Analysis of a Viral Infection Model with Delayed Nonlytic Immune Response

Abstract EN

We investigate the dynamical behavior of a virus infection model with delayed nonlytic immune response.

By analyzing corresponding characteristic equations, the local stabilities of two boundary equilibria are established.

By using suitable Lyapunov functional and LaSalle’s invariance principle, we establish the global stability of the infection-free equilibrium.

We find that the infection free equilibrium E0 is globally asymptotically stable when R0⩽1, and the infected equilibrium without immunity E1 is local asymptotically stable when 1

Under the condition R0>1+bβ/cd we obtain the sufficient conditions to the local stability of the infected equilibrium with immunity E2.

We show that the time delay can change the stability of E2 and lead to the existence of Hopf bifurcations.

The stabilities of bifurcating periodic solutions are studied and numerical simulations to our theorems are provided.