Stability and Hopf bifurcation for a virus infection model with delayed humoral immunity response

In this paper, we investigate the dynamical behavior of a virus infection model with delayed humoral immunity. By using suitable Lyapunov functional and the LaSalleʼs invariance principle, we establish the global stabilities of the two boundary equilibria. If R0<1R0<1, the uninfected equilibrium E0E0 is globally asymptotically stable; if R1<11R1>1, we obtain the sufficient conditions to the local stability of the infected equilibrium with immunity E2E2. The time delay can change the stability of E2E2 and lead to the existence of Hopf bifurcations. The stabilities of bifurcating periodic solutions is also studied. We check our theorems with numerical simulations in the end.