# pos

id: cord-034824-eelqmzdx
pos: NNP
token:
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lemma:
  https://github.com/YangLiangwei/Influential-nodes-identification-in-complex-networksvia-information-entropy


# ent

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id: cord-273429-dl6z8x9h
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  Dandekar R Rackauckas C Barbastathis G title A machine learning aided global diagnostic and comparative tool to assess effect of quarantine control


id: cord-029725-px209lf0
type: EVENT
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  World Health Organization Situation Report 113 Coronavirus Disease World Health Organization Situation Report 3 Coronavirus Disease


id: cord-010719-90379pjd
type: ORG
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  Knowledge Epidemics and Population Dynamics Models for Describing Idea Diffusion Models of Science Dynamics Encounters Between Complexity Theory and Information Sciences Introduction to Percolation Theory


id: cord-010719-90379pjd
type: LAW
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  worm infestations Measurement and Analysis of Worm Propagation on Internet Network Topology Proceedings of the 13th International Conference on Computer Communications


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entity:
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id: cord-188958-id9m3mfk
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  L 2 L 2 L 2 L 2 with size L 10 and periodic boundary conditions We have solved the equations of the SIR


id: cord-191574-1g38scnj
type: DNA
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  Adomian and Laplace Adomian Decomposition Methods date 2020 08 28 journal nan DOI nan sha 26ad48f61f8d6fe11dc94400795cdb6178d3a55c doc_id 191574 cord_uid 1g38scnj The Susceptible Infected Recovered SIR epidemic model


id: cord-184685-ho72q46e
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entity:
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id: cord-184685-ho72q46e
type: CELL_LINE
entity:
  United States COVID 19 Antibody Seroprevalence Actual Coronavirus Infections Vastly Undercounted C D C Data


id: cord-247144-crmfwjvf
type: WORK_OF_ART
entity:
  The Signicance of the Detection Ratio for Predictions on the Outcome of an Epidemic A Message from Mathematical Modelers Preprints Impact


id: cord-310863-jxbw8wl2
type: DNA
entity:
  SIRD class The models are different from each other in terms of the choice for the epidemiological class SIR


id: cord-324993-hs66uf1u
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  Amazonian forest culture COVID 19 Epidemic Compartments Model and Bangladesh International license It is made available under a is the author funder who has granted medRxiv


id: cord-320912-jfeu4tho
type: ORG
entity:
  Transmission Using Outbreak Sizes Outside China Identifying and Interrupting Superspreading Events Implications for Control of Severe Acute Respiratory Syndrome Coronavirus


id: cord-314725-og0ybfzf
type: ORG
entity:
  Mathematical Epidemiology of Infectious Diseases Model Building Analysis and Interpretation Analysis


id: cord-314725-og0ybfzf
type: WORK_OF_ART
entity:
  The SIR Model for Spread of Disease COVID 19 Epidemiology Evolution and Cross Disciplinary Perspectives Mathematics for Life Science and Medicine Inverse Problem Theory and Methods for Model Parameter Estimation Methods for Solving Incorrect Problems Novel Coronavirus 2019


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type: GGP
entity:
  c 0 3 0 35 We note that the initial value of the number of patients at Day 90 sensitively determines the subsequent number of the infected people CC BY ND 4 0 International license It is made available under a perpetuity is the author funder who has granted medRxiv a license to display the preprint


id: cord-332922-2qjae0x7
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entity:
  Detecting Suspected Epidemic Cases Using Trajectory Big Data Bayesian Automatic Relevance Determination for Feature Selection in Credit Default Modelling Sampling Techniques


id: cord-241596-vh90s8vi
type: ORG
entity:
  Simultaneous Strategies for Dynamic Process Optimization A SEIR Model for Control of Infectious Diseases with Constraints An Introduction


id: cord-241596-vh90s8vi
type: ORG
entity:
  Neuroimaging a Systematic Literature Review Dynamic Simulation and Optimization with Inequality Path Constraints Predicting Unobserved Exposures


id: cord-241596-vh90s8vi
type: WORK_OF_ART
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  Cours d Économie Politique F Rouge Modelling the Effect of Changes in Vaccine Effectiveness and Transmission Contact Rates on Pertussis Epidemiology


id: cord-241596-vh90s8vi
type: LAW
entity:
  the Foundations of Public Health Susceptible Exposed Infected Recovery SEIR Model with Immigration Equilibria Points


id: cord-241596-vh90s8vi
type: LAW
entity:
  Application The Epidemiology Diagnosis and Treatment of COVID 19 Multiobjective Evolutionary Algorithms a Comparative Case Study


id: cord-354627-y07w2f43
type: ORG
entity:
  Statistical Correlation for Hydrological Units Prioritization Complete Statistical Analysis to Weather Forecasting Advances


id: cord-354627-y07w2f43
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  Hybrid Model of Artificial Neural Networks Particle Swarm Optimization Comparative Analysis of ANN ICA


id: cord-339425-hdf3blpu
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  Susceptible Infected Removed SIR Model A Case Study of Covid 19 Pandemic date 2020 09 03 journal Front Med Lausanne DOI 10 3389 fmed 2020 556366 sha 59ce9ffb5fbf6c1200fad23306d3a192edfece96 doc_id 339425 cord_uid hdf3blpu


id: cord-339425-hdf3blpu
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  Can We Estimate From Fatality and Infectious Case Data Using the Susceptible Infected Removed SIR Model A Case Study of Covid 19 Pandemic date 2020 09 03


id: cord-342855-dvgqouk2
type: WORK_OF_ART
entity:
  Understanding The Difficulties With Estimation Of Its Fatality Rate Identification and Estimation of the SEIRD Epidemic Model for COVID 19


# url

id: cord-034824-eelqmzdx
domain: github.com
url:
  http://github.com/YangLiangwei/Influential-nodes-identification-in-complex-networksvia-information-entropy


# bib

id: cord-005350-19za0msu
title: Theory of early warning signals of disease emergenceand leading indicators of elimination
author: O’Regan, Suzanne M.
date: 2013-05-31
txt: ./txt/cord-005350-19za0msu.txt
cache: ./cache/cord-005350-19za0msu.txt
extension: .txt
mime: text/plain
url: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7090900/
doi: 10.1007/s12080-013-0185-5
summary:
  Using the stochastic differential equation, we can obtain analytical expressions for statistical signatures of leading indicators and early warning signals, including the power spectrum and autocorrelation function (see Appendix A for details). To investigate the results of this theory for a particular parameter set (Table 7) , we calculated leading indicators of elimination and emergence, assuming alternatively that (a) the mean proportion of infectious individuals is given by the deterministic endemic equilibrium ( → 0 theory) or (b) assuming it is given by the current state of the fast-slow system approaching a transition. We also compared the elimination indicators with those calculated assuming that the mean proportion of infectious individuals was given by the deterministic endemic equilibrium from the limiting case models with no immigration. The goal of our study was to develop the theory of such early warning signals and leading indicators for infectious disease transmission systems that meet the assumptions of the familiar SIS and SIR models and which are forced through a critical transition by changes in transmission.

abstract:
  Anticipating infectious disease emergence and documenting progress in disease elimination are important applications for the theory of critical transitions. A key problem is the development of theory relating the dynamical processes of transmission to observable phenomena. In this paper, we consider compartmental susceptible–infectious–susceptible (SIS) and susceptible–infectious–recovered (SIR) models that are slowly forced through a critical transition. We derive expressions for the behavior of several candidate indicators, including the autocorrelation coefficient, variance, coefficient of variation, and power spectra of SIS and SIR epidemics during the approach to emergence or elimination. We validated these expressions using individual-based simulations. We further showed that moving-window estimates of these quantities may be used for anticipating critical transitions in infectious disease systems. Although leading indicators of elimination were highly predictive, we found the approach to emergence to be much more difficult to detect. It is hoped that these results, which show the anticipation of critical transitions in infectious disease systems to be theoretically possible, may be used to guide the construction of online algorithms for processing surveillance data.


id: cord-007399-qbgz7eqt
title: Effects of quasiperiodic forcing in epidemic models
author: Bilal, Shakir
date: 2016-09-22
txt: ./txt/cord-007399-qbgz7eqt.txt
cache: ./cache/cord-007399-qbgz7eqt.txt
extension: .txt
mime: text/plain
url: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7112454/
doi: 10.1063/1.4963174
summary:
  6, 7 In typical seasonally forced models of infectious diseases, the transmission rate (i.e., the per capita rate at which a susceptible individual interacts with an infectious individual and acquires a new infection) is modulated in a periodic fashion using a sine or cosine function. One of the characteristic features of temporally forced systems is that they possess multiple coexisting attractors: the dynamics sensitively depends on the initial values of state variables. [15] [16] [17] Coexistence of multiple attractors or states has also been observed in the dynamics of epidemic models when the transmission rates are periodically forced. As hinted in the beginning of this paragraph, the models considered here vary in internal feedbacks on disease dynamics in terms of the effect of immune response in regulating the build-up of susceptibles during inter-epidemic periods necessary for fuelling next outbreaks. Previous studies, investigating the effects of periodic modulation in the transmission rate, showed the coexistence of multiple attractors in the dynamics of the SIR family of epidemic models.

abstract:
  We study changes in the bifurcations of seasonally driven compartmental epidemic models, where the transmission rate is modulated temporally. In the presence of periodic modulation of the transmission rate, the dynamics varies from periodic to chaotic. The route to chaos is typically through period doubling bifurcation. There are coexisting attractors for some sets of parameters. However in the presence of quasiperiodic modulation, tori are created in place of periodic orbits and chaos appears via finite torus doublings. Strange nonchaotic attractors (SNAs) are created at the boundary of chaotic and torus dynamics. Multistability is found to be reduced as a function of quasiperiodic modulation strength. It is argued that occurrence of SNAs gives an opportunity of asymptotic predictability of epidemic growth even when the underlying dynamics is strange.


id: cord-007404-s2qnhswe
author: Shu, Panpan
date: 2015-06-04
txt: ./txt/cord-007404-s2qnhswe.txt
cache: ./cache/cord-007404-s2qnhswe.txt
extension: .txt
mime: text/plain
url: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7112466/
doi: 10.1063/1.4922153
summary:
  The existing studies have provided different theoretical predictions for epidemic threshold of the susceptible-infected-recovered (SIR) model on complex networks, while the numerical verification of these theoretical predictions is still lacking. To understand the effectiveness of the variability measure, the distribution of outbreaks sizes is investigated near the epidemic threshold on random regular networks. Considering that the existing theories more or less have some limitations (e.g., the HMF theory neglects the quenched structure of the network; QMF theory ignores dynamical correlations 14 ) , some numerical methods such as the finite-size scaling analysis, 15 susceptibility, 16 and lifetime measure 17 have been proposed to check the accuracies of different theoretical predictions for the SIS model. In this work, we perform extensive numerical simulations of the SIR model on networks with finite size, and present a numerical identification method by analyzing the peak of the epidemic variability 24,25 (i.e., the maximal value of the epidemic variability) to identify the epidemic threshold.

title:
  Numerical identification of epidemic thresholds for susceptible-infected-recovered model on finite-size networks

abstract:
  Epidemic threshold has always been a very hot topic for studying epidemic dynamics on complex networks. The previous studies have provided different theoretical predictions of the epidemic threshold for the susceptible-infected-recovered (SIR) model, but the numerical verification of these theoretical predictions is still lacking. Considering that the large fluctuation of the outbreak size occurs near the epidemic threshold, we propose a novel numerical identification method of SIR epidemic threshold by analyzing the peak of the epidemic variability. Extensive experiments on synthetic and real-world networks demonstrate that the variability measure can successfully give the numerical threshold for the SIR model. The heterogeneous mean-field prediction agrees very well with the numerical threshold, except the case that the networks are disassortative, in which the quenched mean-field prediction is relatively close to the numerical threshold. Moreover, the numerical method presented is also suitable for the susceptible-infected-susceptible model. This work helps to verify the theoretical analysis of epidemic threshold and would promote further studies on the phase transition of epidemic dynamics.


id: cord-010715-91fob3ax
title: Outbreaks in susceptible-infected-removed epidemics with multiple seeds
author: Hasegawa, Takehisa
date: 2016-03-30
txt: ./txt/cord-010715-91fob3ax.txt
cache: ./cache/cord-010715-91fob3ax.txt
extension: .txt
mime: text/plain
url: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7217506/
doi: 10.1103/physreve.93.032324
summary:
  We derive the percolation transition points for the SIR model with multiple seeds to show that as the infection rate increases epidemic clusters generated from each seed percolate before a single seed can induce a global outbreak. To evaluate the time evolution of the SIR dynamics and the total densities of the susceptible and removed nodes in the final states, we consider the approximate master equations (AMEs) [12, 14] . In particular, the gap between λ c1 and λ SIR c indicates that as the infection rate increases, the epidemic clusters generated from each seed percolate before a single seed can induce a global outbreak. We have numerically and analytically shown that the present model with multiple seeds on the RRG percolates at a lower infection rate than the epidemic threshold. The SIR model with numerous seeds shows the percolation transition of the removed and susceptible nodes at λ c1 and λ c2 , respectively.

abstract:
  We study a susceptible-infected-removed (SIR) model with multiple seeds on a regular random graph. Many researchers have studied the epidemic threshold of epidemic models above which a global outbreak can occur, starting from an infinitesimal fraction of seeds. However, there have been few studies of epidemic models with finite fractions of seeds. The aim of this paper is to clarify what happens in phase transitions in such cases. The SIR model in networks exhibits two percolation transitions. We derive the percolation transition points for the SIR model with multiple seeds to show that as the infection rate increases epidemic clusters generated from each seed percolate before a single seed can induce a global outbreak.


id: cord-010719-90379pjd
title: Memory effects on epidemic evolution: The susceptible-infected-recovered epidemic model
author: Saeedian, M.
date: 2017-02-21
txt: ./txt/cord-010719-90379pjd.txt
cache: ./cache/cord-010719-90379pjd.txt
extension: .txt
mime: text/plain
url: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7217510/
doi: 10.1103/physreve.95.022409
summary:
  We also consider the SIR model on structured networks and study the effect of topology on threshold points in a non-Markovian dynamics. In all previous works, the authors rarely discuss the effect of fractional order differential equations and memory on the epidemic thresholds and the macroscopic behavior of epidemic outbreaks. This means that the initial time for taking into account the disease control memory is shifted toward more recent times: thereafter, the dynamics is evolving with a new fraction of susceptible and infected individuals, different from that predicted by the solution of the differential equations. In Sec. II, following Caputo''s approach, we convert the differential equations of the standard SIR model to the fractional derivatives, thereby allowing us to consider memory effects. In order to observe the influence of memory effects, first we rewrite the differential equations (1) in terms of time-dependent integrals as follows:

abstract:
  Memory has a great impact on the evolution of every process related to human societies. Among them, the evolution of an epidemic is directly related to the individuals' experiences. Indeed, any real epidemic process is clearly sustained by a non-Markovian dynamics: memory effects play an essential role in the spreading of diseases. Including memory effects in the susceptible-infected-recovered (SIR) epidemic model seems very appropriate for such an investigation. Thus, the memory prone SIR model dynamics is investigated using fractional derivatives. The decay of long-range memory, taken as a power-law function, is directly controlled by the order of the fractional derivatives in the corresponding nonlinear fractional differential evolution equations. Here we assume “fully mixed” approximation and show that the epidemic threshold is shifted to higher values than those for the memoryless system, depending on this memory “length” decay exponent. We also consider the SIR model on structured networks and study the effect of topology on threshold points in a non-Markovian dynamics. Furthermore, the lack of access to the precise information about the initial conditions or the past events plays a very relevant role in the correct estimation or prediction of the epidemic evolution. Such a “constraint” is analyzed and discussed.


id: cord-016965-z7a6eoyo
title: Human Mobility, Networks and Disease Dynamics on a Global Scale
author: Brockmann, Dirk
date: 2017-10-23
txt: ./txt/cord-016965-z7a6eoyo.txt
cache: ./cache/cord-016965-z7a6eoyo.txt
extension: .txt
mime: text/plain
url: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7121407/
doi: 10.1007/978-3-319-67798-9_19
summary:
  In addition for infected sites to transmit the disease to neighboring susceptible lattice sites, every now and then (with a probability of 1%) they can also Fig. 19 .1) geographic distance to the initial outbreak location is no longer a good predictor of arrival time, unlike in systems with local or spatially limited host mobility infect randomly chosen lattice sites anywhere in the system. A visual inspection of the air-transportation system depicted in Fig. 19 .1 is sufficiently convincing that the significant fraction of long-range connections in global mobility will not only increase the speed at which infectious diseases spread but, more importantly, also cause the patterns of spread to exhibit high spatial incoherence and complexity caused by the intricate connectivity of the air-transportation network. Figure 19 .7 shows that also the model epidemic depicts only a weak correlation between geographic distance to the outbreak location and arrival time.

abstract:
  Disease dynamics is a complex phenomenon and in order to address these questions expertises from many disciplines need to be integrated. One method that has become particularly important during the past few years is the development of computational models and computer simulations that help addressing these questions. In the focus of this chapter are emergent infectious diseases that bear the potential of spreading across the globe, exemplifying how connectivity in a globalized world has changed the way human-mediated processes evolve in the 21st century. The examples of most successful predictions of disease dynamics given in the chapter illustrate that just feeding better and faster computers with more and more data may not necessarily help understanding the relevant phenomena. It might rather be much more useful to change the conventional way of looking at the patterns and to assume a correspondingly modified viewpoint—as most impressively shown with the examples given in this chapter.


