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A Worm Defending Model with Partial Immunization and Its Stability Analysis

Fangwei Wang1, Yong Yang2, Dongmei Zhao1 , and Yunkai Zhang3
1.College of Information Technology, Hebei Normal University, Shijiazhuang 050024, China
2.Network and Information Center, Yunnan University, Kunming 650091, China
3.Department of Information Engineering, Shijiazhuang Institute of Railway Technology, Shijiazhuang 050091, China

Abstract—Internet worms, a great threat to the Internet infrastructure, can propagate horrendously through networks, and reduce network security and cause economic losses. In order to effectively defend against worms, this paper proposes a novel epidemic SVEIR model with partial immunization. In the SVEIR model, we obtain the basic reproduction number for determining whether the worm dies out completely. The global stabilities of infection-free equilibrium and endemic equilibrium are proven using a Lyapunov function and a geometrical approach. The impact of different parameters of this model is studied. Simulation results show that the number of susceptible and infected hosts is consistent with theoretical analysis. The model provides a theoretical foundation for control and forecasting Internet worms.

Index Terms—Network security, Internet worm, stability analysis, endemic equilibrium, partial immunization

Cite: Fangwei Wang, Yong Yang, Dongmei Zhao, and Yunkai Zhang, "A Worm Defending Model with Partial Immunization and Its Stability Analysis," Journal of Communications, vol. 10, no. 4, pp. 276-283, 2015. Doi: 10.12720/jcm.10.4.276-283