Abstract
In this paper, a stochastic HIV/AIDS epidemic model is presented to study the synthetic effect of ART (antiretroviral therapy) and PrEP (pre-exposure prophylaxis) treatments among MSM ( men who have sex with men). Firstly, we give the global stability of disease-free equilibrium and the endemic equilibrium in terms of basic reproduction number R0 for deterministic model. And then the existence of global positive solutions and the existence of unique ergodic stationary distribution under R0S>1 for stochastic model are given. Further, the long-time stochastic dynamic of the model is investigated, including the criteria on the extinction and persistence in mean for the stochastic model. Finally, we give some numerical simulations to illustrate our theoretical results, and the sensitive analysis shows that ART (antiretroviral therapy) and PrEP (pre-exposure prophylaxis) treatments can effectively control the spread of AIDS among MSM population.
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