id: cord-029725-px209lf0
author: Anand, Nikhil
date: 2020-07-24
txt: ./txt/cord-029725-px209lf0.txt
cache: ./cache/cord-029725-px209lf0.txt
extension: .txt
mime: text/plain
url: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7380501/
doi: 10.1007/s41403-020-00151-5
summary:
  Using the available data of the number of COVID-19 positive cases reported in the state of Kerala, and in India till 26th April, 2020 and 12th May 2020, respectively, the parameter estimation problem is converted into an optimization problem with the help of a least squared cost function. Using the estimated set of parameters, the model predicts that in the state of Kerala, by using certain interventions the pandemic can be successfully controlled latest by the first week of July, whereas the [Formula: see text] value for India is still greater than 1, and hence lifting of lockdown from all regions of the country is not advisable. In such a scenario, assuming the present levels of testing, the model predicts that the number of cases in Kerala can be controlled by the first week of June (as shown in Fig. 8 ).

title:
  Predicting the Spread of COVID-19 Using [Formula: see text] Model Augmented to Incorporate Quarantine and Testing

abstract:
  India imposed a nationwide lockdown from 25th March 2020 onwards to combat the spread of COVID-19 pandemic. To model the spread of a disease and to predict its future course, epidemiologists make use of compartmental models such as the [Formula: see text] model. In order to address some of the assumptions of the standard [Formula: see text] model, a new modified version of [Formula: see text] model is proposed in this paper that takes into account the percentage of infected individuals who are tested and quarantined. This approach helps overcome the assumption of homogenous mixing of population which is inherent to the conventional [Formula: see text] model. Using the available data of the number of COVID-19 positive cases reported in the state of Kerala, and in India till 26th April, 2020 and 12th May 2020, respectively, the parameter estimation problem is converted into an optimization problem with the help of a least squared cost function. The optimization problem is then solved using differential evolution optimizer. The impact of lockdown is quantified by comparing the rising trend in infections before and during the lockdown. Using the estimated set of parameters, the model predicts that in the state of Kerala, by using certain interventions the pandemic can be successfully controlled latest by the first week of July, whereas the [Formula: see text] value for India is still greater than 1, and hence lifting of lockdown from all regions of the country is not advisable.


id: cord-034824-eelqmzdx
title: Influential Nodes Identification in Complex Networks via Information Entropy
author: Guo, Chungu
date: 2020-02-21
txt: ./txt/cord-034824-eelqmzdx.txt
cache: ./cache/cord-034824-eelqmzdx.txt
extension: .txt
mime: text/plain
url: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7516697/
doi: 10.3390/e22020242
summary:
  In this paper, we propose the EnRenew algorithm aimed to identify a set of influential nodes via information entropy. Compared with the best state-of-the-art benchmark methods, the performance of proposed algorithm improved by 21.1%, 7.0%, 30.0%, 5.0%, 2.5%, and 9.0% in final affected scale on CEnew, Email, Hamster, Router, Condmat, and Amazon network, respectively, under the Susceptible-Infected-Recovered (SIR) simulation model. The impressive results on the SIR simulation model shed light on new method of node mining in complex networks for information spreading and epidemic prevention. defined the problem of identifying a set of influential spreaders in complex networks as influence maximization problem [57] , and they used hill-climbing based greedy algorithm that is within 63% of optimal in several models. Besides, to make the algorithm practically more useful, we provide EnRenew''s source code and all the experiments details on https://github.com/YangLiangwei/Influential-nodes-identification-in-complex-networksvia-information-entropy, and researchers can download it freely for their convenience.

abstract:
  Identifying a set of influential nodes is an important topic in complex networks which plays a crucial role in many applications, such as market advertising, rumor controlling, and predicting valuable scientific publications. In regard to this, researchers have developed algorithms from simple degree methods to all kinds of sophisticated approaches. However, a more robust and practical algorithm is required for the task. In this paper, we propose the EnRenew algorithm aimed to identify a set of influential nodes via information entropy. Firstly, the information entropy of each node is calculated as initial spreading ability. Then, select the node with the largest information entropy and renovate its l-length reachable nodes’ spreading ability by an attenuation factor, repeat this process until specific number of influential nodes are selected. Compared with the best state-of-the-art benchmark methods, the performance of proposed algorithm improved by 21.1%, 7.0%, 30.0%, 5.0%, 2.5%, and 9.0% in final affected scale on CEnew, Email, Hamster, Router, Condmat, and Amazon network, respectively, under the Susceptible-Infected-Recovered (SIR) simulation model. The proposed algorithm measures the importance of nodes based on information entropy and selects a group of important nodes through dynamic update strategy. The impressive results on the SIR simulation model shed light on new method of node mining in complex networks for information spreading and epidemic prevention.


id: cord-102966-7vdz661d
title: A Fundamental Inconsistency in the SIR Model Structure and Proposed Remedies
author: Nikolaou, M.
date: 2020-05-01
txt: ./txt/cord-102966-7vdz661d.txt
cache: ./cache/cord-102966-7vdz661d.txt
extension: .txt
mime: text/plain
url: http://medrxiv.org/cgi/content/short/2020.04.26.20080960v1?rss=1
doi: 10.1101/2020.04.26.20080960
summary:
  In their landmark 1927 publication Contribution to the Mathematical Theory of Epidemics, 1, 2 Kermack and McKendrick developed a general, if elaborate model structure to capture the dynamics of a fixed-size population comprising compartments of individuals susceptible (S) to a spreading infection, infectious (I), and removed (R) from the preceding two compartments by recovery or death. Starting with the assumption that individuals leave the infectious group at time after infection, we develop in this paper a corresponding mathematical model structure, named delay SIR (dSIR), in the form of a single delay differential equation (DDE) for , and two associated delay algebraic equations, for and in terms of . It turns out (Appendix A) that the following simple remedy can be used to retain the ODE structure of the standard SIR model, while better approximating the DDE dynamics of the more realistic dSIR model structure: The SIR equations for { ′ , ′ }, eqns.

abstract:
  The susceptible-infectious-removed (SIR) compartmental model structure and its variants are a fundamental modeling tool in epidemiology. As typically used, however, this tool may introduce an inconsistency by assuming that the rate of depletion of a compartment is proportional to the content of that compartment. As mentioned in the seminal SIR work of Kermack and McKendrick, this is an assumption of mathematical convenience rather than realism. As such, it leads to underprediction of the infectious compartment peaks by a factor of about two, a problem of particular importance when dealing with availability of resources during an epidemic. To remedy this problem, we develop the dSIR model structure, comprising a single delay differential equation and associated delay algebraic equations. We show that SIR and dSIR fully agree in assessing stability and long-term values of a population through an epidemic, but differ considerably in the exponential rates of ascent and descent as well as peak values during the epidemic. The novel Pade-SIR structure is also introduced as a approximation of dSIR by ordinary differential equations. We rigorously analyze the properties of these models and present a number of illustrative simulations, particularly in view of the recent coronavirus epidemic. Suggestions for further study are made.


id: cord-103598-8umv06ox
title: On a coupled time-dependent SIR models fitting with New York and New-Jersey states COVID-19 data
author: Ambrosio, Benjamin
date: 2020-06-10
txt: ./txt/cord-103598-8umv06ox.txt
cache: ./cache/cord-103598-8umv06ox.txt
extension: .txt
mime: text/plain
url: https://arxiv.org/pdf/2006.05665v1.pdf
doi: 10.20944/preprints202006.0068.v1
summary:
  This article describes a simple Susceptible Infected Recovered (SIR) model fitting with COVID-19 data for the month of march 2020 in New York (NY) state. The model is a classical SIR, but is non-autonomous; the rate of susceptible people becoming infected is adjusted over time in order to fit the available data. In this short article, we first introduce a simple SIR model, in which we adjust a key parameter k standing for a control on the Susceptible-Infected rate, and secondarily the death rate, in order to fit the data of the pandemic in NY state in March 2020, and provide predictions for a near future. Accordingly, the main key points of this article are that, 1) it highlights the dynamics and epidemiological characteristics which have been discussed in press and health policies; It highlights qualitatively how lockdown policies have decreased the spread of the virus and provides prediction and explanation of an upcoming apex, 2) it fits real data provided for the New York state and 3) it fits the data of NJ state by considering coupled equations taking into account the daily fluxes between NY and NJ.

abstract:
  This article describes a simple Susceptible Infected Recovered (SIR) model fitting with COVID-19 data for the month of march 2020 in New York (NY) state. The model is a classical SIR, but is non-autonomous; the rate of susceptible people becoming infected is adjusted over time in order to fit the available data. The death rate is also secondarily adjusted. Our fitting is made under the assumption that due to limiting number of tests, a large part of the infected population has not been tested positive. In the last part, we extend the model to take into account the daily fluxes between New Jersey (NJ) and NY states and fit the data for both states. Our simple model fits the available data, and illustrates typical dynamics of the disease: exponential increase, apex and decrease. The model highlights a decrease in the transmission rate over the period which gives a quantitative illustration about how lockdown policies reduce the spread of the pandemic. The coupled model with NY and NJ states shows a wave in NJ following the NY wave, illustrating the mechanism of spread from one attractive hot spot to its neighbor. }


id: cord-104158-l7s2utqb
title: CoSIR: Managing an Epidemic via Optimal Adaptive Control of Transmission Policy
author: Maheshwari, H.
date: 2020-11-13
txt: ./txt/cord-104158-l7s2utqb.txt
cache: ./cache/cord-104158-l7s2utqb.txt
extension: .txt
mime: text/plain
url: http://medrxiv.org/cgi/content/short/2020.11.10.20211995v1?rss=1
doi: 10.1101/2020.11.10.20211995
summary:
  • We demonstrate that the SIR dynamics map to the well-known Lotka-Volterra (LV) system [8] on interpreting infectious patients as predators and susceptible contacts (i.e., the product of transmission rate and susceptible population) as the prey under specific conditions on the transmission rate. • We derive optimal control policy for transmission rate (CoSIR) using control-Lyapunov functions [45] based on the energy of the system, that is guaranteed to converge to the desired equilibrium, i.e., target infectious levels from any valid initial state. We also discuss extensions to compartmental model variants that involve an incubation period (e.g., delayed SIR, SEIR) as well as control of the infectious period that is influenced by testing and quarantine policy. We now consider the problem of controlling the transmission rate β for the LVSIR model (Fig 2(c) ) to nudge the infectious levels to a desired equilibrium.

abstract:
  Shaping an epidemic with an adaptive contact restriction policy that balances the disease and socioeconomic impact has been the holy grail during the COVID-19 pandemic. Most of the existing work on epidemiological models focuses on scenario-based forecasting via simulation but techniques for explicit control of epidemics via an analytical framework are largely missing. In this paper, we consider the problem of determining the optimal policy for transmission control assuming SIR dynamics, which is the most widely used epidemiological paradigm. We first demonstrate that the SIR model with infectious patients and susceptible contacts (i.e., product of transmission rate and susceptible population) interpreted as predators and prey respectively reduces to a Lotka-Volterra (LV) predator-prey model. The modified SIR system (LVSIR) has a stable equilibrium point, an energy conservation property, and exhibits bounded cyclic behaviour similar to an LV system. This mapping permits a theoretical analysis of the control problem supporting some of the recent simulation-based studies that point to the benefits of periodic interventions. We use a control-Lyapunov approach to design adaptive control policies (CoSIR) to nudge the SIR model to the desired equilibrium that permits ready extensions to richer compartmental models. We also describe a practical implementation of this transmission control method by approximating the ideal control with a finite, but a time-varying set of restriction levels and provide simulation results to demonstrate its efficacy.


id: cord-121428-79wyxedn
title: Social contacts and the spread of infectious diseases
author: Dimarco, G.
date: 2020-09-02
txt: ./txt/cord-121428-79wyxedn.txt
cache: ./cache/cord-121428-79wyxedn.txt
extension: .txt
mime: text/plain
url: https://arxiv.org/pdf/2009.01140v1.pdf
doi: nan
summary:
  The kinetic description leads to study the evolution over time of Boltzmann type equations describing the number densities of social contacts of susceptible, infected and recovered individuals, whose proportions are driven by a classical compartmental model in epidemiology. Inspired by the model considered in [14] for describing a social attitude and making use of the SIR dynamics, we present here a model composed by a system of three kinetic equations, each one describing the time evolution of the distribution of the number of contacts for the subpopulation belonging to a given epidemiological class. Once the system of Fokker-Planck type equations has been derived, in Section 4 we close the SIR-type system of kinetic equations around the Gamma-type equilibria to obtain a SIR model in which the presence and consequently the evolution of the social contacts leads to a non-linear incidence rate of the infectious disease satisfying the compatibility conditions introduced in [33] .

abstract:
  Motivated by the COVID-19 pandemic, we introduce a mathematical description of the impact of sociality in the spread of infectious diseases by integrating an epidemiological dynamic with a kinetic modeling of population-based contacts. The kinetic description leads to study the evolution over time of Boltzmann type equations describing the number densities of social contacts of susceptible, infected and recovered individuals, whose proportions are driven by a classical compartmental model in epidemiology. Explicit calculations show that the spread of the disease is closely related to the mean number of contacts, thus justifying the lockdown strategies assumed by governments to prevent them. Furthermore, the kinetic model allows to clarify how a selective control can be assumed to achieve a minimal lockdown strategy by only reducing individuals undergoing a very large number of daily contacts. This, in turns, could permit to maintain at best the economic activities which would seriously suffer from a total closure policy. Numerical simulations confirm the ability of the model to describe different phenomena characteristic of the rapid spread of an epidemic. A last part is dedicated to fit numerical solutions of the proposed model with experimental data coming from different European countries.


id: cord-131678-rvg1ayp2
author: Ponce, Marcelo
date: 2020-09-02
url: https://arxiv.org/pdf/2009.01091v1.pdf
doi: nan
title:
  covid19.analytics: An R Package to Obtain, Analyze and Visualize Data from the Corona Virus Disease Pandemic

abstract:
  With the emergence of a new pandemic worldwide, a novel strategy to approach it has emerged. Several initiatives under the umbrella of"open science"are contributing to tackle this unprecedented situation. In particular, the"R Language and Environment for Statistical Computing"offers an excellent tool and ecosystem for approaches focusing on open science and reproducible results. Hence it is not surprising that with the onset of the pandemic, a large number of R packages and resources were made available for researches working in the pandemic. In this paper, we present an R package that allows users to access and analyze worldwide data from resources publicly available. We will introduce the covid19.analytics package, focusing in its capabilities and presenting a particular study case where we describe how to deploy the"COVID19.ANALYTICS Dashboard Explorer".


id: cord-140977-mg04drna
title: Methodology for Modelling the new COVID-19 Pandemic Spread and Implementation to European Countries
author: Maltezos, S.
date: 2020-06-27
txt: ./txt/cord-140977-mg04drna.txt
cache: ./cache/cord-140977-mg04drna.txt
extension: .txt
mime: text/plain
url: https://arxiv.org/pdf/2006.15385v2.pdf
doi: nan
summary:
  Based on a proposed parametrization model appropriate for implementation to an epidemic in a large population, we focused on the disease spread and we studied the obtained curves, as well as, we investigated probable correlations between the country''s characteristics and the parameters of the parametrization. where the function c(t) applied in an epidemic spread represents the rate of the infected individuals as the new daily reported cases (DRC) and coincides with the function I(t) in the SIR model, as we can see in the following. The more analytical approach, in the general case from the mathematical point of view, comes from the fundamental study of the epidemic growth and includes a number of terms in a form of double summation related to the inverse Laplace Transform of a rational function given in [8] , referring to the "Earlier stages of an epidemic in a large population".

abstract:
  After the breakout of the disease caused by the new virus COVID-19, the mitigation stage has been reached in most of the countries in the world. During this stage, a more accurate data analysis of the daily reported cases and other parameters became possible for the European countries and has been performed in this work. Based on a proposed parametrization model appropriate for implementation to an epidemic in a large population, we focused on the disease spread and we studied the obtained curves, as well as, we investigated probable correlations between the country's characteristics and the parameters of the parametrization. We have also developed a methodology for coupling our model to the SIR-based models determining the basic and the effective reproductive number referring to the parameter space. The obtained results and conclusions could be useful in the case of a recurrence of this repulsive disease in the future.


id: cord-146213-924ded7t
title: COVID-19 Risk Estimation using a Time-varying SIR-model
author: Kiamari, Mehrdad
date: 2020-08-11
txt: ./txt/cord-146213-924ded7t.txt
cache: ./cache/cord-146213-924ded7t.txt
extension: .txt
mime: text/plain
url: https://arxiv.org/pdf/2008.08140v1.pdf
doi: nan
summary:
  We propose a rigorous hybrid model-and-data-driven approach to risk scoring based on a time-varying SIR epidemic model that ultimately yields a simplified color-coded risk level for each community. We show how this risk score can be estimated using another useful metric of infection spread, $R_t$, the time-varying average reproduction number which indicates the average number of individuals an infected person would infect in turn. First, we obtain the daily effective reproduction number R t of a time-varying SIR model as well as the corresponding confidence Interval. Our code for infection risk calculation uses this data in conjunction with a time-varying SIR-based Bayesian mathematical model to obtain risk estimates and prediction for different communities. A well-known parameter in the classical SIR model is called R0, the effective reproductive number, which measures the average number of infections caused by infectious individuals at the beginning of the epidemic.

