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

Ball, Frank G.; Sirl, David J.

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
• Peer Reviewed: Not Peer Reviewed
• Public URL: https://nottingham-repository.worktribe.com/output/1012360