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