Stationary Distribution and Extinction of Stochastic HTLV-I Infection Model with CTL Immune Response under Regime Switching

Abstract

In this paper, the stochastic HTLV-I infection model with CTL immune response is investigated. Firstly, we show that the stochastic system exists unique positive global solution originating from the positive initial value. Secondly, we obtain that the existence of ergodic stationary distribution of the model by stochastic $Lyapunov$ functions. Thirdly, we establish sufficient conditions for extinction of the infected cells. Finally, numerical simulations are carried out to illustrate the theoretical results.