Analysis of a nonlinear perturbed HLIV model with viral production and multiple latent stages

Abstract

In this paper, we establish and analyze a nonlinear stochastically perturbed HLIV model with viral production and multiple latent stages, which is described by a series of stochastic differential equations with nonlinear perturbations. Firstly, we prove that there exists a unique global positive solution to the proposed model for any positive initial value. Then we adopt a stochastic Lyapunov function method to establish sufficient criteria for the existence and uniqueness of an ergodic stationary distribution of positive solutions to the system. Especially, under some mild conditions which are used to ensure the existence and local asymptotic stability of the endemic equilibrium of the deterministic system, we obtain the exact expression of the probability density around the endemic equilibrium of the deterministic system. In addition, we build up sufficient criteria for wiping out of the infected cells and free viruses. Finally, numerical simulations are performed to illustrate our theoretical findings.