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An SIR epidemic model on a population with random network and household structure, and several types of individuals

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journal contribution
posted on 21.01.2013, 11:05 by Frank Ball, David Sirl
We consider a stochastic SIR (susceptible → infective → removed) epidemic model with several types of individuals. Infectious indi- viduals can make infectious contacts on two levels, within their own ‘household’ and with their neighbours in a random graph represent- ing additional social contacts. This random graph is an extension of the well-known configuration model to allow for several types of in- dividuals. We give a strong approximation theorem which leads to a threshold theorem for the epidemic model and a method for calcu- lating the probability of a major outbreak given few initial infectives. A multitype analogue of a theorem of Ball et al. (2009) heuristically motivates a method for calculating the expected size of such a major outbreak. We also consider vaccination and give some short numerical illustrations of our results.

History

School

  • Science

Department

  • Mathematics Education Centre

Citation

BALL, F.G. and SIRL, D.J., 2012. An SIR epidemic model on a population with random network and household structure, and several types of individuals. Advances in Applied Probability, 44, pp.63-86.

Publisher

© Applied Probability Trust

Version

AM (Accepted Manuscript)

Publication date

2012

ISSN

0001-8678

Language

en