A dynamics stochastic model with HIV infection of CD4+ T-cells driven by Lévy noise. (December 2019) - Cheng, Yan; Li, Mingtao; Zhang, Fumin
Highlights: Described the strong fluctuation of HIV viral infection by introducing a Lévy jump process into the HIV dynamical model. Using the hasminskii-Mao theorem and stochastic Lyapunov function, we show that the model has a unique global positive solution. In order to investigate the sufficient conditions of infected CD4 + T-cells and virus particles persistence in mean, we applied a new method to establish a stochastic Lyapunov function. Abstract: Aim to described this strong fluctuation by introducing a Lévy 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 Lévy 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.