The quasi-stationary distribution of the closed endemic sis model

1 March 1996

journal article
general applied-probablity
Published by Cambridge University Press (CUP) in Advances in Applied Probability

Vol. 28 (03) , 895-932
https://doi.org/10.1017/s0001867800046541

Abstract

The quasi-stationary distribution of the closed stochastic SIS model changes drastically as the basic reproduction ratio R ₀ 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 R ₀ distinctly below 1 and by a normal distribution (continuous!) for R ₀ distinctly above 1. Uniformity of the approximation with respect to R ₀ 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

This publication has 12 references indexed in Scilit:

Stochastic epidemics: major outbreaks and the duration of the endemic period
Journal of Mathematical Biology, 1995
On Ramanujan's Q-function
Journal of Computational and Applied Mathematics, 1995
An Efficient Procedure for Computing Quasi-Stationary Distributions of Markov Chains by Sparse Transition Structure
Advances in Applied Probability, 1994
The stochastic SI model with recruitment and deaths I. comparison with the closed SIS model
Mathematical Biosciences, 1993
On the quasi-stationary distribution of the Ross malaria model
Mathematical Biosciences, 1991
On the distribution of the time to extinction in the stochastic logistic population model
Advances in Applied Probability, 1982
The Asymptotic Expansion of the Incomplete Gamma Functions
SIAM Journal on Mathematical Analysis, 1979
Quasi-stationary distributions of birth-and-death processes
Advances in Applied Probability, 1978
Uniform asymptotic expansions of the incomplete gamma functions and the incomplete beta function
Mathematics of Computation, 1975
On quasi-stationary distributions in absorbing continuous-time finite Markov chains
Journal of Applied Probability, 1967