Aadil Lahrouz

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Abstract. We present in this paper an SIRS epidemic model with saturated incidence rate and disease-inflicted mortality. The Global stability of the endemic equilibrium state is proved by constructing a Lyapunov function. For the stochastic version, the global existence and positivity of the solution is showed, and the global stability in probability and(More)
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(More)
In this paper, we analyze a stochastic Gilpin-Ayala population model with Markovian switching and white noise. The Gilpin-Ayala parameter is also allowed to switch. We establish the global stability of the trivial equilibrium state of the model. Verifiable sufficient conditions which guarantee the extinction and persistence are provided. Furthermore, we(More)
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