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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

Mathematical models have been proven valuable in understanding the population dynamics of viral load in vivo. A proper model may play significant role in a better understanding of the disease and the various drug therapy strategies. Viral infection models have received great attention in recent years [

Recently, there have been a lot of papers on virus dynamics within host; some include the immune response directly [

Time delays cannot be ignored in models for immune response. Antigenic stimulation generating CTLs may need a period of time

This paper is organized as follows. In Section

Considering the existence of the three equilibria, then we have the following conclusions.

Let

If

If

If

Under the above initial conditions (

If

The characteristic equation about

If

The characteristic equation about

If

Define the Lyapunov functional

Let

If

From Theorem

Suppose that (

Suppose the characteristic equation is the form

Let

We choose

In this section, we will study the direction of the Hopf bifurcations and stability of bifurcating periodic solutions by applying the normal theory and the center manifold theorem introduced in [

Let

For

Assume that

If

In order to demonstrate our results and find complex dynamic behavior of system (

The phase diagram of system (

If we choose the following data set:

Local asymptotic stability of the immune-exhausted equilibrium

In addition, we choose a set of parameters:

By Theorem

Stability of

A stable bifurcating periodic solution for

Stability of

A stable bifurcating periodic solution for

A bifurcation diagram in which

As shown in Figures

In this paper, we have studied a virus infection model with delayed nonlytic immune response. We obtain the sufficient and necessary conditions for the existence of the equilibria. Global stability of the infection-free equilibrium has been given by the Lyapunov-LaSalle type theorem. We find that the infection-free equilibrium

The authors declare that there is no conflict of interests regarding the publication of this paper.

^{4+}T-cells

^{+}T cells

^{+}T cells with delayed CTL response