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

  • Richard J. Kryscio (a1) and Claude Lefèvre (a2)


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.


Corresponding author

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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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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