A delayed computer virus propagation model and its dynamics

Highlights: ► Analyze local stability of virus-free and virus equilibrium under no restriction. ► Prove global stability, global attractiveness of virus-free equilibrium. ► Prove that Hopf bifurcation may occur and corresponding critical value is obtained. ► Obtain a sufficient criterion for global stability of virus equilibrium with delays. - Abstract: In this paper, we propose a delayed computer virus propagation model and study its dynamic behaviors. First, we give the threshold value R0 determining whether the virus dies out completely. Second, we study the local asymptotic stability of the equilibria of this model and it is found that, depending on the time delays, a Hopf bifurcation may occur in the model. Next, we prove that, if R0 = 1, the virus-free equilibrium is globally attractive; and when R0 < 1, it is globally asymptotically stable. Finally, a sufficient criterion for the global stability of the virus equilibrium is obtained.