The stability of a worm propagation model with nonlinear incidence rate on complex networks

摘要

There has been a constant barrage of worms over the internet during the recent past. In order to develop appropriate tools for thwarting quick spread of worms, researchers are trying to understand the behavior of the worm propagation with the aid of epidemiological models. In this study, A SIQRS (susceptible-infected-quarantined-removed-susceptible) model with nonlinear incidence rate for the worm propagation on complex networks is presented. Using the mean field theory and the Lyapunov stability theory, the existence of the threshold and how the threshold of this model is concerned with the topology of networks is analyzed, the conditions to the existence of the disease-free equilibrium is established, and globally asymptotically stable of the disease-free equilibrium is studied. We have also analyzed the effect of quarantine on infected nodes in this paper.