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Compound Poisson limits for household epidemics

Research output: Contribution to journalJournal articlepeer-review

Published
<mark>Journal publication date</mark>2005
<mark>Journal</mark>Journal of Applied Probability
Issue number2
Volume42
Number of pages12
Pages (from-to)334-345
Publication StatusPublished
<mark>Original language</mark>English

Abstract

We consider epidemics in populations that are partitioned into small groups known as households. Whilst infectious, a typical infective makes global and local contact with individuals chosen independently and uniformly from the whole population or their own household, as appropriate. Previously, the classical Poisson approximation for the number of survivors of a severe epidemic has been extended to the household model. However, in the current work we exploit a Sellke-type construction of the epidemic process, which enables the derivation of sufficient conditions for the existence of a compound Poisson limit theorem for the survivors of the epidemic. The results are specialised to the Reed-Frost and general stochastic epidemic models.