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Endemic Behaviour of SIS Epidemics with General Infectious Period Distributions

Part of: Stochastic processes

Published online by Cambridge University Press:  22 February 2016

Peter Neal
Peter Neal*
Affiliation:
Lancaster University
*
∗ Postal address: Department of Mathematics and Statistics, Fylde College, Lancaster University, Lancaster LA1 4YF, UK. Email address: p.neal@lancaster.ac.uk
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Abstract

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We study the endemic behaviour of a homogeneously mixing SIS epidemic in a population of size N with a general infectious period, Q, by introducing a novel subcritical branching process with immigration approximation. This provides a simple but useful approximation of the quasistationary distribution of the SIS epidemic for finite N and the asymptotic Gaussian limit for the endemic equilibrium as N → ∞. A surprising observation is that the quasistationary distribution of the SIS epidemic model depends on Q only through

Keywords

SIS epidemicbranching process with immigrationGaussian processquasistationary distribution

MSC classification

Primary: 92D30: Epidemiology
Secondary: 60G10: Stationary processes
Type
Research Article
Information
Advances in Applied Probability , Volume 46 , Issue 1 , March 2014 , pp. 241 - 255
Copyright
© Applied Probability Trust 

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