Stability and Hopf bifurcation in a delayed model for HIV infection of CD4þ T cells

In this paper, we consider a delayed mathematical model for the interactions of HIV infection and CD4þ T cells. We first investigate the existence and stability of the Equilibria. We then study the effect of the time delay on the stability of the infected equilibrium. Criteria are given to ensure that the infected equilibrium is asymptotically stable for all delay. Moreover, by applying Nyquist criterion, the length of delay is estimated for which stability continues to hold. Finally by using a delay s as a bifurcation parameter, the existence of Hopf bifurcation is also investigated. Numerical simulations are presented to illustrate the analytical results.