Stability and Bifurcation Analysis of a Viral Infection Model with Delayed Immune Response∗

In this paper, we study a viral infection model with an immunity time delay accounting for the time between the immune system touching antigenic stimulation and generating CTLs. By calculation, we derive two thresholds to determine the global dynamics of the model, i.e., the reproduction number for viral infection R0 and for CTL immune response R1. By analyzing the characteristic equation, the local stability of each feasible equilibrium is discussed. Furthermore, the existence of Hopf bifurcation at the CTL-activated infection equilibrium is also studied. By constructing suitable Lyapunov functionals, we prove that when R0 ≤ 1, the infection-free equilibrium is globally asymptotically stable; when R0 > 1 and R1 ≤ 1, the CTLinactivated infection equilibrium is globally asymptotically stable; Numerical simulation is carried out to illustrate the main results in the end.