Threshold behavior in a stochastic HTLV‐I infection model with CTL immune response and regime switching

Abstract

We investigate the stochastic HTLV‐I infection model with CTL immune response, which is disturbed by both white and telegraph noises. First, we obtain that the model solution is positive and global. Furthermore, we obtain the existence of ergodic stationary distribution of the solution by stochastic Lyapunov functions with regime switching, and we also establish sufficient conditions for the extinction of system with regime switching. Meanwhile, the threshold between ergodic property and extinction of the stochastic system is acquired. Finally, our theoretical results are verified by numerical simulation.