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On the Extinction of the S–I–S stochastic logistic epidemic

Published online by Cambridge University Press:  14 July 2016

Richard J. Kryscio  and
Claude Lefèvre
Richard J. Kryscio*
Affiliation:
University of Kentuckyn
Claude Lefèvre*
Affiliation:
Université Libre de Bruxelles
*
∗ Postal address: Department of Statistics, College of Arts and Sciences, University of Kentucky, Lexington, KY 40506–0027, USA.
∗∗ Postal address: Université Libre de Bruxelles, Institut de Statistique, Campus Plaine, C.P. 210, Boulevard du Triomphe, B-1050 Bruxelles, Belgium.
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Abstract

We obtain an approximation to the mean time to extinction and to the quasi-stationary distribution for the standard S–I–S epidemic model introduced by Weiss and Dishon (1971). These results are a combination and extension of the results of Norden (1982) for the stochastic logistic model, Oppenheim et al. (1977) for a model on chemical reactions, Cavender (1978) for the birth-and-death processes and Bartholomew (1976) for social diffusion processes.

Keywords

S–I–S EPIDEMICEXPECTED LENGTHQUASI-STATIONARY DISTRIBUTION
Type
Research Papers
Information
Journal of Applied Probability , Volume 26 , Issue 4 , December 1989 , pp. 685 - 694
Copyright
Copyright © Applied Probability Trust 1989 

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Footnotes

Partially supported by a NATO Grant for international collaboration. The research of RJK was partially supported by NSF EPSCoR Grant RII-861 0671.

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