The threshold for a stochastic HIV-1 infection model with Beddington-DeAngelis incidence rate |
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Institution: | 1. School of Mathematics and Statistics, Changshu Institute of Technology, Changshu, Jiangsu 215500, PR China;2. School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin 130024, PR China |
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Abstract: | In this paper, we consider a stochastic HIV-1 infection model with Beddington-DeAngelis incidence rate. Before exploring its long-time behavior we show that there is a global positive solution of this model. Then sufficient conditions for extinction of the disease are established. Moreover, we give sufficient conditions for the existence of a stationary distribution of the model through constructing a suitable stochastic Lyapunov function. The stationary distribution implies that the disease is persistent in the mean. Therefore, a threshold value for the disease to disappear or prevail is obtained. Finally, some numerical examples are illustrated to support our theoretical results. |
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