Global Stability Analysis for a Virus Dynamics Model with Distributed Intracellular Delays and Eclipse Stages

Abstract

This paper investigates the global asymptotic stability of an HIV dynamics model with discrete intracellular delays incorporating Beddington-DeAngelis functional response. An eclipse stage of infected cells (i.e. latently infected cells), not yet producing virus, is included in our models. We consider nonnegativity and boundedness of solutions and global asymptotic stability of the uninfected and infected equilibria (steady states) of the system. We have proved that if the basic reproduction number Ro is less than unity, then the disease-free equilibrium is globally asymptotically stable, and if Ro is greater than unity, then the infected equilibrium is globally asymptotically stable by constructing suitable Lyapunov functionals. The results obtained show that the global dynamics are completely determined by the basic reproduction number R 0 .