Abstract
In this paper, we investigate an SLBRS computer virus model with time delay and impact of antivirus software. The proposed model considers the entering rates of all computers since every computer can enter or leave the Internet easily. It has been observed that there is a stability switch and the system becomes unstable due to the effect of the time delay. Conditions under which the system remains locally stable and Hopf bifurcation occurs are found. Sufficient conditions for global stability of endemic equilibrium are derived by constructing a Lyapunov function. Formulae for the direction, stability, and period of the bifurcating periodic solutions are conducted with the aid of the normal form theory and center manifold theorem. Numerical simulations are carried out to analyze the effect of some of the parameters in the system on the dynamic behavior of the system.
Highlights
Computer viruses are programs created to carry out activities in a computer without consent of its owner
For system ( ), if (H1)-(H3) hold, E∗(S∗, L∗, B∗, R∗) is locally asymptotically stable when τ ∈ [0, τ0); system ( ) undergoes a Hopf bifurcation at E∗(S∗, L∗, B∗, R∗) when τ = τ0 and a family of periodic solutions bifurcate from E∗(S∗, L∗, B∗, R∗). τ0 is defined as in ( )
A delayed SLBRS computer virus model is presented by incorporating the time delay due to the temporary immunity period of the recovered computers based on the model proposed in [27]
Summary
Computer viruses are programs created to carry out activities in a computer without consent of its owner. In [9], Hosseini et al formulated a discrete-time SEIRS model of computer virus propagation in scale-free networks and analyzed the local and global stability of the model. In [10], Ren and Xu investigated an SEIR-KS computer virus propagation model based on the kill signals They studied the local and global stability of the model by applying Routh-Hurwitz criterion and Lyapunov functional method. To overcome the above-mentioned defect, computer virus models with infectivity in latent period have received much attention in recent years [21,22,23,24,25,26]. Considering the temporary immune period of the recovered computers, we incorporate the time delay due to the temporary immunity period into system (1) and obtain the following delayed model:.
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