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 R 0 < 1 , the uninfected equilibrium E 0 is globally asymptotically stable; if R 1 < 1 < R 0 , the infected equilibrium without immunity E 1 is globally asymptotically stable. When R 1 > 1 , we obtain the sufficient conditions to the local stability of the infected equilibrium with immunity E 2 . The time delay can change the stability of E 2 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.