antibiotic resistance are based on impairing the selection of arbs/args, which is just the first event in ar spread. our main goal, as for any other infectious disease, figure | continued would be reducing transmission. this does not mean that selective pressure is not relevant for transmission. indeed, without positive selection, hgt events are not fixed, allowing the enrichment of some args that are consequently more prone to diversification, both because they are more abundant and more frequently subjected to selection (davies, ; martinez, a,b; salverda et al., ) and because they can explore different landscapes when present as merodiploids in multicopy plasmids (rodriguez-beltran et al., ) . therefore, reducing the selective pressure, either due to antibiotics or by other coselecting agents as heavy metals, still stands as a major intervention against ar emergence and transmission. to address this issue, we need to know more on the amount of pollutants, their selective concentrations, and their mechanisms of coselection and cross-selection in different ecosystems. this is a general example illustrating the gaps in knowledge in the ar field that need to be filled as well as strategies that may help in tackling this problem. the figure includes several other examples of the gaps of knowledge (red) that require further studies and the interventions (blue) that may help to tackle ar. have shown that arb frequently present collateral sensitivity to antimicrobial peptides (lázár et al., ) and that, importantly, some antimicrobial peptides present limited resistance or crossresistance (kintses et al., ; spohn et al., ) . from a conservative point of view, based on the use of the drugs we already have, it would be desirable to fight ar using evolution-based strategies for developing new drugs or treatment strategies. regarding this, the exploitation of the evolutionary trade-offs associated with the acquisition of ar, as collateral sensitivity, could allow the rational design of treatments based on the alternation or the combination of pairs of drugs (imamovic and sommer, ; gonzales et al., ; barbosa et al., ; imamovic et al., ) . in addition to interventions that reduce the selective pressure of antibiotics or that implement new therapeutic approaches, reducing transmission is also relevant to fight infections. the development of drugs or conditions (as certain wastewater treatments) able to reduce mutagenesis or to inhibit plasmid conjugation may also help in reducing the spread of resistance (thi et al., ; alam et al., ; lin et al., ; lopatkin et al., ; valencia et al., ; kudo et al., ) . besides specific drugs to reduce the dissemination of the genetic elements involved in ar, socioeconomic interventions to break the bridges that allow transmission between individuals and, most importantly (and less addressed), between resistance entities (hernando-amado et al., ) are needed (figure ) . more efficient animal management, not only allowing less antibiotics use but also reducing animal crowding (and hence ar transmission), as well as improved sanitation procedures, including the universalization of water treatment, will certainly help in this task (berendonk et al., ; manaia, ; hernando-amado et al., ) . notably, wastewater treatment plants are usually communal facilities where the residues of the total population of a city are treated. hospitals are the hotspots of ar in a city; hence, on-site hospital (and eventually onfarm) wastewater treatment may help to reduce the pollution of communal wastewater by antibiotics and arbs (cahill et al., ; paulus et al., ) , hence reducing ar transmission. concerning trade of goods, it is relevant to remark that, although there are strict regulations to control the entrance of animals or plants from sites with zoonotic of plant epidemic diseases (brown and bevins, ) , there are no regulations on the exchange of goods from geographic regions with a high ar prevalence, a feature that might be taken into consideration for reducing the worldwide spread of ar. once arbs are selected and disseminated, interventions based on the ecological and evolutionary (eco-evo) aspects of ar lehtinen et al., ) should be applied to restore (and select for) susceptibility of bacterial populations, as well as to preserve drug-susceptible microbiomes in humans and in animals . eco-evo strategies include the development of drugs specifically targeting arbs. for that, drugs activated by mechanisms of resistance, vaccines targeting high-risk disseminating resistance clones or the resistance mechanisms themselves (kim et al., ; ni et al., ) , or drugs targeting metabolic paths that can be specifically modified in arbs ) might be useful. the use of bacteriovores such as bdellovibrio to eliminate pathogens without the need for antibiotics has been proposed; although its utility for treating infections is debatable, it might be useful in natural ecosystems (shatzkes et al., ) . more recent work suggests that some earthworms may favor the degradation of antibiotics and the elimination of arbs (wikler, ) , a feature that might be in agreement with the finding that arbs are less virulent (and hence might be specifically eliminated when the worm is present) in a caenorhabditis elegans virulence model ruiz-diez et al., ; paulander et al., ; olivares et al., ) . however, the information on the potential use of worms for reducing ar in the field is still preliminary and requires further confirmation. noteworthy, ar is less prone to be acquired by complex microbiomes (mahnert et al., ; wood, ) , a feature that supports the possibility of interventions on the microbiota to reduce ar. among them, fecal transplantation (chapman et al., ; pamer, ) or the use of probiotics able to outcompete arbs (keith and pamer, ) has been proposed as strategies for recovering susceptible microbiomes. the recent crisis of covid- (garrett, ) resembles the pandemic expansion of args and clearly shows that pandemic outbreaks cannot be solved by just applying local solutions. further, unless all population is controlled, and comprehensive public-health protocols are applied to the bulk of the population, such global pandemics will be hardly controlled. the case of covid- is rather peculiar, because we are dealing with a novel virus. very strict interventions have been applied, mainly trying to control something that is a novel, unknown, disease; we have been learning along the pandemic and still ignore what will come further. ar is already a very well-known pandemic affecting humans, animals, and natural ecosystems (anderson, ; verhoef, ) . in this case, we have tools that might predict the outcome, and likely because the degree of uncertainty is lower than in the case of covid- , we have not applied clear, common, and comprehensive procedures to reduce the spread of ar. it is true that we know the evolution of antibiotics consumption and ar prevalence in several countries, and also interventions, mostly based on social norms, have been applied. social norms have reduced the unnecessary prescription of antibiotics, or pharmacy sales without prescription, and the use of antibiotics for fattening animals has been banned in several countries, being still allowed in several others. nevertheless, these actions are not general, and more aggressive, global actions are still needed. coming back to the covid- example, while the aim of health services worldwide is to detect any possible source of sars-cov- , surveillance of infections (eventually by arbs) is not universal. in other words, it does not apply to all citizens in all countries. the reasons can be just political such as the inclusion of immigrants in public health services (scotto et al., ) or the consequence of limited financial resources and technical capacity that countries such as those belonging to the lmic category can face (gandra et al., ) . the problem is not only on citizens, because different non-human reservoirs, such as wastewater, drinking water, or freshwater, may jointly contribute to ar dissemination (hendriksen et al., ) . in this regard, it is important to highlight that low quality of water is regularly associated to poverty. universalization of health services, sanitization, access to clean water, and in general reduction of poverty are relevant step-forward elements for reduction of the burden of infectious diseases in general and of ar in particular. the time has come to tackle ar, and this cannot be done just by taking actions at the individual or even country level, but by taking convergent actions across the globe. as stated by john donne ( ) in his poem, "no man is an island, " written after his recovery from an infectious disease (likely typhus): "no man is an iland, intire of itselfe; every man is a peece of the continent, a part of the maine; if a clod bee washed away by the sea, europe is the lesse, as well as if a promontorie were, as well as if a manor of thy friends or of thine owne were; any mans death diminishes me, because i am involved in mankinde; and therefore never send to know for whom the bell tolls; it tolls for thee." this reflection on how infectious diseases in general should be faced by the society was published at , but the idea behind still applies nowadays, especially for ar. all authors have contributed to the concept of the review and in its writing. jm was supported by grants from the instituto de salud carlos iii [spanish network for research on infectious diseases (rd / / )], from the spanish ministry of economy and competitivity (bio - -r) and from the autonomous community of madrid (b /bmd- ). work in tc and fb laboratory was supported by grants funded by the joint programming initiative in antimicrobial resistance (jpiamr third call, starcs, jpiamr -ac / ), the instituto de salud carlos iii of spain/ministry of economy and competitiveness and the european development regional fund "a way to achieve europe" (erdf) for co-founding the spanish r&d national plan estatal de i + d + i - (pi / ), ciberesp (ciber in epidemiology and public health; cb / / ), the regional government of madrid (ingemics-b /bmd- ) and the fundación ramón areces. the funders did not have any role neither in the design, nor in the writing of the current review. association between decreased susceptibility to a new antibiotic for treatment of human diseases, everninomicin (sch ), and resistance to an antibiotic used for growth promotion in animals surveillance of antimicrobial resistance in bacteria isolated from food animals to antimicrobial growth promoters and related therapeutic agents in denmark reca inhibitors potentiate antibiotic activity and block evolution of antibiotic resistance card : antibiotic resistome surveillance with the comprehensive antibiotic resistance database call of the wild: 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genes and mobile genetic elements in metal polluted urban soils comparing polyvalent bacteriophage and bacteriophage cocktails for controlling antibioticresistant bacteria in soil-plant system microbial mass movements from "one medicine" to "one health" and systemic approaches to health and well-being key: cord- - q ujnjq authors: sanderson, william c.; arunagiri, vinushini; funk, allison p.; ginsburg, karen l.; krychiw, jacqueline k.; limowski, anne r.; olesnycky, olenka s.; stout, zoe title: the nature and treatment of pandemic-related psychological distress date: - - journal: j contemp psychother doi: . /s - - - sha: doc_id: cord_uid: q ujnjq the covid- crisis has created a “mental health pandemic” throughout the world. scientific data are not available to fully understand the nature of the resulting mental health impact given the very recent onset of the pandemic, nevertheless, there is a need to act immediately to develop psychotherapeutic strategies that may alleviate pandemic-related distress. the psychological distress, in particular fear and sadness, is a function of the pandemic’s negative impact upon people’s ability to meet their most basic needs (e.g., physical safety, financial security, social connection, participation in meaningful activities). this paper presents evidence-based cognitive behavioral strategies that should prove useful in reducing the emotional suffering associated with the covid crisis. mental health issues such as anxiety, depression, substance abuse, and suicide were increasing in the u.s. well before the pandemic (substance abuse and mental health services administration ). thus, it is no surprise that the very recent "mental health pandemic" as a result of covid- (covid) will further accelerate the increasing prevalence of these disorders (marques et al. ; strakowski et al. ) as a result of its impact upon people's day-to-day functioning (brooks et al. ) . indeed, a recent survey by the kaiser family foundation found that percent of people reported that the worry or stress tied to covid had a negative effect on their emotional well-being (panchal et al. ) . moreover, many individuals may attempt to cope with these negative psychological effects in unhelpful ways (e.g., alcohol/ substance use) that can actually result in an increased susceptibility to covid- (da et al. ; volkow ) . clearly, the covid crisis is likely to have an enormous negative impact upon mental health if left ignored. the pandemic has disrupted the ability to satisfy core human needs in almost all areas to an alarming extent (e.g., brooks et al. ) . much of the population is worried about meeting their most basic needs (e.g., paying rent, buying food) as a result of economic hardship (e.g., unemployment) as well as an increasing scarcity of resources (e.g., food, cleaning products, personal protective equipment such as masks). people are living in a chronic state of fear of contracting the virus. socially distancing and disconnecting rather than affiliating has increased loneliness and decreased social support, particularly in elderly and disabled populations and those with underlying health conditions. the artificial substitutes for social connection such as online video events often exacerbate, rather than relieve, the feeling of disconnection. people have been removed from the sources of activity that allow them to feel esteem, status, and pleasure (e.g., work, graduation ceremonies, weddings, engaging in sporting activities). the impact upon dating and finding a mate is profound in an era of remaining six feet from others and fearing any close contact may lead to transmission of the virus. finally, for those who are parents, the stress of this role is enormous (e.g., home schooling, explaining the pandemic to young children), and certainly the idea that children will flourish in the present environment seems implausible. given the sudden onset and impact of the pandemic, scientific data are not available to fully understand the nature of the resulting psychological distress, but existing research suggests anxiety, depression, and worsening stress are common reactions (rajkumar ) . people are suffering and reaching out for assistance-there was a need to act immediately in order to develop strategies that may alleviate psychological distress. typically, when we produce a paper or treatment manual we spend months planning, writing, and reviewing it before making it available to others. given the rapidly evolving mental health crisis that occurred, we produced an initial product after only weeks of the first coronavirus cases in new york, which we continued to revise as we learned more about covid-related problems (cf. sanderson et al. ) . to develop this guide, we brainstormed using our clinical observation skills to identify pandemic-related triggers and resultant psychological problems we were seeing in our patients, family, friends-and our own lives. thus, we are confident that the areas identified in the original document ) represent the spectrum of covid related psychological distress. once we created this list we developed strategies that would allow people to manage these negative emotional states using a self-help format (this guide can be accessed at www.psych rescu e-covid .com or at the permanent doi address provided in the reference section). this self-help guide can be used in conjunction with the current paper, which more concisely outlines therapeutic strategies, to maximize the effectiveness of one's intervention. nearly all of the strategies that we included were taken from evidence-based psychological treatments for individuals with anxiety disorders, depression, and related emotional distress (table ). the approach we used is identical to that which led to the development of a variety of evidence-based treatment manuals for psychological disorders (e.g., panic disorder, depression) where basic cognitive behavioral strategies were tailored to address the specific psychopathology of the disorder. we expected that these strategies would prove useful for those suffering from similar emotional states secondary to the challenges associated with the covid crisis. in fact, since so many individuals are struggling as a direct result of the covid crisis, we have started to conceptualize these symptom clusters as a pandemic-related stress disorder (prsd) . while there has been progress, as outlined above, in understanding the nature and interventions for covid related psychological distress, an additional problem has emerged as a result: the already overburdened mental health system must now provide treatment for a substantial wave of persons in need. similar to the concern of flattening the curve for medical disorders to avoid overburdening the healthcare system, mental healthcare may find itself in the position of having more patients than can be reasonably accommodated (marques et al. ) . in fact, it is probable that this substantial increase in patients will last well beyond the pandemic itself (fiorillo and gorwood ) . many individuals, particularly younger generations, are table summary of commonly encountered distress provoking triggers and recommended evidence based therapeutic strategies stimulus control experiencing significant consequences of the economic crisis (e.g., financial uncertainty) that will take considerable time to resolve. a national survey conducted by the national center for health statistics indicated that approximately % of americans reported experiencing symptoms of an anxiety or depressive disorder during the end of may into june , when several states had already started to reopen (cdc ). furthermore, the process of reopening in itself may result in increased feelings of anxiety. as individuals have become accustomed to staying at home for safety, beginning to reintegrate into society is nerve-wracking for many; psychologists have started to refer to these fears as "re-entry anxiety" (dusharme ) . moreover, the centers for disease control and prevention alerted that the second wave of covid- is likely to be far more devastating than the first (sun ). as a result, in line with the suggestions of marques et al. ( ) , we have been examining scalable psychotherapeutic intervention models to increase our proactivity, reach out to those with distress, and attempt to decrease the likelihood of more severe responses later on. schleider ( ) has developed and tested brief, accessible interventions delivered in non-traditional settings (i.e., telepsychology). she found that a single session of a solution-focused consultation was associated with a reduction in psychological distress in adults seeking psychotherapy ). thus, we adopted her approach and have developed and are in the process of field-testing a consultation-oriented intervention (rather than a more traditional "psychotherapy" model) consisting of two -min telepsychology online video sessions (cf. limowski et al. ) . the focus of the first session is to identify factors that appear to be causing the most distress and providing evidence-based strategies for the client to utilize. the focus of the second session, held approximately one week later, is to assess the success of the initial recommendations and to provide additional strategies if necessary. based upon the results of our field-testing we may ultimately increase the number of sessions in this intervention. fear is an emotion provoked by the perception of danger or threat that evolved to protect us and enhance our ability to survive. given that the core concerns of this pandemic are about illness and death, fear is an expected emotion. the first step in working with pandemic-related fear is to validate the person's emotional experience, within reason. it is also important to help the person understand that fear can become one's ally rather than something to get rid of. when channelled appropriately, fear protects the individual as well as others by leading to protective behaviors such as hand washing, mask wearing, social distancing, and minimizing non-essential activities. individuals with obsessive-compulsive disorder (ocd), many of whom hold contamination fears independent from covid, may be particularly impacted by widespread concern over the coronavirus and may require specific adjustments to treatments (fontenelle and miguel ) . however, that being said, what can be modified is one's level of fear. many are at a panic level of fear, meanwhile, the overwhelming majority of people are in fact not overly vulnerable to covid. for those individuals, the following should become their guiding principle: covid- will pass, humankind will survive, almost everyone will still be alive in its aftermath. the scientific evidence clearly supports this statement. to varying degrees media (television, newspapers, social media, websites) coverage of events such as the covid crisis increases one's perception of risk (ropiek ) . there is an old saying in the media: if it bleeds, it leads. the idea is the more horrific the story (e.g., the more frightening), the more likely it will be the headline and receive a lot of time or space in the way the media source covers it. thus, media outlets are biased towards presenting the most threatening scenarios (people dying on ventilators, overfilled morgues, stories of the sickest patients, etc.) and not focused on alternative information which may present a more balanced or nuanced view (e.g., interviewing tens of thousands of people who had no or mild symptoms-overwhelmingly the typical course of covid-or even people that were fairly sick who recovered). consequently, these messages shape the general public's reality of the covid crisis as overall more threatening than it is because of the biased information. it is also worth noting that it is not uncommon for false information to be spread by social media. the news media can be viewed as a stimulus that triggers a certain response (immediate fear, skewed beliefs). since this stimulus is something that everyone does in fact have control over the recommended strategy is stimulus control (borkovec et al. ; mcgowan and behar ) : reduce or eliminate exposure to the stimulus to prevent the undesirable response. while one needs to be informed, watching or reading the news for approximately - min per day should be sufficient to keep up with the necessary information. accurate, non sensationally-oriented, print media is recommended. the johns hopkins coronavirus resource center (https ://coron aviru s.jhu.edu/) meets these criteria and thus, is a highly recommended source to avoid unrealistic risk perception. news from local and state health departments which present factual and locally-oriented information are other reputable sources through which individuals can stay informed. the topic of media information provides an excellent segue to perception of risk (danger). as discussed above, the media impacts beliefs about coronavirus in that it increases the perception of danger by presenting somewhat skewed information. with regard to the experience of fear, for the most part, the more dangerous one perceives something, the greater the amount of fear that is experienced. thus, the therapeutic goal is to help an individual develop accurate risk perception so that his or her fear is in proportion to the threat. the primary strategy to use is cognitive reappraisal (lazarus and alfert ; gross and john ) to identify, examine, and when appropriate reappraise the situation. clearly, coronavirus is a threat. but like most threats, it is not the same for everyone. it is essential to keep in mind that fortunately most everyone will survive coronavirus. the following are several examples of how media consumption distorts a person's risk perception because of the way information is presented: you see covid in extremes: either you do not get it, or you end up on a ventilator. there is no middle ground or shades of grey. you only focus on the worst cases. if a celebrity announces they are covid positive but only have mild or no symptoms, you forget about him or her. but if a celebrity is very ill, that is the example that sticks in your brain. you only focus on the worst outcome and personalize it: you are going to end up hospitalized with covid just because that is a possibility. you lose the distinction between possibility (anything is possible) and probability (what is likely to happen based upon knowledge of base rates). because you feel anxious about this highly contagious virus that everyone else is anxious about, you assume it is dangerous-just because you feel it is. watching media that displays cases and deaths like a scoreboard continues to exaggerate your anxiety further even though proportionally these are relatively low numbers compared to the entire population. central to human behavior is the motivation to stay aliveeven before the covid crisis. if evolution designed the mind for anything it is to guide human survival. as mentioned above, fear is the invariable reaction that occurs when a threat is perceived and it guides our behavior towards maximizing survival (e.g., avoiding and escaping from danger, reducing the threat). some individuals seem to want certainty about their risk and likelihood that nothing bad will happen. unfortunately, the fact is, there is no certainty that one will live beyond this moment. the probability for most everyone is that they will be here tomorrow-that is almost % certain. but since it is possible that something can happen at any moment, it is not a full %. that is a point that must be accepted. otherwise, attempting to gain certainty when it does not exist will exacerbate fear. the following three points are important to keep in mind as we try to help individuals to accept the existential reality of our existence and consequently decrease fear driven by the attempt of obtaining certainty: ( ) one can never be % certain that nothing will happen at any point in the future starting with now, ( ) we take risks every day living our lives, and there is no alternative; very few of us would want to live in a bubble to maximize our safety and give up our lifestyle, ( ) the best one can do is manage risks, not eliminate them fully. in the covid environment, one must ultimately confront death to move forward with some level of comfort. it is important to work towards accepting that we risk our survival every day so that we can live the life we want to live. the best one can do to manage their fear in the coronavirus landscape is to: ( ) acknowledge this reality, ( ) control whatever is reasonably possible (e.g., wear a mask while shopping, wash hands regularly, socially distance), and ( ) move forward and live life. we attempt to get people not to deny the possibility of death, but to do their best to attend to managing risk and focus on realistic probabilities. sadness (depression) is an emotional response that is primarily triggered by the occurrence of personal losses that are important to an individual and cannot easily be restored (e.g., loss of a job, failing a test) or in some instances are not able to be restored (irrevocable losses). these can be tangible losses, such as the death of a loved one or the breakup of a relationship, and they can be more abstract losses, such as failing to live up to one's expectations, or failing to have the marriage that one expected. the most severe form of sadness occurs when a person experiences, or perceives an experience, where the loss cannot be undone. the classic example is the death of a loved one (i.e., bereavement) where the loss is clearly irrevocable. however, it can also apply to a situation where a person believes (perceives) the loss is irrevocable; for example, a person who has a breakup of a relationship and truly believes he/she will never find anyone else. with regard to the pandemic, what most are feeling are the effects of transient losses. for example, if someone misses seeing their friends during this period of social distancing and quarantine, the fact that the sadness is experienced is in fact because what was lost is important. the degree of sadness mirrors the importance of the loss. when irrevocable loss occurs, or is perceived or believed to have occurred, the individual may go into a state of "resignation"-an evolved response to preserve energy when using effort would be futile (the loss is irrevocable so the person needs to adjust rather than continue to attempt to restore it). however, when the resignation is triggered by perceptions of irrevocable losses (e.g., the world is never going to survive this pandemic, there is no way to fix the economy-it will be bad forever, i'll never see my friends again), it can lead to a state of resignation characterized by hopelessness and helplessness. these two states, as well as several other triggers of sadness, end up contributing to and maintaining the intense sadness, and people end up in a downward spiral from which it is difficult to escape. when helping people manage their sadness, the goal is to build their resilience, their ability to increase behavior to access what is important to them. individuals may begin to experience an overwhelming lack of hope for the future as a result of the negative impact of the pandemic and the constant flooding of bleak news reports. while there are many unknowns, it is relatively certain that the transition back to our accustomed lives will not happen in the immediate future. this realization understandably adds to an individual's experience of hopelessness and depressive resigning behavior. as mentioned previously, stimulus control is recommended in order to combat feelings of hopelessness. although it is unhelpful, attending to negative news is in our nature. checking the news frequently may be contributing to hopelessness, even in hopes of more positive announcements. we are often reinforced to check more often due to intermittent segments of uplifting news, or anticipation of positive news, even if the overall message conveyed is overly negative. as aforementioned, individuals are recommended to limit covid- related news consumption to a specified amount (i.e., once a day for min) and are urged to use accurate, non-sensationalized sources (borkovec et al. ; mcgowan and behar ) . reappraisal of hopeless attitudes towards our current situation is also recommended as it is important to keep the reality in mind that for the most part these pandemic-related stressors are not permanent, although they may feel this way when one is in the midst of them. focusing on the notion that humans are resilient and have previously overcome countless tragic crises (e.g., recessions, war, epidemics) is also imperative to provide a context of hope and survival-rather than resignation. (note. for those in crisis, the national suicide prevention lifelife ( - - - or https ://suici depre venti onlif eline .org/chat/) is available / .) relatedly, helplessness is both the belief that a situation will not change and the belief that one is unable to enact change on a situation. in other words, individuals who feel helpless believe that there is nothing they can do to change their undesirable circumstances; they have been convinced that their hopeless feelings are true. unfortunately, helplessness may inadvertently create a self-fulfilling prophecy, that is one may behave in accordance with the predicted or expected outcome, thus creating a reality that confirms the faulty belief (e.g., if you do not study for an exam