abstract:
  Policy-makers require data-driven tools to assess the spread of COVID-19 and inform the public of their risk of infection on an ongoing basis. We propose a rigorous hybrid model-and-data-driven approach to risk scoring based on a time-varying SIR epidemic model that ultimately yields a simplified color-coded risk level for each community. The risk score $Gamma_t$ that we propose is proportional to the probability of someone currently healthy getting infected in the next 24 hours. We show how this risk score can be estimated using another useful metric of infection spread, $R_t$, the time-varying average reproduction number which indicates the average number of individuals an infected person would infect in turn. The proposed approach also allows for quantification of uncertainty in the estimates of $R_t$ and $Gamma_t$ in the form of confidence intervals. Code and data from our effort have been open-sourced and are being applied to assess and communicate the risk of infection in the City and County of Los Angeles.


id: cord-152881-k1hx1m61
title: Susceptible-Infected-Recovered (SIR) Dynamics of COVID-19 and Economic Impact
author: Toda, Alexis Akira
date: 2020-03-25
txt: ./txt/cord-152881-k1hx1m61.txt
cache: ./cache/cord-152881-k1hx1m61.txt
extension: .txt
mime: text/plain
url: https://arxiv.org/pdf/2003.11221v2.pdf
doi: nan
summary:
  This paper aims to help decision making by building a mathematical epidemic model, estimating it using the up-to-date data of COVID-19 cases around the world, making out-of-sample predictions, and discussing optimal policy and economic impact. Due to the high transmission rate and lack of herd immunity, in the absence of mitigation measures such as social distancing, the virus spreads quickly and may infect around 30 percent of the population at the peak of the epidemic. 4 Although the fraction of cases c(t) is likely significantly underestimated because infected individuals do not appear in the data unless they are tested, it does not cause problems for estimating the parameter of interest (the transmission rate β) because under-reporting is absorbed by the constant y 0 in (2.3b), which only affects the onset of the epidemic by a few weeks without changing the overall dynamics (see Figure 5 ).

abstract:
  I estimate the Susceptible-Infected-Recovered (SIR) epidemic model for Coronavirus Disease 2019 (COVID-19). The transmission rate is heterogeneous across countries and far exceeds the recovery rate, which enables a fast spread. In the benchmark model, 28% of the population may be simultaneously infected at the peak, potentially overwhelming the healthcare system. The peak reduces to 6.2% under the optimal mitigation policy that controls the timing and intensity of social distancing. A stylized asset pricing model suggests that the stock price temporarily decreases by 50% in the benchmark case but shows a W-shaped, moderate but longer bear market under the optimal policy.


id: cord-153905-qszvwqtj
title: Modelos SIR modificados para la evoluci''on del COVID19
author: Bizet, Nana Cabo
date: 2020-04-23
txt: ./txt/cord-153905-qszvwqtj.txt
cache: ./cache/cord-153905-qszvwqtj.txt
extension: .txt
mime: text/plain
url: https://arxiv.org/pdf/2004.11352v1.pdf
doi: nan
summary:
  En la sección II se considera el mismo modelo SIR pero en el cual se introduce una ya reconocida propiedad de la presente epidemia: la razón k entre el número de infectados observados (por los sistemas de salud) y el total de infectados, es un número que se estima en el intervalo de 0.1 a 0.2 [5, 12] . Sin embargo, los datos de que se disponen para resolver las ecuaciones a partir de sus condiciones iniciales, en muchos casos son solo la población total del país y los números de infectados y recuperados que detecta el sistema de Salud. Consideremos la solución del sistema de ecuaciones (1,2,3) que describa aproximadamente la lista de valores para el número de los infectados activos y sus incrementos diarios observados por el Sistema de Salud de Cuba entre los días 11.03.20 y 3.04.20.

abstract:
  We study the SIR epidemiological model, with a variable contagion rate, applied to the evolution of COVID19 in Cuba. It is highlighted that an increase in the predictive character depends on understanding the dynamics for the temporal evolution of the rate of contagion $beta^*$. A semi-empirical model for this dynamics is formulated, where reaching $beta^*approx0$ due to isolation is achieved after the mean duration of the disease $tau=1/gamma$, in which the number of infected in the confined families has decreased. It is considered that $beta^*(t)$ should have an abrupt decrease on the day of initiation of confinement and decrease until canceling at the end of the interval $tau$. The analysis describes appropriately the infection curve for Germany. The model is applied to predict an infection curve for Cuba, which estimates a maximum number of infected as less than 2000 in the middle of May, depending on the rigor of the isolation. This is suggested by the ratio between the daily detected cases and the total. We consider the ratio between the observed and real infected cases (k) less than unity. The low value of k decreases the maximum obtained when $beta^*-gamma>0$. The observed evolution is independent of k in the linear region. The value of $beta^*$ is also studied by time intervals, adjusting to the data of Cuba, Germany and South Korea. We compare the extrapolation of the evolution of Cuba with the contagion rate until 16.04.20 with that obtained by a strict quarantine at the end of April. This model with variable $beta^*$ correctly describes the observed infected evolution curves. We emphasize that the desired maximum of the SIR infected curve is not the maximum standard with constant $beta^*$, but one achieved due to quarantine when $tilde R_0=beta^*/gamma<1$. For the countries controlling the epidemic the maxima are in the region in which SIR equations are linear.


id: cord-155015-w3k7r5z9
title: Discontinuous transitions of social distancing
author: Arazi, R.
date: 2020-08-16
txt: ./txt/cord-155015-w3k7r5z9.txt
cache: ./cache/cord-155015-w3k7r5z9.txt
extension: .txt
mime: text/plain
url: https://arxiv.org/pdf/2008.06863v1.pdf
doi: nan
summary:
  To understand social distancing dynamics it is important to combine basic epidemiology models for viral unfold (like SIR) with game theory tools, such as a utility function that quantifies individual or government forecast for epidemic damage and economy cost as the functions of social distancing. The work proceeds with the presentation of the SIR model with induced transitions (SIRIT), almost analytical treatment of this model, the calibration of an epidemic and economy parameters of the model using time series of active cases and causalities during the 1st wave of COVID-19 in Austria, Israel, and Germany, followed by a discussion of obtained results and their implications. The work introduces SIRIT, a standard Susceptible-Infected-Recovered (SIR) model extended with a utility function that predicts induced transitions (IT) of social distancing. The fit of the first social distancing transitions (deviations from SIR model) after COVID-19 climax in Austria, Germany, and Israel, but, demonstrates that β remains constant during the transitions.

abstract:
  The 1st wave of COVID-19 changed social distancing around the globe: severe lockdowns to stop pandemics at the cost of state economies preceded a series of lockdown lifts. To understand social distancing dynamics it is important to combine basic epidemiology models for viral unfold (like SIR) with game theory tools, such as a utility function that quantifies individual or government forecast for epidemic damage and economy cost as the functions of social distancing. Here we present a model that predicts a series of discontinuous transitions in social distancing after pandemics climax. Each transition resembles a phase transition and, so, maybe a general phenomenon. Data analysis of the first wave in Austria, Israel, and Germany corroborates the soundness of the model. Besides, this work presents analytical tools to analyze pandemic waves.


id: cord-159425-fgbruo9l
title: Semi-supervised Neural Networks solve an inverse problem for modeling Covid-19 spread
author: Paticchio, Alessandro
date: 2020-10-10
txt: ./txt/cord-159425-fgbruo9l.txt
cache: ./cache/cord-159425-fgbruo9l.txt
extension: .txt
mime: text/plain
url: https://arxiv.org/pdf/2010.05074v1.pdf
doi: nan
summary:
  This method consists of unsupervised and supervised parts and is capable of solving inverse problems formulated by DEs. We also propose an extension of the SIR model to include a passive compartment P , which is assumed to be uninvolved in the spread of the pandemic (SIRP), presenting a novel machine learning technique for solving inverse problems and improving disease modeling. Then, we introduce the SIRP model and study the pandemic''s evolution by applying the semi-supervised approach to real data, capturing the populations infected and removed by COVID-19 in Switzerland, Spain, and Italy. We examined the effectiveness of the SIRP model and the semi-supervised method by fitting data obtained during the COVID-19 pandemic for three countries: Switzerland, Spain, and Italy [3] . We applied the proposed semi-supervised method on real data to study the COVID-19 spread in Switzerland, Spain, and Italy.

abstract:
  Studying the dynamics of COVID-19 is of paramount importance to understanding the efficiency of restrictive measures and develop strategies to defend against upcoming contagion waves. In this work, we study the spread of COVID-19 using a semi-supervised neural network and assuming a passive part of the population remains isolated from the virus dynamics. We start with an unsupervised neural network that learns solutions of differential equations for different modeling parameters and initial conditions. A supervised method then solves the inverse problem by estimating the optimal conditions that generate functions to fit the data for those infected by, recovered from, and deceased due to COVID-19. This semi-supervised approach incorporates real data to determine the evolution of the spread, the passive population, and the basic reproduction number for different countries.


id: cord-167454-ivhqeu01
title: COVID-19: $R_0$ is lower where outbreak is larger
author: Battiston, Pietro
date: 2020-04-16
txt: ./txt/cord-167454-ivhqeu01.txt
cache: ./cache/cord-167454-ivhqeu01.txt
extension: .txt
mime: text/plain
url: https://arxiv.org/pdf/2004.07827v1.pdf
doi: nan
summary:
  Specifically, we employ daily data on the number of individuals positive to COVID-19 at the municipality level, focusing on a period in which the entire country was subject to a lockdown. Note: fit between data and the corresponding SIR model for Lombardy region (left) and the most affected municipalities at the beginning of our period of interest in absolute and per capita terms, respectively (center, right). In order to shed light on this indeterminacy, we proceed to simulating the SIR model for each municipality until the predicted size of the infected population decreases below either (i) 0.1 cases for one thousands inhabitants or (ii) 0.1 cases 6 and we consider the number of periods elapsed as the outbreak duration. We show that in Lombardy, during a lockdown, the basic reproduction number for COVID-19 reacts negatively to the initial size of an outbreak at the municipality level, an effect which cannot be explained by the population having reached herd immunity.

abstract:
  We use daily data from Lombardy, the Italian region most affected by the COVID-19 outbreak, to calibrate a SIR model individually on each municipality. These are all covered by the same health system and, in the post-lockdown phase we focus on, all subject to the same social distancing regulations. We find that municipalities with a higher number of cases at the beginning of the period analyzed have a lower rate of diffusion, which cannot be imputed to herd immunity. In particular, there is a robust and strongly significant negative correlation between the estimated basic reproduction number ($R_0$) and the initial outbreak size, in contrast with the role of $R_0$ as a emph{predictor} of outbreak size. We explore different possible explanations for this phenomenon and conclude that a higher number of cases causes changes of behavior, such as a more strict adoption of social distancing measures among the population, that reduce the spread. This result calls for a transparent, real-time distribution of detailed epidemiological data, as such data affects the behavior of populations in areas affected by the outbreak.


id: cord-174036-b3frnfr7
title: Spatial Heterogeneity Can Lead to Substantial Local Variations in COVID-19 Timing and Severity
author: Thomas, Loring J.
date: 2020-05-20
txt: ./txt/cord-174036-b3frnfr7.txt
cache: ./cache/cord-174036-b3frnfr7.txt
extension: .txt
mime: text/plain
url: https://arxiv.org/pdf/2005.09850v1.pdf
doi: nan
summary:
  Based on simulations of unrestricted COVID-19 diffusion in 19 U.S cities, we conclude that heterogeneity in population distribution can have large impacts on local pandemic timing and severity, even when aggregate behavior at larger scales mirrors a classic SIR-like pattern. These results demonstrate the potential for spatial network structure to generate highly non-uniform diffusion behavior even at the scale of cities, and suggest the importance of incorporating such structure when designing models to inform healthcare planning, predict community outcomes, or identify potential disparities. In this paper, we examine the potential impact of local spatial heterogeneity on COVID-19, modeling the diffusion of SARS-CoV-2 in populations whose contacts are based on spatially plausible network structures. The disease diffuses through the contact network, with currently infectious individuals infecting susceptible neighbors as a continous time Poisson process with a rate estimated from mortality data (see supplement); recovered or deceased individuals are not considered infectious for modeling purposes.

abstract:
  Standard epidemiological models for COVID-19 employ variants of compartment (SIR) models at local scales, implicitly assuming spatially uniform local mixing. Here, we examine the effect of employing more geographically detailed diffusion models based on known spatial features of interpersonal networks, most particularly the presence of a long-tailed but monotone decline in the probability of interaction with distance, on disease diffusion. Based on simulations of unrestricted COVID-19 diffusion in 19 U.S cities, we conclude that heterogeneity in population distribution can have large impacts on local pandemic timing and severity, even when aggregate behavior at larger scales mirrors a classic SIR-like pattern. Impacts observed include severe local outbreaks with long lag time relative to the aggregate infection curve, and the presence of numerous areas whose disease trajectories correlate poorly with those of neighboring areas. A simple catchment model for hospital demand illustrates potential implications for health care utilization, with substantial disparities in the timing and extremity of impacts even without distancing interventions. Likewise, analysis of social exposure to others who are morbid or deceased shows considerable variation in how the epidemic can appear to individuals on the ground, potentially affecting risk assessment and compliance with mitigation measures. These results demonstrate the potential for spatial network structure to generate highly non-uniform diffusion behavior even at the scale of cities, and suggest the importance of incorporating such structure when designing models to inform healthcare planning, predict community outcomes, or identify potential disparities.


id: cord-175366-jomeywqr
title: Structural Identifiability and Observability of Compartmental Models of the COVID-19 Pandemic
author: Massonis, Gemma
date: 2020-06-25
txt: ./txt/cord-175366-jomeywqr.txt
cache: ./cache/cord-175366-jomeywqr.txt
extension: .txt
mime: text/plain
url: https://arxiv.org/pdf/2006.14295v1.pdf
doi: nan
summary:
  We analyse the structural identifiability and observability of all of the models, considering all plausible choices of outputs and time-varying parameters, which leads us to analyse 255 different model versions. It should be taken into account that in the present work we are interested in assessing structural identifiability and observability both with constant and continuous time-varying model parameters (or equivalently, with unknown inputs), as explained in Remark 1. The recovered state (R) is almost never observable unless it is directly measured (D.M.) as output; the only exceptions are two SEIR models, 31 and 38, for which R is observable under the assumption of time-varying parameters. Changing β from a constant to a time-varying parameter (or equivalently an unknown input) does not change its observability nor that of the other variables in SIR models. Considering the recovery rate γ (Fig. 7) or the latent period κ (Fig. 6) individually as time-varying parameters generally leads to greater observability, except for model 31 (1) .

abstract:
  The recent coronavirus disease (COVID-19) outbreak has dramatically increased the public awareness and appreciation of the utility of dynamic models. At the same time, the dissemination of contradictory model predictions has highlighted their limitations. If some parameters and/or state variables of a model cannot be determined from output measurements, its ability to yield correct insights -- as well as the possibility of controlling the system -- may be compromised. Epidemic dynamics are commonly analysed using compartmental models, and many variations of such models have been used for analysing and predicting the evolution of the COVID-19 pandemic. In this paper we survey the different models proposed in the literature, assembling a list of 36 model structures and assessing their ability to provide reliable information. We address the problem using the control theoretic concepts of structural identifiability and observability. Since some parameters can vary during the course of an epidemic, we consider both the constant and time-varying parameter assumptions. We analyse the structural identifiability and observability of all of the models, considering all plausible choices of outputs and time-varying parameters, which leads us to analyse 255 different model versions. We classify the models according to their structural identifiability and observability under the different assumptions and discuss the implications of the results. We also illustrate with an example several alternative ways of remedying the lack of observability of a model. Our analyses provide guidelines for choosing the most informative model for each purpose, taking into account the available knowledge and measurements.


id: cord-184685-ho72q46e
author: Huang, Tongtong
date: 2020-08-10
txt: ./txt/cord-184685-ho72q46e.txt
cache: ./cache/cord-184685-ho72q46e.txt
extension: .txt
mime: text/plain
url: https://arxiv.org/pdf/2008.05909v1.pdf
doi: nan
summary:
  We present the development of a forecasting model using local fine-grained hospital-level data to track the changes in hospitalization and mortality rates owing to reopening orders in the greater Houston area encompassing nine counties in the state of Texas, USA. We demonstrated our new approach using a policy-aware risk-Stratified Susceptible-Infectious-Recovered Hospitalization-Critical-Dead (SSIR-HCD) model, which compared favorably to existing methods (including our neural network latent space modeling, a nonlinear extension of SIR-HCD). • Epidemiology based dynamic models based on grouping populations into a discrete set of compartments (i.e., states), and defining ordinary differential equations (ODE) rate equations describing the movement of people between compartments: SEIR (Susceptible, Exposed, Infected, Recovered) models and their myriad variants are examples in this category. Our SSIR-HCD model forecasts fine-grained COVID-19 hospitalization and mortality by accounting for the impact of local policies.

