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Title: An SIR epidemic model on a population with random network and household structure, and several types of individuals
Authors: Ball, Frank
Sirl, David
Keywords: Coupling
Final outcome
Local and global contacts
Multitype branching process
Multitype epidemic process
Multitype random graph
Threshold theorem
Issue Date: 2012
Publisher: © Applied Probability Trust
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.
Abstract: 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.
Version: Accepted for publication
URI: https://dspace.lboro.ac.uk/2134/11505
Publisher Link: http://www.appliedprobability.org/
ISSN: 0001-8678
Appears in Collections:Published Articles (Mathematics Education Centre)

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