Modified HIV-1 infection model with delay in saturated CTL immune response

Abstract

We propose a HIV-1 dynamics model with CTL immune response and both infected and immune cell infections. Both actively infected cells and immune cells are incorporated with two time delays. The infected-susceptible and immune-susceptible infection rates are given by saturated incidence. By calculation, we obtain immunity-inactivated reproduction number R₀ and immunity-activated reproduction number R₁. By analyzing the distribution of roots of the corresponding characteristic equations, we study the local stability of an infection-free equilibrium, an immunity-inactivated equilibrium and an immunity-activated equilibrium of the model. We discuss the persistence theory for addressing the long term survival of all components of system.