Stability and Hopf bifurcation of a HIV infection model with CTL-response delay

In this paper, we consider a HIV infection model with CTL-response delay and analyze the effect of time delay on stability of equilibria. We obtain the global stability of the infection-free equilibrium and give sufficient conditions for the local stability of the CTL-absent equilibrium and CTL-present equilibrium. By choosing the CTL-response delay ττ as a bifurcation parameter, we prove that the CTL-present equilibrium is locally asymptotically stable in a range of delays and a Hopf bifurcation occurs as ττ crosses a critical value. Numerical simulations are given to support the theoretical results.