AN EPIDEMIC MODEL WITH REMOVAL-DEPENDENT INFECTION RATE
成果类型：
Article
署名作者：
O'Neill, Philip
署名单位：
University of Bradford
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
发表日期：
1997
页码：
90-109
关键词：
摘要：
This paper is concerned with a model for the spread of an epidemic in a closed, homogeneously mixed population in which new infections occur at rate beta(z)xy/(x+y), where x, y and z denote, respectively, the numbers of susceptible, infective and removed individuals. Thus the infection mechanism depends upon the number of removals to date, reflecting behavior change in response to the progress of the epidemic. For a deterministic version of the model, a recurrent solution is obtained when beta(z) is piecewise constant. Equations for the total size distribution of the stochastic model are derived. Stochastic comparison results are obtained using a coupling method. Strong convergence of a sequence of epidemics to an unusual birth-and-death process is exhibited, and the behavior of the limiting birth-and-death process is considered. An epidemic model featuring sudden behavior change is studied as an example, and a stochastic threshold result analagous to that of Whittle is derived.