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Stability analysis of a worm propagation model with partial immunization

Fangwei Wang, Yong Yang, Dongmei Zhao, Yunkai Zhang

Internet worm attacks the Internet infrastructure, reduces network security and causes economic losses. In order to effectively defend against worms, this paper proposes a novel epidemic SVEIR model with partial immunization. Using this SVEIR model, we obtain the basic reproduction number for determining whether the worm dies out completely. The global stability of worm-free equilibrium is proven using a Lyapunov function. By the use of Hurwitz criterion, the local stability of the unique endemic equilibrium is proven. 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.