Analysis of Two-Worm Interaction Model in Heterogeneous M2M Network

Abstract

With the rapid development of M2M (Machine-to-Machine) networks, the damages caused by malicious worms are getting more and more serious. By considering the influences of the network heterogeneity on worm spreading, we are the first to study the complex interaction dynamics between benign worms and malicious worms in heterogeneous M2M network. We analyze and compare three worm propagation models based on different immunization schemes. By investigating the local stability of the worm-free equilibrium, we obtain the basic reproduction number R0 . Besides, by using suitable Lyapunov functions, we prove that the worm-free equilibrium is globally asymptotically stable if R0 ≤ 1 , otherwise unstable. The dynamics of worm models is completely determined by R0 . In the absence of birth, death and users’ treatment, we obtain the final size formula of worms. This study shows that the nodes with higher node degree are more susceptible to be infected than those with lower node degree. In addition, the effects of various immunization schemes are studied. Numerical simulations verify our theoretical results. The research results are meaningful for us to further understand the spread of worms in heterogeneous M2M network, and enact effectual control tactics.