A dynamics stochastic model with HIV infection of CD4+ T-cells driven by Levy noise

Aim to described this strong fluctuation by introducing a Levy jump process into the HIV dynamical modelA stochastic model that describing the interaction between the CD4(+) T-cells and the free human immunodeficiency virus (HIV) is investigated, a basic biological mechanism which describe the strong fluctuation in environment be considered into the model by introducing Levy process. First, we obtained that the stochastic model admits a unique global positive solution. Then, constructed a function to analyze the extinction of infected the CD4(+) T-cells and virus particles. Next, we investigated the persistence in mean of the infected CD4(+) T-cells, a sufficient condition be established. Finally, some numerical simulations are given to verify the result of theoretical analysis. (C) 2019 Published by Elsevier Ltd.