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Analysis of a stochastic SIR epidemic on a random network incorporating household structure

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posted on 2011-09-28, 10:50 authored by Frank Ball, David Sirl, Pieter Trapman
This paper is concerned with a stochastic SIR (susceptible → infective → removed) model for the spread of an epidemic amongst a population of individuals, with a random network of social contacts, that is also partitioned into households. The behaviour of the model as the population size tends to infinity in an appropriate fashion is investigated. A threshold parameter which determines whether or not an epidemic with few initial infectives can become established and lead to a major outbreak is obtained, as are the probability that a major outbreak occurs and the expected proportion of the population that are ultimately infected by such an outbreak, together with methods for calculating these quantities. Monte Carlo simulations demonstrate that these asymptotic quantities accurately reflect the behaviour of finite populations, even for only moderately sized finite populations. The model is compared and contrasted with related models previously studied in the literature. The effects of the amount of clustering present in the overall population structure and the infectious period distribution on the outcomes of the model are also explored.

History

School

  • Science

Department

  • Mathematics Education Centre

Citation

BALL, F., SIRL, D. and TRAPMAN, P., 2010. Analysis of a stochastic SIR epidemic on a random network incorporating household structure. Mathematical Biosciences, 224 (2), pp. 53-73.

Publisher

© Elsevier

Version

  • AM (Accepted Manuscript)

Publication date

2010

Notes

This article was published in the journal, Mathematical Biosciences [© Elsevier] and the definitive version is available at: http://dx.doi.org/10.1016/j.mbs.2009.12.003

ISSN

0025-5564

Language

  • en

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