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Epidemic model
About: Epidemic model is a research topic. Over the lifetime, 4664 publications have been published within this topic receiving 91509 citations.
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TL;DR: In this article, the authors considered the problem of finding a causal factor which appears to be adequate to account for the magnitude of the frequent epidemics of disease which visit almost every population.
Abstract: (1) One of the most striking features in the study of epidemics is the difficulty of finding a causal factor which appears to be adequate to account for the magnitude of the frequent epidemics of disease which visit almost every population. It was with a view to obtaining more insight regarding the effects of the various factors which govern the spread of contagious epidemics that the present investigation was undertaken. Reference may here be made to the work of Ross and Hudson (1915-17) in which the same problem is attacked. The problem is here carried to a further stage, and it is considered from a point of view which is in one sense more general. The problem may be summarised as follows: One (or more) infected person is introduced into a community of individuals, more or less susceptible to the disease in question. The disease spreads from the affected to the unaffected by contact infection. Each infected person runs through the course of his sickness, and finally is removed from the number of those who are sick, by recovery or by death. The chances of recovery or death vary from day to day during the course of his illness. The chances that the affected may convey infection to the unaffected are likewise dependent upon the stage of the sickness. As the epidemic spreads, the number of unaffected members of the community becomes reduced. Since the course of an epidemic is short compared with the life of an individual, the population may be considered as remaining constant, except in as far as it is modified by deaths due to the epidemic disease itself. In the course of time the epidemic may come to an end. One of the most important probems in epidemiology is to ascertain whether this termination occurs only when no susceptible individuals are left, or whether the interplay of the various factors of infectivity, recovery and mortality, may result in termination, whilst many susceptible individuals are still present in the unaffected population. It is difficult to treat this problem in its most general aspect. In the present communication discussion will be limited to the case in which all members of the community are initially equally susceptible to the disease, and it will be further assumed that complete immunity is conferred by a single infection.
8,238 citations
TL;DR: In this paper, the authors study the interplay between short-scale commuting flows and long-range airline traffic in shaping the spatio-temporal pattern of a global epidemic.
Abstract: Among the realistic ingredients to be considered in the computational modeling of infectious diseases, human mobility represents a crucial challenge both on the theoretical side and in view of the limited availability of empirical data. To study the interplay between short-scale commuting flows and long-range airline traffic in shaping the spatiotemporal pattern of a global epidemic we (i) analyze mobility data from 29 countries around the world and find a gravity model able to provide a global description of commuting patterns up to 300 kms and (ii) integrate in a worldwide-structured metapopulation epidemic model a timescale-separation technique for evaluating the force of infection due to multiscale mobility processes in the disease dynamics. Commuting flows are found, on average, to be one order of magnitude larger than airline flows. However, their introduction into the worldwide model shows that the large-scale pattern of the simulated epidemic exhibits only small variations with respect to the baseline case where only airline traffic is considered. The presence of short-range mobility increases, however, the synchronization of subpopulations in close proximity and affects the epidemic behavior at the periphery of the airline transportation infrastructure. The present approach outlines the possibility for the definition of layered computational approaches where different modeling assumptions and granularities can be used consistently in a unifying multiscale framework.
1,268 citations
TL;DR: In this article, the Kermack-McKendrick deterministic model is generalized, introducing an interaction term in which the dependence upon the number of infectives occurs via a nonlinear bounded function.
Abstract: In this paper the Kermack-McKendrick deterministic model is generalized, introducing an interaction term in which the dependence upon the number of infectives occurs via a nonlinear bounded function which may take into account saturation phenomena for large numbers of infectives. An extension of the well-known threshold theorem is obtained, after a stability analysis of the equilibrium points of the system. A numerical example is carried out in detail.
999 citations
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19 Jul 2000
TL;DR: In this paper, a simple epidemic model: The Reed-Frost model is presented. But it is not a deterministic model and it cannot be used to model the entire population of a population.
