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A new computer virus propagation model with delay and incomplete antivirus ability is formulated and its global dynamics is analyzed. The existence and stability of the equilibria are investigated by resorting to the threshold value

With the rapid developments of information and communication technologies, computer has brought great convenience to our life. While enjoying the convenience from Internet, people have to confront the threat of virus intrusions. As the damaging programs, computer viruses parasitize themselves on a host mainly through the Internet and have also become an enormous threat to computers and network resources. So, understanding and predicting the dynamics of computer virus propagation are, therefore, an important pursuit. Consequently, a number of computer virus propagation models, ranging from conventional

There is something strikingly different between computer viruses and biological viruses: computer viruses in latent status possess infectivity [

One common feature shared by a computer virus is latency [

In this paper, a new computer virus propagation model, which incorporates simultaneously the above-mentioned aspects, is established. The aim is to extend and analyze the

The organization of this paper is as follows. In the next section, we present the mathematical model to be discussed. In Section

Consider the typical

By carefully considering the natures of computer virus, the following assumptions are made.

At time

Since the antivirus ability is incomplete, at time

In this section, we intended to study the dynamical behaviors of model (

It is clear that model (

When

Now, it is the turn to examine the global stability of virus-free equilibrium. The following theorem is obtained.

When

By use of the Lyapunov Direct Method, consider the following function:

Next, we examine the stability of virus equilibrium. After direct computations, the unique virus equilibrium

With

when

When

We consider the following function:

In this section, numerical simulations are carried out to support the analytical conclusion and to illustrate possible behavioral scenarios of the model. Figure

Phase diagram of

Evolutions of

Phase diagram of

Evolutions of

Evolutions of comparison of

Evolutions of

Evolutions of

Evolutions of

Appearance of periodic solutions in the case

In real networks, the outbreak of computer virus usually lags and the antivirus ability of network is not fully complete. Aiming at characterizing these situations, a new computer virus propagation model is established. By theoretical analysis, the following conclusions can be obtained.

If

If

The critical delay

When the delay

When the delay

For virus equilibrium, the larger the delay is, the longer it takes to settle down towards its steady states.

As expected, the increase of the scan rate can reduce the percentage of the breaking-out computers but increase the percentage of the latent ones, which suggests that we run the antivirus software as often as possible.

As expected, the increase of the antivirus ability of the software can reduce the percentage of the infected (latent and breaking-out) computers in the network, which suggests that we invest more in their developments.

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

This work is supported by the National Natural Science Foundation of China under Grant no. 61304117, the Natural Science Foundation of the Jiangsu Higher Education Institutions of China under Grant no. 13KJB520008, and the Doctorate Teacher Support Project of Jiangsu Normal University under Grant no. 12XLR021.