Dynamics analysis of a stochastic HIV model with non-cytolytic cure and Ornstein–Uhlenbeck process

In this paper, we introduce an HIV infection model with virus-to-cell infection, cell-to-cell infection and non-cytolytic cure. Two mean-reverting Ornstein–Uhlenbeck processes are also taken into account in the model. Firstly, it is proved that the stochastic model has a unique positive global solution. The model is found to have at least one stationary distribution by constructing suitable Lyapunov functions if the critical condition $R_0^s>1$. Then, the probability density function near the quasi-positive equilibrium is obtained by solving the corresponding Fokker–Planck equation. The spectral radius method is used to derive the virus extinction under a sufficient condition $R_0^e<1$. Finally, some numerical simulations are carried out.