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An epidemic model with exposure-dependent severities

Part of:Limit theoremsSpecial processes

Published online by Cambridge University Press:  14 July 2016

Frank Ball and
Tom Britton
Frank Ball*
Affiliation:
The University of Nottingham
Tom Britton*
Affiliation:
Stockholm University
*
∗ Postal address: School of Mathematical Sciences, The University of Nottingham, University Park, Nottingham NG7 2RD, UK. Email address: frank.ball@nottingham.ac.uk
∗∗ Postal address: Department of Mathematics, Stockholm University, SE-106 91 Stockholm, Sweden. Email address: tom.britton@math.su.se
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Abstract

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We consider a stochastic model for the spread of a susceptible–infective–removed (SIR) epidemic among a closed, finite population, in which there are two types of severity of infectious individuals, namely mild and severe. The type of severity depends on the amount of infectious exposure an individual receives, in that infectives are always initially mild but may become severe if additionally exposed. Large-population properties of the model are derived. In particular, a coupling argument is used to provide a rigorous branching process approximation to the early stages of an epidemic, and an embedding argument is used to derive a strong law and an associated central limit theorem for the final outcome of an epidemic in the event of a major outbreak. The basic reproduction number, which determines whether or not a major outbreak can occur given few initial infectives, depends only on parameters of the mild infectious state, whereas the final outcome in the event of a major outbreak depends also on parameters of the severe state. Moreover, the limiting final size proportions need not even be continuous in the model parameters.

Keywords

Stochastic epidemicfinal sizebasic reproduction numberinfections of varying severityexposurebranching processcouplingembedded processweak convergencecentral limit theorem

MSC classification

Primary:92D30: Epidemiology
Secondary:60F99: None of the above, but in this section60K99: None of the above, but in this section

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 42 , Issue 4 , December 2005, pp. 932 - 949
Copyright
© Applied Probability Trust 2005 

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