because you believe you will fail, you will in fact fail because you did not study, not because you were destined to fail). additionally, feeling helpless may result in all-or-nothing thinking (e.g., "if i cannot fix the economy, i shouldn't bother ordering takeout from a local restaurant to support them"). taken together, individuals are encouraged to reappraise allor-nothing thoughts (e.g., "the economy is doing poorly but i can do something to make a difference") and expand one's thinking to the "bigger picture" (e.g., "the economy is doing poorly but if everyone did something small, the scale of the impact would be enormous"). the pandemic might also be viewed as an opportunity to develop a new skill (e.g., sewing) that could be used to prompt supportive actions (e.g., distributing masks to others). with these changes in perspective, coupled with engaging in behaviors that are cognitively consistent, individuals can increase their sense of empowerment (i.e., the opposite of helplessness) and move out of the helpless frame. while many will experience grief related to a loss of a loved one due to covid- , this crisis has also introduced an array of non-bereavement related loss (e.g., loss of social connection, jobs, normalcy, economic stability). these losses have been found to instill a similar grief reaction, especially when the loss is directly associated with one's identity (papa et al. ) . the level and intensity of grief varies per individual, as do the order of the stages of grief (i.e., denial or avoidance, anger, bargaining, sadness, and acceptance). while grief reactions are expected as a result of pandemic-related loss, research on grief has indicated several strategies to cope with and process these losses. expressive writing in the form of identifying and naming the experienced loss can help individuals increase awareness of the associated emotions and recognize previous strategies that were effective in coping with that emotion in the past. after naming the losses, outlining ways to move forward in or amend those loss areas can help individuals accept their loss and work towards reproducing what has been lost (e.g., after job loss, reading or attending webinars on new innovations of your field; briggs and pehrsson ) . additionally, social support is largely indicated in grief interventions. while social distancing limits physical social contact, grieving individuals can still access social support. phone and online platforms can increase the social support experience through voice or video methods, in comparison to texting which can be less personal. global quarantine and social distancing regulations have resulted in significantly limited social contact. as a result, many individuals have started to socially and physically resign and are overwhelmed by upsetting thoughts related to loneliness. although these reactions are understandable, they typically exacerbate feelings of social disconnection. instead, individuals are encouraged to validate their feelings, challenge unhelpful thoughts, and problem solve in order to increase connection in novel ways . helpful strategies that can be used to think about the current regulations in a more balanced manner include: relabeling the current guidelines from "social distancing" to "physical distancing;" remembering that individuals are apart now so they can be together later; and reframing the situation as a time to focus on, build, and/or create meaningful relationships. several practical ways to increase connection include but are not limited to: zoom video chats, facetime, netflix movie parties, handwritten letters, video games, virtual exercise classes, online forums, online support groups, virtual game nights, virtual paint nights, virtual book clubs, hugging a stuffed animal, and purchasing long distance friendship lamps. loss of income and loss of social reinforcement are two ways the pandemic has decreased reinforcement among individuals (pfefferbaum and north ) . such losses can decrease effective behaviors leading to psychological distress and increase ineffective behaviors which pose health risks (e.g., socially isolating, avoidance, washing hands irregularly; brooks et al. ) . engaging in a range of activities that balance pleasure, mastery, and social connection is often most helpful for boosting reinforcement and promoting positive moods. for example, cooking different meals at home can be inherently enjoyable (i.e., flavorful food), result in a sense of achievement (i.e., learning a new recipe), and promote social connection (i.e., sharing the recipe or meals with others). with regards to health behaviors that individuals may struggle to implement (e.g., wearing a mask, handwashing), basic principles of contingency management can be used to increase the desired behavior. individuals can set goals for themselves, track their progress, and reward themselves when goals are met. this can be helpful to increase behaviors that are not immediately pleasurable, but are important to do in the current context. as the pandemic continues, many perceive a sense of meaninglessness due to uncontrollable circumstances (e.g., unemployment, decreased social interaction, and various other role losses). the disruptions in daily life lead many individuals to feel a loss of purpose which they normally derive from involvement in careers, caregiving, or other activities. therapeutic approaches that prioritize meaning have been shown to be effective in improving quality of life (breitbart et al. ) . relatedly, as aforementioned, cbt emphasizes increasing engagement in pleasant and masteryoriented activities as a general mood management strategy. a helpful strategy is for individuals to mourn the unavoidable role-related losses while simultaneously shifting focus to aspects in their control. individuals can connect purposefully with the world by engaging in hobbies, learning new skills, keeping a pandemic journal, or helping others. small contributions like phoning someone who lives alone, shopping for others, or donating to causes more directly (e.g., blood drives, buying supplies, fundraising) hold tremendous potential for cultivating a sense of meaning and are activities that can be safely conducted during social distancing efforts. individuals are being exposed to a deluge of negative information about a problem that-at least in the short term-has no clear solution. additionally, given that this negative information is relevant to the current public health crisis, it is unsurprising that individuals are more likely than ever to attend to it. initially, increased attention to negative information may appear to be solution-focused or goal-directed thinking and, due to the current crisis, individuals may be more likely to continue engaging in such behavior. however, individuals can easily become stuck in a cycle of ruminative (i.e., brooding and dwelling) thoughts about the current situation which results in exacerbated emotional distress, agitation, and/or sadness. while this reaction is unsurprising, self-monitoring is recommended to help individuals identify specific external cues (e.g., media consumption, speaking with a friend or relative who catastrophizes), emotional states (e.g., loneliness, sadness, boredom), and locations or times of day (e.g., isolated in home office, late at night) when ruminative thinking is more likely to occur again. increased awareness of cognitive, behavioral, and environmental triggers then creates a personalized guide for what cues the individual should remove or avoid from their environment (e.g., limiting news intake, schedule "socializing" breaks throughout the workday). however, it is important to note that if the "socializing break" is a virtual one; changing one's physical location during the call is crucial to differentiating this break from the workday (i.e., the work environment in one's home). thoughts of hopelessness and helplessness, rumination and worry, and overall negative thinking are expected when individuals are exposed to an overwhelming amount of negative information regarding the pandemic (i.e., death statistics, case increases, economic collapse). in combination with a predisposition to negativity bias, (ito et al. ) a pandemic undoubtedly exacerbates depressive thinking (i.e., negatively oriented news focused on dangers and losses). practicing gratitude is a recommended strategy that may help lessen our negativity bias by transferring a portion of our attention to positive stimuli. individuals can begin to assess what they are thankful for, and deliberately attend to simple moments of pleasure each day to transfer focus to contentment rather than loss. being mindful during pleasurable activities (i.e., recognizing emotions) and when engaging one's senses (i.e., taste of a meal) can help increase awareness of moments for which one can be grateful. similarly, increasing awareness of negative thoughts and of their frequency can help individuals notice the onset of the thought, and engage in a positively salient activity in order to halt the depressive thinking cycle. thought monitoring and cognitive reappraisal are particularly powerful ways to combat depressive thinking as outlined above. finally, engaging in physical exercise (see below for section on sedentary behavior) can be an excellent way to change thoughts through behaviors. guilt has been a frequent consequence of the pandemic. some may discover they tested positive for covid after they were in contact with others, some may be struggling with not being able to actively help during this crisis, healthcare workers may not be able to save patients, and some may be feeling more privileged than others. as a result, individuals are blaming themselves, questioning their behaviors, punishing themselves (whether intentionally or not), and resigning. to manage feelings of guilt, individuals are often encouraged to identify the source of their guilt, evaluate how much responsibility they have for it, take the appropriate amount of responsibility, make reparations for any harm they might have caused, and ultimately forgive themselves. additionally, engaging in prosocial behaviors is recommended (e.g., sending a care package to someone struggling, ordering takeout from local restaurants, reaching out to someone who might be lonely, making a donation) to help with thoughts about not doing enough and increasing one's sense of empowerment. shame occurs when individuals engage in reputation-damaging behaviors or those that have a heavy cost to society (cibich et al. ). in the current context, a positive covid status can be shame-inducing due to the stigma associated with being contagious, as well as the costs it has to society (i.e., potential of infecting others). shame can be problematic if the feeling is so intense that it negatively affects self-esteem and mental health (e.g., feeling worthless despite taking adequate quarantine precautions). shame can also lead to avoidance or ineffective behaviors (e.g., not telling housemates about positive test results). the first step to manage shame is to determine if it is justified or not. shame experienced from disease status per se is not justified, but other behaviors (e.g., not wearing a face covering when symptomatic) can be. shame can be functional if it guides one to rectify a negative behavior (i.e., informing others, taking precautions). for unjustified or excessive shame, identifying and acknowledging the emotion is the first step to reduce the intensity. next, individuals can identify behaviors driven by the emotion and engage in the opposite behavior (the 'opposite action' skill in dialectical behavior therapy; rizvi and linehan ) . to reduce the effects that shame has on self-esteem, it is important to first differentiate qualities of oneself that do not change from having the virus, and to identify and reframe "shame thoughts." for example, instead of not disclosing testing positive for the virus because of thoughts that they are "bad" or "dirty", individuals can be encouraged to disclose it to appropriate people in their lives and see themselves as "brave" and "proud" for socially isolating and taking steps to protect others, which is valuable to society. as aforementioned, the media frequently highlights biased information and often focuses on those who appear to be maximizing productivity and accumulating accolades during this pandemic. the tendency to make comparisons between these featured individuals and ourselves can lead to personal feelings of inadequacy, as well as attempts at radical behavioral changes with goals that may be difficult to attain, resulting in increased feelings of failure and reduced selfesteem (vogel et al. ). while it is common to engage in these comparisons, it may be more helpful to practice reappraisal, recognizing that those featured likely represent only a small percentage of the population, and that what is shown is highly selected for, thus leading to a biased perception (i.e., sitting on the couch and watching television is an activity many individuals participate in, but is not broadcasted as it is not especially attention-grabbing). additionally, rather than setting broad, ambitious goals that may be exceedingly difficult to achieve, focus should be on setting goals that are smaller, observable, specific, and measurable. research has shown that two key factors in maintaining commitment in working towards a goal include ( ) the belief that one can realistically attain the goal, and ( ) importance given to the outcome expected as a result of attaining the goal (locke and latham ) . thus, it is critical to set goals that are challenging enough to feel a sense of accomplishment when achieved, while not being overly onerous. lastly, specificity aids in accountability, and detailing what the goal is and how to measure it, as well as scheduling the time and day during the week to engage in goal-focused activity, can help facilitate action towards reaching a goal. collectively, the population is encountering an increase in daily and repeated frustration (i.e., achieving one's goals is either more difficult or currently impossible). frustrations may be the result of external (e.g., experiencing interrupted internet connection), internal (e.g., low self-confidence after failing to meet work deadlines), or particularly salient (e.g., specific cleaning supplies consistently being out of stock) daily experiences. experiencing frustration may lead to an increase in negative mood and result in maladaptive thinking such as, catastrophizing (e.g., "i am the worst employee ever"), overgeneralizing (e.g., "my internet never works"), and fortune telling (e.g., "if the cleaning product was out of stock at the first store, none of them will have what i need"). additionally, an individual's interpretation of any given event is influenced by a number of factors (e.g., current emotions, life circumstances, relationships, the weather, etc.) and tends to change over time. given the heightened level of emotional distress an individual may be experiencing, interpretation of neutral or even somewhat negative events as catastrophic is expected. cognitive reappraisal is recommended to shift the individual's perception of the increased meaning and significance of these negative events and ultimately decrease negative emotion. furthermore, encouraging individuals to reframe the situation which led to frustration in a more positive way or as an opportunity to increase effortful action and goal-directed behavior (e.g., problem solving) will be helpful. we propose the existence of a condition that can best be described as pandemic-induced claustrophobia; not claustrophobia in the traditional sense of the psychological disorder, but a unique feeling of discomfort related to being "trapped" at home. this "condition" may be particularly prevalent for those living in apartments, in cities where ample space is rare, and/or with several other people. such individuals may feel stir-crazy yet exhausted, exhibit negative affect, and be tempted to break social distancing policies. an effective mental strategy to combat pandemic-specific claustrophobia is cognitive reappraisal. in the current situation, this tactic can take the form of changing one's attributions for the quarantine: viewing staying inside as an intrinsically motivated behavior as opposed to a punitive decree from an external source. an example strategy is thinking of a specific person one knows who is a member of a high-risk population, and telling oneself that one's decision to stay inside is in the service of protecting this person. alternatively, some individuals may interpret stay-at-home orders as prohibitive of going outside even for fresh air or exercise. this type of appraisal may contribute to a feeling of being "trapped." by consciously reframing the situation (e.g., "i should limit my contact with others, but going for walks outside is acceptable"), individuals can feel a greater sense of agency and control over their current circumstances and reduce claustrophobic feelings that may be exaggerated from these misinterpretations. feeling stressed or overwhelmed is one of the most commonly reported emotional experiences of the pandemic; a cumulative effect of being faced with a variety of new challenging circumstances. this response is unsurprising, but also problematic, given that the body responds to stressful external circumstances with increased production of the hormone cortisol. elevated levels of cortisol are associated with numerous negative health consequences-including, ironically, diminished immune response. stress management is therefore crucial for both mental and physical well-being during the pandemic, and one major tool for combating the negative effects of stress is meditation (see section below on lifestyle factors for additional tools to help manage stress, most notably the section on exercise). in fact, numerous studies over recent decades have demonstrated the benefits of meditation for many facets of physical, emotional, and mental health (lynch et al. ). this practice may be particularly relevant at this time given that many individuals do not have access to their regular stress relief outlets (going to the gym, gathering with friends, etc.). an abundance of meditation-related offerings exist online, from formal training programs to guided mindfulness exercises. thus, the first step in establishing a meditation practice is taking the time to explore different meditation resources and determine what type of meditation one finds to be the best personal "fit." by cultivating an enjoyable and sustainable practice, individuals are more likely to remain consistent in their meditation, which is key for reaping maximum health benefits. more than ever, individuals are working from home and spending more time at home, leading to increased contact with families and roommates. stress-induced negative emotions, boredom, and irritability naturally contribute to more conflict in households. of note, incidents of domestic violence have substantially increased worldwide since the onset of stay-athome orders (boserup et al. ) . self-care methods and relaxation strategies can reduce irritability in the long-term, potentially making conflicts less likely to occur. conflict may arise from reductions in privacy or from disagreements about safety precautions due to variability in risk tolerance. individuals are encouraged to recognize that others differ in the extent to which they desire solitude as well as their comfort level in taking health precautions. while there are certain public health guidelines for navigating health behaviors, ideally households can be respectful in conversations and seek a compromise. specific communication strategies are also useful for anticipating, reducing, and navigating interpersonal conflicts. for example, it can be helpful to first become aware of emotions in the moment and take a "time out" as necessary (e.g., counting to , leaving the room) before responding. if tensions are still high, deciding on a future time to have discussions can be effective. communicating using "i" statements and making requests instead of demands are other helpful tactics for more effectively resolving disputes. (note. for anyone affected by abuse and needing support, call - - - , go to thehotline.org, or text loveis to - - - ). research suggests a strong positive relationship between sunlight and serotonin levels (lambert et al. ) , a neurotransmitter central to biological explanations of depression. the pandemic cancelled many outdoor events and shuttered businesses, workplaces, and other establishments. as a result, many are spending more time indoors, away from sunlight. sunlight can promote positive moods, so individuals should aim to get at least min of sunlight each day. this practice could take the form of walking around neighborhoods, sitting outside, or engaging with nature (e.g., hiking, walking near water). several of these suggestions can be combined with other pleasurable activities (e.g., reading, listening to podcasts, making telephone calls). if outdoor activity is still not possible, light therapy lamps can also have antidepressant benefits (kripke ). social distancing efforts are disrupting routines, leading to less daily structure and negatively impacting sleep. many individuals also report increased screen time and anxious thoughts at bedtime, making insomnia a problematic consequence of the pandemic. decades of research show that adequate sleep is necessary for physical health, immune functioning, and mental well-being. cbt for insomnia involves working with dysfunctional beliefs about sleep, utilizing stimulus control, and practicing good sleep hygiene. in addition to getting sunlight and physical exercise throughout the day, keeping a regular sleep schedule, engaging in a relaxing wind down routine, and limiting electronic use before bed are all helpful strategies. if individuals cannot sleep at night, they should go to another part of their home and do a calming activity until they feel sleepy, ensuring that bedrooms are used for sleep only. finally, anxious thoughts should be dealt with prior to bed time (e.g., worry time) and dysfunctional beliefs about sleep (e.g., catastrophic outcomes resulting from not achieving a "perfect" night's sleep) can be addressed with cognitive reappraisal and psychoeducation. telework and home entertainment-common during the pandemic-lead to prolonged sitting and a normalization of sedentary lifestyles. social distancing may greatly reduce individuals' activity levels, since gyms are closed and organized team sports are cancelled. even before the pandemic, many people failed to get the min/week of aerobic exercise recommended by the american heart association. however, physical activity promotes positive moods and can be protective against depression (schuch et al. ) so becoming more active is very important. activities such as walking, running, hiking, or indoor activities (e.g., fitnesscentered video games, zoom yoga classes) are all helpful. individuals who are beginning new exercise routines should consider physical activity as they would any new habit, emphasizing starting small and being consistent. for many, the pandemic has caused a prolonged increase in stress, which often leads to an increase in the consumption of highly palatable high-fat and high-sugar foods (adam and epel ) . the intake of calorically-dense foods has been found to stimulate the reward center of the brain, thus reinforcing this behavior by temporarily reducing negativeaffect. however, consequences of eating such foods include inflammation in the body, which has been linked to various health conditions such as depression (kiecolt-glaser ) . therefore, the strategy of eating such foods to manage stress and increase feelings of well-being is counterproductive. instead, more prudent strategies involve cognitive appraisal, deliberate behavioral changes, and awareness around stimulus control. for example, avoid purchasing these highly caloric foods, since reduced access will likely equate to decreased consumption. additionally, taking advantage of time at home by planning and preparing meals in advance can help override the tendency to reach for highly caloric foods when hungry or stressed. while social connection is of utmost importance during a period of social distancing, a distinct set of challenges related to boundary infringement emerged within the social lives of those asked to stay at home, work at home, and socialize from home. this change is in part a result of a prevalent aspect of the "new normal" which includes the utilization of videoconferencing platforms (e.g., zoom) for work meetings, academic classes, and social calls. individuals working from home were asked to do so within the context of unclear expectations (e.g., increased availability) and increased demands (e.g., homeschooling children). unsurprisingly, individuals struggling with the effects of boundary infringement may react by either withdrawing and avoiding particularly aversive work-related tasks or by being overly accommodating and working increased hours. however, neither of these responses is sustainable; avoidance often leads to increased anxiety and overworking often leads to burnout. a helpful strategy is to develop and implement a behavior management plan in order to set a metaphorical boundary between work and home, given that the physical boundary is no longer in place. in addition, despite the usefulness of video conferencing software, a newly-recognized phenomenon is "zoom fatigue," described in the media as a feeling of being disengaged during video conferences and/or mentally drained after signing off. virtual meetings lack many of the nuances that make in-person interactions feel connected and organic, while also presenting challenges such as internet connectivity issues, background noises, and awkward pauses or moments of cross-talk. as a result, those with many zoom obligations may emotionally withdraw, becoming less participative in work meetings and choosing not to join video calls with friends despite already feeling socially isolated. this unique brand of burnout can be combated with specific behavioral strategies aimed to help individuals re-engage with their zoom activities by treating virtual get-togethers the same way they would treat those events in real life. for example, to get into a "work" mindset, individuals should keep the same pre-work morning routine as they held before the pandemic, create one designated workspace in their home, and practice staying engaged in meetings by asking questions. to help maintain enthusiasm about virtual social activities, individuals should seek to create a clear delineation between work-related video calls and social video calls. this distinction can be accomplished by using different video apps for each kind of call, changing out of one's work clothes at the end of the day and into clothes one would normally wear for social events, and not taking social calls in one's designated workspace area. finally, individuals may benefit from reaching out to family and friends to process feelings of burnout, and recruiting loved ones to help hold them accountable. on the other hand, in the service of "staying connected," individuals may feel pressured to respond quickly to alerts on mobile devices or participate in virtual get togethers even when their time might be better spent in solitude. others may participate in virtual social events only to find themselves begrudgingly talking about news, politics, or the pandemic. for those who feel sufficiently connected, communicating clearly about feelings and intentions using assertive statements is important. setting appropriate boundaries with electronic communications can also be very helpful, either by silencing mobile notifications, lengthening delays before responding to others, or skipping virtual meetups all together if feeling socially "worn out." whatever approach is taken, increasing agency within communications may decrease feelings of resentment and, as a result, make socialization more fulfilling. to address these various concerns, our clinic has created a two-session consultation service for psychological distress related to covid (for materials, see limowski et al. ). the consultation service was advertised on the university clinic's website so that the link could be easily shared by students and faculty. the description is as follows: "in order to offer our expertise in helping individuals cope with psychological distress and emotional difficulties related to covid- , the staff of the anxiety and depression clinic (director: william c. sanderson, phd-a ny state licensed psychologist) is offering a consultation series consisting of two -min online sessions with an adc staff member." clients are asked to provide responses to questions that assess their current and pre-pandemic levels of fear, sadness, and emotional distress on a -point scale, identify and provide information about their most challenging pandemicrelated circumstance, and provide some information about their mental health functioning (e.g., past/current medication use, therapy, diagnosis). sessions are scheduled by email and take place over hipaa compliant zoom. our first session is based on the single-session model used by schleider ( ) and involves targeting one or two main problem areas with cognitive behavioral strategies. our clinic additionally offers a follow-up session one week later to further assist clients in utilizing strategies previously discussed. at time of writing, four clients have completed our brief consultation service. issues addressed most commonly involved managing job-related stress, setting healthy boundaries, practicing sleep hygiene, managing excessive worry related to uncertainties, and reducing alcohol consumption. while of course, these data are very preliminary given the small sample size, it is worth noting that self-report assessment conducted following the second session indicates that the consultation service was of value clients. specifically, clients reported experiencing approximately % reductions in fear, sadness, and general distress over the course of one week following the implementation of the recommended strategies. all clients rated the intervention as "very helpful" in addressing their concerns and developing an action plan (both rated as on a point scale). similarly, therapists conducting these sessions believed they were effective in administering a very focused, useful intervention. these data are promising with regard to delivering a remote, scalable, and effective intervention for those suffering from pandemicrelated psychological distress. as is evident, many individuals are struggling with a plethora of covid-related triggers; however, a variety of therapeutic strategies (indicated above) can be helpful in managing the resulting distress. in fact, highly stressful life events that are often associated with periods of grief and loss are also typically associated with hopeful periods of readjustment and healing (tedeschi and calhoun ) . thus, during the covid crisis, it is possible that many individuals will convey healthy response patterns-some may exhibit resilience (i.e., maintaining baseline functioning in the context of disruption) and others may even experience posttraumatic growth (i.e., improving baseline functioning in the context of disruption) as a result of dealing with a new reality. generally, individuals report experiencing at least one positive change after a potentially traumatic event (e.g., an increased appreciation for life, stronger and closer relationships; tedeschi and calhoun ) . therefore, dealing with the abrupt and ongoing changes of the pandemic can actually have positive psychological effects over time. during the covid crisis, it is understandable that individuals feel down and distressed at times; however, expecting to only feel this way won't allow for the possibility of even momentary health and wellness. instead, a curious, open, and appreciative mindset can promote self-maintenance and growth. commuting time can be repurposed in new and valuable ways, individuals can focus on meaningful activities they may not have had time for previously, and new hobbies can be embraced and potentially result in longterm lifestyle changes. as regulations are slowly lifted, individuals can also begin to practice appreciating life's day to day activities that may have been previously interpreted as mundane or even aversive (e.g., grocery shopping, sitting in traffic, running errands). additionally, being proactive and deliberate with one's actions towards growth (e.g., setting goals) and embracing resilience resources (e.g., individual characteristics and skills, social support within communities, finding a sense of meaning/purpose) are also particularly helpful in cultivating progress (rosenberg ) . importantly, while some may experience resilience and growth, expecting this outcome at all times is unreasonable and unhelpful. there is no "right" way to cope with the pandemic, and growth isn't essential to survive. instead, individuals need to simply do what works best for them during these challenging times. in sum, although the covid crisis has resulted in numerous problems, resilience and growth are not only possible, but probable. however, resilience requires a "growth mindset"-one which acknowledges the negative but also looks for opportunities for improvement. the covid- crisis is expected to have an enormous negative impact upon the mental health of the world's population (marques et al. ; strakowski et al. ) . unfortunately, the mental health system in the u.s.