Dynamical Analysis of Stochastic SIRS Double Epidemic Model with Logistic Growth and Crowley-Martin Incidence Rate
Based on the fact that many diseases coexist in real life and are affected by envi-ronmental noise,a stochastic SIRS double epidemic model with Logistic growth and Crowley-Martin type incidence is established to discuss the effects of Logistic growth,Crowley-Martin type incidence and double epidemic infectious diseases on the global dynamics of the model.It is obtained that the global dynamics of the model is determined by stochastic basic repro-duction number.Firstly,by constructing the Lyapunov function and using the Itô's formula,the existence and uniqueness of the global positive solution are proved,and then,by combining the stochastic basic reproduction number and the constructed Lyapunov function,the sufficient conditions for determining the extinction and persistence of the disease are obtained by using the LaSalle invariance principle.The results show that the environmental change can inhibit the disease under certain conditions.Finally,the correctness of the theoretical results is verified by numerical simulation.
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