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An epidemic model with infector-dependent severity

Part of: Special processes

Published online by Cambridge University Press:  01 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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A stochastic epidemic model is defined in which infected individuals have different severities of disease (e.g. mildly and severely infected) and the severity of an infected individual depends on the severity of the individual he or she was infected by; typically, severe or mild infectives have an increased tendency to infect others severely or, respectively, mildly. Large-population properties of the model are derived, using branching process approximations for the initial stages of an outbreak and density-dependent population processes when a major outbreak occurs. The effects of vaccination are considered, using two distinct models for vaccine action. The consequences of launching a vaccination program are studied in terms of the effect it has on reducing the final size in the event of a major outbreak as a function of the vaccination coverage, and also by determining the critical vaccination coverage above which only small outbreaks can occur.

Keywords

Stochastic epidemicfinal sizebasic reproduction numbervarying severitybranching processdensity dependent population processthreshold behaviour

MSC classification

Primary: 92D30: Epidemiology
Secondary: 60K99: None of the above, but in this section
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 39 , Issue 4 , December 2007 , pp. 949 - 972
Copyright
Copyright © Applied Probability Trust 2007 

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