Abstract
A delayed SEIQRS-V model with quarantine describing the dynamics of worm propagation is considered in the present paper. Local stability of the endemic equilibrium is addressed and the existence of a Hopf bifurcation at the endemic equilibrium is established by analyzing the corresponding characteristic equation. By means of the normal form theory and the center manifold theorem, properties of the Hopf bifurcation at the endemic equilibrium are investigated. Finally, numerical simulations are also given to support our theoretical conclusions.
Highlights
A computer worm is a self-contained program that can spread functional copies of itself or its segments to other systems without depending on another program to host its code [, ]
Theorem For system ( ), if the conditions (H )-(H ) hold, the endemic equilibrium P∗(S∗, E∗, I∗, Q∗, R∗, V∗) is asymptotically stable for τ ∈ [, τ ); a Hopf bifurcation occurs at the endemic equilibrium P∗(S∗, E∗, I∗, Q∗, R∗, V∗) when τ = τ and a family of periodic solutions bifurcate from the endemic equilibrium P∗(S∗, E∗, I∗, Q∗, R∗, V∗) near τ = τ
5 Conclusions Based on the fact that one of the significant features of computer viruses is its latent characteristic, we incorporate the latent period delay into the model considered in the literature [ ] and obtain the delayed SEIQRS-V model describing the worms propagation in a network
Summary
A computer worm is a self-contained program that can spread functional copies of itself or its segments to other systems without depending on another program to host its code [ , ]. Many researchers introduce the quarantine strategy into mathematical models to investigate the spread of the worms in a network [ – ]. In order to describe the dynamics of worm propagation in a network, Kumar et al proposed the following SEIQRS-V model in [ ]:
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