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

We establish a stochastic HIV/AIDS model involving the susceptible with protection awareness within a total population. The mechanism of dynamic behaviors of the stochastic HIV/AIDS model with protection awareness are investigated in order to control the spread of HIV/AIDS. We firstly show that the stochastic model admits a global positive solution with any initial positive values. By constructing Lyapunov functions, the ergodic stationary distribution under the condition , and the extinction under the condition for the stochastic model are further obtained respectively. Moreover, by using positive preserving truncated Euler–Maruyama method (PPTEM), the related numerical simulations are performed, which demonstrate the quantitative properties of persistence and extinction of the solution. Precisely, the increasing of protection efficiency of the susceptible with protection awareness reduces the scale of the infected individuals with AIDS; and the continuous antiretroviral therapy (ART) also benefits the control of the scale of the infected individuals with HIV/AIDS; the media reports with more instructions and details such as taking post-exposure prophylaxis (PEP) within 72 h to help the individuals avoid the infection to meet the 90%–90%–90% plan of WHO.