A stochastic model of HIV infection incorporating combined therapy of HAART driven by Lévy jumps

Abstract

A stochastic HIV infection model of virus-to-cell transmission is proposed, incorporating the antiretroviral drug therapy by introducing efficacy parameters of RTI and PI drugs, considering the Lévy noise for the inherent stochastic biochemical processes. First, we discuss the model existence of a global positive solution and, by applying Itô’s formula, establish a sufficient condition for the extinction of infected CD4+ T-cells and virus particles. Then, for proving the persistence in mean, a special method is investigated to handle the model. It is obtained that if $\tilde{R}_{1}>1$ the infected CD4+ T-cells and virus particles will be persistent in mean. Finally, some numerical simulations are carried out to show the effects of inherent stochastic fluctuation.