Stochastic multi-type SIR epidemics among a population partitioned into households

Ball, Frank G. and Lyne, Owen D. (2001) Stochastic multi-type SIR epidemics among a population partitioned into households. Advances in Applied Probability, 33 (1). pp. 99-123. ISSN 0001-8678. (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

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We consider a stochastic model for the spread of an SIR (susceptible --> infective --> removed) epidemic among a closed, finite population that contains several types of individuals and is partitioned into households. The infection rate between two individuals depends on the types of the transmitting and receiving individuals and also on whether the infection is local (i.e., within a household) or global (i.e., between households). The exact distribution of the final outcome of the epidemic is outlined. A branching process approximation for the early stages of the epidemic is described and made fully rigorous, by considering a sequence of epidemics in which the number of households tends to infinity and using a coupling argument. This leads to a threshold theorem for the epidemic model. A central limit theorem for the final outcome of epidemics which take off is derived, by exploiting an embedding representation.

Item Type: Article
Uncontrolled keywords: epidemic process; final outcome; local and global contacts; multitype branching process; coupling; threshold theorem; weak convergence; central limit theorems; embedded process
Subjects: H Social Sciences > HA Statistics
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science
Depositing User: Judith Broom
Date Deposited: 19 Dec 2007 18:20
Last Modified: 29 May 2014 15:06
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