Global stability analysis of a delayed HIV model with saturated infection rate

Laboratory of Mathematics and Applications, Faculty of Sciences and Technologies, University Hassan II of Casablanca, PO Box 146, Mohammedia, Morocco

^a e-mail: jaouaddanane@gmail.com
^b e-mail: allali@hotmail.com

Abstract

In this paper, the global stability of a delayed HIV model with saturated infection rate infection is investigated. We incorporate two discrete delays into the model; the first describes the intracellular delay in the production of the infected cells, while the second describes the needed time for virions production. We also derive the global properties of this two-delay model as function of the basic reproduction number R₀. By using some suitable Lyapunov functions, it is proved that the free-equilibrium point is globally asymptotically stable when R₀ ≤ 1, and the endemic equilibrium point is globally asymptotically stable when R₀ ≥ 1. Finally, in order to support our theoretical findings we have illustrate some numerical simulations.