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A household SIR epidemic model incorporating time of day effects

Part of: Stochastic processes Markov processes

Published online by Cambridge University Press:  21 June 2016

Peter Neal
Peter Neal*
Affiliation:
Lancaster University
*
* Postal address: Department of Mathematics and Statistics, Fylde College, Lancaster University, Lancaster LA1 4YF, UK. Email address: [email protected]
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Abstract

During the course of a day an individual typically mixes with different groups of individuals. Epidemic models incorporating population structure with individuals being able to infect different groups of individuals have received extensive attention in the literature. However, almost exclusively the models assume that individuals are able to simultaneously infect members of all groups, whereas in reality individuals will typically only be able to infect members of any group they currently reside in. In this paper we develop a model where individuals move between a community and their household during the course of the day, only infecting within their current group. By defining a novel branching process approximation with an explicit expression for the probability generating function of the offspring distribution, we are able to derive the probability of a major epidemic outbreak.

Keywords

Birth–death processbranching processhouseholds SIR epidemic model

MSC classification

Primary: 92D30: Epidemiology
Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60G10: Stationary processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 53 , Issue 2 , June 2016 , pp. 489 - 501
Copyright
Copyright © Applied Probability Trust 2016 

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