Global analysis of HIV-1 dynamics with Hill type infection rate and intracellular delay

The mass action infection law, the most frequently used transmission process in the theoretical studies of disease dynamics, has been challenged in various ways. Hill type infection rate is supposed to be a better alternative to mass action law. In the first phase of this paper, we study a basic HIV model with Hill type infection rate. In the second phase, we modify our basic model with intracellular delay ττ that measures the time between the first effective contact between a virus and a healthy CD4+ T cell and the latter becomes productively infective. Mathematical results like well-posedness, permanence, local stability and global stability of both the delayed and non-delayed systems are studied. It is observed that the endemic equilibrium is locally and globally asymptotically stable if the virus replication factor is greater than a threshold value and unstable otherwise. In the latter case, the disease-free steady state occurs and is proved to be globally asymptotically stable. Our simulation results shed different insights on drug therapy when various perturbations are given to the system. It is shown that multi-blockers drug therapy is more appropriate in the treatment of HIV patients in comparison to any mono-blocker drug therapy.