SIR epidemics with stages of infection. (September 2016)

• Record Type: Journal Article
• Authors: Lefèvre, Claude; Simon, Matthieu
• Is Part Of: Advances in applied probability. Volume 48:Number 3(2016)
• Page Start: 768
• Page End: 791
• Publication Date: 2016-09
• Subjects: Epidemic model, -- final size and severity, -- phase-type distribution, -- Markovian or semi-Markovian infection process, -- matrix analytic method; Primary 60J20, -- Secondary 60K15, -- 92D30; Probabilities -- Periodicals; Stochastic models -- Periodicals; Electronic journals; Periodicals; 519.2
• DOI: 10.1017/apr.2016.27
• Languages: English
• ISSNs: 0001-8678

Abstract

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).