Effects of a Discrete Time Delay on an HIV Pandemic

We investigate the effects of a discrete time delay on the disease progression of a human immunodeficiency virus (HIV) pandemic. We consider a model of the cell-free viral spread of HIV in a well-mixed compartment such as the bloodstream. A discrete time delay is introduced to take into account the time between the infection of a CD4(+) T cell and the emission of viral particles at the cellular level. We first investigate the effects of the delay on the virulence of the HIV strains. We derive an analytical expression of the evolutionary stable strategy (ESS), and characterize how changes in the delay could alter that evolutionary optimum. Our analysis will show that the ESS of the HIV strains does not depend on the delay; however, the virulence of the HIV strains may increase as a consequence of increasing the delay time. We then present an analytic stability analysis of the endemically infected equilibrium. We also present a novel numerical analysis of the stability and bifurcation process of the same equilibrium using numerical tools. With the numerical methods, we are able to reach the same conclusion as reached analytically.