Abstract
In this paper we extend the classical SIS epidemic model from a deterministic framework to a stochastic one. We also study the long time behavior of the stochastic system. We mainly establish conditions for the extinction of disease from the population as well as the persistence of disease under different conditions. In the case of persistence, we show the existence of a stationary distribution. we found that the introduction of stochastic noise changes the basic reproduction number. The presented results are demonstrated by numerical simulations.
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The authors are grateful to the editor and the anonymous reviewers for their careful reading and valuable suggestions which improved the quality of the paper.
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Lahrouz, A., Settati, A. & Akharif, A. Effects of stochastic perturbation on the SIS epidemic system. J. Math. Biol. 74, 469–498 (2017). https://doi.org/10.1007/s00285-016-1033-1
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DOI: https://doi.org/10.1007/s00285-016-1033-1