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A threshold limit theorem for the stochastic logistic epidemic

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

Håkan Andersson  and
Boualem Djehiche
Håkan Andersson*
Affiliation:
Stockholm University
Boualem Djehiche*
Affiliation:
Royal Institute of Technology
*
∗Postal address: Department of Mathematics, Stockholm University, S-106 91 Stockholm, Sweden. Email address: hakan@matematik.su.se.
∗∗Postal address: Department of Mathematics, Royal Institute of Technology, S-100 44 Stockholm, Sweden.
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Abstract

The time until extinction for the closed SIS stochastic logistic epidemic model is investigated. We derive the asymptotic distribution for the extinction time as the population grows to infinity, under different initial conditions and for different values of the infection rate.

Keywords

Birth and death processepidemic processentropytime to extinctioncoupling

MSC classification

Primary: 92D30: Epidemiology
Secondary: 60J27: Continuous-time Markov processes on discrete state spaces
Type
Research Papers
Information
Journal of Applied Probability , Volume 35 , Issue 3 , September 1998 , pp. 662 - 670
Copyright
Copyright © Applied Probability Trust 1998 

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