Dynamics of an HIV/AIDS transmission model with protection awareness and fluctuations

We establish a stochastic HIV/AIDS model for the individuals with protection awareness and reveal how plays its important role in control of AIDS. firstly show that there exists global positive solution model. By constructing Lyapunov functions, ergodic stationary distribution when $R_{0}^{s}>1$ extinction $R_{0}^{e}<1$ are obtained. A number numerical simulations by using preserving truncated Euler-Maruyama method (PPTEM) performed to illustrate theoretical results. Our new results detailed publicity has great impact on AIDS compared extensive publicity, while continuous antiretroviral therapy (ART) is helpful HIV/AIDS.