A Stochastic HIV Infection Model with Latent Infection and Antiretroviral Therapy

Recent studies have demonstrated that the latent infection is a major obstacle to the viral elimination in HIV infection process. In this paper, we formulate a stochastic HIV infection model to include both latent infection and combination drug therapies. We derive that the model solution is unique and positive, and the solution is global. By constructing appropriate stochastic Lyapunov functions, the existence of an ergodic stationary distribution is obtained when the critical condition is greater than one. Furthermore, through rigorous analysis and deduction, the extinction of the virus is established under certain conditions. Numerical simulations are performed to show that small intensity of white noises can maintain the existence of a stationary distribution, while large intensity of white noises is beneficial to the extinction of the virus.