Global Dynamics for an HIV Infection Model with Crowley-Martin Functional Response and Two Distributed Delays

Abstract

In this paper, an HIV dynamics model with two distributed intracellular delays incorporating Crowley-Martin functional response infection rate is investigated. The authors take into account multiple stage disease transmission and the latently infected cells (not yet producing virus) in our system. The authors consider nonnegativity, boundedness of solutions, and global asymptotic stability of the system. By constructing suitable Lyapunov functionals and using the Lyapunov-LaSalle invariance principle, the authors prove the global stability of the infected (endemic) equilibrium and the diseasefree equilibrium for time delays. The authors have proven that if the basic reproduction number R0 is less than unity, then the disease-free equilibrium is globally asymptotically stable, and if R0 is greater than unity, then the infected equilibrium is globally asymptotically stable. The results obtained show that the global dynamic behaviors of the model are completely determined by the basic reproduction number R0 and that the time delay does not affect the global asymptotic properties of the model.