Virus infection model under nonlinear perturbation: Ergodic stationary distribution and extinction

Abstract

In order to study the effect of nonlinear perturbation on virus infection of target cells, in this paper, we propose a stochastic virus infection model with multitarget cells and exposed state. Firstly, by constructing novel stochastic Lyapunov functions, we theoretically prove that the solution of the stochastic model is positive and global. Secondly, we obtain the existence and uniqueness of an ergodic stationary distribution of the stochastic system and the exact expression of probability density function around a quasi-endemic equilibrium if Rs>1, and we establish a sufficient condition Re<1 for the extinction of infected cells and virus. Finally, we present examples and numerical simulations to verify our theoretical results.