-and perhaps other places in the world-is not well poised to deal with the psychological distress associated with the pandemic. given the novelty of this situation, specific treatments have not yet been developed to target the pandemic-related triggers that are resulting in a significant amount of stress. in addition, the present system may not be able to meet the current and future increased need for mental health services and thus, scalable interventions will be necessary to better distribute the resources available to a greater number of individuals. it is important to note that based upon responses to similar stressors, most individuals, even if acutely distressed, are likely to recover on their own once the pandemic passes (rauch et al. ) . indeed, humans are resilient! nevertheless, providing evidence-based cognitive behavioral emotion regulation skills to those experiencing significant distress in the moment has obvious value in that it can facilitate increased comfort as well as decrease the likelihood of more severe problems emerging down the road. if mental health professionals view all psychological distress as a "normal" response to the pandemic, and thus not requiring intervention, this may ultimately lead to significantly worse mental health outcomes for many individuals down the road. as a result, identification and an appropriate level of treatment for those with pandemic-related mental health issues now-ranging from providing self-help information to brief specific interventions to longer term psychotherapeutic treatment-is critical to prevent the development of a mental health pandemic that lasts beyond the covid- crisis. the data were not collected. conflict of interest the authors declared that they have no conflict of interest. informed consent there was no need for informed consent. stress, eating and the reward system stimulus control applications to the treatment of worry alarming trends in us domestic violence during the covid- pandemic individual meaning-centered psychotherapy for the treatment of psychological and existential distress: a randomized controlled trial in patients with advanced cancer use of bibliotherapy in the treatment of grief and loss: a guide to current counseling practices the psychological impact of quarantine and how to reduce it: rapid review of the evidence mental health household pulse survey moving beyond 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during a pandemic physical activity and incident depression: a meta-analysis of prospective cohort studies single-session consultation for emotional and behavioral health open pilot trial of a singlesession consultation service for clients on psychotherapy waitlists new projections on suicide, substance abuse, and covd- [video key substance use and mental health indicators in the united states: results from the national survey on drug use and health center for behavioral health statistics and quality, substance abuse and mental health services administration cdc director warns second wave of coronavirus is likely to be even more devastating posttraumatic growth: conceptual foundations and empirical evidence social comparison, social media, and self-esteem collision of the covid- and addiction epidemics publisher's note springer nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations key: cord- -d y r di authors: marshall, j. a.; thompson, w. l.; gust, i. d. title: coronavirus‐like particles in adults in melbourne, australia date: - - journal: j med virol doi: . /jmv. sha: doc_id: cord_uid: d y r di coronavirus‐like particle(s) (cvlp) are faecal‐derived pleomorphic membrane bound virus‐like particles characterised by a fringe of clubshaped spikes that measure about nm in length. the association of cvlp with a variety of social, clinical, and epidemiological factors was examined after a month survey of faeces received for routine testing at an infectious diseases hospital. cvlp was found most commonly in three groups: first, intellectually retarded individuals who were usually inmates of institutions; second, recent overseas travellers who were either indochinese refugees/immigrants or were overseas travellers who had usually visited developing communities for lengthy periods; and, third, male homosexuals who had a history of multiple sexual contacts and/or venereal disease. it was concluded that the excretion of cvlp had a strong association with unhygienic living or working conditions irrespective of any clinical symptoms the individual might show. coronavirus-like particle(s (cvlp) is the name applied to a group of pleomorphic membrane-bound viruslike particles characterised by a distinct fringe of spikes [macnaughton and davies, . cvlp are found in faeces, and negative-staining electron microscopy is the only reliable method for their detection [macnaughton and davies, . the precise nature, clinical significance, and epidemiology of cvlp are poorly understood [macnaughton and davies, ; kidd et al., . although cvlp are commonly detected in developing communities [mathan et al., ; marshall et al., ; sitbon, ; kidd et al., , they appear less common in developed communities [macnaughton and davies, . however, there have been few detailed controlled surveys of cvlp in developed communities, and the precise relationship between cvlp excretion in developed and developing communities is not clear. this study examines the question using adults in melbourne, australia, as the test population. fairfield infectious diseases hospital is the chief centre for the diagnosis and management of infectious diseases in the state of victoria, australia, and as such receives a wide range of specimens from a variety of individuals. during the course of a month period from january, , to september, , over , faecal specimens from individuals aged years and over were processed and examined by electron microscopy. these specimens were chiefly from patients with a history of gastroenteritis, although faecal specimens were also received from other patients and healthy persons temporarily resident in the hospital. this study is based on the cases found in the course of the survey when cvlp were detected and detailed records were available. in of these patients, which are referred to as gastroenteritis cases, diarrhoea was a major symptom prior to admission. in the remaining eight cases, diarrhoea was either absent or only a minor symptom prior to admission. in seven of these eight nongastroenteritis cases, a variety of illnesses was recorded, including hepatitis (two cases), malaria, pneumonia, malignant mesothelioma, leprosy, and chest infection. the remaining nongastroenteritis case was apparently healthy. a control group for the gastroenteritis excretors of cvlp was chosen as follows: a control case was selected for each experimental case by using the first recorded individual after the experimental in the laboratory log book, who was years old or more and who was within * years of age of the experimental, who had symptoms of diarrhoea prior to admission, for whom no cvlp were detected, and for whom detailed records were available. this control group therefore represents a random selection of gastroenteritis cases matched in age and time of collection to the cvlpexcreting gastroenteritis group. the two experimental groups and the control group represented exclusively inpatients at fairfield hospital. faecal samples were processed as described by iver et al. [ ] . briefly, faecal specimens were prepared as a % (w/v) suspension in hank's complete balanced salt solution, vigorously shaken, then centrifuged twice at low speed to deposit debris. the clarified supernatant was then concentrated and further purified by ultracentrifugation through a sucrose cushion. initially the purified concentrated faecal specimens were examined after negative staining with % phosphotungstic acid (ph . ) on mesh formvar-carbon-coated grids. at least four grid squares were examined for each specimen using a philips electron microscope. virus and virus-like particles were photographed and measured from photographic negatives. catalase crystals, with half the lattice spacing taken to be . nm, were used as a calibration standard. in all positive specimens, cvlp numbered, on average, at least one particle per grid square. in a further systematic study of the morphology of cvlp, a total of randomly selected cvlp were photographed from of the individuals positive for cvlp. in each case, between and cvlp were photographed. cvlp varied greatly in shape and size both within an individual and from individual to individual. they varied in shape from roughly round or ovoid to highly irregular ( fig. la) . cvlp measured along their longest axis (excluding spikes) could vary from as little as nm to more than nm. the variability in size of cvlp appears to arise from the capacity of larger cvlp to break up into smaller particles through the formation of constrictions (fig. lb) . particles with constrictions were seen in of cases studied in detail, although the actual incidence of these particles was low, with only identified in particles studied. cvlp were recognised with confidence by virtue of their fringe of club shaped spikes (figs. - ), which had a length of about nm (mean k s.d. = . . nm, n = ; measured from one spike from one particle from each of individuals). sometimes the appearance of the spikes was obscured by a fuzziness on the cvlp. the fuzziness could vary in intensity as well as in the proportion of spikes it covered (fig. ) . the morphology of the spikes varied both within an individual and from individual to individual, but there were two basic forms: spikes with one terminal bleb and spikes with two terminal blebs (fig. ) . a systematic analysis of cvlp from individuals indicated that cvlp with spikes with one bleb and cvlp with spikes with two blebs occurred in the same individual in ( %) cases. in of individuals, thread-like fibres were seen radiating from the fringe of spikes of some cvlp (fig. ) . cvlp with fibres were noted in a total of of particles studied in detail. thus cvlp have a varied morphology but can be defined as pleomorphic particles characterised by a fringe of spikes with an average length of about nm. the spikes have a minimum of one terminal bleb and frequently exhibit a second bleb. cvlp excretors could be classified into six categories based on their recent social history (table i) . intellectually handicapped and institutionalised. individuals who were intellectually handicapped and institutionalised made up about one-third of all cvlp excretors in the gastroenteritis group (table i) . of these, five were from one institution, two were from a second institution, and one was from a third institution, indicating that cvlp excretion was not restricted to any one institution. intellectually handicapped and institutionalised individuals were not found in the control group (table i) . intellectually handicapped and not institutionalised. one individual who was intellectually handicapped but not institutionalised was in the cvlp-excreting gastroenteritis group (table i) . this -year-old pensioner lived with her -year-old mother in a house described as being "in a dilapidated state." recent overseas travellers. the most common group excreting cvlp (both with and without gastroenteritis) was recently arrived overseas travellers i.e., those who had arrived from overseas within months of being admitted to fairfield hospital (table i ). an examination of the travel itinerary of overseas travellers excreting cvlp and those travellers not excreting cvlp suggests that places visited and lifestyle are related to the excretion of cvlp, although total time overseas is not related. the mean time spent in "developing communities" was significantly longer for travellers with gastroenteritis excreting cvlp, excluding indochinese refugeeslimmigrants (mean -t s.e. = -t weeks; n = ) compared to travellers who were not excreting cvlp (mean k s.e. = k weeks, n = ) (p < . , student's t test). it is also notable that seven of the overseas travellers excreting cvlp were indochinese refugeeshmmigrants, whereas no such individuals were found in the control group. on the other hand, there was no significant difference in mean total time overseas between overseas travellers with gastroenteritis excreting cvlp excluding indochinese refugees/ immigrants (mean k s.e. = k weeks; n = ) and travellers not excreting cvlp (mean * s.e. = t weeks; n = ) ( p > . ; student's t test). health workers. one individual, a nurse, could be classified only in this category (table i) . another nurse was noted in the gastroenteritis control group (table i) . nothing in their respective histories gave any clue to how one may have become "infected" with cvlp but not the other. it was also noted that a number of other individuals in the experimental and control groups were health care workers (table i) . these included two nurses in the group of recent overseas travellers in the cvlp excreting gastroenteritis group, two nurses in the group of six recent overseas travellers in the gastroenteritis control group, and one nurse who had a history of multiple sexual contacts and/or venereal disease in the cvlp-excreting nongastroenteritis group (table i) . it must be concluded that as health care workers fall equally into both experimental (individuals with gastroenteritis excreting cvlp) and control (individuals with gastroenteritis not excreting cvlp) groups, being a health care worker is not in itself a risk factor for the excretion of cvlp. individuals with a history of multiple sexual contacts andlor venereal disease. two individuals, both male homosexuals, belonged to this category in the cvlp excreting gastroenteritis group (table i) . one of them admitted to numerous sexual contacts and at a later admission was found to have antibody to hiv (human immunodeficiency virus). the second admitted to a past history of gonorrhoea. (in addition, one over-seas traveller with gastroenteritis, a male airline steward who was excreting cvlp, was also noted to be a homosexual with a history of multiple sexual contacts and venereal disease). one individual belonging to this category was noted in the cvlp-excreting nongastroenteritis group (table i) . he was a homosexual and admitted having "contacts." all four individuals admitted to homosexual contacts within months of admission. one case belonging to this category was noted in the gastroenteritis control (no cvlp) group (table i ). an examination of this case history, however, points to a marked difference from those individuals excreting cvlp. this former female prostitute had, apparently, ceased these activities years previously after migrat- ( ) ( ) ( ) "figure in brackets gives percentage of total for that column. htwo of these individuals were also nurses. one had worked in a refugee camp in somalia while overseas and the other had worked for days after arriving from overseas. 'one of these individuals was also a male homosexual with a history of multiple sexual contacts and venereal disease. dtwo of these individuals were also nurses by profession. this individual was also a nurse. in general, in the first five of the above categories, there is a n obvious close association with "poor hygiene" over a period of time. in the histories of individuals in the unclassified category of the gastroenteritis control group, no such relationship with poor hygiene was noted. it can then be seen that % of cvlp excretors with gastroenteritis had no obvious association with poor hygiene compared to % of the control group. statistical analysis showed that the difference between these two groups was highly significant ( p < . ; x test). in the cvlp-excreting nongastroenteritis group, only one of eight individuals had no obvious association with poor hygiene (table i) . ing to australia to marry. there was a suspicion of a past history of syphilis. unclassified. one individual ( %) of the cvlp excretors with gastroenteritis does not fall into any of the above five categories, compared to % in the control group (table i) . although the morphology of cvlp is well documented [ macnaughton and davies, , a number of novel observations in this study contribute to a n understanding of the variability of morphology of cvlp. first, smaller particles appear to arise through the formation of constrictions in larger particles. second, particles with spikes with one bleb and particles with spikes with two blebs quite commonly occur in the same individual. it is possible the outer bleb has a tendency to break off, resulting in the formation of one blebbed spikes. the general description of cvlp in this study accords closely to the general description of cvlp in other reports [macnaughton and davies, . the occasional finding of fuzzy material on cvlp seen in this study may represent antibody on the particles. the frequent observation of fine thread-like fibres on many cvlp found in this study has not been previously noted. these fibres could represent thread-like debris that have adhered to the cvlp. the results of this survey show that excretors of cvlp in melbourne generally belong to three groups: intellectually handicapped individuals, recent overseas travellers who had spent some time in developing communities, and some homosexuals. the intellectually handicapped individuals excreting cvlp were mainly inmates of institutions. the recent overseas travellers excreting cvlp were commonly refugees or immigrants from developing communities or were overseas travellers who had visited developing communities for lengthy periods. the homosexuals excreting cvlp were all male and had a history of multiple sexual contacts andlor venereal disease. the findings of a number of studies of cvlp in special population groups in developed communities are consistent with the general conclusions of this study. both kern et al. [ and riordan et al. [ noted cvlp quite commonly in male homosexuals, some of whom developed aids. moore et al. [ ] detected cvlp quite frequently in a centre for the intellectually retarded. although the findings of this study do not exclude the possibility that "infection" with cvlp may cause gastroenteritis, the results show that cvlp excretion and poor hygiene are closely related, irrespective of the clinical symptoms of the individual excreting the particles. this appears to be the factor linking all excretors of cvlp in developed and developing communities alike. the nature and clinical significance of cvlp are controversial. although the morphology of these particles is consistent with that of an enveloped virus, biochemical and serological studies, to date, appear confusing [gerna et al., ; mortensen et al., ; resta et al., ; battaglia et al., ; schnagl et al., . the results of this study should aid further work by pinpointing the precise morphology of cvlp and the groups most likely to be found excreting the particles. human enteric coronaviruses: further characterization and immunoblotting of viral proteins human enteric coronaviruses: antigenic relatedness to human coronavirus oc and possible etiologic role in viral gastroenteritis detection of coronavirus-like particles in homosexual men with acquired immunodeficiency and related lymphadenopathy syndrome shedding of coronavirus-like particles by children in lesotho human enteric coronaviruses. brief review coronavirus-like particles and other agents in the faeces of children in efate pleomorphic virus-like particles in human faeces coronaviruses in training centre for intellectually retarded. lancet i coronaviruslike particles in human gastrointestinal disease prolonged outbreak of norwalk gastroenteritis in an isolated guest house isolation and propagation of a human enteric coronavirus enteric coronavirus in symptomless homosexuals characteristics of australian human enteric coronavirus-like particles: comparison with human respiratory coronavirus and duodenal brush border vesicles human-enteric-coronaviruslike particles (cvlp) with different epidemiological characteristics the authors thank dr. l. irving for assistance and barbara gray for typing 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- -idv cio authors: devita, maria; bordignon, alessandra; sergi, giuseppe; coin, alessandra title: the psychological and cognitive impact of covid- on individuals with neurocognitive impairments: research topics and remote intervention proposals date: - - journal: aging clin exp res doi: . /s - - - sha: doc_id: cord_uid: idv cio nan the novel coronavirus (covid- ) that emerged in wuhan, china, in december rapidly spread within hubei province, and by january , had extended to up to countries. highly contagious and dangerous, covid- quickly impacted governments and public health systems, so that almost the entire world had to adopt the clinical and social tools that had previously been successfully deployed on a massive and unprecedented scale in china. quarantine, social distancing, and community containment are the public health measures that have recently, as in the past, been taken to separate people to interrupt transmission and thereby prevent person-to-person spread of this disease [ ] . however, quarantine brings with it also important psychological sequelae, as recently reported in the general chinese population [ ] , so that the world health organization (who) promptly provided guidelines for dealing with this problem. an increasing amount of data is becoming available on the psychological and social problems resulting from covid- and the interventions to tackle them in the general population [ ] ; yet little attention is being paid to elderly population and, in particular, to a frail subgroup of this age: individuals with neurocognitive disorders. the "stayhome" disposition and the sudden upheaval of daily life routines are in themselves difficult to tolerate by healthy and/or younger people, but can become even more burdensome for older persons with diseases that involve cognitive impairments, no less. for them, a daily routine is fundamental as a behavioral therapeutic approach to control the typical behavioral and psychological symptoms of dementia (bpsd) of disease, as psychomotor agitation, wandering and aggression. the opportunity to leave the house and to go out is a great source of indirect cognitive stimulation, thanks to the variety of environmental stimuli and the multiple possible chances of social exchange. finally, also the possible motor impairments associated to quarantine should not be underestimated: a forced reduction of motor/physical activity can cause, particularly in older individuals with neurocognitive disorders, a progressive loss of personal and instrumental autonomy, as well as a possible worsening of other agingrelated clinical problems, as sarcopenia, with a consequent increased risk of falls, and subsequent medical geriatrics complications. with this background, the present point of view paper aims to focus on a particularly frail population, namely on individuals with neurocognitive disorders, that have been relatively neglected up to now by the literature on the covid- pandemic. to do that, on a first section, this paper puts forward research topics aimed at deeper investigation of the indirect cognitive and psycho-affective effects of covid- quarantine on individuals with neurocognitive disorders. beyond providing selected points for discussion and highlighting some open issues, this paper suggests to consider remote assessment tools to be implemented not just during extraordinary periods, such as that of covid- , but also as a future and possible method of clinical practice. in the second section, "remote interventions" (ri) are proposed to be validated to provide neuropsychological assistance to persons with neurocognitive disorders, but also psychological and psychoeducational support for their caregivers during the pandemic but also for the next future. a first issue that we believe should be carefully considered results directly from the impositions of covid- quarantine: the need of developing and/or standardizing remote assessment tools for older people with neurocognitive impariments. although concerns may arise about the actual feasibility and reliability of such methodology, previous studies showed how diagnostic interviewing and several neuropsychological tests (e.g., the mmse, verbal fluency, the clock test) conducted "via video teleconference and traditional face-to-face conditions have good agreements even with persons with cognitive impairments and dementia" [ ] . during the lockdown, a number of clinicians and researchers have proposed research protocols, all motivated by the various scientific, clinical, social and psychological issues associated with covid- . however, so far, no one thought about remote neuropsychological evaluation, although it was proved to be previously successfully applied, clashing with the lack of measurements for collecting the necessary data instead, which poses a big challenge for the near future. the use of proxy reports, questionnaires administered by telephone (despite not being standardized for this application), and the creation of new "ad hoc" inventories could respond to the need for emergency tools able to overcome the social distancing in place to safeguard patient health. when covid- quarantine ends, all the remote modalities deployed up till then will be evaluated and carefully considered; if found to be accurate, these new measures will likely constitute alternative, "at distance" methods that allow social distancing to be maintained; this is particularly important for older individuals. these new methods will also be of interest to all the centers for cognitive decline and dementia with large numbers of individuals to diagnose every day, and therapeutic prescriptions to renew periodically. although the face-to-face clinical visit is undoubtedly always fundamental for cognitive impairment diagnosis and follow-up, remote assessment could be a valid transitional measure for public health needs in the coming months, and would guarantee continuity in patient care (against the currently imposed, though necessary, interruption), while reducing the risk of contagion and the consequent potential negative outcome of infection. the use of remote measurements could also be useful in speeding up and facilitating the massive collection of data that researchers and clinicians have to tackle daily. older individuals are among the most frail populations exposed to covid- contagion. as showed by the literature daily updated, it particularly concerns older people causing severe lungs and systemic inflammatory sequelae often requiring hospitalization and the subsequent, well known, related medical complications. this issue is even truer for individuals with neurocognitive disorders that are "the frailest among the frailest". for them, hospitalization, acute inflammatory status associated with possible marked hypoxia often triggers delirium, whose general negative impact is well known. furthermore, even a milder covid- infection could cause collateral disturbances, such as hyporexia, certainly caused by the disease itself, but also due to the hypo-anosmia and dysgeusia often associated with this virus' infection and to a worsening of the nutritional status and malnutrition. beyond these clinical and medical considerations, it should be highlighted that living with the covid- pandemic could be really dramatic for these persons as they may have difficulties in remembering to wear a mask, or in understanding public health information and the constraints imposed, and hence in complying with them (it should be noted that some behavioral diseases, such as "wandering" or disinhibition, can aggravate the overall situation). these difficulties, aside from representing a further potential burden to caregivers, also place people with neurocognitive disorders to an increased risk of contagion, nourishing a dangerous vicious cycle. a series of further questions seem in need of answering. for example, are individuals with cognitive impairment aware of the spread of covid- and its effects? are they able to experience distress as other people do? could the potential lack of awareness (i.e., anosognosia) be a "protective" factor for people with cognitive impairments, so that, having lost part of their "world consciousness", they are not affected by fear, distress and psychological malaise? or, on the contrary, could anosognosia be considered a major risk factor because it makes them less prone to the application of preventive measures and consequently they are more exposed to infectious risk with even serious complications? is it possible that quarantine "forces" family members, like children and grandchildren, to give more constant care to older people? these changes can, of course, be a possible source of stress and behavioral problems. however, might it not also be that older people benefit from the greater proximity of their loved ones? although great attention is paid to olders' biomedical care, fewer efforts are made for their psychological and cognitive well-being. this latter, in particular, should not be underestimated, since clinicians will potentially be witness of a population whose profile might be extremely changed during this period of pandemic. in particular, if cognitive stimulation training (cst) is highly recommended for individuals with neurocognitive disorders, it merits even greater endorsement during covid- -related social isolation. without dwelling on the well-known beneficial effects of cst on individuals with cognitive impairments, this point of view paper would like to suggest that clinicians, and neuropsychologists in particular, to design and validate specific individual and group remote csts. given the impossibility of carrying out the routine clinical examinations that older people with cognitive impairment are involved in on a weekly basis, remote and online cognitive training sessions should be planned and carried out with the aim of maintaining general orientation-to-reality, and stimulating, albeit in a milder way, overall cognition. with the presence of a caregiver, an internet connection and the use of now widespread technological devices, cst could be carried out individually or in groups with ease and in comfort. the possibility of using this method in "normal" times is not excluded, as it would be a means of reaching those individuals who cannot physically take part in cst for organizational reasons (face-to-face interventions are undoubtedly to be preferred). according to previous studies using remote neuropsychological tools with people with neurocognitive disorders, specific technological expertise is not required by examiners. neuropsychologists that already have the adequate conditions allowing in their clinical practice to carry out csts would