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SIR epidemics with stages of infection

Part of: Special processes Markov processes

Published online by Cambridge University Press:  19 September 2016

Claude Lefèvre  and
Matthieu Simon
Claude Lefèvre*
Affiliation:
Université Libre de Bruxelles
Matthieu Simon*
Affiliation:
Université Libre de Bruxelles
*
* Postal address: Département de Mathématique, Université Libre de Bruxelles, Campus de la Plaine C.P. 210, B-1050 Bruxelles, Belgium.
* Postal address: Département de Mathématique, Université Libre de Bruxelles, Campus de la Plaine C.P. 210, B-1050 Bruxelles, Belgium.
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Abstract

In this paper we are concerned with a stochastic model for the spread of an epidemic in a closed homogeneously mixing population when an infective can go through several stages of infection before being removed. The transitions between stages are governed by either a Markov process or a semi-Markov process. An infective of any stage makes contacts amongst the population at the points of a Poisson process. Our main purpose is to derive the distribution of the final epidemic size and severity, as well as an approximation by branching, using simple matrix analytic methods. Some illustrations are given, including a model with treatment discussed by Gani (2006).

Keywords

Epidemic modelfinal size and severityphase-type distributionMarkovian or semi-Markovian infection processmatrix analytic method

MSC classification

Primary: 60J20: Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
Secondary: 60K15: Markov renewal processes, semi-Markov processes 92D30: Epidemiology
Type
Research Article
Information
Advances in Applied Probability , Volume 48 , Issue 3 , September 2016 , pp. 768 - 791
Copyright
Copyright © Applied Probability Trust 2016 

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