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Gaussian approximation of some closed stochastic epidemic models

Published online by Cambridge University Press:  14 July 2016

Frank J. S. Wang
Frank J. S. Wang*
Affiliation:
University of Montana
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Abstract

A generalization of Bailey's general epidemic model is considered. In this generalized model, it is assumed that the probability of any particular susceptible becoming infected during the small time interval (t, t + Δt) is α(X(t))Δt + o(Δt), for some function a, where X(t) is the proportion of infected individuals in the entire population, the probability that an infected individual is infected for at least a length of time t is F(t), and recovered individuals are permanently immune from further attack. In this paper, central limit theorems are obtained for the proportion of infected individuals and the proportion of susceptibles in the entire population.

Keywords

EPIDEMIC MODELGAUSSIAN PROCESSCENTRAL LIMIT THEOREMBIVARIATE GAUSSIAN RANDOM FUNCTIONVOLTERRA INTEGRAL EQUATIONRESOLVENT KERNELPARTIAL DIFFERENTIAL EQUATIONSKOROHOD TOPOLOGY
Type
Research Papers
Information
Journal of Applied Probability , Volume 14 , Issue 2 , June 1977 , pp. 221 - 231
Copyright
Copyright © Applied Probability Trust 1977 

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