substitute the "canonical" time for these face-to-face interventions with remote ones, thus not requiring extra resources in terms of time and costs. the eurostat's statistics on information and communication technologies (icts) show that in close to half ( %) of the elderly population-defined as those aged - years-in the eu- used the internet at least once a week. this figure could be compared with the situation a decade earlier in , when just % of the elderly population was using the internet on a regular basis (at least once a week) [ ] . it is true that a certain reticence still persists among older adults in using icts, specifically in italy; however, data seem to suggest that this digital divide is being gradually overcoming. carers of individuals with dementia always deserve particular attention, but especially so in this extraordinary period of quarantine when caregiving in general-or cohabitationcan be extremely hard. with respect to "canonical" interventions in the care of people with cognitive impairments, successful, non-pharmacological treatment is desirable, as is actively involving caregivers in supportive psychological and "strategic" programs to deal with dementia. we propose making remote and online information and education sessions available to monitor patients' well-being and provide caregivers with, on the one hand, information and clarification regarding possible cognitive, behavioral and affective changes occurring during quarantine, and, on the other hand, the suggestions and strategies that clinicians normally give to their patients during routine practice, and that are probably needed even more in these times. the extraordinary spread of covid- has brought-and will soon bring more-new, alternative methods for use in research and clinical practice with the elderly population. we believe that these represent an opportunity to reinforce classical geriatric and neuropsychological methodologies and approaches in studying normal and pathological aging, not only during the covid- pandemic but also in the near future, by providing remote tools able to reach those individuals who do not have the physical, social and/or affective means of obtaining adequate and constant care. funding this research received no specific grant from any funding agency in the public, commercial or not-for-profit sectors, and to our knowledge. ) isolation, quarantine, social distancing and community containment: pivotal role for old-style public health measures in the novel coronavirus ( -ncov) outbreak immediate psychological responses and associated factors during the initial stage of the coronavirus disease (covid- ) epidemic among the general population in china psychological intervention measures during the covid- pandemic teleneuropsychology: evidence for video teleconference-based neuropsychological assessment peopl e_in_the_eu_stati stics _on_an_agein g_socie ty#senio r_citiz ens_onlin e_.e . . _silve r_surfe rs publisher's note springer nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations conflict of interest there are no conflicts of interest associated with this publication. this study was carried out with respect to human and animal rights.informed consent for this type of study, formal consent is not required. key: cord- - jx u js authors: sulmasy, daniel p. title: “diseases and natural kinds” date: journal: theor med bioeth doi: . /s - - -x sha: doc_id: cord_uid: jx u js david thomasma called for the development of a medical ethics based squarely on the philosophy of medicine. he recognized, however, that widespread anti-essentialism presented a significant barrier to such an approach. the aim of this article is to introduce a theory that challenges these anti-essentialist objections. the notion of natural kinds presents a modest form of essentialism that can serve as the basis for a foundationalist philosophy of medicine. the notion of a natural kind is neither static nor reductionistic. disease can be understood as making necessary reference to living natural kinds without invoking the claim that diseases themselves are natural kinds. the idea that natural kinds have a natural disposition to flourish as the kinds of things that they are provides a telos to which to tether the notion of disease – an objective telos that is broader than mere survival and narrower than subjective choice. it is argued that while nosology is descriptive and may have therapeutic implications, disease classification is fundamentally explanatory. sickness and illness, while referring to the same state of affairs, can be distinguished from disease phenomenologically. scientific and diagnostic fallibility in making judgments about diseases do not diminish the objectivity of this notion of disease. diseases are things, not kinds. injury is a concept parallel to disease that also makes necessary reference to living natural kinds. these ideas provide a new possibility for the development of a philosophy of medicine with implications for medical ethics. twenty-five years ago, in the pages of this journal, david c. thomasma and edmund d. pellegrino challenged the field by arguing that medical ethics must begin with the philosophy of medicine. before his untimely death, dave let us know that such a comprehensive philosophy of medicine -one that could serve as a foundation for medical ethics -still eluded us. perhaps, he seemed to suggest, it had only become more difficult to achieve. in , he wrote, practice of medicine today, the movement back towards foundations will be difficult indeed. in this essay, dedicated to david's memory, i would like to set forth a possible new direction for pursuing this challenge. as he noted, such an endeavor amounts to swimming upstream against the currents of contemporary ''bioethics.'' despite the difficulties, however, it would appear that substantial new work in analytic philosophy might (surprisingly) lead to the sort of foundation for the philosophy of medicine and medical ethics that david sought. the notion of natural kinds has become very important in contemporary anglo-american philosophy, but scholars have not yet taken seriously how the notion that human beings are a natural kind might have implications for the philosophy of medicine and medical ethics. i will not attempt to lay out all of the implications of this idea in a single essay. rather, i will attempt to explain the notion of a natural kind, and to outline some of the ways in which this notion might help to illuminate a few fundamental questions about disease and health care. in the long run, a philosophy of medicine based centrally upon the notion of the human as a natural kind might be exactly the sort of foundation for medical ethics that david thomasma sought. essences have not been very popular in recent philosophy. positivists, for instance, complained that they had never seen one. the philosophy of medicine has also largely discarded essentialism as a sort of lingering, outmoded aristotelian habit of speech, or as jensen has written, ''the child of a static (pre-darwinian) view of nature.'' jensen goes on to say that, ''a unit of classification is a human construct,'' and argues that since diseases are evolving entities, they cannot be assigned essences, which are necessarily static. the idea that all classifications are human constructs is not new. it traces its origins to th century nominalism. but mere nominalism is not radical enough for the st century. for the post-modern bioethicist, medical terms are all socially constructed and thus, little more than disguised attempts to assert power and domination over others. thus, one group of postmodern feminists has critiqued the research agenda in women's health, writing that the concept to which the word 'woman' refers is '''crowded with the overdeterminations of male supremacy,' and... contaminated with misogyny and sexism.'' they argue further that 'gender' and 'sex' are also tainted with essentialism. the idea of pure sex difference uninfluenced by social constructions presupposes a mythical time prior to gendering. since it is impossible to be both inside culture and outside it at the same time, sexual differences are always already informed by gender. poststructuralist critiques have demonstrated that women's bodies and their experiences are only knowable through the discourses that constitute them, so both sex and gender are socially constructed. nonetheless, to advance their own political agenda of claiming power for women and righting past injustices, they advocate a cynical appropriation of the essentialist terms 'woman', 'sex', and 'gender' as tools for their movement. we argue that a ''strategic essentialism,'' as advanced by spivak, provides feminists the theoretical ground from which to argue their political agendas. in this formulation, essentialist categories such as woman/women, sex, or gender are used strategically to achieve specific purposes or aims. in spivak's terms, strategic essentialism is the ''strategic use of a positivist essentialism in a scrupulously visible political interest.'' in this sense, the strategy suits the situation, and the essentialized term (i.e., woman) becomes a mobilizing slogan aimed at specific political ends. in an academic climate such as this, small wonder that dave thomasma thought that the movement back to foundationalism would be difficult. and yet, powerful arguments are emerging in recent analytic philosophy that are making the concept of essentialism not only respectable once again, but even changing the antiessentialist received view. consider the work of saul kripke on identity and necessity. kripke has argued that ''identity statements are necessary and not contingent.'' he has used the term ''rigid designator'' to describe what might in an earlier era have been called an essential characteristic of a thing. a rigid designator is ''a term that designates the same object in all possible worlds.'' he does not imply that the thing must exist, of necessity, in all possible worlds, but rather that if it were to exist in any possible world, the rigid designator would designate it in that world. this is not trivial or obscure in its consequences for medical ethics. every time, for instance, that one requests a substituted judgment, the question is framed as a contrary to fact conditional that posits a possible world that is not our own. a clinician asks the daughter of a comatose patient, ''what would your mother, mrs. penelope smith, have wanted in terms of life sustaining treatment if she were able to speak to us today?'' kripke would insist that the mrs. penelope smith to whom we refer in the possible world in which comatose people's thoughts can be understood is not some other person who happens to look like mrs. penelope smith, but is identical with the mrs. penelope smith lying in the bed in the icu. it is this woman's values we are after. it is critically important to note that this routine exercise in clinical ethics, the elicitation of a substituted judgment, hailed by purportedly anti-essentialist bioethicists everywhere, is not even conceptually possible unless there is something akin to the essence of mrs. penelope smith. she is rigidly designated by her name. baruch brody's analysis would also support this interpretation, but on more forthrightly essentialist, aristotelian grounds. brody argues that ''identity across possible worlds is prior to rigid designation,'' and that something must already have been picked out as the same in any possible world before it can be designated as such. kripke's work on naming, identity, and natural necessity has also been complemented and even extended by david wiggins' work on natural kinds. wiggins has developed the notion of ''sortal predicates'' by which entities of a certain kind are picked out, identified, and re-identified over time. he has come to the conclusion that the predicate calculus simply cannot account for much of what is (particularly living things) unless it is enriched by the addition of the concept of a sortal predicate. in other words, one cannot say ''smith is the same man i saw yesterday'' without predicating that smith and the man i saw yesterday belong to the same natural kind (in this case, man). and if this is the case, then wiggins says, we must embrace at least a ''modest'' form of essentialism. these essences are not platonic forms. as wiggins puts it, essences are not ''fancied vacuities parading in the shadow of familiar things as the ultimate explanation of everything that happens in the world. they are the natures whose possession by their owners is the precondition of their owners being divided from rest of reality as anything at all.'' with respect to the philosophy and ethics of medicine, one would think it obvious that at least this sort of modified essentialism would be necessary in order to function in the clinical world. but while this might be obvious to clinicians, it has not been obvious to philosophers. how might the concept of natural kinds bridge the gap between the common sense essentialism of clinicians and the philosophy of medicine? building on the work of putnam, wiggins very clearly, if densely, tells what a natural kind entails: the determination of a natural kind stands or falls with the existence of law-like principles that will collect together the actual extension of the kind around an arbitrary good specimen of it; and these law-like principles will also determine the characteristic development and typical history of members of this extension. diseases and natural kinds i will argue that one cannot understand human disease unless one understands that human beings are a natural kind. this is not to argue that diseases are natural kinds, but that the concept of a disease must make necessary reference to a natural kind. if one is sincerely interested in acquiring knowledge about a subject, rather than beginning with obscure cases proposed as counterarguments in support of all manner of skeptical conclusions, one should begin by studying what is common and paradigmatic. the concept of natural kinds provides a framework for doing so. taking biology, pathology, plant science, human medicine, and veterinary medicine very seriously seems critical to any contemporary discussion of the general notion of disease. in this light, the following points are worth noting: ( ) a disease is always a disease of (at least one) living natural kind. for example, powdery mildew is a disease that afflicts members of at least one living natural kind -rosemary bushes (rosmarinus officinalis). but it is not a disease of the human natural kind. human diseases are diseases of members of the human natural kind. ( ) diseases can afflict more than one natural kind. plants other than rosemary, such as grapes and roses, can become diseased with powdery mildew. dogs and human beings both can be afflicted with myasthenia gravis. ( ) diseases of one natural kind may be caused by another natural kind -e.g. -erysiphe spp. and sphaerotheca spp. are among the natural kinds causing powdery mildew. plasmodium falciparum causes one type of malaria in human beings. but clearly not all diseases are caused by one natural kind invading another. there is no known pathogenic natural kind that causes myasthenia gravis. the important point is that to understand any of the conditions named above as diseases, one must understand how these conditions diseases and natural kinds affect the afflicted individual as the kind of thing that it is. there are law-like principles that determine the characteristic history and typical patterns of development that collect together the actual extension of those individual entities one calls members of the human natural kind. in fact, two arbitrary, good specimens of this natural kind have been picked out, radiologically dissected, and their anatomical features placed on line at the national library of medicine in bethesda, maryland. and amazingly enough, the average man or woman (or even child), is easily able to tell which entities belong to this natural kind (and their sex), in the absence of technical anatomical knowledge and without reference to a political agenda. one can also readily recognize those deviations from the characteristic development and typical history that render some members of this natural kind defective. so, children born with syndactyly (webbed fingers) are defective members of the human natural kind. they are not members of some other natural kind, say dolphins. to say something is a defective x implies that one knows what kind of thing an x is. without at least this much essentialism, medicine would not even be conceptually possible. natural kinds have a natural teleology. to say that they have characteristic patterns of development and typical histories implies a teleology. anthony lisska has called the properties that determine the pattern of development of a natural kind its ''dispositional predicates.'' the successful unfolding of these dispositions over developmental time -a program and a pattern -allows the individual to flourish as the kind of thing that it is. natural kinds have dispositions. this much teleology must be granted. uranium undergoes a characteristic pattern of radioactive decay. various types of stars have dispositional predicates. they develop and change over periods of time that may seem long by human standards, but there is a pattern by which a star's history must unfold temporally if it is to behave as the kind of thing that it is. dispositional predicates seem especially characteristic of living natural kinds. in fact, philippa foot has written that the word 'good' is an attributive adjective, not a predicative adjective, and cannot be understood apart from an understanding of what kind of thing something is. so, for instance, the word 'good', as used in the phrase, ''good roots,'' cannot be understood unless one knows that it is being attributed to a rosemary bush and not to a rhinoceros. having deep roots would not be good for a rhinoceros. natural kinds have natural tendencies. much of the scientific enterprise consists of coming better to understand these natural tendencies. this teleology is natural. it does not imply the anthropomorphizing of things or the ascribing of conscious goal-directed activity to them, nor does it imply that there is a deity that directs their development. that natural kinds have law-like principles that determine how they develop and flourish as the kinds of things that they are is simply a fact about the world as we encounter it. natural kinds are not timeless, changeless platonic entities. the concept of a natural kind is perfectly compatible with biological evolution. that living natural kinds evolve over time is simply one of the law-like generalizations that characterize them. some will go extinct. some may change so dramatically that they become a new natural kind. but for human medicine (as well as veterinary medicine and botany), the slow time frame of evolutionary change is just not significant for clinical pathology and practice. human understanding of the law-like generalizations that determine the characteristic development and typical history of natural kinds may also change over time. but this does not mean that the kind has changed, merely our understanding of it. this understanding has a mind-to-world direction of fit -i.e. -our understanding must be better fitted to the kind; the kind is not shaped to our understanding of it. thus, there is scientific progress in medicine. humoral theories of disease have been abandoned. bloodletting has been replaced by plasmaphoresis. but the gene of mendel and the gene of watson and crick are one and the same gene, now understood in greater depth. genetics is the study of one aspect of the lawlike principles that determine the characteristic development and typical history of living natural kinds. we understand human genetic principles better now than we did years ago. but it is still the same natural kind that is studied and treated by human medicinethe human natural kind. the idea of a natural kind is not reductionistic. the fundamental way that complex systems are understood is through a hierarchical analysis of their structure, recognizing that there is both ''top-down'' and ''bottom-up'' causation along the hierarchical levels. natural kinds can be understood at multiple hierarchical levels of organization, and lower levels of organization are neither individually nor jointly sufficient to explain higher levels of organization, or even sufficient to ask the questions that would be relevant to the understanding of the kind at that higher level of organization. these properties, those that can only be understood in relation to the hierarchical level of organization to which they belong, are said to be ''emergent.'' that is to say, they ''supervene'' only at successively higher levels of organization, but cannot be fully explained by lower levels of organization. thus, physics is insufficient to explain chemistry, chemistry is insufficient to explain biology, biology is insufficient to explain psychology, and psychology is insufficient to explain morality. for example, cell walls contain both quarks and l-mesons, but quarks and l-mesons cannot explain what a cell wall is. this does not preclude the work by which scientists can arrive at partial explanations of various states of affairs of a given natural kind, considered at a given level of organization, by invoking an understanding of one or another state of affairs of lower levels of organization of the kind. thus, at a chemical level, understanding that a base pair mutation results in the substitution of valine for glycine at the th position of the b chain of the hemoglobin molecule provides a substantial causal explanation for sickle cell disease. this information is useful and important. it has diagnostic and therapeutic implications. but as an explanation of what sickle cell disease is, it is radically incomplete. one cannot understand this disease without also understanding the biology of plasmodium falciparum, the ecological concept of inclusive fit, population genetics, patterns of migration, the physiology of blood flow, the existence of capillaries, the biology of pain, and the concept of infarction, none of which can be fully reduced to chemistry. the chemical explanation deepens the biological explanation, but only biology and levels of scientific hierarchy above the biological (so-called ''top-down causation'') fully explain the biological phenomena. a moral, rational, living natural kind can be understood, nonreductionistically, at multiple, hierarchically arranged levels of organization at which level-specific properties emerge, featuring both top-down and bottom-up causation. for the human natural kind, these might be sketched out as: evolutionary ecology sociology, economics, history psychology physiology anatomy molecular biology and genetics physics the domain of medicine is primarily the domain of the biology of individual members of the human natural kind -particularly the levels of anatomy, physiology, and psychology. those law-like principles that determine the characteristic development and typical history of members of this natural kind at these hierarchical levels of scientific understanding are the subject of medicine as an applied science. these are the biological principles of the kind. this is not to say that physics and sociology are irrelevant to medicine -patients can develop cancer because of radon exposure and economic factors may help to explain why a particular patient came to be exposed to radon. there is both top-down and bottom-up causation. but medical science cannot claim to be the complete human science. it must have boundaries if it is to be a field of inquiry distinguished from others. and this is determined by its praxis, with its emphasis on caring for the individual with disturbed biology at the level of experience and function. so, for example, molecular biology matters intensely to medicine because it can explain alterations in anatomy, physiology, and psychology and offer possibilities for corrective intervention. there can be ''allied'' sciences of medical sociology, medical economics, public health, and medical ethics. there is also a field of medical engineering, applying physics to medical care. but these fields merit the adjective, 'medical' precisely because they can help to explain or can help produce effective interventions in matters of anatomy, physiology, and psychology. this much being said, i am now ready to offer a formal definition of disease. a disease is a class of states of affairs of individual members of a living natural kind x, that: ( ) disturbs the internal biological relations (law-like principles) that determine the characteristic development and typical history of members of the kind, x, ( ) in a pattern of disturbance shared with at least one other member of the kind, x. ( ) the aim of this classification must be to provide at least a provisional basis for explaining the causes and/or natural history of a disturbance in the internal biological relations of the affected members of x (and, if x is a self-reflective natural kind, can serve as an explanation of the illness of those so affected), ( ) and at least some individuals of whom (or which) this class of states of affairs can be predicated are, by virtue of that state, inhibited from flourishing as xs. i must further explicate this fairly dense definition. a. a disease is not a natural kind. it is a classification of a certain state of affairs that can occur in members of particular living natural kinds. b. the ''biological internal relations (law-like principles)'' encompass anatomy, physiology, and psychology. not all variations in the law-like principles that govern natural kinds at these levels of organization are diseases, but only those variations that also meet the other criteria. c. there are no diseases that are unique to particular individuals. individuals may be sick or ill, but until the pattern of disturbance is detected in other members of the kind, it is not a disease. disease is a scientific concept and concerns more than the individual. d. the purpose of disease classification (nosology) is, in the first place, explanatory. even if the disease does not provide a causal explanation for the illness, the purpose of bringing a pattern of disturbance under a particular name is to predict an expected natural history and provide the first step towards explanation. even if the explanation is not scientific by contemporary standards (e.g., possession by demons or angry ancestors), the classification of a pattern of disturbance in the law-like principles that govern the biological organization of a living natural kind as a disease serves an explanatory function. e. the hope of medical practice is that better explanatory knowledge of a disease will provide better treatment. the th and th centuries rewarded medicine handsomely for pursuing explanatory knowledge of diseases. the eventual payoff was better therapy. but the aim of nosology is fundamentally explanatory, not therapeutic. f. there can be asymptomatic disease. but if a pattern of disturbance in the law-like biological principles that determine the characteristic development and typical history of a living natural kind is to be called a disease, at least some individuals with the disease must be inhibited from flourishing as the kinds of things that they are. for example, prostate cancer at age may be ''incidental'' and never interfere with a man's flourishing. but unless prostate cancer interfered with at least some men's flourishing, it would not be called a disease. g. the telos in this definition is that the individual should flourish as the kind of thing that it is. this is an important difference from christopher boorse's specification of the telos in his definition of disease as survival and reproduction. survival and reproduction might be sufficient for an amoeba to flourish as the kind of thing that it is. but survival is scarcely enough for a rosemary bush, never mind a human being. a rosemary bush might survive a bout of powdery mildew, live a normal lifespan, and reproduce well. but while infected, it is not flourishing as a rosemary bush. likewise, a human being with a coronavirus infection has a disease (the common cold). it is almost inconceivable that this could affect her survival or reproduction. but while infected, she fails to flourish as the kind of thing she is. h. setting as the telos the flourishing of the individual as the kind of thing that it is also explains why it can be controversial to classify as diseases certain patterns of variation in the law-like biological principles that determine the characteristic development and typical history of a living natural kind. in particular, patterns of human behavior are most susceptible to being controversially called diseases. but this does not undermine the definition of a disease. it is only to say that the task of deciding whether to designate as disease a pattern of variation in the lawlike principles that govern a thing as a member of a kind will have some very clear cases. by virtue of being the kinds of things that they are, human beings are incredibly varied -biologically, psychologically, and socially. human beings make choices, some of which preclude one good in order to pursue another. there is, therefore, a subject-relativity to the flourishing of human beings that ought not be confused with subjectivity. thus, human flourishing includes a certain diversity, and this diversity is objectively good. while the purpose of this essay is not to engage in a discussion of medical ethics, it must be stated that this diversity is not morally unbounded. human choices ought not detract from the common good (as integrally understood) and ought not undermine the basic conditions by which human beings flourish as the kinds of things that they are. with minor variations, i accept the by-now classical distinction between disease and illness, and i also accept the distinction between sickness and illness, but with a significant variation on the use of these terms. in sum, i hold that these three words designate three ways of referring to the same state of affairs -individually, socially, and scientifically -corresponding to the terms sickness, illness, and disease, respectively. sickness and illness are not the same as disease. distinctions between these terms have phenomenological and sociological meaning for human beings. while the first two terms, in particular, are largely synonymous in ordinary language, they can be used as technical terms to stipulate different phenomenological and sociological aspects of the lived experience of diseased human beings. sickness, as i use the term, is a state of disturbed internal biological relations that appears (from a non-professional perspective) to be inhibiting the individual from flourishing as the kind of thing that it is. individual members of any living natural kind, whether a rosemary bush or a fruit fly, can be said to be sick. generally, this disturbed state has observable manifestations, but not always. to know that an individual member of a kind is sick, one can observe the pattern of disturbance, and, with at least some knowledge of what it takes for such a kind of thing to flourish, one can make the judgment that the individual is sick. if a crow is walking around in clockwise circles and is not flying, not flapping its wings, not eating, and not cawing, most adult north american observers who know enough about what a crow is and how it typically behaves can make the judgment that the bird is sick. one can also ask for a report (from an individual capable of so reporting) about abnormal sensations or other subjective indications of disturbed biology associated with diminished flourishing. before one hears a report from the individual, however, one can make one's own judgment and simply ask for confirmation, saying, ''you look as if you are sick.'' illness is a socially mediated (but also unscientific) judgment about the exact same state of affairs to which sickness refers. illness connotes the recognition of a pattern, but is not a judgment that is made with an explanatory intention. an individual