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February 1997 An epidemic model with removal-dependent infection rate
Philip O'Neill
Ann. Appl. Probab. 7(1): 90-109 (February 1997). DOI: 10.1214/aoap/1034625253


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.


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Philip O'Neill. "An epidemic model with removal-dependent infection rate." Ann. Appl. Probab. 7 (1) 90 - 109, February 1997.


Published: February 1997
First available in Project Euclid: 14 October 2002

zbMATH: 0871.92027
MathSciNet: MR1428750
Digital Object Identifier: 10.1214/aoap/1034625253

Primary: 60J27 , 92D30

Keywords: Birth-and-death process , coupling , deterministic and stochastic models , epidemics , size of epidemic , strong convergence , threshold theorems

Rights: Copyright © 1997 Institute of Mathematical Statistics

Vol.7 • No. 1 • February 1997
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