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

Ball, Frank G.; Sirl, David J.; Trapman, Pieter

Authors

Frank G. Ball

David J. Sirl

Pieter Trapman



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.

Journal Article Type Article
Publication Date Jan 1, 2009
Journal Advances in Applied Probability
Print ISSN 0001-8678
Publisher Applied Probability Trust
Peer Reviewed Peer Reviewed
Volume 41
Issue 3
APA6 Citation Ball, F. G., Sirl, D. J., & Trapman, P. (2009). Threshold behaviour and final outcome of an epidemic on a random network with household structure. Advances in Applied Probability, 41(3),
Keywords Branching process; coupling; epidemic process; final outcome; households; local and global contacts; random graph; susceptibility set; threshold theorem
Publisher URL http://www.appliedprobability.org/content.aspx?Group=journals&Page=apjournals
Related Public URLs http://projecteuclid.org/euclid.aap/1253281063
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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