A delayed SLB computer virus propagation model with infectivity in latent period is proposed in this paper. We establish sufficient conditions for local stability of the positive equilibrium and existence of Hopf bifurcation by analyzing distribution of the roots of the associated characteristic equation and applying the Hopf bifurcation theorem. Furthermore, properties of the Hopf bifurcation are determined by using the normal form theory and the center manifold theorem. Finally, numerical simulations supporting the theoretical analysis are carried out.

Due to their striking features such as destruction, polymorphism, and unpredictability [

In recent years, people have paid attention to the necessity of monitoring computer viruses in the Internet and proposed many mathematical models to depict the spread of computer viruses in the Internet based on the classic epidemic models [

However, system (

The remainder of this paper is organized as follows. Local stability and existence of Hopf bifurcation for system (

According to the analysis in [

Obviously, if condition

For

From the analysis above, we know that if the coefficients of system (

If condition

And then, we will verify the transversality condition. From (

It is clear that if condition

If conditions

In the previous section, we have obtained the conditions under which a Hopf bifurcation occurs and a family of periodic solutions bifurcate from the positive equilibrium

Let

Then,

For

By the discussion in the previous section, we know that

On the other hand, since

In the remainder of this section, we use the same notations as those used by Xu and He [

Define

In order to get the expression of

From (

In what follows, we will find out

From (

For system (

the sign of

the sign of

the sign of

In this section, we try to present some numerical simulations for system (

By a simple computation, we get

The phase plot of the states

The phase plot of the states

In addition, we also find that onset of the Hopf bifurcation can be delayed if the values of the parameters

A new epidemic model of computer virus with time delay has been proposed in this paper. Compared with the model considered in the literature [

It is found that when the value of the time delay is below the critical value

The authors declare that there are no competing interests regarding the publication of this paper.

This research was supported by the Natural Science Foundation of Anhui Province (nos. 1608085QF145 and 1608085QF151) and the Natural Science Foundation of the Higher Education Institutions of Anhui Province (no. KJ2015A144).