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Title: Threshold behaviour and final outcome of an epidemic on a random network with household structure
Authors: Ball, Frank
Sirl, David
Trapman, Pieter
Keywords: Branching process
Final outcome
Epidemic process
Local and global contacts
Random graph
Susceptibility set
Threshold theorem
Issue Date: 2009
Publisher: © Applied Probability Trust
Citation: BALL, F., SIRL, D. and TRAPMAN, P., 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.
Abstract: In this paper we consider 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.
Description: This article was published in the journal, Advances in Applied Probability [© Applied Probability Trust] and the definitive version is available at http://dx.doi.org/10.1239/aap/1253281063
Version: Accepted for publication
DOI: 10.1239/aap/1253281063
URI: https://dspace.lboro.ac.uk/2134/8864
Publisher Link: http://dx.doi.org/10.1239/aap/1253281063
ISSN: 0001-8678
Appears in Collections:Published Articles (Mathematics Education Centre)

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