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Asymptotic analysis of the general stochastic epidemic with variable infectious periods

Part of: Limit theorems

Published online by Cambridge University Press:  14 July 2016

A. N. Startsev
A. N. Startsev*
Affiliation:
Institute of Mathematics, Uzbek Academy of Sciences
*
∗ Postal address: Institute of Mathematics, Uzbek Academy of Sciences, Ul. Khodjaeva 29, Akademgorodok, 700143 Tashkent, Uzbekistan.
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Abstract

A generalisation of the classical general stochastic epidemic within a closed, homogeneously mixing population is considered, in which the infectious periods of infectives follow i.i.d. random variables having an arbitrary but specified distribution. The asymptotic behaviour of the total size distribution for the epidemic as the initial numbers of susceptibles and infectives tend to infinity is investigated by generalising the construction of Sellke and reducing the problem to a boundary crossing problem for sums of independent random variables.

Keywords

epidemicssize of epidemicvariable infectious periodlimit theoremsnon-Markovian model

MSC classification

Primary: 92D30: Epidemiology
Secondary: 60F17: Functional limit theorems; invariance principles
Type
Research Papers
Information
Journal of Applied Probability , Volume 38 , Issue 1 , March 2001 , pp. 18 - 35
Copyright
Copyright © by the Applied Probability Trust 2001 

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