Threshold Dynamics of a Non-Linear Stochastic Viral Model with Time Delay and CTL Responsiveness

Abstract

This article focuses on a stochastic viral model with distributed delay and CTL responsiveness. It is shown that the viral disease will be extinct if the stochastic reproductive ratio is less than one. However, when the stochastic reproductive ratio is more than one, the viral infection system consists of an ergodic stationary distribution. Furthermore, we obtain the existence and uniqueness of the global positive solution by constructing a suitable Lyapunov function. Finally, we illustrate our results by numerical simulation.

Keywords

• stochastic viral model
• time delayed
• CTL responsiveness
• ergodic stationary distribution
• extinction