Dynamics and Control of Worm Epidemic Based on Mobile Networks by SEIQR-Type Model with Saturated Incidence Rate

Abstract

The mobile networks have increasingly facilitated our daily life but are also breeding grounds for malicious worms, which are considered as the main threat to cyber security. The purpose of this paper is to analyze the dynamics of worm propagation and to control the worm epidemic based on mobile-phone networks. Accordingly, we establish an SEIQR-type model to explore the worm epidemic with saturated incidence rate. This paper shows that if the basic reproduction number is less than 1, the worm-free equilibrium is asymptotically stable, and the epidemic of worm will eventually disappear and remain under control; in addition, if the basic reproduction number is greater than 1, the asymptotical stability of worm-existence equilibrium is derived to imply that the epidemic will remain persistent and uncontrollable. Our results give new insights to mobile network security, namely, that is predicting the worm spreading tendency, identifying the epidemic control strategies, and estimating the worm popularity level. Numerical experiments are conducted to show the rationality of our obtained results and the effectiveness of the control strategies.