Statistics Seminars: Stochastic and deterministic SIS household epidemics
5 May 2006 00:00 in CM107"The SIS (Susceptible -> Infective -> Susceptible) epidemic model is the simplest epidemic model which exhibits endemic behaviour. Most of the `classical' results for stochastic epidemic models are asymptotic results as the population size becomes infinitely large. Therefore the implicit homogeneously mixing assumption of the SIS epidemic becomes increasingly unrealistic, and so, over the last fifteen years considerable attention has been devoted to the analysis of the spread of infectious diseases in heterogeneously mixing populations. The prime example is the household epidemic model which has been studied extensively for the SIR epidemic model. However very little has progress has been made with the SIS epidemic model.
In this talk I shall consider the SIS household epidemic model. We shall study both the stochastic and deterministic model. In particular we show how Markov chains can be utilised to obtain the equilibrium distribution of the deterministic model. We shall also consider the fluctuations of the stochastic model about the deterministic trajectory."
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