title:
  Population stratification enables modeling effects of reopening policies on mortality and hospitalization rates

abstract:
  Objective: We study the influence of local reopening policies on the composition of the infectious population and their impact on future hospitalization and mortality rates. Materials and Methods: We collected datasets of daily reported hospitalization and cumulative morality of COVID 19 in Houston, Texas, from May 1, 2020 until June 29, 2020. These datasets are from multiple sources (USA FACTS, Southeast Texas Regional Advisory Council COVID 19 report, TMC daily news, and New York Times county level mortality reporting). Our model, risk stratified SIR HCD uses separate variables to model the dynamics of local contact (e.g., work from home) and high contact (e.g., work on site) subpopulations while sharing parameters to control their respective $R_0(t)$ over time. Results: We evaluated our models forecasting performance in Harris County, TX (the most populated county in the Greater Houston area) during the Phase I and Phase II reopening. Not only did our model outperform other competing models, it also supports counterfactual analysis to simulate the impact of future policies in a local setting, which is unique among existing approaches. Discussion: Local mortality and hospitalization are significantly impacted by quarantine and reopening policies. No existing model has directly accounted for the effect of these policies on local trends in infections, hospitalizations, and deaths in an explicit and explainable manner. Our work is an attempt to close this important technical gap to support decision making. Conclusion: Despite several limitations, we think it is a timely effort to rethink about how to best model the dynamics of pandemics under the influence of reopening policies.


id: cord-186927-b8i85vo7
title: Incentives, lockdown, and testing: from Thucydides's analysis to the COVID-19 pandemic
author: Hubert, Emma
date: 2020-09-01
url: https://arxiv.org/pdf/2009.00484v1.pdf
doi: nan
abstract:
  We consider the control of the COVID-19 pandemic via incentives, through either stochastic SIS or SIR compartmental models. When the epidemic is ongoing, the population can reduce interactions between individuals in order to decrease the rate of transmission of the disease, and thus limit the epidemic. However, this effort comes at a cost for the population. Therefore, the government can put into place incentive policies to encourage the lockdown of the population. In addition, the government may also implement a testing policy in order to know more precisely the spread of the epidemic within the country, and to isolate infected individuals. We provide numerical examples, as well as an extension to a stochastic SEIR compartmental model to account for the relatively long latency period of the COVID-19 disease. The numerical results confirm the relevance of a tax and testing policy to improve the control of an epidemic. More precisely, if a tax policy is put into place, even in the absence of a specific testing policy, the population is encouraged to significantly reduce its interactions, thus limiting the spread of the disease. If the government also adjusts its testing policy, less effort is required on the population side, so individuals can interact almost as usual, and the epidemic is largely contained by the targeted isolation of positively-tested individuals.


id: cord-187462-fxuzd9qf
title: Modelling the spread of Covid19 in Italy using a revised version of the SIR model
author: Palladino, Andrea
date: 2020-05-18
txt: ./txt/cord-187462-fxuzd9qf.txt
cache: ./cache/cord-187462-fxuzd9qf.txt
extension: .txt
mime: text/plain
url: https://arxiv.org/pdf/2005.08724v2.pdf
doi: nan
summary:
  We started from a simple Susceptible, Infected, Recovered (SIR) model and we added the condition that, after a certain time, the basic reproduction number $R_0$ exponentially decays in time, as empirically suggested by world data. Hence, at a given time t from the beginning of the spreading of the epidemic, I(t) and S(t) are the number of infected people present in the population and the number of vulnerable people that have not contracted the virus yet, respectively, while R(t) is the sum of the ones that have developed immunity (recovered) or deceased and are therefore removed from the susceptible count. Although a simulation with the standard SIR appears to be adequate to describe an epidemic spreading in a sample where all the initial conditions remain constant throughout the period of time, it is not sufficient when it comes to a more complex and realistic situation such as the population of a given country, where the parameters of the model are influenced by other external factors.

abstract:
  In this paper, we present a model to predict the spread of the Covid-19 epidemic and apply it to the specific case of Italy. We started from a simple Susceptible, Infected, Recovered (SIR) model and we added the condition that, after a certain time, the basic reproduction number $R_0$ exponentially decays in time, as empirically suggested by world data. Using this model, we were able to reproduce the real behavior of the epidemic with an average error of 5%. Moreover, we illustrate possible future scenarios, associated to different intervals of $R_0$. This model has been used since the beginning of March 2020, predicting the Italian peak of the epidemic in April 2020 with about 100.000 detected active cases. The real peak of the epidemic happened on the 20th of April 2020, with 108.000 active cases. This result shows that the model had predictive power for the italian case.


id: cord-187700-716af719
title: Epidemic Spreading in a Social Network with Facial Masks wearing Individuals
author: Lee, Duan-Shin
date: 2020-10-31
txt: ./txt/cord-187700-716af719.txt
cache: ./cache/cord-187700-716af719.txt
extension: .txt
mime: text/plain
url: https://arxiv.org/pdf/2011.00190v1.pdf
doi: nan
summary:
  In this paper, we present a susceptible-infected-recovered (SIR) model with individuals wearing facial masks and individuals who do not. The disease transmission rates, the recovering rates and the fraction of individuals who wear masks are all time dependent in the model. We determine the fraction of individual who wear masks by a maximum likelihood estimation, which maximizes the transition probability of a stochastic susceptible-infected-recovered model. We develop a bond percolation analysis to predict the eventual fraction of population who are infected, assuming that parameters of the SIR model do not change anymore. Specifically, we propose a time dependent susceptible-infected-recovered (SIR) model with two types of individuals. From the data published by John Hopkins University [5] we progressively estimate the time dependent disease transmission rates and the recovery rates of the SIR model. In this report, we presented a time dependent SIR model, in which some individuals wear facial masks and some do not.

abstract:
  In this paper, we present a susceptible-infected-recovered (SIR) model with individuals wearing facial masks and individuals who do not. The disease transmission rates, the recovering rates and the fraction of individuals who wear masks are all time dependent in the model. We develop a progressive estimation of the disease transmission rates and the recovering rates based on the COVID-19 data published by John Hopkins University. We determine the fraction of individual who wear masks by a maximum likelihood estimation, which maximizes the transition probability of a stochastic susceptible-infected-recovered model. The transition probability is numerically difficult to compute if the number of infected individuals is large. We develop an approximation for the transition probability based on central limit theorem and mean field approximation. We show through numerical study that our approximation works well. We develop a bond percolation analysis to predict the eventual fraction of population who are infected, assuming that parameters of the SIR model do not change anymore. We predict the outcome of COVID-19 pandemic using our theory.


id: cord-188958-id9m3mfk
title: Containing a pandemic: Nonpharmaceutical interventions and the"second wave"
author: Vrugt, Michael te
date: 2020-09-30
txt: ./txt/cord-188958-id9m3mfk.txt
cache: ./cache/cord-188958-id9m3mfk.txt
extension: .txt
mime: text/plain
url: https://arxiv.org/pdf/2010.00962v1.pdf
doi: nan
summary:
  Recently [12] , we have proposed an extension of the SIR model based on dynamical density functional theory (DDFT) [13] [14] [15] [16] that incorporates social distancing in the form of a repulsive interaction potential. In this work, we use the SIR-DDFT model and an extended susceptible-infected-recovereddead (SIRD) model with hysteresis to investigate the effects of various containment strategies with model parameters adapted to the current COVID-19 outbreak in Germany. We compare the effects of face masks and social distancing/isolation and of various threshold values (of the number of infected persons) for imposing and lifting restrictions. This is an important advantage, since it allows to distinguish the effects of two of the main NPIs that were implemented against the COVID-19 outbreak: Face masks and other hygiene measures such as frequent hand washing reduce c, i.e., they decrease the probability of an infection in case of contact.

abstract:
  In response to the worldwide outbreak of the coronavirus disease COVID-19, a variety of nonpharmaceutical interventions such as face masks and social distancing have been implemented. A careful assessment of the effects of such containment strategies is required to avoid exceeding social and economical costs as well as a dangerous"second wave"of the pandemic. In this work, we combine a recently developed dynamical density functional theory model and an extended SIRD model with hysteresis to study effects of various measures and strategies using realistic parameters. Depending on intervention thresholds, a variety of phases with different numbers of shutdowns and deaths are found. Spatiotemporal simulations provide further insights into the dynamics of a second wave. Our results are of crucial importance for public health policy.


id: cord-189434-nrkvbdu4
title: Analytical Mechanics Allows Novel Vistas on Mathematical Epidemic Dynamics Modelling
author: Steinmann, Paul
date: 2020-06-06
txt: ./txt/cord-189434-nrkvbdu4.txt
cache: ./cache/cord-189434-nrkvbdu4.txt
extension: .txt
mime: text/plain
url: https://arxiv.org/pdf/2006.03961v1.pdf
doi: nan
summary:
  In both cases, Hamilton''s equations in terms of a suited Hamiltonian as well as Hamilton''s principle in terms of a suited Lagrangian are considered in minimal and extended phase and state space coordinates, respectively. Taken together, the time re-parameterized SIR model obeys Hamiltonian structure and identifies the relation between the gradient G(Z) ∈ R 2 of the Hamiltonian H(Z) in minimal phase space coordinates and the forcing term F (Z) ∈ R 2 as Clearly, the Euler-Lagrange equation in minimal state space coordinates coincides with the single, non-linear ODE formulation of the time re-parameterized SIR model in Eq. 7. Using again Hamilton''s equation Q • = 2Λ · J and exploiting the skew-symmetry of the symplectic matrix, i.e. Λ · J = −J · Λ, recovers once more the already previously established relation between the gradient G(Q) ∈ R 2 of the Hamiltonian H(Q) (in extended state space coordinates) and the forcing term

abstract:
  This contribution aims to shed light on mathematical epidemic dynamics modelling from the viewpoint of analytical mechanics. To set the stage, it recasts the basic SIR model of mathematical epidemic dynamics in an analytical mechanics setting. Thereby, it considers two possible re-parameterizations of the basic SIR model. On the one hand, it is proposed to re-scale time, while on the other hand, to transform the coordinates, i.e. the independent variables. In both cases, Hamilton's equations in terms of a suited Hamiltonian as well as Hamilton's principle in terms of a suited Lagrangian are considered in minimal and extended phase and state space coordinates, respectively. The corresponding Legendre transformations relating the various options for the Hamiltonians and Lagrangians are detailed. Ultimately, this contribution expands on a multitude of novel vistas on mathematical epidemic dynamics modelling that emerge from the analytical mechanics viewpoint. As result, it is believed that interesting and relevant new research avenues open up when exploiting in depth the analogies between analytical mechanics and mathematical epidemic dynamics modelling.


id: cord-190296-erpoh5he
title: On COVID-19 Modelling
author: Schaback, Robert
date: 2020-05-11
txt: ./txt/cord-190296-erpoh5he.txt
cache: ./cache/cord-190296-erpoh5he.txt
extension: .txt
mime: text/plain
url: https://arxiv.org/pdf/2005.07004v1.pdf
doi: nan
summary:
  This contribution starts in section 2 with a rather elementary reconciliation of the standard SIR model for epidemics, featuring the central notions like Basic Reproduction Number, Herd Immunity Threshold, and Doubling Time, together with some critical remarks on their abuse in the media. To run this hidden model with constant N = S + M + H + C, one needs initial values and good estimates for β and γ, which are not the ones of the Johns Hopkins Data Model of section 3.3. These yield estimates for the parameters of the full SIR model that replace the earlier time series from the Johns Hopkins Data Model in section 3.3. Note that the only ingredients beside the Johns Hopkins data are the number k for the k-day rule, the Infection Fatality Rate γ IF from the literature, and the backlog m for estimation of constants from time series.

abstract:
  This contribution analyzes the COVID-19 outbreak by comparably simple mathematical and numerical methods. The final goal is to predict the peak of the epidemic outbreak per country with a reliable technique. This is done by an algorithm motivated by standard SIR models and aligned with the standard data provided by the Johns Hopkins University. To reconstruct data for the unregistered Infected, the algorithm uses current values of the infection fatality rate and a data-driven estimation of a specific form of the recovery rate. All other ingredients are data-driven as well. Various examples of predictions are provided for illustration.


id: cord-190495-xpfbw7lo
title: Safety-Critical Control of Compartmental Epidemiological Models with Measurement Delays
author: Molnar, Tamas G.
date: 2020-09-22
txt: ./txt/cord-190495-xpfbw7lo.txt
cache: ./cache/cord-190495-xpfbw7lo.txt
extension: .txt
mime: text/plain
url: https://arxiv.org/pdf/2009.10262v1.pdf
doi: nan
summary:
  We introduce a methodology to guarantee safety against the spread of infectious diseases by viewing epidemiological models as control systems and by considering human interventions (such as quarantining or social distancing) as control input. We consider a generalized compartmental model that represents the form of the most popular epidemiological models and we design safety-critical controllers that formally guarantee safe evolution with respect to keeping certain populations of interest under prescribed safe limits. The parameters β 0 = 0.33 day −1 , γ = 0.2 day −1 and N = 33 × 10 6 of the SIR model were fitted following the algorithm in [10] to the recorded number of confirmed cases I + R [31] between March 25 and August 9, 2020, while the control input u(t), that represents the level of quarantining and social distancing, was identified from mobility data [32] based on the medium time people spent home.

abstract:
  We introduce a methodology to guarantee safety against the spread of infectious diseases by viewing epidemiological models as control systems and by considering human interventions (such as quarantining or social distancing) as control input. We consider a generalized compartmental model that represents the form of the most popular epidemiological models and we design safety-critical controllers that formally guarantee safe evolution with respect to keeping certain populations of interest under prescribed safe limits. Furthermore, we discuss how measurement delays originated from incubation period and testing delays affect safety and how delays can be compensated via predictor feedback. We demonstrate our results by synthesizing active intervention policies that bound the number of infections, hospitalizations and deaths for epidemiological models capturing the spread of COVID-19 in the USA.


id: cord-191574-1g38scnj
author: Harko, Tiberiu
date: 2020-08-28
txt: ./txt/cord-191574-1g38scnj.txt
cache: ./cache/cord-191574-1g38scnj.txt
extension: .txt
mime: text/plain
url: https://arxiv.org/pdf/2009.00434v1.pdf
doi: nan
summary:
  The series representations of the time evolution of the SIR model with vital dynamics are compared with the exact numerical solutions of the model, and we find that, at least for a specific range of parameters, there is a good agreement between the Adomian and Laplace-Adomian semianalytical solutions, containing only a small number of terms, and the numerical results. In the present work we consider the possibility of obtaining some accurate semianalytical solutions of the equations of the SIR model with vital dynamics by using the Adomian and the Laplace-Adomian Decomposition Methods, respectively. In order to obtain some approximate solutions of the basic evolution equation we will apply to it both the Adomian and the Laplace-Adomian Decomposition Methods, We obtain in each case the recurrence relations giving the successive terms in the Adomian series representation as a function of the Adomian polynomials.

title:
  Series solution of the Susceptible-Infected-Recovered (SIR) epidemic model with vital dynamics via the Adomian and Laplace-Adomian Decomposition Methods

abstract:
  The Susceptible-Infected-Recovered (SIR) epidemic model as well as its generalizations are extensively used for the study of the spread of infectious diseases, and for the understanding of the dynamical evolution of epidemics. From SIR type models only the model without vital dynamics has an exact analytic solution, which can be obtained in an exact parametric form. The SIR model with vital dynamics, the simplest extension of the basic SIR model, does not admit a closed form representation of the solution. However, in order to perform the comparison with the epidemiological data accurate representations of the time evolution of the SIR model with vital dynamics would be very useful. In the present paper, we obtain first the basic evolution equation of the SIR model with vital dynamics, which is given by a strongly nonlinear second order differential equation. Then we obtain a series representation of the solution of the model, by using the Adomian and Laplace-Adomian Decomposition Methods to solve the dynamical evolution equation of the model. The solutions are expressed in the form of infinite series. The series representations of the time evolution of the SIR model with vital dynamics are compared with the exact numerical solutions of the model, and we find that, at least for a specific range of parameters, there is a good agreement between the Adomian and Laplace-Adomian semianalytical solutions, containing only a small number of terms, and the numerical results.


id: cord-194157-ak2gc3nz
title: Parameter estimation in the SIR model from early infections
author: Clum, Charles
date: 2020-08-10
txt: ./txt/cord-194157-ak2gc3nz.txt
cache: ./cache/cord-194157-ak2gc3nz.txt
extension: .txt
mime: text/plain
url: https://arxiv.org/pdf/2008.04286v1.pdf
doi: nan
summary:
  We introduce a simple algorithm that uses the early infection times from a sample path of the SIR model to estimate the parameters this model, and we provide a performance guarantee in the setting of locally tree-like graphs. Section 3 gives the proof of our main result: that our approach provides decent estimates of λ and µ in the setting of locally tree-like graphs. For example, it is known that for every fixed choice of d ∈ N with d > 1 and c ∈ (0, 1 4 ), there exists γ > 0 such that a random d-regular graph on n vertices is (c log d−1 n, n −γ )-locally tree-like with probability approaching 1 as n → ∞; see Proposition 4.1 in [2] . For each n, consider the SIR model on G n with parameters λ and µ, and let E ∞ denote the event that U (∞) contains a vertex of distance greater than r from U (0).

