Threshold behaviour and final outcome of an epidemic on a random network with household structure

Ball, Frank G. and Sirl, David J. and Trapman, Pieter (2009) Threshold behaviour and final outcome of an epidemic on a random network with household structure. Advances in Applied Probability, 41 (3). pp. 765-796.

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Abstract

This paper considers a stochastic SIR (susceptible-infective-removed) epidemic model in which individuals may make infectious contacts in two ways, both within 'households' (which for ease of exposition are assumed to have equal size) and along the edges of a random graph describing additional social contacts. Heuristically-motivated branching process approximations are described, which lead to a threshold parameter for the model and methods for calculating the probability of a major outbreak, given few initial infectives, and the expected proportion of the population who are ultimately infected by such a major outbreak. These approximate results are shown to be exact as the number of households tends to infinity by proving associated limit theorems. Moreover, simulation studies indicate that these asymptotic results provide good approximations for modestly-sized finite populations. The extension to unequal sized households is discussed briefly.

Item Type:Article
Uncontrolled Keywords:Branching process; coupling; epidemic process; final outcome; households; local and global contacts; random graph; susceptibility set; threshold theorem
Schools/Departments:Faculty of Science > School of Mathematical Sciences
ID Code:1299
Deposited By:Sirl, Dr David
Deposited On:19 May 2010 11:22
Last Modified:21 Jun 2011 14:55

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