manifests a pattern of disturbed internal biological relations and appears not to be flourishing (is sick). another observer further adduces that this pattern of disturbance is not unique, and that this judgment has been made regarding other members of the kind. unscientifically, one judges, ''this illness is something that has been going around.'' in a rational, self-reflective, and socially interdependent natural kind such as the human, the individual, subjectively appreciated state that i have called sickness must generally be validated by other member(s) of the kind, thus allowing the ill individual to assume ''the sick role.'' disease serves as an explanatory designation for the same state of affairs. this individual's sickness, the illness that has been ''going around,'' is explained by judging that the individual suffers from a disease, e.g., influenza. human disease is therefore also social, but its aim is scientific -an explanation for the observed biological disturbance that does, scientifically, cause at least some individuals, so afflicted, to fail to flourish as the kinds of things that they are. symptoms are the sensory signals by which a sensible natural kind is alerted that internal biological relations are askew. when symptoms are sensed by self-reflective individuals, such individuals can use these sense data to judge that they suffer from sickness -feeling feverish, nauseated, pruritic, being in pain, etc. many living natural kinds have such signals. many of these signals have biological purpose -e.g. -pain may signal that a behavioral response to avoid the offending stimulus is in order. some are biologically inappropriate, or appropriate in the short-term but not in the long-term. symptoms are ultimately subjective, even if the cause of the symptoms is not. among the members of self-reflective natural kinds, symptoms assume meaning. one author has recently suggested the primary symptom is der unheimliche (a sense of not being at home in oneself). an individual sensing symptoms is often initially uncertain of the veracity of a symptom complex or its meaning. this leads the individual to seek validation by others. when this occurs, the patient enters the sick role and concludes, ''i am ill.'' disease, by contrast, is a class of patterns of actual disturbance in the internal biological relations of members of a living natural kind that can explain the sickness of individuals of whom the disease can be predicated. disease can also explain the sickness or illness of afflicted individuals if the natural kind in question is self-reflective and social. diagnosis is the art by which specialists determine that an individual's illness can be explained by a particular disease. this art requires recognizing a pattern of disturbance that typifies the state of affairs that defines the particular disease. diagnosis is an epistemic project. the data are the symptoms (if the individual has the linguistic capacity to report on internal sensations), and signs. signs are observable manifestations of disturbances in the internal relations or law-like principles that determine the characteristic development and typical history of sick members of the kind to which the individual belongs. signs are what others (e.g., doctors and nurses) observe as the effects of illness. some symptoms cannot be observed and can only be reported, for example, the symptom of seeing yellow halos around lights. some signs are only observed directly by others, and cannot be experienced subjectively, or even observed of oneself directly, such as an asymptomatic change in the surface of the retina. often, signs and symptoms will be intrinsically linked. the same phenomenon can have two sides -it can be experienced as a symptom and observed as a sign. for example, a patient may experience the symptom of feeling feverish. if a doctor observes this patient, the doctor will note that the patient has, perhaps among other signs, a fever. a diagnosis is a disease name that has been judged to be predicable of a state of affairs of a given member of a given natural kind, serving at least as a provisional explanation for the observed pattern of disturbance in the internal, kind-typical, biological relations of the individual. a diagnosis is a judgment that the pattern of disturbance in an individual can be classified as belonging to a named disease. diseases are thus classes of disturbed states of affairs in natural kinds. a diagnosis is a judgment that a certain state of affairs in a particular individual belongs to a certain class. lonergan's distinction between classical and statistical heuristic structures provides an important insight into the ways that diseases are currently understood. from a scientific point of view, there are two basic ways of understanding phenomena -classically and statistically. in classical science, the data converge upon some formula or understanding, such as pv = nrt, or e= mc , or the notion that stars form clusters called galaxies. in statistical science, one appreciates that the phenomenon of interest is itself stochastic, and that one can only understand this phenomenon by coming to know a value such as a mean, from which this inherently non-systematic process cannot systematically deviate. so, for instance, one comes to know that the mean temperature in paris in july is °c, or that the mean temperature of the background cosmic microwave radiation in space is . °k. this distinction is also helpful in understanding medical science, some of which is understood via a classical heuristic structure, and some of which is understood via a statistical heuristic structure. so, for instance, classical physiological laws obtained in medicine, such as the henderson-hasselbach equation: ph = pk a þ log ½conjugate base ½weak acid . the data about acid-base balance in the human natural kind converge upon this formula. but other processes can only be understood statistically, such as the fact that the ulnar artery is absent in about % of members of the human natural kind. diseases likewise are understood both classically and statistically. pneumococcal pneumonia is an example of a classical disease. the data converge on a particular description of the pattern of disturbance in the internal biological relations afflicting individual members of the human natural kind. this does not mean there will be no variations. in fact, the variation one sees in biology is greater than the variation one sees in physics. there is variation even in physics, and a classical law such as pv = nrt does not describe each measurement of pressure, temperature, molar quantity, and volume, but the for-diseases and natural kinds mula upon which multiple such measurements converge. likewise, the data do converge on a classical description of pneumococcal pneumonia even if it is not true that each and every case of pneumococcal pneumonia is exactly the same. there are also statistical diseases. since human diseases are disturbances in the biological law-like properties that govern the typical history and characteristic development of the human natural kind, it is not the mean value or central tendency but variations from the mean that are of concern to medicine. medicine characterizes some such variations as diseases, to the extent that they also fulfill the other criteria for classifying something as a disease -especially that they inhibit human flourishing. thus, some statistical variations (such as the absence of an ulnar artery) are not classified as diseases, while others (such as hypertension) are classified as diseases. the patterns of reasoning by which one makes the judgment that a particular state of affairs in a particular individual belongs to the class defined by a particular disease are multiple and complexdeductive, analogical, statistical, pragmatic, and more. a full discussion of diagnostic reasoning is beyond the scope of this essay. the philosophical literature on diseases has raged on for decades as a pitched battle between realists and anti-realists. the modest essentialism that accompanies the notion of natural kinds provides the basis for a modified form of realism about disease. the view proposed here may provide a solution to the problems posed by previous defenses of disease realism. diseases are not primary existents. 'systemic lupus erythematosis' does not pick out a primary existent, but a class of states of affairs occurring in members of a natural kind(s). diseases are not natural kinds, but states of affairs. diseases have no essences. saying this does not imply, however, that diseases have no objective basis, or are merely human constructions, or that diseases are merely value judgments. diseases make necessary reference to natural kinds, and natural kinds admit of at least a modest essentialism. it is essentialism about living natural kinds and their natural dispositions that provides the foundation for realism about diseases. the patterns of disturbance that one classifies as diseases are not arbitrary. it is the pattern of disturbed internal biological relation-ships in the natural kind that imposes itself upon the observer; the observer does not impose the pattern upon the affected members of the kind. that is to say, there is a mind-to-world direction of fit -the mind of the observer must conform to the world for the observer's beliefs about disease to be true. the world is the standard by which the observer's beliefs are judged. further, many diseases of one natural kind are caused by other natural kinds, and the pattern of disturbed development of a diseased natural kind may reflect the flourishing of the one causing the disease (e.g., in malaria, the illness of a member of the human natural kind is explained by the characteristic development and typical history of plasmodium falciparum). thus, the essentialism of two natural kinds may necessarily be invoked in defining some diseases. arguments are often proposed in (roughly) the following form: it was once thought that x was a disease. now, we no longer think that x is a disease. therefore diseases are social constructions. such arguments seem superficially to be sound, but they are specious. that the medical community can change its beliefs about disease does not imply that diseases are constructed by physicians according to the mores of their era. an alternative interpretation is that the former belief or the present belief or both are wrong. medical judgments are fallible. but fallibility does not imply subjectivity. for example, it may turn out that edwin hubble was wrong and that the universe is not expanding. but whether hubble was right or wrong depends upon the universe, not upon the mental states of human beings. in thinking about fallibility in medicine, it is important to distinguish two types of fallible judgment about disease -scientific judgments and diagnostic judgments. among scientific judgments about diseases, there are two sub-types, both of which are fallible: ( ) one may judge incorrectly that what appears to be a pattern of disturbance in the law-like principles governing the internal biological relations of a natural kind constitutes a disease (i.e., one may be wrong in one's scientific judgment that apparent pattern x is a disease) and ( ) one may incorrectly formulate a causal explanation for the pattern of disturbance picked out by a disease name (i.e., one may be wrong in one's judgment about the cause of x). the objective basis for disease classification must be that it makes necessary reference to a natural kind and to disturbances in the internal biological relations that inhibit at least some of the affected members of the kind from flourishing as the kinds of things they are. i will argue that, at the end of the day, this is what settles the question of whether a certain observable pattern constitutes disease. those who offer putative counter-examples, such as the th century medical theory that a slave's habitual tendency to try to escape was a disease (''drapetomania''), do not in any way thereby provide the slightest bit of proof that disease is a ''value-judgment.'' the objective basis for deciding this matter is to ask whether a desire no longer to be a slave is a disturbance in the internal biological relations that inhibits afflicted members of the human natural kind from flourishing as the kinds of things they are. if someone once thought this was true of slaves who wanted to escape, this opinion is simply wrong on both counts. it might be understandable that someone would render such an erroneous opinion given the socioeconomic and historical conditions under which physicians who made such judgments lived. but it is an absolute non-sequitor to conclude that this implies that all diseases are value judgments and that therefore appendicitis is simply a human construct. that judgments are fallible does not mean that they have no objective basis. behaviors are particularly susceptible to this sort of error. even today, whether some behaviors (such as homosexuality or substance abuse) are diseases can be hotly contested by various groups. but again, this does not mean that there is no basis for settling the case. the basis for settling this question is the same: whether there is at least a plausible biological explanation and whether the behavior inhibits human beings from flourishing as the kind of things that they are. that we are not % settled on what constitutes human flourishing does not mean that there is no basis for making such judgments or that there are not thousands of other clear cut cases (such as appendicitis and malaria) where it is obvious that the observed pattern of kind-atypical activity has a biological basis and that this pattern inhibits human flourishing. medical science can also be mistaken in its causal explanations about diseases. malaria (as its name implies) was once attributed to ''bad air.'' thus, a pattern of disturbance in the law-like characteristics governing the typical development and history of human beings was noted, cases fitting this pattern were carefully classified according to patterns of fever, and each thought to have a particular biological explanation. that explanation made epidemiological sense, and it ultimately fit with the causes of malaria as presently under-stood -anopheles mosquitoes, carriers of the malarial parasites, breed where the air is ''bad.'' doubtless our future understanding of malaria will deepen further than our understanding today. but the ''mal'aria'' of medieval italy and the disease we know today are not two different diseases. they are the same disease, better understood. the fact that we can incorporate previous observations into deeper explanations of the same disease is inconsistent with the assertion that diseases are merely human constructions. throughout the history of medical science, all we have ever tried to do has been to shape our minds better to fit the world as we encounter it. the fact that we have made mistakes does not mean that disease concepts are merely subjectively or intersubjectively chosen values. the ultimate standard of the truth about malaria and other disease concepts is in the world, not in our heads. that is how we can learn that we have been mistaken in our views about diseases. human medical science will establish the criteria for deciding that a particular pattern of disturbance in the biological internal relations of an individual member of the human natural kind falls within the extension of each disease category. one can be mistaken in the criteria that one establishes, because the pattern one is attempting to capture has an objective unity. one discovers that unity; one does not create it. in lonerganian terminology, a disease is a real thing, even if it is not a natural kind. one can progress in one's understanding of a thing. for example, the medical community once judged that a diagnosis of the condition known as lyme disease required manifestations of an oligoarthritis. as more research was conducted, it was noted that oligoarthritis was one stage in this disease, and that earlier stages had different manifestations such as an erythema migrans rash. the pattern of disturbance in the internal biological relations of the human natural kind to which the disease name 'lyme disease' refers did not change. our scientific understanding of lyme disease changed and the diagnostic criteria were adjusted. mistakes are also possible in diagnostic judgments. whether someone does or does not have a disease is fallible judgment, as all physicians (and medical students) know well. mistakes are possible at multiple levels. first one must correctly interpret the observable signs and the communicated symptoms (history and physical). second, one must be knowledgeable about the patterns of signs and symptoms manifested by the diseases as they are classified by the medical science of one's era (differential diagnosis). third, one must be knowledgeable about the appropriate confirmatory tests (diagnostic testing), and sufficiently experienced to use only those that are necessary (diagnostic elegance). fourth, in the setting of uncertainty, one must avoid the extremes of rashness (making a diagnosis before there are sufficient data) and indecisiveness (deferring judgment when sufficient data are at hand). the art of medicine is the mediation between medical science (concerned with universals) and the individual who must be diagnosed and treated. diagnosis is a judgment about individuals. as aristotle has said, the doctor does not cure 'a man' universally taken, except accidentally, but callias or socrates or someone else to whom also the essence of man happens to belong. if, then, someone without the experience has the theory and knows the universal but is ignorant of the individual included under this universal, he will often fail to cure; for it is rather the individual that is curable. (metaphysics a - ) . the fact that one can be mistaken in applying the science of one's era in making a judgment about whether a particular disease name can be correctly applied to a particular pattern of disturbance in the internal biological relations of an individual member of the human natural kind does not imply that diseases are value judgments. the logic of diagnosis is intensional. the ultimate standard for whether or not one has correctly applied the disease name (as defined by the science of one's day) to a particular patient is the match between that definition and the state of affairs that actually exists in the affected individual member of the human natural kind who is being diagnosed. further, the fact that the standards that are given for defining a disease must, to some extent, be arbitrary and admit of borderline cases, does not mean that diseases are primarily human constructions and value judgments. one must be careful not to confuse the epistemological with the ontological. definition is an epistemic exercise. whatever definition one gives will exclude some cases and include others, because this is what a definition does. giving intensional definitions for ontologically real entities is an inherently fallible enterprise. in a definition of multiple myeloma, for instance, one must arrive at cutoff values, currently set at > % plasma cells in the bone marrow and > . gms/dl of an igg m-protein. as every experienced clinician knows, some individuals who do not meet these criteria actually have multiple myeloma. however, this only means that the reality to which the definition points is prior to the definition. the definition is open to revision, based on its ability to correctly classify cases as belonging to the recurring pattern of disturbance in internal biological relations of the human natural kind that the definition is attempting to capture. there will be mistakes. some cases will only come to be knowable as the pattern of disturbance in the individual progresses along its own natural history. there will also be borderline cases in which the diagnostic judgment will be difficult. but as anscombe once remarked (in a quote she attributes to samuel johnson), ''the fact of twilight does not mean there is no difference between night and day.'' borderline cases do not suffice to refute objectivity. thus, one must conclude that none of these sources of fallibility in reasoning about diseases provides a philosophical justification for radical skepticism about the realism with which clinicians must undertake the tasks of studying and diagnosing diseases. diseases are objective perturbations in the reality of the natural kinds of which they can be predicated. finally, something must be said about the distinction between disease and injury. i am very sympathetic to the spirit of boorse's defense against those who criticize his theory for failing to make this distinction. this distinction is not fundamental to the notion of disease. however, i do think the distinction has some usefulness and should be maintained by the philosophy of medicine. injury and disease are highly related but distinct concepts. the words are used quite distinctly by both medical laypersons and medical professionals. the sub-specialists who treat diseases (e.g., internists, pediatricians, and family physicians) are different from those who treat injuries (e.g., orthopedists, burn surgeons, and trauma physicians). so, it is probably worthwhile to maintain the distinction. nonetheless, disease and injury are sufficiently related that the definition of injury is really parallel to that already given for disease. like disease, injury makes necessary reference to the notion of a living natural kind. an injury is a state of affairs of an individual member of a living natural kind x, that: ( ) disrupts the physical structure or physical integrity that is characteristic of the developmental stage and is typical of the history of members of the kind, x, and ( ) this state of affairs inhibits the individual from flourishing as an x. this definition of injury is parallel to the definitions of sickness and illness. that is to say, it is a ''lay'' definition. unfortunately, there is no ready-made cluster of synonyms that one can use to distinguish the various phenomenological and sociological aspects of injury to parallel the vocabulary of sickness, illness, and disease discussed above. instead one can therefore call this lay definition, injury sense . in this sense, one can say, as a medical layperson, in parallel to the notion of sickness, ''my finger is bleeding,'' or ''i hurt my wrist.'' parallel to the sociology i associated with the word, 'illness,' the injured sense individual may seek intersubjective validation. while the same definition applies, there is therefore a usage we can call injury sense . thus, my - / year old nephew asks, ''do i have a splinter, uncle danny?'' or someone says, ''you broke your wrist,'' or ''you've burned your hand rather badly.' ' however, there are many specific injuries that are more like diseases than they are like sickness or illness in that they have been named and categorized by medical science. in the absence of synonyms to use as technical terms, one can call this injury sense . this sense of injury can be defined in a manner more formally parallel to the definition of disease. a named injury (injury sense ) is a class of states of affairs of individual members of a living natural kind x, that: ( ) disrupts the physical structure or physical integrity that is characteristic of the developmental stage and is typical of the history of members of the kind, x, ( ) in a pattern of disruption shared with at least one other member of the kind, x. ( ) the aim of this classification must be to provide at least a provisional basis for explaining the causes and/or natural history of this disruption in members of x (and, if x is a self-reflective natural kind, can serve as an explanation of the injury sense of those so affected), ( ) and at least some individuals of whom this class of states of affairs can be predicated are, by virtue of that state, inhibited from flourishing as xs. thus the physician says, ''you have a non-displaced colle's fracture,'' or ''this is a second-degree burn injury involving . % of the body surface.'' this is scientific, explanatory vocabulary. the notion of injury sense is parallel to the notion of disease in every way. while it is a different class of states of affairs of the biology of living natural kinds, injuries (sense ), like diseases, can be predicated of any living natural kind. and the concept of injury sense , like the concept of disease, is objective, even if scientific and diagnostic judgments regarding injuries can be just as fallible as those regarding diseases. the notion of natural kinds can be a powerful starting point for the philosophy of medicine. it provides a philosophically credible basis for objectivity about diseases. the modest essentialism that accompanies the notion of a natural kind meets most objections raised in the literature. it provides a basis for discussion of value in disease discourse, while maintaining that such values are objective and inherent in the dispositional predicates of natural kinds in accordance with a theory of natural goodness and the teleology of a thing flourishing as the kind of thing that it is. it provides a basis for disease realism while avoiding the pitfalls of characterizing diseases as natural kinds themselves. it may provide just the sort of foundation for the philosophy of medicine upon which to develop a medical ethics, following the plan david thomasma outlined for us but could not carry out before his untimely death. philosophy of medicine as the source for medical ethics antifoundationalism and the possibility of a moral philosophy of medicine a critique of essentialism in medicine,'' in health, disease, and causal explanations in medicine abstracting women: essentialism in women's health research identity and necessity naming and necessity,'' in semantics of natural language sameness and substance see the debate about the notion of diseases as natural kinds: robert d'amico however, the inference both seem to share, that if disease is not a natural kind then it must be a ''value judgment aquinas' theory of natural law: an analytic reconstruction philippa foot, natural goodness intentionality: an essay in the philosophy of mind on the moral nature of the universe concepts of health,'' in health care ethics: an introduction autonomy, subject-relativity, and subjective and objective theories of well-being in bioethics four basic notions of the common good dependent rational animals: why human beings need the virtues - ; and his later refinements of this distinction in ''a rebuttal on health while i accept more or less the same distinction, i am using the terms 'illness' and 'sickness' in the opposite manner as has become standard in the philosophy of medicine (see bjørn hofman since it is preferable to assign to technical terms the use that is closest to ordinary language, i propose a reversal of the standard use of these terms. i will use 'sickness' to refer to the individual's own subjective experience of disturbed internal biological relations, or to an observer's assessment of the disturbed state of an individual. i will use 'illness' to refer to the intersubjectively supported, socially mediated understanding of the same state of affairs. so, we often say that a dog is ''sick,'' but we do not usually say that a dog is ''ill das unheimliche: towards a phenomenology of illness insight: a study of human understanding i am tempted to argue that ''statistical'' diseases are only epidemiological risk factors for classical ones, but i will not explore this hypothesis further in this essay a variation on this fallacious line of argument is the illicit inference that since there are heated arguments in the present about whether certain states such as homosexuality or menopause or aging or infertility are diseases, one must conclude that diseases are socially constructed. this is the tack taken by arthur l. caplan in ''the 'unnaturalness' of aging -give me a reason to live report on the diseases and physical peculiarities of the negro race,'' in health, disease, and illness: concepts in medicine plasma cell neoplasms,'' in principles and practice of oncology war and murder toward a pragmatic theory of disease.'' in what is disease war and murder.'' in war and morality concepts of health.'' in health care ethics: an introduction on the distinction between disease and illness a rebuttal on health the unnaturalness of aging -give me a reason to live.'' in health, disease, and illness report on the diseases and physical peculiarities of the negro race.'' in health, disease, and illness: concepts in medicine is disease a natural kind the foundations of bioethics natural goodness on the triad disease, illness and sickness a critique of essentialism in medicine.'' in health, disease, and causal explanations in medicine identity and necessity.'' in identity and individuation naming and necessity.'' in semantics of natural language theory of natural law: an analytic reconstruction insight: a study of human understanding dependent rational animals: why human beings need the virtues abstracting women: essentialism in womens health research plasma cell neoplasms.'' in principles and practice of oncology on the moral nature of the universe minneapolis definitions of health and illness in the light of american values and social structure.'' in patients, physicians, and illness dis-ease about kinds: reply to damico intentionality: an essay in the philosophy of mind four basic notions of the common good das unheimliche: towards a phenomenology of illness philosophy of medicine as the source for medical ethics antifoundationalism and the possibility of a moral philosophy of medicine autonomy, subject-relativity, and subjective and objective theories of well-being in bioethics sameness and substance key: cord- -mo mvwch authors: huang, jiechen; wang, juan; xia, chengyi title: role of vaccine efficacy in the vaccination behavior under myopic update rule on complex networks date: - - journal: chaos solitons fractals doi: . /j.chaos. . sha: doc_id: cord_uid: mo mvwch how to effectively prevent the diffusion of infectious disease has become an intriguing topic in the field of public hygienics. to be noted that, for the non-periodic infectious diseases, many people hope to obtain the vaccine of epidemics in time to be inoculated, rather than at the end of the epidemic. however, the vaccine may fail as a result of invalid storage, transportation and usage, and then vaccinated individuals may become re-susceptible and be infected again during the outbreak. to this end, we build a new framework that considers the imperfect vaccination during the one cycle of infectious disease within the spatially structured and heterogeneous population. meanwhile, we propose a new vaccination update rule: myopic update rule, which is only based on one focal player’s own perception regarding the disease outbreak, and one susceptible individual makes a decision to adopt the vaccine just by comparing the perceived payoffs vaccination with the perceived ones of being infected. extensive monte-carlo simulations are performed to demonstrate the imperfect vaccination behavior under the myopic update rule in the spatially structured and heterogeneous population. the results indicate that healthy individuals are often willing to inoculate the vaccine under the myopic update rule, which can stop the infectious disease from being spread, in particular, it is found that the vaccine efficacy influences the fraction of vaccinated individuals much more than the relative cost of vaccination on the regular lattice, meanwhile, vaccine efficacy is more sensitive on the heterogeneous scale-free network. current results are helpful to further analyze and model the choice of vaccination strategy during the disease outbreaks. over the past two decades, the outbreak of infectious diseases has been threatening the safety of human lives and properties, such as the severe acute respiratory syndrome sars [ ] , h n [ ] , ebola [ ] and so on. thus, how to prevent the extensive outbreaks of epidemics has become a challenging topic in the field of public health [ ] [ ] [ ] . meanwhile, the difference of population