A dynamics stochastic model with HIV infection of CD4+ T-cells driven by Lévy noise. (December 2019)

• Record Type: Journal Article
• Authors: Cheng, Yan; Li, Mingtao; Zhang, Fumin
• Is Part Of: Chaos, solitons and fractals. Volume 129(2019)
• Page Start: 62
• Page End: 70
• Publication Date: 2019-12
• Subjects: Stochastic model -- Lévy noise -- Within-host HIV infection -- Persistence in mean; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2019.07.054
• Languages: English
• ISSNs: 0960-0779

Abstract

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.