Global properties of delayed-HIV dynamics models with differential drug efficacy in cocirculating target cells

The objective of this work is to investigate the qualitative behaviors of three HIV dynamical models with two types of cocirculating target cells and intracellular discrete time delay. In the two types of target cells, the drug efficacy is assumed to be different. The models take into account both short-lived infected cells and long-lived chronically infected cells. The incidence rate of infection is given by bilinear and saturation functional response in the first and second model, respectively, while it is given by a general function in the third model. Lyapunov functionals are constructed and LaSalle’s invariance principle is applied to prove the global asymptotic stability of all equilibria of the models. In the first two models, we have derived the basic reproduction number R0. It has been proven that the disease-free equilibrium is globally asymptotically stable (GAS) when R0 ≤ 1, and the endemic equilibrium is GAS when R0 > 1. For the third model, we have derived R0 and established a set of sufficient conditions for global stability of both disease-free and endemic equilibria of the model. At the end theoretical results have been checked by numerical simulations.