distribution, religious belief and regional differences may greatly affect the spread of infectious diseases, for example, refs. [ ] [ ] [ ] [ ] explore the impact of various topological structures within the population on the infectious diseases spread, and it is convincingly found that heterogeneous networks may quicken the disease spreading within the population, even lead to the absence of epidemic threshold [ ] . meanwhile, the individual reactions to infectious diseases may also substantially influence the diffusion processes of epidemics. one of the most striking cases regarding the outbreaks was h n pandemic in [ ] , which induced around , deaths. during the outbreaks of h n , the suppression of epidemic processes can not only be attributed to the public measures, but also through personal and uncoordinated responses, that is, the human behavior has noticeably interfered with the epidemic spreading. in the long run, human behavior has been intricately correlated with the contagion of infectious diseases. in medieval ages, the deadly bubonic plague rendered many people to avoid and flee away from the sick and their close contacts so that their own immunity can be secured [ ] . similarly, the villagers of yorkshire in eyam tried to voluntarily quarantine themselves to stop the spread of the plague from that village [ ] . in , during the outbreak of sars, many citizens spontaneously wear the face masks, some schools are temporarily closed and the students are imperatively required to stay at home so as to avoid the further epidemic infection as much as possible [ ] . in addition, protective behavior when confronting the epidemics has also been observed in many other contexts, such as measles-mumps-rubella(mmr) [ ] , tuberculosis(tb) [ ] and hiv [ ] etc. while the impact of human behaviors on the epidemic spreading process has often been mentioned anecdotally, the accurate modeling or quantitative models are relatively fewer regarding their nature, property, or the effect they may have on the spread of the disease. at present, mathematical models have been put forward to study the role of human behavior in the context of social population, such as escape panic [ ] , pedestrian trails [ ] , but effort s to quantitatively explore the role of human behavior in the large-scale epidemics generally focus on assessing the effectiveness of various public health measures including the social distancing, school closure etc. in the recent years, there are many fields and methods to help us to study infectious disease [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] , however, there is an increasing attention about the effect of spontaneous individual action or response strategy on the progression of an infectious disease, in which this kind of spontaneous actions may highly restrain from the further diffusion of epidemics and even change the fate of outbreaks. thus, it is of great significance to fully understand the interacting mechanisms between the human behavior and disease dynamics within the specified population. it is worth mentioning that funk et al. [ ] systematically summarized the related works and provided a taxonomy framework of behavior-disease models. on the one hand, they classify these models according to source and type of information that individuals base their neighbors on, in which source of information may be local or global and the type of information that individuals change their behaviors are prevalence-based or belief-based; on the other hand, they classify the previous works based on the impact of individual behavior changes on the disease dynamics, which include the following three aspects: (i) the disease state; (ii) model parameters (infection or recovering rate); and (iii) the network contact structure relevant for the spread of epidemics. in particular, for some preventable infectious diseases with the help of vaccines, the epidemic outbreaks are intricately linked with the individual vaccination behavior since the vaccines can help the vaccinators not to be infected by a specific disease. meanwhile, these vaccinators may indirectly protect their nearest neighbors with whom they contact, and then these neighbors may choose not to vaccinate again (that is, free-ride the vaccinators) so as to avoid the necessary vaccine fees or other potential risk and side effects. henceforth, the vaccination behavior may dominate the evolutionary process of vaccine preventable diseases. among them, bauch and earn [ ] seminally utilized the game theory to model the dilemmatic situation for an individual facing with the epidemics, and they proposed a class of vaccination game to denote the individual decision making and found that, for the well-mixed population, the nash equilibrium is never to vaccinate if the vaccination cost is higher than that of being infected; but there exists a nash equilibrium yielding a suboptimal vaccinated fraction if the vaccine cost is lower than that of being infected. as a further step, complex networks, beyond the well-mixed topology, provide a unified platform to characterize the topology of real-world populations, where the nodes represent individuals and links mimic the contacts among them [ ] . thus, under framework of game theory, many works are devoted to exploring the interplay between contact patterns, behavioral responses and disease dynamics. as an example, fu et al. [ ] found that heterogeneous networks, such as scale-free ones, can induce a broad range of vaccinating actions of many individuals since highdegree hubs with many neighbors become voluntary vaccinators more probably in order to reduce the risk of being infected. after that, zhang et al. [ ] demonstrated that the hubs may largely inhibit the outbreaks of infectious diseases under the voluntary vaccination policy. in the meantime, various subsidy policies on controlling the epidemic spreading have been determined from the socioeconomic perspectives within the well-mixed and networked population [ ] [ ] [ ] [ ] [ ] [ ] . furthermore, most previous works [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] often assume that the vaccine has a perfect efficacy, which will endow the complete immunity for the inoculated individuals, but an interesting topic is on how the epidemic spreads when the vaccine is not fully effective for the disease (i.e., % efficacy)? besides, in the vaccination game, whether an individual decides to vaccinate the vaccine or not will be often determined by the estimated payoff, and the vaccinating decision may be transferred from one player to another one inside the population according to a specific role model during the outbreaks. nevertheless, under some real-world scenarios, some individuals are not willing to imitate the behaviors of others as a result of special belief, religion, opinion and even awareness of a disease. according to the above description, in the real world, when a new epidemic starts to outbreak, people want to take some measures to protect themselves immediately. generally, inoculating the vaccine is considered as an effective measure, but the vaccine may fail as result of invalid storage, transportation and usage, and then rendered that the vaccinated individuals may confront the risk of being infected. henceforth, some individuals make a decision to vaccinate just judge by themselves and don't consider their neighbors. thus, in order to deeply analyze the role of vaccine efficacy and spontaneous individual decision mechanism in the outbreak of vaccine preventable diseases, we propose a vaccination game model to explore the impact of imperfect vaccine efficacy and myopic update rule in the spatially structure and heterogeneous populations. the rest of this paper is structured as follows. firstly, we depict the new vaccination game model in section in detail. then, section provides extensive numerical simulation results, which are obtained in the regular lattice and heterogeneous scalefree networks, respectively. lastly, in section , we end this paper with some conclusions and point out the potential works in the future. as mentioned above, we consider the vaccination game for a class of emerging epidemics within the structured population, where the vaccine can be obtained after the epidemic spreads. thus, in the current model, all individuals have no chances to vaccinate at the initial time step ( t = ). after that, each time step ( t ≥ ) is divided into two elementary sub-steps: one step is for the decision of inoculating the vaccine; the other one is used to model the process of epidemic spreading. among them, for the epidemic sub-steps including t = , we leverage the frequently used susceptible-infective-recovery (sir) compartment model to characterize the evolution of epidemics, where each individual may lie in the susceptible (s), infective (i) or recovery (r) state. during the vaccination decision sub-steps, each susceptible individual needs to assess the risk of being infected, and then make the decision whether he will vaccinate or not. regarding the sir model, any susceptible individual may be infected through the contact with infective neighbors and the transmission rate along each infective link is assumed to be β. meanwhile, the infected individual can be cured with the recovering rate μ, and the recovered one will not be infected again or infect any other healthy ones. hence, the probability that the susceptible player i without inoculating the vaccine will be infected by all possible infective neighbors can be written as follows, where k i in f denotes the total number of infected neighbors of the focal player i . the epidemic continues until there are no more newly infected individuals. as for the individual vaccination decision, each susceptible one will evaluate the risk of being infected and compare the difference between the vaccine cost ( c v ) and the potential expenses once he has been infected. without loss of generality, we fix the infection cost c i = , while the vaccine cost is usually lower than c i and then its relative cost can be re-scaled as < c = c v /c i < . in order to quantitatively perform the decision, by borrowing from the terms in game theory, we assume that the decision process is based on the comparison between the perceived payoffs of vacci-nation i v and the perceived payoffs of being infected i nv if he is not vaccinated, which can be expressed as follows, respectively, where λ i denotes the potential infection probability that can be calculated according to eq. ( ) . then, the susceptible agent i will independently decide to inoculate the vaccine with the following fermi-like probability, where k represents the impact of the noise or its reverse / k means the strength of strategy selection, which reflects the uncertainty of vaccination strategy adoption. here, we term this vaccination decision as the myopic update rule just based on one player's own perception, which is different from imitating the vaccination strategy of others in many previous works [ , , [ ] [ ] [ ] [ ] [ ] . when k → , agent i is totally rational and whether he will vaccinate or not is fully determined by comparing i v and i nv , on the contrary, when k → ∞ , agent i will randomly perform the vaccination choice. in addition, we consider the imperfect vaccination program, that is, the vaccine efficacy is not % and the vaccination may fail as a result of incorrect transportation, storage, and usage of vaccine. thus, we introduce an independent parameter θ to characterize the vaccine failure rate, which implies that the susceptible individual to choose the vaccination is still kept in the susceptible state with the probability θ , while the probability changing from s into v ( s → v ) state is set to be ( − θ ). once the healthy individual decides to vaccinate, he will have a chance to enter into the vaccinated ( v ) state, the sir epidemic dynamics will evolve into the sirv model as illustrated in fig. , in which the successfully vaccinated individual will be equivalent to the r-type one at the next time step, that is, the successfully vaccinated (v-type) agent does not get the infection or infect others, either. we do not know when does vaccine fails, so that at each propagating time step, inoculation individuals are judged whether the vaccine is fails or not. to be noted, the vaccinated healthy individuals will not be vaccinated again during this epidemics even if the vaccine lost its effect. in order to further explore the impact of network topology on the evolutionary process under the imperfect vaccination, we simulate the current mechanism on l × l regular lattices and scale-free networks with n = l nodes, respectively. initially, we stochastically choose i = individuals as the infective seeds within the population, and other ( n − i ) individuals are kept in the susceptible state, and thus there have no vaccinators. at t = step, the system starts the evolution according to the sir model. after that, from t = , each susceptible agent has the opportunity to receive the vaccination and then the system carries out the evolution of epidemics based on the above-mentioned two elementary steps. the system continuously evolves until there are no infective individuals. in addition, the current results are averaged over independent runs so that the large fluctuations can be removed. in all the numerical simulations, the population size is fixed to be n = . in the homogenous topology, we use the regular lattice satisfying the periodic boundary with the size l = as the underlying networks, and each individual has nearest neighbors (that is, the von-neumann neighborhood). as for the heterogeneous topology, we generate the scale-free network by using the configuration model, in which the average degree is fixed to be < k > = and the power exponent is set to be γ = . in this section, we conduct extensive numerical simulations to demonstrate the vaccination behavior on the regular lattices and scale-free networks, respectively. among them, we mainly discuss the influence of vaccine cost c and failure rate θ on the collective vaccination level within the population. without loss of generality, we set the value of parameters in the sir model as β = . and γ = / , which are identical with those in ref. [ ] . first, we investigate the equilibrium fraction of both vaccinated ( ρ v ) and recovered ( ρ r ) state individual size for different values of relative cost of vaccination c and vaccine failure rate θ . fig. plots . (yellow triangle), respectively. on the one hand, for a specific vaccine failure rate θ , ρ v declines with the increase of the relative vaccination cost c , while ρ r increases as c augments, which means that the vaccination cost will markedly affect the willingness of individuals to inoculate the vaccine. as an example, when c ≤ . , ρ v and ρ r can almost keep the similar vaccination level as c increases; however, c > . leads to the substantial reduction of ρ v and the continuous rising of ρ r since the vaccination cost is comparable to the infection cost; in particular, ρ v will be dramatically reduced when c is up to . , even tends to zero as the vaccination cost is too high, especially for c = . . on the other hand, under the same vaccination cost c, ρ v decreases as the vaccine failure rate becomes higher, for instance, the fraction of adopting the vaccination strategy under c = . is much less than that with c = . , which implies that the vaccinated fraction within the whole population will be a little more sensitive to the vaccine failure rate. then, we discuss the influence of the noise factor k on the vaccination behavior within the population in fig. , where we set σ = k , termed as the strength of selection ( < σ < ∞ ), as and . , which are slightly different from that in fig. . likewise, it can be clearly shown that ρ v declines and ρ r increases slowly when the relative cost of vaccination c lies between and . . afterwards, when the relative cost of vaccination c is more than . , the greater the noise selection strength, the more rapidly the varying trend of ρ v and ρ r . in fact, as the strength of selection increases, individuals become much more rational and will not tend to take the vaccination strategy since they will take their own economic cost and the related interests, say, free-riding behavior, into account. in particular, the relative cost c is beyond . , or the vaccine loss rate is higher (i.e., θ = . ), the un-vaccination behavior of rational individuals become much more prominent, and thus it is unable to prevent the outbreaks of epidemics, which can be observed from the larger ρ r as c > . or θ = . . next, in order to fully check the impact of relative vaccination cost c and the vaccine failure rate θ on the vaccination behavior, fig. illustrates the evolution of ρ v and ρ r within the broader ranges of c and θ . it is clearly indicated that at the lower vaccine failure rates (say, θ < . ), the fraction of vaccinated individuals is often more than half of the total population, even if relative cost of vaccination c is large (e.g., . ); meanwhile, a plethora of vacci- thus, creating the high quality vaccine is significant, which greatly determines the individual vaccination inclination. furthermore, to deeply understand individual state change in the lattice as sirv model evolves, we record the evolutionary snapshots of individual states at various time steps for θ = . , c = . and θ = . , c = . in fig. . among them, the upper eight panels denote the snapshots under θ = . and c = . , while the lower eight panels represent the ones for θ = . and c = . . at time step t = , there are no vaccinated individuals on the lattice and only i = randomly infected seeds, and then the epidemic starts to propagate at this time. after that ( t ≥ ), the susceptible individuals have the opportunity to determine whether they will inoculate the vaccine or not. it is clearly observed that most individuals choose to vaccinate under these two cases when epidemic begins to spread. however, when θ = . is lower, there is fewer vaccinated individuals to become susceptible, and then most of vaccinated individuals are immunized, in which the epidemic is hard to spread and finally tends to be extinct. reversely, for the higher vaccine failure rate (i.e., θ = . ), the vaccine is easy to be invalid, many vaccinated individuals become susceptible due to the loss of vaccine efficacy. therefore, the epidemic can be pandemic and then most of individuals enter the recovered state in the end. all these results again demonstrate that the vaccine efficacy plays the significant role in the evolution of vaccination behavior of epidemic outbreaks within the structured population. in the real world, many networks are often heterogeneous, and thus it is necessary to understand the mechanics of myopic update rule better on heterogeneous topology. to this end, we formulated the game of taking the vaccine on the scale-free network. here, we generate the scale-free network with , node under the configuration model, where the average degree of the whole network is equal to and the power exponent . after the fundamental networks are created, the system evolves according to the sirv model, which is identical with the iteration procedure on regular lattices, and the epidemic continues until there are no more newly infected individuals. first of all, we plot the time courses of fraction of susceptible, vaccinated and recovered individuals for different the relative cost of vaccination c and vaccine failure rate θ in fig. . in all panels, the red, blue and yellow lines denote the evolution of susceptible, recovered and vaccinated individuals, respectively. it can be found that the vaccinated individuals increase rapidly in a very short time, and then reach a peak. vaccinated individuals are rarely become susceptible because of the vaccine failure θ is lower (as shown in fig. a,c) so that the number of recovered ones increases a little and arrives at the equilibrium quickly, which states clearly that the epidemic is eliminated and has not become pandemic. due to the vaccine failure rate, the fraction of vaccinated individuals goes down and then tends to be zero after reaching the peak. however, when the value of vaccine failure rate θ is raised (as shown in fig. b,d) , even though the vaccinated individuals increase rapidly, they become susceptible quickly due to the high vaccine failure rate θ , it can't prevent the epidemic spread so that the number of recovered individuals increases. additionally, we found that for the value of vaccine failure rate θ = . , whatever the values of relative cost of vaccination c , the number of recovered agents is the same as that at the equilibrium. generally, when the epidemic starts to spread, many susceptibles take the vaccine in the population at a short due to the perception of infection risk. also, this vaccination behavior is almost widespread regardless of the values of relative cost of vaccination c and vaccine failure rate θ . at the lower vaccine failure rate, vaccinated individuals are hard to become susceptible, which leads to the disease propagates difficultly and be eliminated as soon as possible. these results are also consistent with the work of zhang et al. [ ] , since the hub nodes are often vaccinated immediately after the disease starts to spread. but for the higher vaccine failure rate, the vaccinated individuals become susceptible quickly, the disease can outbreak. we also consider the equilibrium fraction of both vaccinated ( ρ v ) and recovered ( ρ r ) state individual size for different values of it can be found that in the figs. and , whatever the ways of vaccination, the epidemic can outbreak and vaccinated individuals are more sensitive to the vaccine failure rate. therefore, except β = . , we consider the epidemic evolution of sirv model under the lower transmission rate β = . . meanwhile, we set the i = initial infective seeds as the top largest degree nodes, which is here termed as the hub infection scheme. correspondingly, we call the randomly selecting one for the generous case as the random infection. in summary, based on the sir epidemic dynamics, we investigate the imperfect vaccine immunity under the myopic update rule in different foundation topology including the regular lattice and scale-free networks, where the focal player makes the vaccination decision just according to his own judgement about the epidemic situation. extensive numerical simulations show that most unvaccinated susceptible individuals are willing to inoculate the vaccine under the myopic update rule, whatever the type of network is, in particular for the lower vaccine cost ( c ≤ . ) and failure rate ( θ ≤ . ). after the epidemic starts to propagate, and most of individuals change their strategies to adopt the vaccine in a short time since the individual can estimate the infection risk at the early stage, which leads the epidemics to be hard to spread within the population. however, due to the failure of vaccine or the free-riding behavior of susceptible individuals, vaccinated individuals become susceptible again and then confront the risk of being infected, which creates the potential epidemics situation. to be of great interest, we find that the impact of vaccine failure rate on the vaccination coverage becomes much higher, when compared to the role of the relative cost of vaccine. for example, the value of vaccine failure rate θ is usually assumed to be no more than %, or else most vaccinated individuals become re-susceptible again. at a fixed θ , the fraction of vaccinated individuals almost keep unchanged when the relative vaccine cost is not beyond c = . , but this value will become lower and lower after c is more than . , which is basically consistent with the reality of vaccine usage. on the contrary, on the scale-free networks, the number of vaccinated individuals is more sensitive to the effect on vaccine failure rate θ . hub nodes have a stronger inclination to adopt the vaccine under the myopic update rule, which can effectively prevent the diffusion of epidemics. hence, the disease will be eliminated quickly in heterogeneous topology. however, when the values of vaccine failure rate increase a little bit, hub nodes become susceptible and cannot prevent the epidemic spread, which leads to the epidemic outbreak. meanwhile, when the relative cost of vaccination c increases, unvaccinated susceptible individuals are not willing to choose the vaccination strategy, which can not stop the outbreak of infectious diseases. when the vaccine failure rate further increases, such as . , the number of vaccinated individuals decays to zero before the epidemic is eliminated, which is almost equivalent with the classic sir model. anyway, current results are conducive to better understanding the individual vaccination behaviors when confronting the real epidemics. the authors declare that they do not have any financial or nonfinancial conflict of interests. transmission dynamics of the etiological agent of sars in hong kong: impact of public health interventions novel influenza a (h n ) pregnancy working group. h n influenza virus infection during pregnancy in the usa an outbreak of 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sir-based disease spreading and awareness diffusion on multiplex networks modelling the influence of human behavior on the spread of infectious diseases: a review vaccination and the theory of games epidemic dynamics on complex networks imitation dynamics of vaccination behavior on social networks hub nodes inhibit the outbreak of epidemic under voluntary vaccination policy evaluation for the subsidy for influenza vaccination in elderly does subsidy work? price elasticity of demand for influenza vaccination among the elderly in japan impacts of subsidy policies on vaccination decisions in contact networks simulation analysis of vaccination subsidy with abm approach preferential imitation can invalidate targeted subsidy policies on seasonal-influenza diseases subsidy strategy based on history information can stimulate voluntary vaccination behaviors on seasonal diseases effects of behavioral response and vaccination policy on epidemic spreading -an approach based on evolutionary-game dynamics a susceptible-infected epidemic model with voluntary vaccinations group interest versus self-interest in smallpox vaccination policy imitation dynamics predict vaccinating behavior impact of committed individuals on vaccination behavior the impact of imitation on vaccination behavior in social contact networks the influence of social norms on the dynamics of vaccinating behavior for paediatric infectious diseases risk assessment for infectious disease and its impact on voluntary vaccination behavior in social networks can influenza epidemics be prevented by voluntary vaccination? this project is financially supported by the national natural science foundation of china (nsfc) (grant nos. and ). key: cord- -lze ye q authors: bialasiewicz, luiza; eckes, christina title: ‘individual sovereignty’ in pandemic times – a contradiction in terms? date: - - journal: polit geogr doi: . /j.polgeo. . sha: doc_id: cord_uid: lze ye q nan over the past months, appeals to 'individual sovereignty' have brought together a wide range of political actors across europe, united in their rejection of face masks, 'social distancing', and other forms of stateimposed regulation of behavior and mobility. opposition to state efforts to govern the spread of the pandemic has created, indeed, the most unlikely of coalitions-from anarchists and natural health proponents to anti-vaxxers and libertarians of all stripes (from the radical-ecological to the right-nativist)-all mobilizing around a purported defense of 'personal freedoms' and 'individual rights' against the sovereign power of states. in this short piece, we take to task the notion of 'individual sovereignty' which has been invoked by these movements to contest the pandemic powers of the state. our aim is to point out some fundamental contradictions that underpin such claims-making, from a legal and political-geographic point of view. as simpson notes in his commentary, the impacts of both the pandemic and of the extension of state powers in attempting to contain it have been profoundly unequal across space and across different bodies, deemed more or less worthy of protection and care. while cognizant of the inherent inequalities (if not directly violence) of state pandemic-politics, we wish to draw attention here also to the potential perils that the contestation of state powers may bring when it throws into question the very bases of democratic collectivity. by highlighting how the claims of today's protest movements ably meld neoliberal appeals to 'individual responsibility' with a mystified and depoliticized notion of 'sovereignty' evacuated of its collective content, we add to mitropoulos's argument that the absence of collective action under pandemic circumstances conditions life chances on private wealth. in articulating their claims to 'individual sovereignty', many of the european protesters against covid- measures have appealed to the language of 'fundamental rights'. in both the german and dutch contexts, for instance, protesters have invoked constitutional protections in their calls for "the restoration of fundamental rights" (baumgartner et alia, ; nrc, ) . likewise, the leaders of the protest in rome in early june, which brought together the italian far-right and the gilet arancioni, presented themselves as "the guarantors of democracy" (merlo, ) . in the political imaginary of these protesters, 'fundamental rights' connote universal moral claims. they are understood as something that pertains to individuals, and that is actionable by individuals. as such, they are envisioned as capable of transcending and restricting, if needed, the political power of the state. yet fundamental rights, as they are codified by law, are always also an expression of national (or at times supra-national claims to) sovereignty. they are partial, based on a political choice, and subject to politically introduced limits (ignatieff, ) . understood as a formal recognition of certain political values (and not others), codified in a particular way, and backed by the threat of enforcement, fundamental rights are both a confinement and an expression of public powers. this double role of fundamental rights is what defines their essential role in ensuring that the inherent tension between individual autonomy and collective self-rule, i.e. sovereignty, does not result in the destruction of one or the other. jürgen habermas eloquently expresses for pandemic times what this tension is aimed to ensure: "if democratic citizens only obey the general laws that they have given to themselves, and all together, they cannot agree to policies that, contrary to their equality, jeopardize the lives of some for the sake of everyone else's interests" (habermas in habermas & günther, ) . along with the language of fundamental rights, the protests across various european cities have also appealed to another powerful notion, that of 'popular sovereignty'. protests in stuttgart and berlin have invoked the slogan 'wir sind das volk' ('we are the people') (höhn, ) while in the italian context, the gilet arancioni gathered around the chant of 'quando tutto crolla, l'ultima frontiera della democrazia è il popolo!' (when everything collapses, the last frontier of democracy is the people!') (berizzi, ) . 