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Stochastic and deterministic analysis of SIS household epidemics

Research output: Contribution to journalJournal articlepeer-review

Published
<mark>Journal publication date</mark>12/2006
<mark>Journal</mark>Advances in Applied Probability
Issue number4
Volume38
Number of pages26
Pages (from-to)943-968
Publication StatusPublished
<mark>Original language</mark>English

Abstract

We analyse SIS epidemics among populations partitioned into households. The analysis considers both the stochastic and deterministic models and, unlike in previous analyses, we consider general infectious period distributions. For the deterministic model, we prove the existence of an endemic equilibrium for the epidemic if and only if the threshold parameter, R*, is greater than 1. Furthermore, by utilising Markov chains we show that the total number of infectives converges to the endemic equilibrium as t → ∞. For the stochastic model, we prove a law of large numbers result for the convergence, to the deterministic limit, of the mean number of infectives per household. This is followed by the derivation of a Gaussian limit process for the fluctuations of the stochastic model.