abstract:
  A standard model for epidemics is the SIR model on a graph. We introduce a simple algorithm that uses the early infection times from a sample path of the SIR model to estimate the parameters this model, and we provide a performance guarantee in the setting of locally tree-like graphs.


id: cord-212912-t5v11gs0
title: Prospects and limits of SIR-type Mathematical Models to Capture the COVID-19 Pandemic
author: Barwolff, Gunter
date: 2020-04-13
txt: ./txt/cord-212912-t5v11gs0.txt
cache: ./cache/cord-212912-t5v11gs0.txt
extension: .txt
mime: text/plain
url: https://arxiv.org/pdf/2004.06522v1.pdf
doi: nan
summary:
  Especially a good choice of $beta$ as the number of others that one infected person encounters per unit time (per day) influences the adequateness of the results of the model. We use the European Centre for Disease Prevention and Control [2] as a data for the COVID-19 infected people for the period from December 31st 2019 to April 8th 2020. For the iterative Gauss-Newton method we guessed the respective periods for every country by a visual inspection of the graphs of the infected people over days. The numerical tests showed that a very early start of the lockdown resulting in a reduction of the infection rate β results in the typical Gaussian curve to be delayed by I; however, the amplitude (maximum value of I) doesn''t really change. The interesting points in time are those where the acceleration of the numbers of infected people increases or decreases, respectively.

abstract:
  For the description of a pandemic mathematical models could be interesting. Both for physicians and politicians as a base for decisions to treat the disease. The responsible estimation of parameters is a main issue of mathematical pandemic models. Especially a good choice of $beta$ as the number of others that one infected person encounters per unit time (per day) influences the adequateness of the results of the model. For the actual COVID-19 pandemic some aspects of the parameter choice will be discussed. Because of the incompatibility of the data of the Johns-Hopkins-University to the data of the German Robert-Koch-Institut we use the COVID-19 data of the European Centre for Disease Prevention and Control (ECDC) as a base for the parameter estimation. Two different mathematical methods for the data analysis will be discussed in this paper and possible sources of trouble will be shown. As example of the parameter choice serve the data of the USA and the UK. The resulting parameters will be used estimated and used in W.,O. Kermack and A.,G. McKendrick's SIR model. Strategies for the commencing and ending of social and economic shutdown measures are discussed. The numerical solution of the ordinary differential equation system of the modified SIR model is being done with a Runge-Kutta integration method of fourth order. At the end the applicability of the SIR model could be shown essentially. Suggestions about appropriate points in time at which to commence with lockdown measures based on the acceleration rate of infections conclude the paper.


id: cord-220116-6i7kg4mj
title: Social distancing and epidemic resurgence in agent-based Susceptible-Infectious-Recovered models
author: Mukhamadiarov, Ruslan I.
date: 2020-06-03
txt: ./txt/cord-220116-6i7kg4mj.txt
cache: ./cache/cord-220116-6i7kg4mj.txt
extension: .txt
mime: text/plain
url: https://arxiv.org/pdf/2006.02552v1.pdf
doi: nan
summary:
  To determine the robustness of our results and compare the influence of different contact characteristics, we ran our stochastic model on four distinct spatially structured architectures, namely i) regular two-dimensional square lattices, wherein individuals move slowly and with limited range, i.e., spread diffusively; ii) two-dimensional small-world networks that in addition incorporate substantial long-distance interactions and contaminations; and finally on iii) random as well as iv) scale-free social contact networks. For both the two-dimensional regular lattice and small-world structure, a similar sudden drop in the total number of infected individuals ( Figure 6B ) requires a considerably longer mitigation duration: In these dynamical networks, the repopulation of nodes with infective individuals facilitates disease spreading, thereby diminishing control efficacy. In this study, we implemented social distancing control measures for simple stochastic SIR epidemic models on regular square lattices with diffusive spreading, two-dimensional Newman-Watts small-world networks that include highly infective long-distance connections, and static contact networks, either with random connectivity or scale-free topology.

abstract:
  Once an epidemic outbreak has been effectively contained through non-pharmaceutical interventions, a safe protocol is required for the subsequent release of social distancing restrictions to prevent a disastrous resurgence of the infection. We report individual-based numerical simulations of stochastic susceptible-infectious-recovered model variants on four distinct spatially organized lattice and network architectures wherein contact and mobility constraints are implemented. We robustly find that the intensity and spatial spread of the epidemic recurrence wave can be limited to a manageable extent provided release of these restrictions is delayed sufficiently (for a duration of at least thrice the time until the peak of the unmitigated outbreak) and long-distance connections are maintained on a low level (limited to less than five percent of the overall connectivity).


id: cord-222193-0b4o0ccp
title: A simple statistical physics model for the epidemic with incubation period
author: Saakian, David B.
date: 2020-04-13
txt: ./txt/cord-222193-0b4o0ccp.txt
cache: ./cache/cord-222193-0b4o0ccp.txt
extension: .txt
mime: text/plain
url: https://arxiv.org/pdf/2004.05778v1.pdf
doi: nan
summary:
  Based on the classical SIR model, we derive a simple modification for the dynamics of epidemics with a known incubation period of infection. We use the proposed model to analyze COVID-19 epidemic data in Armenia. Moreover, it is crucial to consider the final incubation period of the disease to construct a correct model for the COVID-19 case. In this study, we derive a system of integro-differential equations based on the rigorous master equation that adequately describes infection dynamics with an incubation period, e.g., COVID-19. In fact, the real data allows us to measure three main parameters: the exponential growth coefficient at the beginning of the epidemic; the minimum period of time, in which an infected person can transmit the infection; and the maximum period, when an infected person ceases to transmit the infection. In this paper, we introduced a version of SIR model for infection spreading with known incubation period. This model was applied to analyze the COVID-19 epidemic data in Armenia.

abstract:
  Based on the classical SIR model, we derive a simple modification for the dynamics of epidemics with a known incubation period of infection. The model is described by a system of integro-differential equations. Parameters of our model directly related to epidemiological data. We derive some analytical results, as well as perform numerical simulations. We use the proposed model to analyze COVID-19 epidemic data in Armenia. We propose a strategy: organize a quarantine, and then conduct extensive testing of risk groups during the quarantine, evaluating the percentage of the population among risk groups and people with symptoms.


id: cord-229937-fy90oebs
title: Global analysis of the COVID-19 pandemic using simple epidemiological models
author: Amaro, J. E.
date: 2020-05-14
txt: ./txt/cord-229937-fy90oebs.txt
cache: ./cache/cord-229937-fy90oebs.txt
extension: .txt
mime: text/plain
url: https://arxiv.org/pdf/2005.06742v1.pdf
doi: nan
summary:
  The Death or ''D'' model is a simplified version of the SIR (susceptible-infected-recovered) model, which assumes no recovery over time, and allows for the transmission-dynamics equations to be solved analytically. The evolution of the COVID-19 pandemic in several countries (China, Spain, Italy, France, UK, Iran, USA and Germany) shows a similar behavior in concord with the D-model trend, characterized by a rapid increase of death cases followed by a slow decline, which are affected by the earliness and efficiency of the lockdown effect. These results are in agreement with more accurate calculations using the extended SIR model with a parametrized solution and more sophisticated Monte Carlo grid simulations, which predict similar trends and indicate a common evolution of the pandemic with universal parameters. Additionally, D-model calculations are benchmarked with more sophisticated and reliable calculations using the extended SIR (ESIR) and Monte Carlo Planck (MCP) models -also developed in this work -which provide similar results, but allow for a more coherent spatial-time disentanglement of the various effects present during a pandemic.

abstract:
  Several analytical models have been used in this work to describe the evolution of death cases arising from coronavirus (COVID-19). The Death or `D' model is a simplified version of the SIR (susceptible-infected-recovered) model, which assumes no recovery over time, and allows for the transmission-dynamics equations to be solved analytically. The D-model can be extended to describe various focuses of infection, which may account for the original pandemic (D1), the lockdown (D2) and other effects (Dn). The evolution of the COVID-19 pandemic in several countries (China, Spain, Italy, France, UK, Iran, USA and Germany) shows a similar behavior in concord with the D-model trend, characterized by a rapid increase of death cases followed by a slow decline, which are affected by the earliness and efficiency of the lockdown effect. These results are in agreement with more accurate calculations using the extended SIR model with a parametrized solution and more sophisticated Monte Carlo grid simulations, which predict similar trends and indicate a common evolution of the pandemic with universal parameters.


id: cord-241596-vh90s8vi
author: Libotte, Gustavo Barbosa
date: 2020-04-15
url: https://arxiv.org/pdf/2004.07397v2.pdf
doi: nan
title:
  Determination of an Optimal Control Strategy for Vaccine Administration in COVID-19 Pandemic Treatment

abstract:
  During decades, mathematical models have been used to predict the behavior of physical and biologic systems, and to define strategies aiming the minimization of the effects regarding different types of diseases. In the present days, the development of mathematical models to simulate the dynamic behavior of novel coronavirus disease (COVID-19) is considered an important theme due to the quantity of infected people worldwide. In this work, the aim is to determine an optimal control strategy for vaccine administration in COVID-19 pandemic treatment considering real data from China. For this purpose, an inverse problem is formulated and solved in order to determine the parameters of the compartmental SIR (Susceptible-Infectious-Recovered) model. To solve such inverse problem, the Differential Evolution (DE) algorithm is employed. After this step, two optimal control problems (mono- and multi-objective) to determine the optimal strategy for vaccine administration in COVID-19 pandemic treatment are proposed. The first consists of minimizing the quantity of infected individuals during the treatment. The second considers minimizing together the quantity of infected individuals and the prescribed vaccine concentration during the treatment, i.e., a multi-objective optimal control problem. The solution of each optimal control problems is obtained using DE and Multi-Objective Differential Evolution (MODE) algorithms, respectively. The results regarding the proposed multi-objective optimal control problem provides a set of evidences from which an optimal strategy for vaccine administration can be chosen, according to a given criterion.


id: cord-243070-0b06zk1q
title: Epidemic control via stochastic optimal control
author: Lesniewski, Andrew
date: 2020-04-14
txt: ./txt/cord-243070-0b06zk1q.txt
cache: ./cache/cord-243070-0b06zk1q.txt
extension: .txt
mime: text/plain
url: https://arxiv.org/pdf/2004.06680v3.pdf
doi: nan
summary:
  This results in a system of forward backward stochastic differential equations, which is amenable to numerical solution via Monte Carlo simulations. In this note we study the problem of optimal control of an epidemic modeled by means of a stochastic extension of the SIR model (see Section 2 for definition). The optimal control problem is recast as the stochastic minimum principle problem and formulated in terms of a system of forward backward stochastic differential equations (FBSDE). If a vaccine against the disease is unavailable, we set u 1 = 0 in the equation above, which yields the following controlled process: Using Ito''s lemma, we verify that these two conditions lead to the following nonlinear partial differential equation for the value function, namely the stochastic Hamilton-Jacobi-Bellman equation: Under this running cost function, the optimal policy is to implement a draconian isolation regime, which leads to a rapid drop in infections, while keeping the susceptible fraction of the population at a very high level.

abstract:
  We study the problem of optimal control of the stochastic SIR model. Models of this type are used in mathematical epidemiology to capture the time evolution of highly infectious diseases such as COVID-19. Our approach relies on reformulating the Hamilton-Jacobi-Bellman equation as a stochastic minimum principle. This results in a system of forward backward stochastic differential equations, which is amenable to numerical solution via Monte Carlo simulations. We present a number of numerical solutions of the system under a variety of scenarios.


id: cord-247144-crmfwjvf
author: Bodova, Katarina
date: 2020-05-14
txt: ./txt/cord-247144-crmfwjvf.txt
cache: ./cache/cord-247144-crmfwjvf.txt
extension: .txt
mime: text/plain
url: https://arxiv.org/pdf/2005.06933v1.pdf
doi: nan
summary:
  We observe that the time series of active cases in individual countries (the difference of the total number of confirmed infections and the sum of the total number of reported deaths and recovered cases) display a strong agreement with polynomial growth and at a later epidemic stage also with a combined polynomial growth with exponential decay. Note that the inflection points of the function I = I(t) are located at T ± I = (α ± √ α) T G , particularly the time t = T − I plays an important role in the observed epidemic data as it corresponds to a moment at which the growth of the number of active cases reaches its maximum and starts to decrease. The simple PGED model, i.e., the universal scaling 7 and nonlinear fitting of the parameters from the data, can be used for as a predictive tool for the number of the reported active cases, particularly in countries in the growth phase.

title:
  Emerging Polynomial Growth Trends in COVID-19 Pandemic Data and Their Reconciliation with Compartment Based Models

abstract:
  We study the reported data from the COVID-19 pandemic outbreak in January - May 2020 in 119 countries. We observe that the time series of active cases in individual countries (the difference of the total number of confirmed infections and the sum of the total number of reported deaths and recovered cases) display a strong agreement with polynomial growth and at a later epidemic stage also with a combined polynomial growth with exponential decay. Our results are also formulated in terms of compartment type mathematical models of epidemics. Within these models the universal scaling characterizing the observed regime in an advanced epidemic stage can be interpreted as an algebraic decay of the relative reproduction number $R_0$ as $T_M/t$, where $T_M$ is a constant and $t$ is the duration of the epidemic outbreak. We show how our findings can be applied to improve predictions of the reported pandemic data and estimate some epidemic parameters. Note that although the model shows a good agreement with the reported data we do not make any claims about the real size of the pandemics as the relation of the observed reported data to the total number of infected in the population is still unknown.


id: cord-248050-apjwnwky
author: Vrugt, Michael te
date: 2020-03-31
txt: ./txt/cord-248050-apjwnwky.txt
cache: ./cache/cord-248050-apjwnwky.txt
extension: .txt
mime: text/plain
url: https://arxiv.org/pdf/2003.13967v2.pdf
doi: nan
summary:
  title: Effects of social distancing and isolation on epidemic spreading: a dynamical density functional theory model We present an extended model for disease spread based on combining an SIR model with a dynamical density functional theory where social distancing and isolation of infected persons are explicitly taken into account. In this article, we present a dynamical density functional theory (DDFT) [18] [19] [20] [21] for epidemic spreading that allows to model the effect of social distancing and isolation on infection numbers. While DDFT is not an exact theory (it is based on the assumption that the density is the only slow variable in the system [50, 51] ), it is nevertheless a significant improvement compared to the standard diffusion equation as it allows to incor-porate the effects of particle interactions and generally shows excellent agreement with microscopic simulations.

title:
  Effects of social distancing and isolation on epidemic spreading: a dynamical density functional theory model

abstract:
  For preventing the spread of epidemics such as the coronavirus disease COVID-19, social distancing and the isolation of infected persons are crucial. However, existing reaction-diffusion equations for epidemic spreading are incapable of describing these effects. We present an extended model for disease spread based on combining an SIR model with a dynamical density functional theory where social distancing and isolation of infected persons are explicitly taken into account. The model shows interesting nonequilibrium phase separation associated with a reduction of the number of infections, and allows for new insights into the control of pandemics.


id: cord-253461-o63ru7nr
title: Temporal Analysis of COVID-19 Peak Outbreak
author: Tewari, A.
date: 2020-09-13
txt: ./txt/cord-253461-o63ru7nr.txt
cache: ./cache/cord-253461-o63ru7nr.txt
extension: .txt
mime: text/plain
url: https://doi.org/10.1101/2020.09.11.20192229
doi: 10.1101/2020.09.11.20192229
summary:
  Intent of this research is to explore how a specific class of mathematical models namely Susceptible-Infected-Removed model can be utilized to forecast peak outbreak timelines of COVID-19 epidemic amongst a population of interest starting from the date of first reported case. With this in mind, SIR model is explored in current research to forecast peak COVID-19 outbreak over a large population in India. DISCUSSION This research was conducted to evaluate the feasibility of application of SIR model to predict peak COVID-19 outbreak timeline from the date of first reported case for the 10 largest states in India which together constitute more than 74% or almost 3/4 th of total population in India. For 9 out of 10 largest states in India included in the research, chosen SIR model could predict peak outbreak timeline from the date of the first reported case with error of +/-6 days or less and Standard Deviation (SD) in error = 5.83 day.

abstract:
  Intent of this research is to explore how a specific class of mathematical models namely Susceptible-Infected-Removed model can be utilized to forecast peak outbreak timelines of COVID-19 epidemic amongst a population of interest starting from the date of first reported case. Till the time of this research, there was no effective and universally accepted vaccine to control transmission and spread of this infection. COVID-19 primarily spreads in population through respiratory droplets from an infected person cough and sneeze which infects people who are in proximity. COVID-19 is spreading contagiously across the world. If health policy makers and medical experts could get early and timely insights into when peak infection rate would occur after first reported case, they could plan and optimize medical personnel, ventilators supply, and other medical resources without over-taxing the infrastructure. The predictions may also help policymakers devise strategies to control the epidemic, potentially saving many lives. Thus, it can aid in critical decision-making process by providing actionable insights into COVID-19 outbreak by leveraging available data.