'the people' which today's protesters invoke are the 'real people', the 'silent majority', contesting an illegitimate state that is simply a proxy for corporate (read: big pharma) interests and other sinister 'elite' and 'foreign' agendas. the 'virus madness' group leading the protests in the netherlands (now called 'virus truth') is indicative, having focused its campaign on 'giving voice to the will of the people', through court appeals as well as direct actions protests. we can certainly identify here a continuity with the sort of sovereigntist-populist language that we have become accustomed to in the past years: a political imaginary reliant, as cas mudde ( : ) has discussed extensively in the european press: see among others baumgartner et alia ( ), mastrobuoni ( ) and seymour ( ) , and our comments in bialasiewicz and muehlenhoff ( argued, upon a vision of society "separated into two homogeneous and antagonistic groups: 'the pure people' versus 'the corrupt elite', and which argues that politics should be an expression of the 'volonté générale' of the people". in this sense, as nadia urbinati ( a) points out, populist rhetoric "violates the synecdoche of modern representative democracy (that is, the claim of a 'part' to represent 'the whole')" by claiming to embody "one part only, the 'authentic' or 'good' part, which by this very reason is legitimate to rule for its own good" (urbinati, a, p. ). the invocations of today's protesters thus recall pre-covid populist rhetoric. as jan-werner müller ( ) has remarked, the "claim to monopoly of properly representing the people" has remained "the political business model of populists" in pandemic times. all the while, we would argue, the focus has undergone a transformation: from appeals to an imagined national 'people' to an emphasis also on personal or individual 'sovereignty', that now becomes the site of basic rights to be defended against the 'sanitary dictatorship' of state institutions presented as "fundamentally illegitimate" (müller, ) . we would like to focus on unpacking this notion of 'individual sovereignty' in the remainder of this commentary in order to point out its inherent contradictions, while also cautioning how it may risk giving populist rhetoric another perilous tool with which to contest the modern constitutional democratic state. within modern constitutional democratic states, individual autonomy is expressed and protected through fundamental rights, which have a double-edged relationship with sovereignty. on the one hand, fundamental rights are, in their specific codified form, an expression of a sovereign choice; on the other hand, they protect individual liberty and autonomy (or self-rule) and limit the exercise of sovereignty. individual autonomy is thus necessary to create the conditions of the very collective self-rule or 'collective autonomy' that is the essence of sovereignty (habermas, ) . indeed, the collective autonomy of any polity is dependent on individual autonomy, in the sense that collective will-forming requires that individual participants actually possess the liberty to make decisions and to determine their actions (habermas, ) . the enjoyment and also enforcement of fundamental rights is central to protecting individual autonomy. procedural and substantive rights allow the equal and free participation of all in the collective will-forming (habermas, ; zürn, ) . they ensure that all participants are treated as individually autonomous. howeverand this is crucial to remember in the current momentindividual autonomy requires collective self-rule under democratic procedures, a collective rule that is able to supply the necessary (collective) public goods that can make the individual autonomous, e.g., public safety and public health. sovereignty is always an expression of a political relationship between the ruler and the ruled-in the modern constitutional democratic state, between the state and the people (loughlin, ) . when the concept of sovereignty is associated with individual autonomy under a different namenamely, the notion of 'individual sovereignty' -the core essence of sovereignty, namely the political and collective, is lost. the political and the collective is essential to sovereignty in the very sense of the word: if it is lost, the concept changes its meaning and becomes unrecognizable. this is not simply a conceptual or terminological problem. as adopted in political discourse, such a notion becomes deeply misleading and charged with a neoliberal conception of the state that denies its fundamental characteristic of being collective. 'individual sovereignty' simply makes no sense in light of the historical and conceptual meaning of sovereignty. sovereignty, while conceptually blurred and contested, does have a very specific core meaning in the modern european constitutional state. in this core meaning, sovereignty connects state authority with democracy and collective self-rule. 'individual sovereignty', by contrast, equates sovereignty with the liberal (rather than democratic) value of individual self-rule. it decouples the concept from its very essence and hence robs it of any meaning. in our pandemic times, when the inherent tension between individual autonomy and collective self-rule becomes particularly stark, it is especially important to protect the collective and the 'common good' from terminological usurpation. italian political philosopher pier aldo rovatti ( ) writing about responses to the pandemic in his essay 'when the i becomes us' asks how we can reverse that which nadia urbinati ( b) identifies as the populist 'me the people' political style that has dominated european politics in the past few years, now articulated simply under a different rubric, that of 'individual sovereignty'. rovatti suggests that while governments may be tempted to ensure compliance with covid- measures through appeals to 'individual responsibility', this framing is inherently perilous. such an individualized response to the pandemic, which places the individual in the position of the (collective) sovereign, conflates individual autonomy with collective self-rule. in doing so, it obscures the rights of the diverse collective to protection from individual behaviours that can take an excessive toll on the health care system (a common good) and on the individual autonomy of those whose lives will be imperiled by infection. the authors declare that there is no conflict of interest. protests in germany see fringe mix with the mainstream gilet arancioni e casa pound in piazza a roma contro il governo. la repubblica personal sovereignty in pandemics: or, why do today's sovereigntists reject state sovereignty? open democracy state sovereignty as social construct between facts and norms: contributions to a discourse theory of law and democracy kein grundrecht gilt grenzenlos coronavirus rallies: germany's growing anti-lockdown movement human rights as politics and idolatry ten tenets of sovereignty germania, medicina alternativa e profughi: cosi il covid alimenta le vecchie e nuove fake news. la repubblica as italian protesters have termed the state's pandemic emergency powers informative in this regard is habermas' procedural account of democratic legitimacy, which presumes that a collective will can only be formed in a legally structured political community (habermas, , p. ), in which courts guarantee equal subjective liberties, equal membership rights, and legal protection of these rights see, among others, the extensive discussion in nia_coronavirus_true_pandemia_coronavirus- /?ref=rhpptp-bh-i -c -p -s . -t destre, ressa in piazza populists are likely to benefit from the coronavirus pandemic. institute for human sciences dansen op dj jean en ageren tegen vaccin en big pharma virus veritas. milano: il saggiatore give them liberty, or give them covid- . why the hard right is fighting lockdown antiestablishment and the substitution of the whole with one of its parts me the people: how populism transforms democracy deliberative democracy and constitutional review key: cord- -g bsul u authors: voinson, marina; alvergne, alexandra; billiard, sylvain; smadi, charline title: stochastic dynamics of an epidemic with recurrent spillovers from an endemic reservoir date: - - journal: journal of theoretical biology doi: . /j.jtbi. . . sha: doc_id: cord_uid: g bsul u abstract most emerging human infectious diseases have an animal origin. while zoonotic diseases originate from a reservoir, most theoretical studies have principally focused on single-host processes, either exclusively humans or exclusively animals, without considering the importance of animal to human transmission (i.e. spillover transmission) for understanding the dynamics of emerging infectious diseases. here we aim to investigate the importance of spillover transmission for explaining the number and the size of outbreaks. we propose a simple continuous time stochastic susceptible-infected-recovered model with a recurrent infection of an incidental host from a reservoir (e.g. humans by a zoonotic species), considering two modes of transmission, ( ) animal-to-human and ( ) human-to-human. the model assumes that (i) epidemiological processes are faster than other processes such as demographics or pathogen evolution and that (ii) an epidemic occurs until there are no susceptible individuals left. the results show that during an epidemic, even when the pathogens are barely contagious, multiple outbreaks are observed due to spillover transmission. overall, the findings demonstrate that the only consideration of direct transmission between individuals is not sufficient to explain the dynamics of zoonotic pathogens in an incidental host. recent decades have seen a surge of emerging infectious diseases (eids), with up to forty new diseases recorded since the s ( jones et al., ) . sixty percent of emerging human infectious diseases are zoonotic, i.e. are caused by pathogens that have an animal origin ( jones et al., ; taylor et al., ) . the world health organization defines zoonotic pathogens as "pathogens that are naturally transmitted to humans via vertebrate animals". the epidemics caused by eids impact the societal and economical equilibria of countries by causing unexpected deaths and illnesses thereby increasing the need for health care infrastructures and by interfering with travel ( morens and fauci, ) . moreover, the risk of eids being transmitted to humans from wildlife is increasing because of the recent growth and geographic expansion of human populations, climate change and deforestation, which all in-crease the number of contacts between humans and potential new pathogens ( jones et al., ; keesing et al., ; murray and daszak, ) . given most eids have an animal origin, it is crucially important to understand how infections spread from animal to human populations, i.e. by spillover transmission. there is numerous empirical evidence that the epidemiological dynamics of infectious diseases is highly dependent on the transmission from the reservoir (the reservoir will be defined following ashford's definition ( ) , i.e. a pathogen is persistent in the environment of the incidental host, see table for details). the start of an outbreak is promoted by a primary contact between the reservoir and the incidental host (i.e. host that becomes infected but is not part of the reservoir) leading to the potential transmission of the infection to the host population. moreover, multiple outbreaks are commonly observed during an epidemic of zoonotic pathogens in human populations, for instance in the case of the epidemic of the nipah virus between and ( luby et al., ) . with regards to the ebola virus, some twenty outbreaks have been recorded since the discovery of the virus in ( de la vega et al., ) . this number of outbreaks undoubtedly underestimates the https://doi.org/ . /j.jtbi. . . - /© elsevier ltd. all rights reserved. definitions of a reservoir from the literature. the reservoir is mostly used as defined by the centre for disease control and prevention (cdc) . two other definitions have been proposed to clarify and complete the notion of reservoir in the case of zoonotic pathogens. on the one hand, haydon et al. ( ) define the reservoir from a practical point of view in order to take into account all hosts epidemiologically connected to the host of interest (i.e. target host), to implement better control strategies. on the other hand, ashford ( ) establishes a more generalizable definition: for a given pathogen there is a single reservoir. authors refs "any animal, person, plant, soil, substance or combination of any of these in which the infectious agent normally lives" centre for disease control and prevention ( ) "all hosts, incidental or not, that contribute to the transmission to the target host (i.e. the population of interest) in which the pathogen can be permanently maintained" haydon et al. ( ) "an ecologic system in which an infectious agent survives indefinitely" ashford ( ashford ( , total number of emergences because not all emergences necessarily lead to the spread of the infection from an animal reservoir to the host population ( jezek et al., ) . while the reservoir has an important role for causing the emergence of outbreaks, the role of spillover transmission on the incidental epidemiological dynamics is rarely discussed. empirically, it is generally difficult to distinguish between direct transmission and transmission from the reservoir. only in the case of non-communicable diseases it is easily possible to measure the importance of the recurrent transmission from the reservoir, since all infected individuals originate from a contact with the reservoir. for instance, the h n virus, for which most human cases are due to a contact with an infected poultry, approximately spillovers have been listed during the epidemic of ( zhou et al., ) . for pathogens that are able to propagate from one individual to another, the origin of the infection can be established according to patterns of contacts during the incubation period ( chowell et al., ; luby et al., ). most often, if an infected individual has been in contact with another infected individual in his recent past, direct transmission is considered as the likeliest origin of the infection. however, both individuals might have shared the same environment and thus might have been independently infected by the reservoir. this leads to overestimating the proportion of cases that result from person-to-person transmission. moreover, when the pathogen infects an individual and the latter does not produce secondary cases then the detection of emergence is unlikely. pathogen spillover is often neglected in epidemiological theoretical models. it is generally assumed that the epidemiological dynamics of outbreaks is driven by the ability of the pathogen to propagate within hosts. for instance, a classification scheme for pathogens has been proposed by wolfe et al. ( ) , including five evolutionary stages in which the pathogen may evolve ranging from an exclusive animal infection (stage i) to an exclusive human infection (stage v) ( fig. ) ( wolfe et al., ) . the intermediate stages are those found for the zoonotic pathogens (stages ii-iv). lloyd-smith et al. ( ) , proposed to enhance the classification scheme by differentiating the stages ii-iv by the ability of pathogens to propagate between individuals in the incidental host (i.e. as a function of the basic reproductive ratio r ): the noncontagious pathogens ( r = , stage ii), pathogens barely contagious inducing stuttering chains of transmission ( < r < , stage iii) and contagious pathogens inducing large outbreaks ( r > , stage iv) ( lloyd-smith et al., ) . however, the role of the reservoir is not clearly defined, and spillover effects on the epidemiological dynamics are not discussed. only a few models have investigated the dynamics of eids by taking into account explicitly the transmission from the reservoir to the incidental host. lloyd-smith et al. ( ) have analysed modelling studies of zoonotic pathogens and concluded that models incorporating spillover transmission are dismayingly rare. more recent models aimed at investigating the dynamics of eids by taking into account the spread of the pathogen using multihost processes but disregarding the persistence of the pathogen in the reservoir ( singh et al., ) , or by focusing on the dynamics and conditions of persistence of the pathogen between two populations ( fenton and pedersen, ) . models that have considered an endemic reservoir are disease-specific and do not generate generalizable dynamics ( chowell et al., ; nieddu et al., ) . more recently, singh and myers ( ) developed a susceptible-infected-recovered (sir) stochastic model coupled with a constant force of infection. the authors are mostly interested in the effect of population size and its impact on the size of an outbreak. however, this approach does not allow teasing apart the contribution of the incidental host transmission from that of the transmission from the reservoir in modulating the dynamics of zoonotic pathogens. in this paper, we aim to provide general insights into the dynamics of a zoonotic pathogen (i.e. pathogens classified in stages ii-iv) emerging from a reservoir and its ability to propagate in an incidental host. to do so, we developed a continuous time stochas- fig. . representation of the classification scheme of pathogens proposed by wolfe et al. ( ) . a pathogen may evolve from infecting only animals (stage i) to infecting only humans (stage v). each stage corresponds to a specific epidemiological dynamics in the incidental host. stage ii corresponds to few spillovers from animals (e.g. bats) to humans with no possible transmission between humans. stage iii corresponds to few stuttering chains of transmission between humans that go extinct (no outbreaks). stage iv corresponds to large outbreaks in human population but the pathogen cannot be maintained without the reservoir. tic model that can dissociate the effect of between-host (i.e. direct) transmission from the effect of spillover (i.e. reservoir) transmission. a multi-host process with a reservoir and an incidental host is considered. the epidemiological processes are stochastic, which is particularly relevant in the case of transmission from the reservoir and more realistic because only a small number of individuals are expected to be infected at the beginning of an outbreak. the model makes a number of assumptions. first, the epidemiological processes are much faster than the demographic processes. second, the pathogen in the reservoir is considered as endemic and might contaminate recurrently the incidental host. third, an individual cannot become susceptible after having been infected. as a consequence, the total number of susceptible individuals in the incidental host decreases during the epidemic. this is what is expected for an epidemic spreading locally during a short period of time (at the scale of a few thousands individuals during weeks or months, depending on the disease and populations considered). we then harness the model to predict the effects of both spillover transmission and direct transmission on the number and the size of outbreaks. outbreaks occur when the number of cases of disease increases above the epidemiological threshold. in the case of non emerging infectious diseases, an epidemiological threshold is used to gauge the start of outbreaks. for instance for the seasonal influenza the epidemiological threshold is calculated depending on the incidence of the disease during the previous years ( tay et al., ) . in the case of emerging infectious diseases, no incidence is normally expected in the population so from a small number of infected individuals, the outbreak can be considered to spread. we show that, regarding the epidemiological dynamics, the recurrent emergence of the pathogen from the reservoir in the incidental host is as important as the transmission between individuals of the incidental host. we conclude by discussing the implications of these results for the classification of pathogens proposed by lloyd-smith et al. ( ) . a continuous time stochastic susceptible-infected-recovered (sir) compartmental transmission model ( kermack and mckendrick, ) with recurrent introduction of the infection into an incidental host by a reservoir is considered ( fig. ). our goal here is not to study a disease in particular but to provide general insights of the reservoir effect on the epidemiological dynamics of the incidental host. the infection is assumed to propagate quickly relatively to other processes such as pathogen evolution and demographic processes. the reservoir is defined as a compartment where the pathogen is persistently maintained, this pathogen is then considered as endemic. the population is fully mixed. an individual can be infected through two types of transmission, from the reservoir by the spillover transmission and by direct contact between individuals. we neglect the possibility for reverse infection from the incidental host to the reservoir. the incidental host is composed of n individuals. the infection can spillover by contact between the reservoir and the incidental host at rate τ s where s is the number of susceptible individuals and τ is the rate at which an individual becomes infected from the reservoir. in the incidental host, the infection can propagate by direct contact at rate βsi where i is the number of infected individuals and β is the individual rate of infection transmission. an infected individual can recover at rate γ . the propensity of the pathogen to be transmitted between individuals within host is expressed in terms of the basic reproductive ratio of the pathogen, r , which is widely used in epidemiology. r corresponds to the average number of secondary infections produced by an infected individual in an otherwise susceptible population. in a deterministic model, for a pathogen to invade the population, r must be larger than in the absence of reservoir. in a stochastic model, the higher the r the higher the probability for the pathogen to invade the population. in a sir model, the basic reproductive ratio r equals to βn / γ . individuals in the recovered compartment do not contribute anymore to the transmission process. since we assume that demographic processes are slower than epidemic processes, the number of susceptible individuals decreases during the epidemic due to the consumption of susceptible by the infection until the extinction of the susceptible population. in other words, in our model, r will decrease because of the successive spillovers from the reservoir. we expect this to occur especially at short space and time scales (a local population during the course of weeks or months). to analyse the dynamics in the incidental host, three statistics will be studied (i) the mean number of outbreaks, (ii) the mean size of the recurrent outbreaks during an epidemic and (iii) the individuals mean size of the largest outbreak occurring during an epidemic. we consider the appearance of an outbreak when the incidence of the infection exceeds the threshold c and define the maximum size of an outbreak as the largest number of infected individuals during the largest outbreak. stochastic simulations. the epidemiological dynamics described previously can be simulated with the following algorithm (simulations were run in c++). the population state is assumed to be known at time t . a total event rate ( ), only depending of the state of the population at time t , is calculated for each iteration. a) the total event rate of the continuous time stochastic sir model is given by: b) the next event time is t = t + δ where δ is exponentially distributed with parameter . c) the next event to occur is randomly chosen: direct transmission, spillover transmission or recover with respective probabilities βsi / , τ s / and γ i / . we performed stochastic individual-based simulations of the epidemics with spillover transmission, using rates as presented in fig. . the incidental host is initially ( t = ) composed of susceptible individuals ( n = s = ). the infection is considered as endemic in the reservoir. simulations are stopped when there are no susceptible individuals anymore. an outbreak begins when the number of infected individuals reaches the epidemiological threshold c ( c = infected individuals in the simulations) and ends when there is no infected individuals anymore ( i = ). stochastic simulations were run for values of the basic reproductive ratio ( r ) ranging from to and of the spillover transmission ( τ ) ranging from − to − , , simulations are performed for each parameter set. all other parameter values are detailed in table . approximation by a branching process. the epidemiological model with recurrent introduction of the infection into an incidental host by a reservoir can be approximated by a branching process with immigration from the reservoir to the incidental host at the beginning of the infectious process (thus assuming that individual "birth" and "death" rates of infected individuals are constant during the starting phase of an outbreak). the individual birth and death rates are respectively βn , the transmission rate and γ , the recovery rate. the immigration rate corresponds to the spillover rate, τ n , at the beginning of the infection. in other words, we assume that the number of susceptibles is n to study the beginning of the infection, which is a good approximation as long as few individuals have been infected. we distinguish between two regimes in the incidental host, the subcritical regime when r < and the supercritical regime when r > . we suppose that at time t = a single individual is infected by the spillover transmission. as illustrated in fig. , three patterns are observed (i) a stuttering chain of transmission that goes extinct, i.e. infection spreads inefficiently, (corresponding to stage ii in wolfe's classification, see served are wider for a higher threshold value (compare fig. a and b), whereas stage iii is narrower. when the direct and the spillover transmissions are low, it is more difficult for the infection to reach a higher threshold. thus, there are more stuttering chains of transmission. in the same way, when the direct or the spillover transmission is high, a large outbreak is observed then some stuttering chains of transmission occur but do not reach the epidemiological threshold. for both values of epidemiological threshold ( fig. (a) and (b)), a "bulb" is observed in the stage iii where the direct transmission is high. after the occurrence of a large outbreak, the susceptible population became small. hence the next excursion is very unlikely to reach the epidemiological threshold. however, a high enough spillover transmission rate is able to counterbalance the small effective r and to produce other outbreaks after the large one. the "bulb" is less pronounced in the case of a higher threshold ( fig. (b) ) because the susceptible population consumed during the large outbreak is important leading to the failure for the next excursion to reach a high epidemiological threshold. we aim at approximating the mean number of outbreaks in the case where the spillover transmission rate τ and the reproductive number r are small (subcritical case corresponding to r < ). the method of approximation is the following: let us denote by s i the number of susceptible individuals at the beginning of the i th excursion. during the i th excursion, we set this number of susceptibles to its initial value s i , and consider that the rate of new infections is βis i . we thus obtain a branching process with individual birth (infection) rate βs i and individual death (recovery) rate γ . when there is no more infected individuals, we compute the mean number of recovered individuals produced by this branching process excursion, denoted by e [ k(s i , β, γ )] , and make the approximation that where e [ k(s i , β, γ )] can be computed and equals (see ( ) in other words, the initial number of susceptible individuals for the ( i + )th excursion is the initial number of susceptible individuals for the i th excursion minus the mean number of recovered individuals produced during the i th excursion under our branching process approximation. we repeat the procedure for the ( i + )th excursion, and so on, until k satisfies s k > and s k + ≤ (no susceptible anymore). in order to be considered as an outbreak, an excursion has to exceed c individuals, where we recall that c is the epidemiological threshold. under our branching process approximation, the probability for the i th excursion to reach the epidemiological threshold (see appendix a ) is: as a consequence, our approximation of the mean number of out- where s = n, and the s i 's are computed as described in ( ) . the mean number of outbreaks computed with the branching process is a good approximation compared to numerical simulations for a small spillover transmission ( − ≤ τ ≤ − ) ( fig. ) . the spillover transmission added in our model introduces the infection recurrently and allows the infection to spread even for a pathogen barely contagious ( r < ). according to fig. when r < the number of outbreaks increases when the direct transmission between individuals increases. indeed, the higher the direct transmission, the higher the probability for the excursions to reach the epidemiological threshold ( c ). the number of outbreaks can be high because when the direct transmission is smaller than , the infection spreads inefficiently and does not consume a large number of susceptibles allowing the next excursion to exceed the epidemiological threshold. fig. shows that the average number of outbreaks is a non-monotonic function of the direct transmission ( r ) and the spillover transmission ( τ ). more precisely, fig. (b) shows that for intermediate and low values of spillover transmission ( − ≤ τ ≤ − ), the average number of outbreaks increases until r ∼ then decreases until it reaches one outbreak when the direct transmission is high ( r > . ). moreover, we observed an increasing number of outbreaks with τ when the pathogen is barely contagious. by contrast, in fig. (a), we show that the average number of outbreaks decreases when τ becomes large ( τ . − ). the supercritical case ( r > ) is now considered and the spillover transmission rate ( τ ) is still supposed small. process approximation, respectively. the average number of outbreaks approximated is evaluated when the spillover transmission τ is small. for the numerical simulations, τ = − has been chosen. there is a break in the dotted curve (branching process) because our approximation is not valid in the critical regime (when r is close to ). in this case, two different types of excursions occur in the incidental host: (i) a large outbreak which consumes, with a probability close to one, a large proportion of susceptible individuals and (ii) multiple excursions before and after a large outbreak which each consumes few susceptible individuals. we let o before ( n, β, γ ) and o after ( n, β, γ ) denote the number of outbreaks occurring respectively before and after the large outbreak. because r > , the probability to have one large outbreak is close to one. hence we make the approximation that one large outbreak occurs during the epidemic, and the total number of outbreaks ( o total to be part of outbreaks occurring before the large one, an excursion has to satisfy two conditions (i) to have a size higher than the epidemiological threshold c , and (ii) to be of a size not too large otherwise it would correspond to the large outbreak. to be more precise, this condition will correspond to the fact that the supercritical branching process used to approximate this excursion does not go to infinity. as a consequence, o before ( n, β, γ ) can be approximated by (see appendix b ) : to approximate the number of outbreaks after the large outbreak ( o after ( n, β, γ ) ), we need to know how many susceptible individuals remain in the population. the number of susceptibles consumed before the large outbreak is negligible with respect to the number of susceptibles consumed during the large outbreak. hence we can consider that the initial state of the large outbreak is n susceptibles, one infected individual and no recovered individual. which has one trivial solution ( s = n) and a non-trivial solution with no explicit expression denoted n after ( n, β, γ ) . after the large outbreak, the reproductive ratio for the next excursions, denoted r a f ter , is subcritical ( r a f ter < ) (see appendix b ) and the number of outbreaks after the large one, denoted o after , can be approximated using eqs. ( ) -( ) . the branching process approximations of the mean number of outbreaks in the supercritical regime, depicted in fig. , are close to the mean number of outbreaks computed by numerical simulations when the recurrent infection from the reservoir is small. the number of outbreaks decreases when the pathogen becomes highly contagious to reach one outbreak when r > . . when the infection