Analysis of a nonlinear stochastic perturbed HIV model with CD4+ T cells

Abstract

Considering that the consequences of human immunodeficiency virus (HIV) infection may lead to exhaustion of $\text{CD4}^{+}$ T cells, this paper investigates a nonlinear stochastic perturbed HIV epidemic model. First, the stochastic Lyapunov function approach is used to establish the condition $\mathcal{R}_{0}^{S}>1$ of having a stationary distribution with the ergodicity property. The approximate probability density around the endemic equilibrium of the stochastic system is then derived by solving the Fokker-Planck equation. In addition, we provide the requirements for disease eradication. Finally, some numerical test results and relevant pictures are given.