Modeling and hopf bifurcation analysis of benign worms with quarantine strategy

Abstract

Since the Morris worm occurred in 1988, malwares have threatened the network persistently. With rapid development of the Internet, network security issues become increasingly serious. Recently, the benign worms become a new active countermeasure to deal with the worm threat. In this paper, we propose a compositive-hybrid benign worm propagation model with quarantine strategy. Usually, quarantine strategy will lead to a time delay, and the worm propagation system will be unstable and out of control with the time delay increases. Then the existence condition and the stability of the positive equilibrium are derived. Through our derivation and analysis, the threshold s0 of Hopf bifurcation is obtained. The system will be stable when time delay s\s0. In addition, numerical experiments are performed and the effect of benign worms is displayed by comparing with the model that do not include benign worms. Furthermore, simulation experiments are carried out to verify our conclusions..