id: cord-258018-29vtxz89
title: A SIR model assumption for the spread of COVID-19 in different communities
author: Cooper, Ian
date: 2020-06-28
txt: ./txt/cord-258018-29vtxz89.txt
cache: ./cache/cord-258018-29vtxz89.txt
extension: .txt
mime: text/plain
url: https://www.sciencedirect.com/science/article/pii/S0960077920304549?v=s5
doi: 10.1016/j.chaos.2020.110057
summary:
  The data in [29] for China, South Korea, India, Australia, USA, Italy and the state of Texas (communities) are organised in the form of time-series where the rows are recordings in time (from January to June, 2020), and the three columns are, the total cases I d tot (first column), number of infected individuals I d (second column) and deaths D d (third column). Assuming the published data are reliable, the SIR model (1) can be applied to assess the spread of the COVID-19 disease and predict the number of infected, removed and recovered populations and deaths in the communities, accommodating at the same time possible surges in the number of susceptible individuals. In this work, we have augmented the classic SIR model with the ability to accommodate surges in the number of susceptible individuals, supplemented by recorded data from China, South Korea, India, Australia, USA and the state of Texas to provide insights into the spread of COVID-19 in communities.

abstract:
  In this paper, we study the effectiveness of the modelling approach on the pandemic due to the spreading of the novel COVID-19 disease and develop a susceptible-infected-removed (SIR) model that provides a theoretical framework to investigate its spread within a community. Here, the model is based upon the well-known susceptible-infected-removed (SIR) model with the difference that a total population is not defined or kept constant per se and the number of susceptible individuals does not decline monotonically. To the contrary, as we show herein, it can be increased in surge periods! In particular, we investigate the time evolution of different populations and monitor diverse significant parameters for the spread of the disease in various communities, represented by countries and the state of Texas in the USA. The SIR model can provide us with insights and predictions of the spread of the virus in communities that the recorded data alone cannot. Our work shows the importance of modelling the spread of COVID-19 by the SIR model that we propose here, as it can help to assess the impact of the disease by offering valuable predictions. Our analysis takes into account data from January to June, 2020, the period that contains the data before and during the implementation of strict and control measures. We propose predictions on various parameters related to the spread of COVID-19 and on the number of susceptible, infected and removed populations until September 2020. By comparing the recorded data with the data from our modelling approaches, we deduce that the spread of COVID-19 can be under control in all communities considered, if proper restrictions and strong policies are implemented to control the infection rates early from the spread of the disease.


id: cord-264248-wqkphg2e
title: Hasty Reduction of COVID-19 Lockdown Measures Leads to the Second Wave of Infection
author: Hazem, Y.
date: 2020-05-26
txt: ./txt/cord-264248-wqkphg2e.txt
cache: ./cache/cord-264248-wqkphg2e.txt
extension: .txt
mime: text/plain
url: http://medrxiv.org/cgi/content/short/2020.05.23.20111526v1?rss=1
doi: 10.1101/2020.05.23.20111526
summary:
  For the study in hand, this model is used to forecast the infection rate if the lockdown measures are reduced by 25% on the 1st of June 2020 or the 1st of July 2020; hence, the impact of delaying this step is also investigated. 23.20111526 doi: medRxiv preprint in lockdown measures and predicts the evolution of the number of infected cases until the end of 2020 following the assumed conditions. . https://doi.org/10.1101/2020.05.23.20111526 doi: medRxiv preprint more affected by reopening as they have not fully conquered COVID-19 yet; hence, the hasty reduction of quarantine measures might lead to even higher infection rates that has happened before during the Spanish flu [21; 22] . In conclusion, this study offers a quantifiable prediction of how reducing the lockdown measures shall lead to the second wave of COVID-19 in the United States, Germany, the United Kingdom, Italy, Spain, and Canada.

abstract:
  The outbreak of COVID-19 has an undeniable global impact, both socially and economically. March 11th, 2020, COVID-19 was declared as a pandemic worldwide. Many governments, worldwide, have imposed strict lockdown measures to minimize the spread of COVID-19. However, these measures cannot last forever; therefore, many countries are already considering relaxing the lockdown measures. This study, quantitatively, investigated the impact of this relaxation in the United States, Germany, the United Kingdom, Italy, Spain, and Canada. A modified version of the SIR model is used to model the reduction in lockdown based on the already available data. The results showed an inevitable second wave of COVID-19 infection following loosening the current measures. The study tries to reveal the predicted number of infected cases for different reopening dates. Additionally, the predicted number of infected cases for different reopening dates is reported.


id: cord-270519-orh8fd1c
title: Bayesian modeling of COVID-19 cases with a correction to account for under-reported cases
author: Oliveira, A. C. S. d.
date: 2020-05-25
url: http://medrxiv.org/cgi/content/short/2020.05.24.20112029v1?rss=1
doi: 10.1101/2020.05.24.20112029
abstract:
  The novel of COVID-19 disease started in late 2019 making the worldwide governments came across a high number of critical and death cases, beyond constant fear of the collapse in their health systems. Since the beginning of the pandemic, researchers and authorities are mainly concerned with carrying out quantitative studies (modeling and predictions) overcoming the scarcity of tests that lead us to under- reporting cases. To address these issues, we introduce a Bayesian approach to the SIR model with correction for under-reporting in the analysis of COVID-19 cases in Brazil. The proposed model was enforced to obtain estimates of important quantities such as the reproductive rate and the average infection period, along with the more likely date when the pandemic peak may occur. Several under-reporting scenarios were considered in the simulation study, showing how impacting is the lack of information in the modeling.


id: cord-273429-dl6z8x9h
author: Dandekar, R.
date: 2020-07-24
txt: ./txt/cord-273429-dl6z8x9h.txt
cache: ./cache/cord-273429-dl6z8x9h.txt
extension: .txt
mime: text/plain
url: https://doi.org/10.1101/2020.07.23.20160697
doi: 10.1101/2020.07.23.20160697
summary:
  Figure 2 shows the comparison of the model-estimated infected and recovered case counts with actual Covid-19 data for the highest affected European countries as of 1 June 2020, namely: Russia, UK, Spain and Italy, in that order. Figure 6 shows reasonably good match between the model-estimated infected and recovered case counts with actual Covid-19 data for the highest affected North American states (including states from Mexico, the United States, and Canada) as of 1 June 2020, namely: New York, New Jersey, Illinois and California. Figure 10 shows reasonably good match between the model-estimated infected and recovered case count with actual Covid-19 data for the highest affected Asian countries as of 1 June 2020, namely: India, China and South Korea. Figure 13 shows reasonably good match between the model-estimated infected and recovered case count with actual Covid-19 data for the highest affected South American countries as of 1 June 2020, namely: Brazil, Chile and Peru.

title:
  A machine learning aided global diagnostic and comparative tool to assess effect of quarantine control in Covid-19 spread

abstract:
  We have developed a globally applicable diagnostic Covid-19 model by augmenting the classical SIR epidemiological model with a neural network module. Our model does not rely upon previous epidemics like SARS/MERS and all parameters are optimized via machine learning algorithms employed on publicly available Covid-19 data. The model decomposes the contributions to the infection timeseries to analyze and compare the role of quarantine control policies employed in highly affected regions of Europe, North America, South America and Asia in controlling the spread of the virus. For all continents considered, our results show a generally strong correlation between strengthening of the quarantine controls as learnt by the model and actions taken by the regions' respective governments. Finally, we have hosted our quarantine diagnosis results for the top $70$ affected countries worldwide, on a public platform, which can be used for informed decision making by public health officials and researchers alike.


id: cord-277094-2ycmxcuz
author: Ifguis, Ousama
date: 2020-06-02
txt: ./txt/cord-277094-2ycmxcuz.txt
cache: ./cache/cord-277094-2ycmxcuz.txt
extension: .txt
mime: text/plain
url: https://doi.org/10.1155/2020/9769267
doi: 10.1155/2020/9769267
summary:
  Since the epidemic of COVID-19 was declared in Wuhan, Hubei Province of China, and other parts of the world, several studies have been carried out over several regions to observe the development of the epidemic, to predict its duration, and to estimate its final size, using complex models such as the SEIR model or the simpler ones such as the SIR model. Also, as the number of infected cases is increasing, it is necessary for modellers to estimate the severity of the epidemic in terms of the total number of people infected, the total number of confirmed cases, the total number of deaths, and basic reproduction and to predict the duration of the epidemic, the arrival of its peak, and its final size. Our simulation study on the optimization of the final size of COVID-19 epidemic evolution in the Kingdom of Morocco, with the SIR model, has allowed us to accurately predict the peak of the infected and death cases (Table 2) , although the number of people tested is very low, about 3,079, until 31 March 2020.

title:
  Simulation of the Final Size of the Evolution Curve of Coronavirus Epidemic in Morocco using the SIR Model

abstract:
  Since the epidemic of COVID-19 was declared in Wuhan, Hubei Province of China, and other parts of the world, several studies have been carried out over several regions to observe the development of the epidemic, to predict its duration, and to estimate its final size, using complex models such as the SEIR model or the simpler ones such as the SIR model. These studies showed that the SIR model is much more efficient than the SEIR model; therefore, we are applying this model in the Kingdom of Morocco since the appearance of the first case on 2 March 2020, with the objective of predicting the final size of the epidemic.


id: cord-279112-ajdkasah
author: Rojas, S.
date: 2020-09-13
txt: ./txt/cord-279112-ajdkasah.txt
cache: ./cache/cord-279112-ajdkasah.txt
extension: .txt
mime: text/plain
url: https://www.sciencedirect.com/science/article/pii/S2590054420300282?v=s5
doi: 10.1016/j.csfx.2020.100047
summary:
  This comment shows that data regarding cumulative confirmed cases from the coronavirus COVID-19 disease outbreak, in the period December 31, 2019–June 29, 2020 of some countries reported by the European Centre for Disease Prevention and Control, can be adjusted by the exact solution of the Kermack – McKendrick approximation of the SIR epidemiological model. In a recent article published in this journal [1] , after some (unnecessary) considerations, the author presents the logistic function (equation (8) in [1] ) as an alternative solution of the differential equation known as the Kermack and McKendrick 1927 approximation [2] of the SIR epidemiological model [3, 4] in order to fit data regarding the cumulative confirmed of COVID-19 infected cases from some countries.

title:
  Comment on “Estimation of COVID-19 dynamics “on a back-of-envelope”: Does the simplest SIR model provide quantitative parameters and predictions?”

abstract:
  This comment shows that data regarding cumulative confirmed cases from the coronavirus COVID-19 disease outbreak, in the period December 31, 2019–June 29, 2020 of some countries reported by the European Centre for Disease Prevention and Control, can be adjusted by the exact solution of the Kermack – McKendrick approximation of the SIR epidemiological model.


id: cord-280683-5572l6bo
title: Panel forecasts of country-level Covid-19 infections()
author: Liu, Laura
date: 2020-10-16
url: https://api.elsevier.com/content/article/pii/S030440762030347X
doi: 10.1016/j.jeconom.2020.08.010
abstract:
  We use a dynamic panel data model to generate density forecasts for daily active Covid-19 infections for a panel of countries/regions. Our specification that assumes the growth rate of active infections can be represented by autoregressive fluctuations around a downward sloping deterministic trend function with a break. Our fully Bayesian approach allows us to flexibly estimate the cross-sectional distribution of slopes and then implicitly use this distribution as prior to construct Bayes forecasts for the individual time series. We find some evidence that information from locations with an early outbreak can sharpen forecast accuracy for late locations. There is generally a lot of uncertainty about the evolution of active infection, due to parameter and shock uncertainty, in particular before and around the peak of the infection path. Over a one-week horizon, the empirical coverage frequency of our interval forecasts is close to the nominal credible level. Weekly forecasts from our model are published at https://laurayuliu.com/covid19-panel-forecast/.


id: cord-288884-itviia7v
title: Stochastic Compartmental Modelling of SARS-CoV-2 with Approximate Bayesian Computation
author: Chandra, Vedant
date: 2020-04-01
txt: ./txt/cord-288884-itviia7v.txt
cache: ./cache/cord-288884-itviia7v.txt
extension: .txt
mime: text/plain
url: https://doi.org/10.1101/2020.03.29.20046862
doi: 10.1101/2020.03.29.20046862
summary:
  We fit this model to the latest epidemic data with an approximate Bayesian computation (ABC) technique. Within this SIR-ABC framework, we extrapolate long-term infection curves for several regions and evaluate their steepness. Armed with the ability to generate stochastic infection and recovery curves from starting parameters, we turn to fitting the starting parameters from real-world epidemic data. We therefore employ an approximate Bayesian computation (ABC) technique to compare our simulations to observations and recover the posterior distributions of β and γ (Figure 1 ). The general goal of ABC is to sample the posterior distributions of simulation parameters such that the simulations match the observed data. Given a simulated epidemic and the observed data, we quantify the difference between both the infectious and recovered population curves to obtain a distance In this proof-of-concept study, we apply approximate Bayesian computation to fit stochastic epidemic models to real world data.

abstract:
  In this proof-of-concept study, we model the spread of SARS-CoV-2 in various environments with a stochastic susceptible-infectious-recovered (SIR) compartmental model. We fit this model to the latest epidemic data with an approximate Bayesian computation (ABC) technique. Within this SIR-ABC framework, we extrapolate long-term infection curves for several regions and evaluate their steepness. We propose several applications and extensions of the SIR-ABC technique.


id: cord-289325-jhokn5bu
title: Effects of distribution of infection rate on epidemic models
author: Lachiany, Menachem
date: 2016-08-11
url: https://doi.org/10.1103/physreve.94.022409
doi: 10.1103/physreve.94.022409
abstract:
  A goal of many epidemic models is to compute the outcome of the epidemics from the observed infected early dynamics. However, often, the total number of infected individuals at the end of the epidemics is much lower than predicted from the early dynamics. This discrepancy is argued to result from human intervention or nonlinear dynamics not incorporated in standard models. We show that when variability in infection rates is included in standard susciptible-infected-susceptible ([Formula: see text]) and susceptible-infected-recovered ([Formula: see text]) models the total number of infected individuals in the late dynamics can be orders lower than predicted from the early dynamics. This discrepancy holds for [Formula: see text] and [Formula: see text] models, where the assumption that all individuals have the same sensitivity is eliminated. In contrast with network models, fixed partnerships are not assumed. We derive a moment closure scheme capturing the distribution of sensitivities. We find that the shape of the sensitivity distribution does not affect [Formula: see text] or the number of infected individuals in the early phases of the epidemics. However, a wide distribution of sensitivities reduces the total number of removed individuals in the [Formula: see text] model and the steady-state infected fraction in the [Formula: see text] model. The difference between the early and late dynamics implies that in order to extrapolate the expected effect of the epidemics from the initial phase of the epidemics, the rate of change in the average infectivity should be computed. These results are supported by a comparison of the theoretical model to the Ebola epidemics and by numerical simulation.


id: cord-293148-t2dk2syq
author: Nadini, Matthieu
date: 2020-09-22
txt: ./txt/cord-293148-t2dk2syq.txt
cache: ./cache/cord-293148-t2dk2syq.txt
extension: .txt
mime: text/plain
url: https://www.ncbi.nlm.nih.gov/pubmed/32984500/
doi: 10.1007/s41109-020-00299-7
summary:
  In the more realistic scenario of a core-periphery structure with multiple locations, we unexpectedly find that the time spent by agents in their base location does not influence the endemic prevalence in the SIS model and the epidemic size in the SIR model, which are measures of the overall fraction of population that is affected by the disease. Here, we propose a one-dimensional model that provides some analytical intuitions on the influence that the randomness α, the probability of jumping outside the base location p, and the presence of a core-periphery structure have in the evolution of SIS and SIR epidemic processes. We consider the two-dimensional agent-based model and numerically study the influence of the randomness α, the probability of jumping outside the base location p, and the presence of a core-periphery structure on the evolution of SIS and SIR epidemic processes.

title:
  A multi-agent model to study epidemic spreading and vaccination strategies in an urban-like environment

abstract:
  Worldwide urbanization calls for a deeper understanding of epidemic spreading within urban environments. Here, we tackle this problem through an agent-based model, in which agents move in a two-dimensional physical space and interact according to proximity criteria. The planar space comprises several locations, which represent bounded regions of the urban space. Based on empirical evidence, we consider locations of different density and place them in a core-periphery structure, with higher density in the central areas and lower density in the peripheral ones. Each agent is assigned to a base location, which represents where their home is. Through analytical tools and numerical techniques, we study the formation mechanism of the network of contacts, which is characterized by the emergence of heterogeneous interaction patterns. We put forward an extensive simulation campaign to analyze the onset and evolution of contagious diseases spreading in the urban environment. Interestingly, we find that, in the presence of a core-periphery structure, the diffusion of the disease is not affected by the time agents spend inside their base location before leaving it, but it is influenced by their motion outside their base location: a strong tendency to return to the base location favors the spreading of the disease. A simplified one-dimensional version of the model is examined to gain analytical insight into the spreading process and support our numerical findings. Finally, we investigate the effectiveness of vaccination campaigns, supporting the intuition that vaccination in central and dense areas should be prioritized.


