A stochastic HIV infection model with T-cell proliferation and CTL immune response

A stochastic HIV infection model with T-cell proliferation and CTL immune response is formulated to investigate the effect of environmental fluctuations on the HIV viral dynamics. We obtain that the model solution is positive and global, and analyze the extinction of the model. We also derive a critical condition R₀^s when R₀^s is greater than one, the existence of ergodic stationary distribution of the model solution is established by constructing suitable Lyapunov functions. Numerical simulations are performed to investigate the effect of white noises on model behavior, we investigate that the small intensities of white noise can maintain the irregular recurrence of HIV virus and CTL immune response, while the larger ones may be help to the elimination of the virus and CTL immune response, and the medium intensities of white noises may cause both the persistence and extinction on model dynamics behavior.