An epidemic model of HIV transmission with two stochastic perturbations

We studied an epidemic model regarding the spread of HIV. Based on the original deterministic model, the model introduces two stochastic perturbations for the transmission coefficients β and $\beta ^{\prime}$ ; one is infectious individuals, and the other is pre-AIDS patients. The existence and uniqueness of the solution are proved using the Lyapunov function method, and the persistence and extinction conditions in the mean are given. Finally, our results are verified through numerical simulations.