Global properties of HIV infection models with nonlinear incidence rate and delay-discrete or distributed.

In this paper, we study the global properties of two mathematical models which describe the interaction of the human immunodeficiency virus (HIV) with two classes of target cells, CD4+ T cells and macrophages. The incidence rate of virus infection is given by the Crowley-Martin functional response. The first model has two types of discrete delays while the second one incorporates two types of distributed delays to describe the time needed for infection of cell and virus replication. The basic reproduction number R0 is identified which completely determines the global dynamics of the models. By constructing suitable Lyapunov functionals, we have proven that if R0 ≤ 1 then the uninfected steady state is globally asymptotically stable (GAS), and if R0 > 1 then the infected steady state exists and it is GAS. [ABSTRACT FROM AUTHOR]