id: cord-297161-ziwfr9dv
title: TESTING INFORMED SIR BASED EPIDEMIOLOGICAL MODEL FOR COVID-19 IN LUXEMBOURG
author: Sauter, T.
date: 2020-07-25
txt: ./txt/cord-297161-ziwfr9dv.txt
cache: ./cache/cord-297161-ziwfr9dv.txt
extension: .txt
mime: text/plain
url: http://medrxiv.org/cgi/content/short/2020.07.21.20159046v1?rss=1
doi: 10.1101/2020.07.21.20159046
summary:
  The model thereby enables a dynamic inspection of the pandemic and allows estimating key figures, like the number of overall detected and undetected COVID-19 cases and the infection fatality rate. Such models allow describing the dynamics of mutually exclusive states such as Susceptible (S) which for COVID-19 is assumed to be the entire population of a country, a region or city, the number of Infected (I) and Removed (R) that often combines (deaths and recovered), as well as the number of Exposed (E) for SEIR models. As the number of performed tests strongly influences the dynamic analysis of the COVID-19 pandemic in a country or region, we developed a novel SIR based epidemiological model (SIVRT, Figure 1 ) which allows the integration of this key information. In summary, the novel testing informed SIVRT model structure allows to describe and analyze the COVID-19 pandemic data of Luxembourg in dependency of the number of performed tests.

abstract:
  The interpretation of the number of COVID-19 cases and deaths in a country or region is strongly dependent on the number of performed tests. We developed a novel SIR based epidemiological model (SIVRT) which allows the country-specific integration of testing information and other available data. The model thereby enables a dynamic inspection of the pandemic and allows estimating key figures, like the number of overall detected and undetected COVID-19 cases and the infection fatality rate. As proof of concept, the novel SIVRT model was used to simulate the first phase of the pandemic in Luxembourg. An overall number of infections of 13.000 and an infection fatality rate of 1,3% was estimated, which is in concordance with data from population-wide testing. Furthermore based on the data as of end of May 2020 and assuming a partial deconfinement, an increase of cases is predicted from mid of July 2020 on. This is consistent with the current observed rise and shows the predictive potential of the novel SIVRT model.


id: cord-303030-8unrcb1f
title: Social distancing versus early detection and contacts tracing in epidemic management
author: Gaeta, Giuseppe
date: 2020-07-16
txt: ./txt/cord-303030-8unrcb1f.txt
cache: ./cache/cord-303030-8unrcb1f.txt
extension: .txt
mime: text/plain
url: https://arxiv.org/pdf/2003.14102v3.pdf
doi: 10.1016/j.chaos.2020.110074
summary:
  In this paper we discuss the different effects of these ingredients on the epidemic dynamics; the discussion is conducted with the help of two simple models, i.e. the classical SIR model and the recently introduced variant A-SIR (arXiv:2003.08720) which takes into account the presence of a large set of asymptomatic infectives. In the SIR model [1] [2] [3] [4] [5] , a population of constant size (this means the analysis is valid over a relatively short time-span, or we should consider new births and also deaths not due to the epidemic) is subdivided in three classes: Susceptibles, Infected (and by this also Infectives), and Removed. Acting on α or on β to get the same γ will produce different timescales for the dynamics; see Fig. 1 , in which we have used values of the parameters resulting from our fit of early data for the Northern Italy COVID-19 epidemic [7] .

abstract:
  Different countries – and sometimes different regions within the same countries – have adopted different strategies in trying to contain the ongoing COVID-19 epidemic; these mix in variable parts social confinement, early detection and contact tracing. In this paper we discuss the different effects of these ingredients on the epidemic dynamics; the discussion is conducted with the help of two simple models, i.e. the classical SIR model and the recently introduced variant A-SIR (arXiv:2003.08720) which takes into account the presence of a large set of asymptomatic infectives.


id: cord-310863-jxbw8wl2
title: A data first approach to modelling Covid-19
author: PRASAD, J.
date: 2020-05-26
txt: ./txt/cord-310863-jxbw8wl2.txt
cache: ./cache/cord-310863-jxbw8wl2.txt
extension: .txt
mime: text/plain
url: https://doi.org/10.1101/2020.05.22.20110171
doi: 10.1101/2020.05.22.20110171
summary:
  We use the procedure to fit a set of SIR and SIRD models, with time dependent contact rate, to Covid-19 data for a set of 45 most affected countries. We find that SIR and SIRD models with constant transmission coefficients cannot fit Covid-19 data for most countries (mainly because social distancing, lockdown etc., make those time dependent). Some of the most important problems related to Covid-19 research are (1) estimating the controlling parameters of the pandemic, (2) making short term predictions using mathematical-statistical modeling which can help in mitigating policies (3) simulating the growth of the epidemic by taking into account as many contributing effects as possible and (4) quantifying the impact of mitigation measures, such as lockdown etc [ea20j] . One of the main reasons to consider these models has been that the Covid-19 data is available only for the Susceptible, Infected, Recovered and Dead compartments (for the notations used here and other places in the present work see table (1)).

abstract:
  The primary data for Covid-19 pandemic is in the form of time series for the number of confirmed, recovered and dead cases. This data is updated every day and is available for most countries from multiple sources. In this work we present a two step procedure for model fitting to Covid-19 data. In the first step, time dependent transmission coefficients are constructed directly from the data and, in the second step, measures of those (minimum, maximum, mean, median etc.,) are used to set priors for fitting models to data. We call this approach a "data driven approach" or "data first approach". This scheme is complementary to Bayesian approach and can be used with or without that for parameter estimation. We use the procedure to fit a set of SIR and SIRD models, with time dependent contact rate, to Covid-19 data for a set of 45 most affected countries. We find that SIR and SIRD models with constant transmission coefficients cannot fit Covid-19 data for most countries (mainly because social distancing, lockdown etc., make those time dependent). We find that any time dependent contact rate, which falls gradually with time, can help to fit SIR and SIRD models for most of the countries. We also present constraints on transmission coefficients and basic reproduction number R0~ as well as effective reproduction number R(t). The main contributions of our work are as follows. (1) presenting a two step procedure for model fitting to Covid-19 data (2) constraining transmission coefficients as well as R0~ and R(t), for a set of most affected countries and (3) releasing a python package PyCov19 that can used to fit a set of compartmental models with time varying coefficients to Covid-19 data.


id: cord-311183-5blzw9oy
author: Malavika, B.
date: 2020-06-27
url: https://www.ncbi.nlm.nih.gov/pubmed/32838058/
doi: 10.1016/j.cegh.2020.06.006
title:
  Forecasting COVID-19 epidemic in India and high incidence states using SIR and logistic growth models

abstract:
  BACKGROUND: Ever since the Coronavirus disease (COVID-19) outbreak emerged in China, there has been several attempts to predict the epidemic across the world with varying degrees of accuracy and reliability. This paper aims to carry out a short-term projection of new cases; forecast the maximum number of active cases for India and select high-incidence states; and evaluate the impact of three weeks lock down period using different models. METHODS: We used Logistic growth curve model for short term prediction; SIR models to forecast the cumulative, maximum number of active cases and peak time; and Time Interrupted Regression model to evaluate the impact of lockdown and other interventions. RESULTS: The predicted cumulative number of cases for India was 58,912 (95% CI: 57,960, 59,853) by May 08, 2020 and the observed number of cases was 59,695. The model predicts a cumulative number of 1,02,974 (95% CI: 1,01,987, 1,03,904) cases by May 22, 2020 As per SIR model, the maximum number of active cases is projected to be 57,449 on May 18, 2020. The time interrupted regression model indicates a decrease of 149 daily new cases after the lock down period which is statistically not significant. CONCLUSION: The Logistic growth curve model predicts accurately the short-term scenario for India and high incidence states. The prediction through SIR model may be used for planning and prepare the health systems. The study also suggests that there is no evidence to conclude that there is a positive impact of lockdown in terms of reduction in new cases.


id: cord-314725-og0ybfzf
title: Dynamics of COVID-19 Using Inverse Problem for Coefficient Identification in SIR Epidemic Models
author: Marinov, Tchavdar T.
date: 2020-07-15
txt: ./txt/cord-314725-og0ybfzf.txt
cache: ./cache/cord-314725-og0ybfzf.txt
extension: .txt
mime: text/plain
url: https://www.sciencedirect.com/science/article/pii/S2590054420300221?v=s5
doi: 10.1016/j.csfx.2020.100041
summary:
  Abstract This work deals with the inverse problem in epidemiology based on a SIR model with time-dependent infectivity and recovery rates, allowing for a better prediction of the long term evolution of a pandemic. The method is used for investigating the COVID-19 spread by first solving an inverse problem for estimating the infectivity and recovery rates from real data. This work aims to create a method that can accurately identify the time dependent parameters of the SIR system using real data and then use the computed parameter values to predict the spread of the epidemics. The inverse problem for estimating the time-dependent transmission and removal rates in the SIR epidemic model is derived and solved. The inverse problem for estimating the time-dependent transmission and removal rates in the SIR epidemic model is derived and solved.

abstract:
  Abstract This work deals with the inverse problem in epidemiology based on a SIR model with time-dependent infectivity and recovery rates, allowing for a better prediction of the long term evolution of a pandemic. The method is used for investigating the COVID-19 spread by first solving an inverse problem for estimating the infectivity and recovery rates from real data. Then, the estimated rates are used to compute the evolution of the disease. The time-depended parameters are estimated for the World and several countries (The United States of America, Canada, Italy, France, Germany, Sweden, Russia, Brazil, Bulgaria, Japan, South Korea, New Zealand) and used for investigating the COVID-19 spread in these countries.


id: cord-316393-ozl28ztz
title: Global analysis of the COVID-19 pandemic using simple epidemiological models
author: Enrique Amaro, José
date: 2020-10-22
url: https://api.elsevier.com/content/article/pii/S0307904X20306028
doi: 10.1016/j.apm.2020.10.019
abstract:
  Several analytical models have been developed in this work to describe the evolution of fatalities arising from coronavirus COVID-19 worldwide. The Death or ‘D’ model is a simplified version of the well-known SIR (susceptible-infected-recovered) compartment model, which allows for the transmission-dynamics equations to be solved analytically by assuming no recovery during the pandemic. By fitting to available data, the D-model provides a precise way to characterize the exponential and normal phases of the pandemic evolution, and it can be extended to describe additional spatial-time effects such as the release of lockdown measures. More accurate calculations using the extended SIR or ESIR model, which includes recovery, and more sophisticated Monte Carlo grid simulations – also developed in this work – predict similar trends and suggest a common pandemic evolution with universal parameters. The evolution of the COVID-19 pandemic in several countries shows the typical behavior in concord with our model trends, characterized by a rapid increase of death cases followed by a slow decline, typically asymmetric with respect to the pandemic peak. The fact that the D and ESIR models predict similar results – without and with recovery, respectively – indicates that COVID-19 is a highly contagious virus, but that most people become asymptomatic (D model) and eventually recover (ESIR model).


id: cord-318525-nc5rtwtd
title: Scaling analysis of COVID-19 spreading based on Belgian hospitalization data
author: Smeets, Bart
date: 2020-03-30
txt: ./txt/cord-318525-nc5rtwtd.txt
cache: ./cache/cord-318525-nc5rtwtd.txt
extension: .txt
mime: text/plain
url: https://doi.org/10.1101/2020.03.29.20046730
doi: 10.1101/2020.03.29.20046730
summary:
  Studies on the outbreak of COVID-19 in the Hubei province and the rest of mainland China show that the temporal evolution of confirmed cases can be classified in three distinct regimes: 1) an initial exponential growth phase, 2) an extended phase of power law growth kinetics indicative of a small world network structure, with a universal growth exponent of µ ≈ 2.1, and 3) a slow inflection to a plateau phase, following a parabolic profile in double logarithmic scale [1] . This model was recently extended to include symptomatic quarantined individuals (X), resulting in the ''SIR-X'' model, which was successfully applied to predict the spreading kinetics and assess containment policies for COVID-19 in China [4] , and is currently being used to monitor the number of confirmed COVID-19 cases in various countries [5] .

abstract:
  We analyze the temporal evolution of accumulated hospitalization cases due to COVID-19 in Belgium. The increase of hospitalization cases is consistent with an initial exponential phase, and a subsequent power law growth. For the latter, we estimate a power law exponent of ≈ 2.2, which is consistent with growth kinetics of COVID-19 in China and indicative of the underlying small world network structure of the epidemic. Finally, we fit an SIR-X model to the experimental data and estimate the effect of containment policies in comparison to their effect in China. This model suggests that the base reproduction rate has been significantly reduced, but that the number of susceptible individuals that is isolated from infection is very small. Based on the SIR-X model fit, we analyze the COVID-19 mortality and the number of patients requiring ICU treatment over time.


id: cord-318688-ditadt8l
author: Mitarai, O.
date: 2020-09-20
url: http://medrxiv.org/cgi/content/short/2020.09.18.20197723v1?rss=1
doi: 10.1101/2020.09.18.20197723
title:
  Suppression of COVID-19 infection by isolation time control based on the SIR model and an analogy from nuclear fusion research

abstract:
  The coronavirus disease 2019 (COVID-19) has been damaging our daily life after declaration of pandemic. Therefore, we have started studying on the characteristics of Susceptible-Infectious-Recovered (SIR) model to know about the truth of infectious disease and our future. After detailed studies on the characteristics of the SIR model for the various parameter dependencies with respect to such as the outing restriction (lockdown) ratio and vaccination rate, we have finally noticed that the second term (isolation term) in the differential equation of the number of the infected is quite similar to the "helium ash particle loss term" in deuterium-tritium (D-T) nuclear fusion. Based on this analogy, we have found that isolation of the infected is not actively controlled in the SIR model. Then we introduce the isolation control time parameter q and have studied its effect on this pandemic. Required isolation time to terminate the COVID-19 can be estimated by this proposed method. To show this isolation control effect, we choose Tokyo for the model calculation because of high population density. We determine the reproduction number and the isolation ratio in the initial uncontrolled phase, and then the future number of the infected is estimated under various conditions. If the confirmed case can be isolated in 3~8 days by widely performed testing, this pandemic could be suppressed without awaiting vaccination. If the mild outing restriction and vaccination are taken together, the isolation control time can be longer. We consider this isolation time control might be the only solution to overcome the pandemic when vaccine is not available.


id: cord-319435-le2eifv8
author: Rahman, Mohammad Mahmudur
date: 2020-04-23
txt: ./txt/cord-319435-le2eifv8.txt
cache: ./cache/cord-319435-le2eifv8.txt
extension: .txt
mime: text/plain
url: https://doi.org/10.1101/2020.04.19.20071415
doi: 10.1101/2020.04.19.20071415
summary:
  To estimate the impact of social distancing we assumed eight different scenarios, the predicted results confirmed the positive impact of this type of control strategies suggesting that by strict social distancing and lockdown, COVID-19 infection can be under control and then the infection cases will steadily decrease down to zero. In this study, we attempt to estimate the final epidemic size of COVID-19 using the classic compartmental susceptible-infected-recovered (SIR) model [9] . The SIR model presents the increase of decrease information of an outbreak based on some initial data i.e. total given population (N), the infection rate of the infectious disease (β), the recovery rate of the disease (Ɣ), initial susceptible population (S0), initial infected population (I0) and the initial recovered population (R0). The SIR model base prediction of infection curve was compared with the confirmed cases ( Figure 02 ).

title:
  Impact of control strategies on COVID-19 pandemic and the SIR model based forecasting in Bangladesh.

abstract:
  COVID-19 is transmitting worldwide drastically and infected nearly two and half million of people sofar. Till date 2144 cases of COVID-19 is confirmed in Bangladesh till 18th April though the stage-3/4 transmission is not validated yet. To project the final infection numbers in Bangladesh we used the SIR mathematical model. We also tried to demonstrate the impact of control strategies like social distancing on the COVID-19 transmission. Due to large population and socio-economic characteristics, we assumed 60% social distancing and lockdown can be possible. Assuming that, the predicated final size of infections will be 3782558 on the 92th day from the first infections. To estimate the impact of social distancing we assumed eight different scenarios, the predicted results confirmed the positive impact of this type of control strategies suggesting that by strict social distancing and lockdown, COVID-19 infection can be under control and then the infection cases will steadily decrease down to zero.


id: cord-320912-jfeu4tho
author: Fukui, M.
date: 2020-06-12
url: http://medrxiv.org/cgi/content/short/2020.06.11.20128058v1?rss=1
doi: 10.1101/2020.06.11.20128058
title:
  Power Laws in Superspreading Events: Evidence from Coronavirus Outbreaks and Implications for SIR Models

abstract:
  While they are rare, superspreading events (SSEs), wherein a few primary cases infect an extraordinarily large number of secondary cases, are recognized as a prominent determinant of aggregate infection rates (R0). Existing stochastic SIR models incorporate SSEs by fitting distributions with thin tails, or finite variance, and therefore predicting almost deterministic epidemiological outcomes in large populations. This paper documents evidence from recent coronavirus outbreaks, including SARS, MERS, and COVID-19, that SSEs follow a power law distribution with fat tails, or infinite variance. We then extend an otherwise standard SIR model with estimated power law distributions, and show that idiosyncratic uncertainties in SSEs will lead to large aggregate uncertainties in infection dynamics, even with large populations. That is, the timing and magnitude of outbreaks will be unpredictable. While such uncertainties have social costs, we also find that they on average decrease the herd immunity thresholds and the cumulative infections because per-period infection rates have decreasing marginal effects. Our findings have implications for social distancing interventions: targeting SSEs reduce not only the average rate of infection (R0) but also its uncertainty. To understand this effect, and to improve inference of the average reproduction numbers under fat tails, estimating the tail distribution of SSEs is vital.


