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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 pth moment(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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