Analysis and control of an age-structured HIV-1 epidemic model with different transmission mechanisms

• Main Authors: Xiaoyan Wang, Junyuan Yang, Fei Xu
• Format: Article
• Language: English
• Published: SpringerOpen 2018-01-01
• Series: Advances in Difference Equations
• Subjects: infection age; antiretroviral therapy; cell-to-cell transmission; Lyapunov functional
• Online Access: http://link.springer.com/article/10.1186/s13662-017-1455-0

Abstract In this paper, we propose a within-host HIV-1 epidemic model with cell-to-virus and cell-to-cell transmission. By mathematical analysis, we obtain the basic reproduction number R 0 $\mathcal {R}_{0}$ , which determines the viral persistence and the basic reproduction number R 0 cc $\mathcal {R}_{0}^{\mathrm{cc}}$ with respect to cell-to-cell transmission which is not strong enough, i.e., it is less than 1. If the basic reproduction number is less than 1, then the viral-free steady state E 0 $E_{0}$ is globally asymptotically stable, which is proved by fluctuation lemma and comparison method; if R 0 > 1 $\mathcal {R}_{0}>1$ is greater than 1, the endemic steady state E ∗ $E^{*}$ is globally asymptotically stable, which is proved by constructing the Lyapunov functional. Antiretoviral therapy is implemented to suppress the viral replication. Protease inhibitors for cell-to-cell transmission play an important role in controlling cell-to-cell infection. Under some circumstances, the effects of the cell-to-cell infection process are more sensitive than those of cell-to-virus transmission.