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 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}