Dynamics of stochastic HTLV‐I infection model with nonlinear CTL immune response.

In this paper, the dynamics of stochastic human T‐cell leukemia virus type I (HTLV‐I) infection model with cytotoxic T lymphocyte (CTL) immune response is investigated. First, we show that the stochastic model exists as a unique positive global solution originating from the positive initial value. Second, we demonstrate that the stochastic model is stochastically permanent and stochastically ultimately bounded for any positive initial value. Third, we establish sufficient conditions for the existence of ergodic stationary distribution of the stochastic model. Fourth, the threshold R0∗ between extinction and persistence of the virus is obtained. Finally, numerical simulations are carried out to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]