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The quasi-stationary distribution of the closed endemic sis model

Part of: Markov processes

Published online by Cambridge University Press:  01 July 2016

Ingemar Nåsell
Ingemar Nåsell*
Affiliation:
The Royal Institute of Technology, Stockholm
*
∗ Postal address: Department of Mathematics, The Royal Institute of Technology, S-l0044 Stockholm, Sweden.
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Abstract

The quasi-stationary distribution of the closed stochastic SIS model changes drastically as the basic reproduction ratio R0 passes the deterministic threshold value 1. Approximations are derived that describe these changes. The quasi-stationary distribution is approximated by a geometric distribution (discrete!) for R0 distinctly below 1 and by a normal distribution (continuous!) for R0 distinctly above 1. Uniformity of the approximation with respect to R0 allows one to study the transition between these two extreme distributions. We also study the time to extinction and the invasion and persistence thresholds of the model.

Keywords

STOCHASTIC LOGISTIC MODELCLOSED STOCHASTIC SIS MODELTIME TO EXTINCTIONTHRESHOLD OF STOCHASTIC MODELUNIFORM ASYMPTOTIC APPROXIMATION

MSC classification

Primary: 60J27: Continuous-time Markov processes on discrete state spaces 92D30: Epidemiology
Type
General Applied Probablity
Information
Advances in Applied Probability , Volume 28 , Issue 3 , September 1996 , pp. 895 - 932
Copyright
Copyright © Applied Probability Trust 1996 

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