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

Ball, Frank G.; Sirl, David J.

Authors

FRANK BALL frank.ball@nottingham.ac.uk
Professor of Applied Probability

David J. Sirl



Abstract

We consider a stochastic SIR (susceptible → infective → removed) epidemic model with several types of individuals. Infectious individuals can make infectious contacts on two levels, within their own ‘household’ and with their neighbours in a random graph representing additional social contacts. This random graph is an extension of the well-known configuration model to allow for several types of individuals. We give a strong approximation theorem which leads to a threshold theorem for the epidemic model and a method for calculating 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.

Citation

Ball, F. G., & Sirl, D. J. An SIR epidemic model on a population with random network and household structure and several types of individuals. Manuscript submitted for publication

Journal Article Type Article
Deposit Date Jan 11, 2011
Publicly Available Date Mar 28, 2024
Peer Reviewed Not Peer Reviewed
Public URL https://nottingham-repository.worktribe.com/output/1012360

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