Abstract
In this paper, we investigate dynamical behaviors for a stochastic malaria model by introducing the effect of environmental white noise on transmission dynamics of malaria. Firstly, the distance between stochastic solutions and the disease-free equilibrium of the corresponding deterministic model is estimated in the time mean sense by constructing stochastic Lyapunov functions. Particularly, by the comparison theorem of stochastic differential equations and the law of large numbers, sufficient conditions for the extinction of the disease are obtained in the special case. Next, the existence of the unique ergodic stationary distribution is proved by constructing a suitable Lyapunov function. Finally, the model is used to simulate the human malaria data in Yunnan province and predict the trend of malaria in Yunnan.
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