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The Probability of Containment for Multitype Branching Process Models for Emerging Epidemics

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

Simon E. F. Spencer  and
Philip D. O‘Neill
Simon E. F. Spencer*
Affiliation:
University of Warwick
Philip D. O‘Neill*
Affiliation:
University of Nottingham
*
∗Postal address: Department of Statistics, University of Warwick, Coventry CV4 7AL, UK. Email address: s.e.f.spencer@warwick.ac.uk
∗∗Postal address: School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK. Email address: philip.oneill@nottingham.ac.uk
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Abstract

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This paper is concerned with the definition and calculation of containment probabilities for emerging disease epidemics. A general multitype branching process is used to model an emerging infectious disease in a population of households. It is shown that the containment probability satisfies a certain fixed point equation which has a unique solution under certain conditions; the case of multiple solutions is also described. The extinction probability of the branching process is shown to be a special case of the containment probability. It is shown that Laplace transform ordering of the severity distributions of households in different epidemics yields an ordering on the containment probabilities. The results are illustrated with both standard epidemic models and a specific model for an emerging strain of influenza.

Keywords

Branching processepidemicinfluenzastochastic epidemic

MSC classification

Secondary: 92D30: Epidemiology 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Type
Research Article
Information
Journal of Applied Probability , Volume 48 , Issue 1 , March 2011 , pp. 173 - 188
Copyright
Copyright © Applied Probability Trust 2011 

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