is introduced in the incidental host by the spillover transmission, the probability to reach the epidemiological threshold depends on the direct transmission between individuals. when the direct transmission increases the infection spreads more efficiently consuming a large number of susceptible individuals allowing few or no other excursion to reach the epidemiological threshold and producing only one outbreak when r > . . we now focus on the effect of the spillover transmission with a pathogen barely contagious ( r < ) on the number of outbreaks. we exclude for the sake of simplicity the cases very close to the critical case, that is to say, − r is not too close to . because we consider the subcritical case ( r < ), the excursions are small and at the beginning of the epidemiological dynamics, we make the approximation that the spillover transmission rate is constant equal to τ n , and the direct transmission rate is equal to βni . we thus consider a birth and death process with constant immigration rate τ n , individual birth rate βn and individual death rate γ . we are interested in the effect of the parameter τ on the mean number of outbreaks. in particular we aim at estimating the value of τ maximising the mean number of outbreaks, denoted τ opt . a first quantity which will help giving us an idea of the order of magnitude of the values of τ to be considered is the mean number of infected individuals at large times. this quantity, denoted m i , equals (see for instance eq. ( . ) in bailey, ) : in particular, when the mean number of infected individuals is much larger than c , and when on the contrary the mean number of infected individuals is negligible with respect to c . let us first consider the first case ( eq. ( ) ), and choose α > such that then we can show (see appendix c. ), that the probability p c that a first infection by the reservoir gives rise to an outbreak (that is to say the number of infected individuals reaches c before ) is larger than: moreover, we can show that if an excursion reaches the level c , it has a probability close to one to lead to a large outbreak consuming a large number of susceptible individuals. thus only few stuttering chains of transmission will emerge. in fig. (a) , when τ is large ( τ > − thus τ n/ (cγ ( − r )) ≥ ), only one outbreak is observed because the large number of spillovers prevents the outbreak from dying out. let us now consider the second case ( eq. ( ) ). recall that in the case of emerging infectious diseases, the threshold c can be considered as small. hence we may consider without loss of generality that ( ) implies: in this case, we can prove (see appendix c. ) that the probability that the number of infected individuals is higher than the threshold c is : thus the probability for the number of infected individuals to reach the epidemiological threshold c is small under condition ( ) . as a consequence, few outbreaks will occur. indeed, the successive spillovers by the reservoir will produce outbreaks with a small probability, but will nevertheless consume susceptible individuals, until there is no more susceptible in the population. according to fig. (a) , when a small effect of spillover transmission ( τ < − ) and a small reproductive ratio ( r ≤ . ) are considered ( τ n/ (cγ ( − r )) < . − ) then the number of outbreaks is small. in the case of a slightly higher direct transmission rate ( r = . ), each spillover has a non negligible probability to become an outbreak (more precisely . when c = ) and the number of outbreaks is higher. we thus predict that the number of outbreaks will tend to be large when the average size of an excursion is close to the epidemiological threshold ( m i c ). these observations allow us to give a first rough upper bound of the optimal value τ opt . indeed, if the mean number of infected individuals ( e [ i ]) is equal to c , the ra- represents the variance of the number of infected individuals, see appendix c. ) and whose value belongs to [ . , ] when c = for the values of r considered, which is large. moreover in this case the distribution of i is skewed to the right (see fig. c . ). this implies that the number of infected individuals will be larger than c a large fraction of the time producing outbreaks which do not go extinct before a new infection by the reservoir, and thus producing few outbreaks. hence we may conclude that τ opt is smaller than the τ leading to a mean number of infected individuals c . for instance for the parameters considered in fig. (a) , this gives that τ opt is smaller than: let us now be more precise on the estimation of τ opt . to this aim, we will apply two results of the theory of branching processes with immigration. the first one, which can be found in bailey ( , eq. ( . )) describes the total infectious lines over the course of the infection, denoted by m : notice that m is necessarily larger than as an infection from the reservoir is needed to generate the first infectious line. the second result is the mean number of infectious lines expected to be present at any time, that is to say in the theory of branching processes the number of distinct immigrants which have descendants alive at a given moment. for large times, this mean number ( m i ) is equal to: pardoux, ) , where e [ t ] denotes the mean lifetime of a branching process without immigration, with individual birth rate βn , individual death rate γ , and initial state . this expression can be computed explicitly (see appendix c. . ) and equals: thus leading to the expression: we will divide an excursion into m / m i blocks of m i simultaneous infectious lines (thus without immigration). the idea for such an estimation is the following: it is known that if a poisson process has k jumps during a time interval, the jumps are uniformly distributed during this time interval. as the infections by the reservoir follow approximately a poisson process with parameter τ n , and we know that in expectation m infections by the reservoir occur before all infected individuals are removed, we divide the epidemic in homogeneous blocks. we choose these blocks to have an initial number of m i infected individuals to allow the use of results on branching processes with immigration. the initial number of infected individuals in each block is thus m i , and as a consequence the infection has a probability to reach the threshold c (see appendix c. ). hence the probability for the whole excursion to reach the threshold c can be approximated by we want this probability to be not too close to , otherwise most susceptible individuals would be consumed without giving rise to an outbreak. we also want this probability to be not too close to . indeed, as we have shown in the beginning of this section, this would correspond to a case where τ n / γ is much larger than c( − r ) and once the infected number of individuals has reached the value c it would be very likely to reach a large value and consume a large number of susceptible individuals. as a consequence, we would have at the limit only one large outbreak. we thus choose to equalize this probability to one half to get an estimation of τ opt . notice that this choice is arbitrary but has only a small effect on the final results. for instance, a choice of . or . would give very close results. the most important is to stay away from and . as a conclusion, τ opt is estimated as the unique solution to: the unicity of the solution is proved in appendix c. . fig. (b) presents the values of τ maximising the number of outbreaks and their estimations (dots) obtained by the branching process approximations. the estimates derived under the branching process approximation give good results, with error ranging from to % regardless the value of the epidemiological threshold ( table ) . values of the optimal spillover transmission from numerical simulations and estimations. the optimal spillover transmission is calculated for r being equal to . , . , . , and . . we present the values of the optimal spillover for two values of epidemiological threshold c = (bold) and c = (not bold). the errors are ranging from to % with a mean error of %. to get the estimation of τ opt we have made several approximations. first we have considered that the spillover rate by the reservoir is constant equal to τ n , whereas it is decreasing and equals to τ s , and that the rate of direct transmission due to infected individuals in the population is βni and not βsi . we believe that these approximations are reasonable because the probability for an excursion to reach the threshold decreases with the consumption of susceptible individuals, and as a consequence, most of the outbreaks will occur at the beginning of the process. however, the real τ opt should be a little bit higher than the one we estimate, to counterbalance the fact that the real infection rates (by the reservoir and the infected individuals) are smaller than the one we use in our calculations. this may explain why in most of the cases we underestimate the real τ opt (see table ). the following approximation we made is the decomposition of the excursions into blocks with an initial number of individuals m i . in the real process there are no simultaneous infections by the reservoir. however this approximation allows to take into account previous infections by the reservoir whose infectious lines are still present. when the ratio, v ar[ i ] / e [ i ] = τ n/γ , is small (see appendix c. ), the value of i stays close to its expectation and few outbreaks occur, as the number of infected individuals rarely reaches . for instance, for r = . and τ = . . − , τ n / γ ∼ . . as decreasing τ increases this ratio, this could explain why we overestimate τ opt for small values of r (because smaller values of r necessitate higher values of τ to get the same probability to reach the threshold c ). during the epidemic, a large outbreak can occur depending on the value of the direct transmission ( r ) and the spillover transmission ( τ ) and corresponds to the largest number of infected individuals. to analyse the effect of the recurrent emergence of the pathogen on the size of the largest outbreak, we model the largest outbreak by a sir deterministic model with a spillover transmission: since no explicit expression of the size of the outbreak can be obtained with the deterministic model, we estimated it using numerical analyses. fig. shows that the maximal number of infected individuals during the largest outbreak increases with the direct transmission ( r ) and the spillover transmission ( τ ). when the direct transmission ( r ) is small, the size of the largest outbreak can differ by orders of magnitude with varying spillover transmission ( τ ). furthermore, a large outbreak can be observed for a pathogen barely contagious ( r < ) when the recurrent emergence of the pathogen is high ( τ − ). zoonotic pathogens constitute one of the most pressing concerns with regards to future emerging diseases, but studies investigating the importance of the role of animal reservoirs for the epidemiological dynamics of infectious diseases are lacking. indeed, most theoretical works only consider pathogen transmission between conspecifics for predicting disease epidemiology. here, we build a continuous time stochastic sir model to consider the statistical process underlying a spillover transmission, i.e. transmission from an animal reservoir to a host. we analyse the model to predict the number and the size of outbreaks as a function of both the spillover transmission and within host. the model shows that spillover transmission influences the epidemiological dynamics as much as the transmission by direct contact between individuals. three different dynamics are observed, ranging from the absence of outbreaks to a single large outbreak. the findings have implications for ( ) modelling the dynamics of eids, ( ) understanding the occurrence of outbreaks in the case of pathogens that are barely contagious and ( ) control strategies. in our results, the appearance of outbreaks depends on both the transmission from the reservoir and the direct transmission between individuals. generally, the occurrence of epidemics in humans is attributed to the ability of the pathogen to propagate between individuals. in the case of a single-host process, the notion of the basic reproductive ratio r seems sufficient to evaluate the spread of the pathogen in a population entirely composed of susceptible individuals. in eids, r is also used to gauge the risk of pandemics. in this way, lloyd-smith et al. ( ) delineate the three stages identified for a zoonotic pathogen ( wolfe et al., ) by using the ability of the pathogen to spread between individuals. each stage corresponds to a specific epidemiological dynamics ranging from a non-contagious pathogen making an outbreak impossible (stage ii, r = ) to a barely contagious pathogen with few outbreaks and stuttering chains of transmission (stage iii, r < ) to a contagious pathogen making a large outbreak possible (stage iv, r > ). the aim of the wolfe's classification is to establish each stage at which a zoonotic pathogen may evolve to be adapted to human transmission only, in order to identify pathogens at potential risk of pandemics. however, in our model, by taking into account the recurrent emergence of the pathogen from the reservoir, the three dynamics that define the three stages will depend on both the spillover transmission and the direct transmission of the pathogen between individuals. the results suggest that in the case of pathogen spilling recurrently over an incidental host, the direct transmission should not be the only parameter to consider. the presence of a reservoir and its associated recurrent spillovers dramatically impact the epidemiological dynamics of infectious diseases in the incidental host. without transmission from the reservoir, the probability to have an outbreak when the pathogen is barely contagious only depends on the direct transmission between individuals, and the outbreak rapidly goes extinct. by contrast, the results show that the recurrent emergence of the pathogen from a reservoir increases the probability to observe an outbreak. spillover transmission enhances the probability to both observe longer chains of transmission and reach the epidemiological threshold (i.e. threshold from which an outbreak is considered) even for a pathogen barely contagious. moreover, this coupling model (reservoir-human transmission) allows the appearance of multiple outbreaks depending on both the ability of the pathogen to propagate in the population and the transmission from the reservoir. zoonotic pathogens such as mers, ebola or nipah are poorly transmitted between individuals ( r estimated to be less than ) ( althaus, ; chowell et al., ; luby et al., ; zumla et al., ) yet outbreaks of dozens/hundreds/thousands of infected individuals are observed. we argue that, as suggested by our model, the human epidemic caused by eids could be due to a recurrent spillover from an animal reservoir. in the case of zoonotic pathogens, it is of primary importance to distinguish between primary cases (i.e. individuals infected from the reservoir) and secondary cases (i.e. individuals infected from another infected individual) to specify which control strategies to implement and how to optimize public health resources. according to the stochastic sir model coupled with a reservoir analysed here, the same dynamics can be observed depending on the relative contribution of the transmission from the reservoir and the direct transmission by contact with an infected individual (see fig. ). for example, a large outbreak is observed either for a high spillover transmission or for a high direct transmission. the proposed stochastic model makes it possible to understand the effects of the infection from the reservoir or from direct transmission on the epidemiological dynamics in an incidental host when empirically this distinction is difficult. empirically, the origin of the infection is established by determining the contact patterns of in-fected individuals during the incubation period. thereafter, the role of control programs implemented could be evaluated in order to determine better strategies. we have considered that the reservoir is a unique population in which the pathogen can persist, which is a simplifying assumption. the pathogen is then endemic in the reservoir and the reservoir has a constant force of infection on the incidental host. the reservoir can be seen as an ecological system comprising several species or populations in order to maintain the pathogen indefinitely ( haydon et al., ) . for example, bat and dromedary camel ( camelus dromedarius ) populations are involved in the persistence of mers-cov and in the transmission to human populations ( sabir et al., ) . in these cases, the assumptions of a constant force of infection can be valid because the pathogen is endemic. however, zoonotic pathogens can spill over multiple incidental hosts and they can infect each other. in the case of the ebola virus, which infects multiple incidental hosts such as apes, gorillas and monkeys ( ghazanfar et al., ) , the principal mode of contamination of the human population is the transmission from non-human primate populations. moreover, the contact patterns between animals and humans is one of the most important risk factors in the emergence of avian influenza outbreaks ( meyer et al., ) . these different epidemiological dynamics with transmission either from the reservoir or from other incidental hosts can largely impact the dynamics of infection observed in the human population, and the investigations of those effects can enhance our understanding of zoonotic pathogens dynamics. in our model, we make a second simplifying assumption by considering that the infection propagates quickly relatively to other processes such as pathogen evolution and demographic processes. this assumption can be not valid in the case of low emergence of the pathogen from the reservoir. indeed, the time between two spillovers can be long and makes the evolution of the pathogen possible inside the reservoir. moreover, during the time between two spillovers, the demography in the incidental host can vary and impact the propagation of the pathogen. in the case of low spillover transmission in the incidental host, the effect of both pathogen evolution and demographic processes can be a topic for future research on the epidemiological dynamics of emerging infectious diseases. in this paper, we have argued that the conventional way for modelling the epidemiological dynamics of endemic pathogens in an incidental host should be enhanced to account for spillover transmission in addition to conspecifics transmission. we have shown that our continuous time stochastic sir model with a reservoir produces similar dynamics to those found empirically (see the classification scheme for pathogens from wolfe et al., ) . this model can be used to better understand the ways in which eids transmission routes impact disease dynamics. in this appendix, we derive results on the branching process approximation stated in section . the main idea of this approximation is the following: when the epidemiological process is subcritical ( r < ), an excursion will modify the state of a small number of individuals with respect to the total population size. during the i th excursions, the direct transmission rate βsi will stay close to βs i i where s i denotes the number of susceptibles at the beginning of the i th excursion. hence, if we are interested in the infected population, the rate βs i i can be seen as a constant individual birth rate βs i . similarly, γ i , which is the rate at which an individual in the population recovers, can be interpreted as a constant individual death rate γ in the population of infected individuals. in this section, we focus on the number of outbreaks when r < and when the rate of introduction of the infection by the reservoir is small ( τ ). that is to say, we consider that each introduction of the infection by the reservoir occurs after the end of the previous excursion created by the previous introduction of the infection by the reservoir. according to eq. ( ) , this approximation is valid as long as the ratio τ / β is small. we first approximate the mean number of susceptible individuals consumed by an excursion. let us consider a subcritical branching process with individual birth rate βn and individual death rate γ . as this process is subcritical, we know that the excursion will die out in a finite time and produce a finite number of individuals. then from britton and pardoux ( ) or van der hofstad ( ) , if we denote by k [ n, β, γ ] the total number of individuals born during the lifetime of this branching process (counting the initial individual), we know that: where p denotes a probability, and hence where e is the expectation. by definition, an excursion is considered as an outbreak only if the maximal number of individuals infected at the same time during this excursion is larger than an epidemiological threshold that we have denoted by c . hence in order to approximate the number of outbreaks we still have to compute the probability for an excursion to be an outbreak. this is a classical result in branching process theory which can be found in athreya and ney ( ) for instance. p (n, β, γ ) : = p ( more than c individuals infected at a given time ) = γ /βn − (γ /βn) c − . (a. ) with these results in hands, the method to approximate the mean number of outbreaks is the following: the probability that the first excursion is an outbreak is fig. a. . probability for an excursion to be of size k . the situation is indicated for a reproductive ratio ( r ) varying from . to . . the number of susceptibles at the beginning of the second excursion is approximated by the second excursion has a probability γ /βs − (γ /βs ) c − to be an outbreak. the number of susceptibles at the beginning of the third excursion is approximated by and the third excursion has a probability γ /βs − (γ /βs ) c − to be an outbreak. the procedure is iterated as long as there is still a positive number of susceptible individuals. this gives . we now focus on the case r = βn/γ > . in this case the approximating branching process is supercritical and go to infinity with a positive probability. in the case where the epidemic process describes small excursions, the branching process approximation is still valid, but in the case where it describes a large excursion, then a large fraction of susceptible individuals is consumed and the branching approximation is not valid anymore. however, as all the quantities (susceptible, infected and recovered individuals) are large, a mean field approximation is a good approximation of the process. here the mean field approximation is the deterministic sir process, whose dynamics is given by: let us first focus on the small excursions occurring before the large one. as they are small, they can be approximated by a branching process. here, unlike in the previous section, the approximating branching process z is supercritical, as βn > γ . we compute its probability to drift to infinity: as we will see, a supercritical branching process with individual birth rate βn and individual death rate γ conditioned to go extinct has the same law as a subcritical branching process with individual birth rate γ and individual death rate βn . indeed, if we denote by z n the successive values of this branching process, we get for every couple of natural numbers ( n, k ): where p (a | b ) denotes the probability of the event a when b is realised. we used again in this series of equalities classical results on branching processes that can be found in athreya and ney ( ) . as a consequence, if we denote by g [ n, β, γ ] the number of susceptible individuals consumed by the excursion of a supercritical branching process with individual birth rate βn and individual death rate γ conditioned to go extinct, we get: , and the probability for this excursion to have a size bigger than the epidemiological threshold c is as the number of susceptible individuals stays large until the large excursion occurs, we may keep n as the initial number of susceptibles at the beginning of the excursions instead of replacing it by their mean value, as we have done in the previous section. the different quantities we have just computed allow us to approximate the number of small excursions before the large excursion: in expectation, we have as k and l ( k ) are small with respect to n , this can be approximated by finally, notice that in (b. ) , s is a decreasing quantity, and i is a non-negative quantity, which varies continuously. hence ˙ i = i(βs − γ ) has to be negative before i hits . as a consequence, this ensures that the epidemic is subcritical after the large outbreak. in this section, we focus on the effect of the reservoir transmission rate (parameter τ ) on the number of outbreaks when the infection is subcritical ( r < ). the idea is the following: first, as excursions of subcritical branching processes are small, we can make the approximation that, at the beginning, the infection rate by the reservoir is constant equal to τ n , and that the direct transmission rate is equal to βni . making this approximation allows us to handle the two processes of infection (by contact and by the reservoir) independently, and to use known results on branching processes with immigration. recall that i denotes the number of infected individuals. we first assume ( ) and prove inequality ( ) . let us choose α > such then for any ≤ k ≤ c − , the jump rates of the process i are: this implies that once one individual is infected, the probability for the number of simultaneously infected individuals to reach c before the recovery of all infected individuals is larger than the probability that a birth and death process with initial state and birth ( b ) and death ( d ) rates satisfying b d reaches the state c . applying (a. ) , we deduce that this probability p c c. satisfies: . this proves ( ) . moreover, as α has been taken large, the infectious process stays supercritical (in the sense that the next event is more likely to be an infection than a recovery) until a size k satisfying and thus if the number of infected individuals reaches c it is likely to reach a large value and consume a large number of susceptible individuals. as we approximate the infection process by a branching process with constant immigration, the law of i under this approximation converges to a well-known law, provided by eq. ( . ) in bailey ( ) : from this law, we can deduce the probability for i to be equal to any integer k : and thus, the probability for i to be larger than c is recall that we assumed that we thus get the following inequality now let us notice that for any i ≥ : − r we thus get where to get the last inequality we computed the maximum of the function x → xa x − for a = ( + r ) / . as a conclusion, for a fixed r < and a small enough τ , the probability for the number of infected individuals at a given time to be higher than c is bounded by a function of r time τ n / (cγ ( − r )) . this probability is thus small when the last term is small. recall eq. (c. ) . it allows us to compute the variance of i , as follows: in particular, e [ i] = τ n γ . in this section we provide an expression for the term e [ t ] which appears in the definition of m i (see eq. ( ) ). this expression derives from the following equality, which can be found in athreya and ney ( ) . let t ≥ and t denotes the extinction time of the excursion of a branching process, with one individual at time . then we have this allows one to compute the expectation of t as follows: where we made an integration by parts. thus recall that if we consider a branching process with individual birth rate βn , individual death rate γ , and initial state k ≤ c , the probability for this process to reach the size c is athreya and ney, for instance). we use this result to approximate the probability for a block of the excursion to reach the threshold c by where we recall that m i is the mean number of simultaneous excursions generated by different infections from the reservoir. notice that this is an approximation, as m i is not necessarily an integer. we end this appendix with the proof of the unicity of the solution to ( ) . to simplify the notations, we introduce the function f , which at x associates: first we notice that f is only defined for x ≤ c . otherwise the term in brackets would be negative. second, notice that if x ≤ and for any c ≥ and r < , this shows that if x ≤ , f ( x ) > / . we now determine the sign of f ( x ) for x belonging to the interval [ , c ]. a direct computation gives: as the two logarithms are negative for x belonging to ( , c ), we deduce that f ( x ) < for x belonging to ( , c ). as f ( ) > / and f (c) = , we conclude that f (x ) = / has a unique solution on the interval ( , c ). this is equivalent to the fact that (c. ) has a unique solution τ opt which belongs to this ends the proof. estimating the reproduction number of ebola virus (ebov) during the outbreak in west africa what it takes to be a reservoir when is a reservoir not a reservoir? branching processes the elements of stochastic processes with applications to the natural sciences centre for disease control and prevention synthesizing data and models for the spread of mers-cov, : key role of index cases and hospital transmission ebolavirus evolution: past and present community epidemiology framework for classifying disease threats ebola, the killer virus identifying reservoirs of infection: a conceptual and practical challenge ebola between outbreaks: intensied ebola hemorrhagic fever surveillance in the democratic republic of the congo global trends in emerging infectious diseases impacts of biodiversity on the emergence and transmission of infectious diseases a contribution to the mathematical theory of epidemics epidemic dynamics at the human-animal interface recurrent zoonotic transmission of nipah virus into humans movement and contact patterns of long-distance free-grazing ducks and avian influenza persistence in vietnam emerging infectious diseases: threats to human health and global stability human ecology in pathogenic landscapes: two hypotheses on how land use change drives viral emergence extinction pathways and outbreak vulnerability in a stochastic ebola model processus de markov et applications: algorithmes, réseaux, génome et finance: cours et exercices corrigés co-circulation of three camel coronavirus species and recombination of mers-covs in saudi arabia outbreak statistics and scaling laws for externally driven epidemics the structure of infectious disease outbreaks across the animal-human interface exploring a proposed who method to determine thresholds for seasonal influenza surveillance risk factors for human disease emergence random graphs and complex networks origins of major human infectious diseases biological features of novel avian influenza a (h n ) virus middle east respiratory syndrome the authors have been supported by the "chair modélisation mathématique et biodiversité" of veolia environnement-ecole polytechnique-museum national d'histoire naturelle-fondation x, france. outbreaks. now we focus on the large excursion. we use eq. (b. ) to approximate its dynamics. this equation is well-known, and it is easy to obtain the equation satisfied by the final number of susceptible individuals: from (b. )in particular, if we are interested in the time t f when there is no more infected individual and we suppose that at time there is only one infected individual we getthat is to say, s ( t f ) and s ( ) are related by the equationrigorously, the value of s ( ) depends on the number of susceptible individuals consumed by the small excursions before the large excursion, but we have seen that this number is small compared to the population size, n . hence the number of susceptible individuals remaining after the large excursion can be approximated by the smallest solution of:notice that it is easy to have an idea of the error caused by a small variation of the initial state. indeed, if we denote by s f the smallest solution of (b. ) and by s f − l(k ) the solution when