The final size and severity of a generalised stochastic multitype epidemic model

Frank Ball, Damian Clancy

Research output: Contribution to journalArticle

Abstract

We consider a stochastic model for the spread of an epidemic amongst a population split into m groups, in which infectives move among the groups and contact susceptibles at a rate which depends upon the infective's original group, its current group, and the group of the susceptible. The distributions of total size and total area under the trajectory of infectives for such epidemics are analysed. We derive exact results in terms of multivariate Gontcharoff polynomials by treating our model as a multitype collective Reed-Frost process and slightly adapting the results of Picard and Lefevre (1990). We also derive asymptotic results, as each of the group sizes becomes large, by generalising the method of Scalia-Tomba (1985), (1990).
Original languageEnglish
Pages (from-to)721-736
Number of pages16
JournalAdvances in Applied Probability
Volume25
Issue number4
DOIs
Publication statusPublished - 1993

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