A Differential Equation Model of HIV Infection of CD4+ T‐Cells with Delay

Abstract

An epidemic model of HIV infection of CD4 + T‐cells with cure rate and delay is studied. We include a baseline ODE version of the model, and a differential‐delay model with a discrete time delay. The ODE model shows that the dynamics is completely determined by the basic reproduction number R 0 < 1. If R 0 < 1, the disease‐free equilibrium is asymptotically stable and the disease dies out. If R 0 > 1, a unique endemic equilibrium exists and is globally stable in the interior of the feasible region. In the DDE model, the delay stands for the incubation time. We prove the effect of that delay on the stability of the equilibria. We show that the introduction of a time delay in the virus‐to‐healthy cells transmission term can destabilize the system, and periodic solutions can arise through Hopf bifurcation.