Qualitative analysis for a delayed epidemic model with latent and breaking-out over the Internet

Abstract

We generalize a delayed computer virus model, known as the SLBQRS model in a computer network, by introducing the time delay due to the period that the antivirus software uses to clean viruses in the breaking out computers and the quarantined computers. By choosing the delay as the parameter, we prove the existence of a Hopf bifurcation as the delay crosses a critical value. Moreover, we study properties of the Hopf bifurcation by applying the center manifold theorem and the normal form theory. Finally, we carry out numerical simulations to support the obtained theoretical conclusions.