id: cord-321984-qjfkvu6n
title: A Review of Multi‐Compartment Infectious Disease Models
author: Tang, Lu
date: 2020-08-03
txt: ./txt/cord-321984-qjfkvu6n.txt
cache: ./cache/cord-321984-qjfkvu6n.txt
extension: .txt
mime: text/plain
url: https://www.ncbi.nlm.nih.gov/pubmed/32834402/
doi: 10.1111/insr.12402
summary:
  Despite relying on a valid infectious diseases mechanism, deterministic approaches have several drawbacks: (i) the actual population in each compartment at a given time is never accurately measured because we only obtain an observation around the mean; (ii) the nature of disease transmission and recovery is stochastic on the individual level and thus never certain; and (iii) without random component in the model, it is neither possible to learn model parameters (e.g. R 0 ) from available data nor to assess prediction uncertainty. In an early stage of the current COVID-19 pandemic, the daily infection and death counts reported by health agencies are highly influenced by the availability of testing kits, reporting delays, reporting and attribution schemes, and under-ascertainment of mild cases in public health surveillance databases (see discussions in Angelopoulos et al., 2020; Banerjee et al., 2020) ; both disease transmission rate and time to recovery or death are also highly uncertain and vary by population density, demographic composition, regional contact network structure and non-uniform mitigation schemes (Ray et al., 2020) .

abstract:
  Multi‐compartment models have been playing a central role in modelling infectious disease dynamics since the early 20th century. They are a class of mathematical models widely used for describing the mechanism of an evolving epidemic. Integrated with certain sampling schemes, such mechanistic models can be applied to analyse public health surveillance data, such as assessing the effectiveness of preventive measures (e.g. social distancing and quarantine) and forecasting disease spread patterns. This review begins with a nationwide macromechanistic model and related statistical analyses, including model specification, estimation, inference and prediction. Then, it presents a community‐level micromodel that enables high‐resolution analyses of regional surveillance data to provide current and future risk information useful for local government and residents to make decisions on reopenings of local business and personal travels. r software and scripts are provided whenever appropriate to illustrate the numerical detail of algorithms and calculations. The coronavirus disease 2019 pandemic surveillance data from the state of Michigan are used for the illustration throughout this paper.


id: cord-324993-hs66uf1u
title: Flattening the COVID 19 curve in susceptible forest indigenous tribes using SIR model
author: Adwibowo, A.
date: 2020-05-25
txt: ./txt/cord-324993-hs66uf1u.txt
cache: ./cache/cord-324993-hs66uf1u.txt
extension: .txt
mime: text/plain
url: https://doi.org/10.1101/2020.05.22.20110254
doi: 10.1101/2020.05.22.20110254
summary:
  Using the Susceptible Infectious Recovered (SIR) model, the spread of the COVID 19 under 3 intervention scenarios (low, moderate, high) is simulated and predicted in indigenous tribe populations. While, in the scenario of high intervention, the COVID 19 peaks can be reduced to values ranging from 53% to 15% .To conclude, the simulated interventions tested by SIR model have reduced the pandemic peak and flattened the COVID 19 curve in indigenous populations. The COVID 19 SIR model of indigenous tribe populations living in remote Yasuni rainforest enclaves with simulated 25% (low), 50% (moderate), and 75% (high) interventions (x axis: days, y axis: proportion of total population). 1101 The indigenous tribe populations and COVID 19 cases in Amazon rainforest enclaves including Lagartococha, Callarú, and Yasuni are presented in the Figure 2 . The proposed SIR model in this study simulates the widespread of COVID throughout indigenous tribe populations living in remote Lagartococha and Yasuni rainforests.

abstract:
  COVID 19 is a global threat and globally spreading. The international cooperation involving indigenous peoples and local communities is urgently required in joint prevention to control the epidemic. Currently, many indigenous populations are continuing to face COVID 19. This study is concerned about the dynamic of COVID 19 pandemic among indigenous populations living in the remote Amazon rainforest enclaves. Using the Susceptible Infectious Recovered (SIR) model, the spread of the COVID 19 under 3 intervention scenarios (low, moderate, high) is simulated and predicted in indigenous tribe populations. The SIR model forecasts that without intervention, the epidemic peak may reach within 10 20 days. Nonetheless the peak can be reduced with strict interventions. Under low intervention, the COVID 19 cases are reduced to 73% and 56% of the total populations. While, in the scenario of high intervention, the COVID 19 peaks can be reduced to values ranging from 53% to 15% .To conclude, the simulated interventions tested by SIR model have reduced the pandemic peak and flattened the COVID 19 curve in indigenous populations. Nonetheless, it is mandatory to strengthen all mitigation efforts, reduce exposures, and decrease transmission rate as possible for COVID 19 containment.


id: cord-326631-7gd3hjc3
title: Generality of the Final Size Formula for an Epidemic of a Newly Invading Infectious Disease
author: Ma, Junling
date: 2006-04-08
txt: ./txt/cord-326631-7gd3hjc3.txt
cache: ./cache/cord-326631-7gd3hjc3.txt
extension: .txt
mime: text/plain
url: https://www.ncbi.nlm.nih.gov/pubmed/16794950/
doi: 10.1007/s11538-005-9047-7
summary:
  More recent analyses have established that the standard final size formula is valid regardless of the distribution of infectious periods, but that it fails to be correct in the presence of certain kinds of heterogeneous mixing (e.g., if there is a core group, as for sexually transmitted diseases). We then proceed to generalize these results in three new directions, showing that the standard formula remains valid (i) regardless of the number of distinct infectious stages, (ii) if the mean contact rate is itself arbitrarily distributed and (iii) for a large class of spatially heterogeneous contact structures. Since this substage trick can be applied equally well to any infectious stage, Anderson and Watson''s (1980) conclusion that the final size in an SIR model with Gamma distributed infectious periods is given by the usual formula (5) now generalizes to an arbitrary number of stages, each with Gamma distributed durations.

abstract:
  The well-known formula for the final size of an epidemic was published by Kermack and McKendrick in 1927. Their analysis was based on a simple susceptible-infected-recovered (SIR) model that assumes exponentially distributed infectious periods. More recent analyses have established that the standard final size formula is valid regardless of the distribution of infectious periods, but that it fails to be correct in the presence of certain kinds of heterogeneous mixing (e.g., if there is a core group, as for sexually transmitted diseases). We review previous work and establish more general conditions under which Kermack and McKendrick's formula is valid. We show that the final size formula is unchanged if there is a latent stage, any number of distinct infectious stages and/or a stage during which infectives are isolated (the durations of each stage can be drawn from any integrable distribution). We also consider the possibility that the transmission rates of infectious individuals are arbitrarily distributed—allowing, in particular, for the existence of super-spreaders—and prove that this potential complexity has no impact on the final size formula. Finally, we show that the final size formula is unchanged even for a general class of spatial contact structures. We conclude that whenever a new respiratory pathogen emerges, an estimate of the expected magnitude of the epidemic can be made as soon the basic reproduction number ℝ(0) can be approximated, and this estimate is likely to be improved only by more accurate estimates of ℝ(0), not by knowledge of any other epidemiological details.


id: cord-332922-2qjae0x7
title: Bayesian inference of COVID-19 spreading rates in South Africa
author: Mbuvha, Rendani
date: 2020-08-05
url: https://www.ncbi.nlm.nih.gov/pubmed/32756608/
doi: 10.1371/journal.pone.0237126
abstract:
  The Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pandemic has highlighted the need for performing accurate inference with limited data. Fundamental to the design of rapid state responses is the ability to perform epidemiological model parameter inference for localised trajectory predictions. In this work, we perform Bayesian parameter inference using Markov Chain Monte Carlo (MCMC) methods on the Susceptible-Infected-Recovered (SIR) and Susceptible-Exposed-Infected-Recovered (SEIR) epidemiological models with time-varying spreading rates for South Africa. The results find two change points in the spreading rate of COVID-19 in South Africa as inferred from the confirmed cases. The first change point coincides with state enactment of a travel ban and the resultant containment of imported infections. The second change point coincides with the start of a state-led mass screening and testing programme which has highlighted community-level disease spread that was not well represented in the initial largely traveller based and private laboratory dominated testing data. The results further suggest that due to the likely effect of the national lockdown, community level transmissions are slower than the original imported case driven spread of the disease.


id: cord-335141-ag3j8obh
title: FFP3 reusable respirators for COVID-19; adequate and suitable in the healthcare setting
author: Higgins, G.C.
date: 2020-06-30
txt: ./txt/cord-335141-ag3j8obh.txt
cache: ./cache/cord-335141-ag3j8obh.txt
extension: .txt
mime: text/plain
url: https://doi.org/10.1016/j.bjps.2020.06.002
doi: 10.1016/j.bjps.2020.06.002
abstract: nan
summary:
  The British Association of Plastic, Reconstructive and Aesthetic Surgeons, the British Society for Surgery of the Hand and the Royal College of Surgeons of England, have all issued guidance: both encouraging patients to avoid risky pursuits, which could result in accidental injuries and to members how to prioritise and optimise services for trauma and urgent cancer work. We have adapted our Hand Trauma Service to a ''One Stop Hand Trauma and Therapy'' clinic, where patients are assessed, definitive surgery performed and offered immediate post-operative hand therapy where therapists make splint and give specialist advice on wound care and rehabilitation including an illustrated hand therapy guide. Local assessment of our practice is ongoing but we have found that this model has enabled a cohort of vulnerable plastic surgery trainees to successfully continue to work whilst reducing the risk of exposure to COVID-19 and providing gold standard care for patients.


id: cord-339425-hdf3blpu
author: Ahmetolan, Semra
date: 2020-09-03
url: https://doi.org/10.3389/fmed.2020.556366
doi: 10.3389/fmed.2020.556366
title:
  What Can We Estimate From Fatality and Infectious Case Data Using the Susceptible-Infected-Removed (SIR) Model? A Case Study of Covid-19 Pandemic

abstract:
  The rapidly spreading Covid-19 that affected almost all countries, was first reported at the end of 2019. As a consequence of its highly infectious nature, countries all over the world have imposed extremely strict measures to control its spread. Since the earliest stages of this major pandemic, academics have done a huge amount of research in order to understand the disease, develop medication, vaccines and tests, and model its spread. Among these studies, a great deal of effort has been invested in the estimation of epidemic parameters in the early stage, for the countries affected by Covid-19, hence to predict the course of the epidemic but the variability of the controls over the course of the epidemic complicated the modeling processes. In this article, the determination of the basic reproduction number, the mean duration of the infectious period, the estimation of the timing of the peak of the epidemic wave is discussed using early phase data. Daily case reports and daily fatalities for China, South Korea, France, Germany, Italy, Spain, Iran, Turkey, the United Kingdom and the United States over the period January 22, 2020–April 18, 2020 are evaluated using the Susceptible-Infected-Removed (SIR) model. For each country, the SIR models fitting cumulative infective case data within 5% error are analyzed. It is observed that the basic reproduction number and the mean duration of the infectious period can be estimated only in cases where the spread of the epidemic is over (for China and South Korea in the present case). Nevertheless, it is shown that the timing of the maximum and timings of the inflection points of the proportion of infected individuals can be robustly estimated from the normalized data. The validation of the estimates by comparing the predictions with actual data has shown that the predictions were realized for all countries except USA, as long as lock-down measures were retained.


id: cord-339789-151d1j4n
author: Hong, Hyokyoung G.
date: 2020-07-21
url: https://arxiv.org/pdf/2004.05730v3.pdf
doi: 10.1371/journal.pone.0236464
title:
  Estimation of time-varying reproduction numbers underlying epidemiological processes: A new statistical tool for the COVID-19 pandemic

abstract:
  The coronavirus pandemic has rapidly evolved into an unprecedented crisis. The susceptible-infectious-removed (SIR) model and its variants have been used for modeling the pandemic. However, time-independent parameters in the classical models may not capture the dynamic transmission and removal processes, governed by virus containment strategies taken at various phases of the epidemic. Moreover, few models account for possible inaccuracies of the reported cases. We propose a Poisson model with time-dependent transmission and removal rates to account for possible random errors in reporting and estimate a time-dependent disease reproduction number, which may reflect the effectiveness of virus control strategies. We apply our method to study the pandemic in several severely impacted countries, and analyze and forecast the evolving spread of the coronavirus. We have developed an interactive web application to facilitate readers’ use of our method.


id: cord-342855-dvgqouk2
title: Mathematical Modeling of Coronavirus Reproduction Rate with Policy and Behavioral Effects
author: Anzum, R.
date: 2020-06-18
url: https://doi.org/10.1101/2020.06.16.20133330
doi: 10.1101/2020.06.16.20133330
abstract:
  In this paper a modified mathematical model based on the SIR model used which can predict the spreading of the corona virus disease (COVID-19) and its effects on people in the days ahead. This model takes into account all the death, infected and recovered characteristics of this disease. To determine the extent of the risk posed by this novel coronavirus; the transmission rate (R0) is utilized for a time period from the beginning of spreading virus. In particular, it includes a novel policy to capture the R0 response in the virus spreading over time. The model estimates the vulnerability of the pandemic with a prediction of new cases by estimating a time-varying R0 to capture changes in the behavior of SIR model implies to new policy taken at different times and different locations of the world. This modified SIR model with the different values of R0 can be applied to different country scenario using the real time data report provided by the authorities during this pandemic. The effective evaluation of R0 can forecast the necessity of lockdown as well as reopening the economy.


id: cord-346951-kvh9qt65
title: Predication of Pandemic COVID-19 situation in Maharashtra, India
author: KUMAR, SUNNY
date: 2020-04-11
url: https://doi.org/10.1101/2020.04.10.20056697
doi: 10.1101/2020.04.10.20056697
abstract:
  Presently, the world is infected by COVID 19 virus which has created an emergency public health. For controlling the spreading of the virus, we have to prepare for precaution and futuristic calculation for infection spreading. The coronavirus affects the population of the world including Inia. Here, we are the study the virus spreading rate on the Maharashtra state which is part of India. We are predicting the infected people by the SIR model. SIR model is one of the most effective models which can predict the spreading rate of the virus. We have validated the model with the current spreading rate with this SIR model. This study will help to stop the epidemic spreading because it is in the early stage in the Maharashtra region.


id: cord-349898-nvi8h77t
title: COVID‐19 pandemic and information diffusion analysis on Twitter
author: Dinh, Ly
date: 2020-10-22
url: https://www.ncbi.nlm.nih.gov/pubmed/33173813/
doi: 10.1002/pra2.252
abstract:
  The COVID‐19 pandemic has impacted all aspects of our lives, including the information spread on social media. Prior literature has found that information diffusion dynamics on social networks mirror that of a virus, but applying the epidemic Susceptible‐Infected‐Removed model (SIR) model to examine how information spread is not sufficient to claim that information spreads like a virus. In this study, we explore whether there are similarities in the simulated SIR model (SIRsim), observed SIR model based on actual COVID‐19 cases (SIRemp), and observed information cascades on Twitter about the virus (INFOcas) by using network analysis and diffusion modeling. We propose three primary research questions: (a) What are the diffusion patterns of COVID‐19 virus spread, based on SIRsim and SIRemp? (b) What are the diffusion patterns of information cascades on Twitter (INFOcas), with respect to retweets, quote tweets, and replies? and (c) What are the major differences in diffusion patterns between SIRsim, SIRemp, and INFOcas? Our study makes a contribution to the information sciences community by showing how epidemic modeling of virus and information diffusion analysis of online social media are distinct but interrelated concepts.


id: cord-354627-y07w2f43
title: COVID-19 Pandemic Prediction for Hungary; a Hybrid Machine Learning Approach
author: pinter, g.
date: 2020-05-06
url: http://medrxiv.org/cgi/content/short/2020.05.02.20088427v1?rss=1
doi: 10.1101/2020.05.02.20088427
abstract:
  Several epidemiological models are being used around the world to project the number of infected individuals and the mortality rates of the COVID-19 outbreak. Advancing accurate prediction models is of utmost importance to take proper actions. Due to a high level of uncertainty or even lack of essential data, the standard epidemiological models have been challenged regarding the delivery of higher accuracy for long-term prediction. As an alternative to the susceptible-infected-resistant (SIR)-based models, this study proposes a hybrid machine learning approach to predict the COVID-19 and we exemplify its potential using data from Hungary. The hybrid machine learning methods of adaptive network-based fuzzy inference system (ANFIS) and multi-layered perceptron-imperialist competitive algorithm (MLP-ICA) are used to predict time series of infected individuals and mortality rate. The models predict that by late May, the outbreak and the total morality will drop substantially. The validation is performed for nine days with promising results, which confirms the model accuracy. It is expected that the model maintains its accuracy as long as no significant interruption occurs. Based on the results reported here, and due to the complex nature of the COVID-19 outbreak and variation in its behavior from nation-to-nation, this study suggests machine learning as an effective tool to model the outbreak. This paper provides an initial benchmarking to demonstrate the potential of machine learning for future research.


