Effects of stochastic perturbation on the SIS epidemic system

A Lahrouz, A Settati, A Akharif - Journal of mathematical biology, 2017 - Springer
Journal of mathematical biology, 2017Springer
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 …
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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