Abstract: I: Stochastic Modelling.- 1. Introduction.- 1.1. Stochastic versus deterministic models.- 1.2. A simple epidemic model: The Reed-Frost model.- 1.3. Stochastic epidemics in large communities.- 1.4. History of epidemic modelling.- Exercises.- 2. The standard SIR epidemic model.- 2.1. Definition of the model.- 2.2. The Sellke construction.- 2.3. The Markovian case.- 2.4. Exact results.- Exercises.- 3. Coupling methods.- 3.1. First examples.- 3.2. Definition of coupling.- 3.3. Applications to epidemics.- Exercises.- 4. The threshold limit theorem.- 4.1. The imbedded process.- 4.2. Preliminary convergence results.- 4.3. The casemn/n??> 0 asn? ?.- 4.4. The casemn=mfor alln.- 4.5. Duration of the Markovian SIR epidemic.- Exercises.- 5. Density dependent jump Markov processes.- 5.1. An example: A simple birth and death process.- 5.2. The general model.- 5.3. The Law of Large Numbers.- 5.4. The Central Limit Theorem.- 5.5. Applications to epidemic models.- Exercises.- 6. Multitype epidemics.- 6.1. The standard SIR multitype epidemic model.- 6.2. Large population limits.- 6.3. Household model.- 6.4. Comparing equal and varying susceptibility.- Exercises.- 7. Epidemics and graphs.- 7.1. Random graph interpretation.- 7.2. Constant infectious period.- 7.3. Epidemics and social networks.- 7.4. The two-dimensional lattice.- Exercises.- 8. Models for endemic diseases.- 8.1. The SIR model with demography.- 8.2. The SIS model.- Exercises.- II: Estimation.- 9. Complete observation of the epidemic process.- 9.1. Martingales and log-likelihoods of counting processes.- 9.2. ML-estimation for the standard SIR epidemic.- Exercises.- 10. Estimation in partially observed epidemics.- 10.1. Estimation based on martingale methods.- 10.2. Estimation based on the EM-algorithm.- Exercises.- 11. Markov Chain Monte Carlo methods.- 11.1. Description of the techniques.- 11.2. Important examples.- 11.3. Practical implementation issues.- 11.4. Bayesian inference for epidemics.- Exercises.- 12. Vaccination.- 12.1. Estimating vaccination policies based on one epidemic.- 12.2. Estimating vaccination policies for endemic diseases.- 12.3. Estimation of vaccine efficacy.- Exercises.- References.
914 citations
TL;DR: A new epidemic model is proposed that discriminates between infected individuals depending on whether they have been diagnosed and on the severity of their symptoms, and shows how the basic reproduction number can be redefined in the new framework, thus capturing the potential for epidemic containment.
Abstract: In late December 2019, a novel strand of Coronavirus (SARS-CoV-2) causing a severe, potentially fatal respiratory syndrome (COVID-19) was identified in Wuhan, Hubei Province, China and is causing outbreaks in multiple world countries, soon becoming a pandemic. Italy has now become the most hit country outside of Asia: on March 16, 2020, the Italian Civil Protection documented a total of 27980 confirmed cases and 2158 deaths of people tested positive for SARS-CoV-2. In the context of an emerging infectious disease outbreak, it is of paramount importance to predict the trend of the epidemic in order to plan an effective control strategy and to determine its impact. This paper proposes a new epidemic model that discriminates between infected individuals depending on whether they have been diagnosed and on the severity of their symptoms. The distinction between diagnosed and non-diagnosed is important because non-diagnosed individuals are more likely to spread the infection than diagnosed ones, since the latter are typically isolated, and can explain misperceptions of the case fatality rate and of the seriousness of the epidemic phenomenon. Being able to predict the amount of patients that will develop life-threatening symptoms is important since the disease frequently requires hospitalisation (and even Intensive Care Unit admission) and challenges the healthcare system capacity. We show how the basic reproduction number can be redefined in the new framework, thus capturing the potential for epidemic containment. Simulation results are compared with real data on the COVID-19 epidemic in Italy, to show the validity of the model and compare different possible predicted scenarios depending on the adopted countermeasures.
858 citations