Stability Analysis of a SEIQRS Model with Graded Infection Rates for Internet Worms

Abstract

Internet worms have drawn a significant attention owing to their enormous threats to the Internet infrastructure and services. In order to effectively defend against them, this paper proposes a novel epidemic SEIQRS model with graded infection rates for Internet worms. Using this SEIQRS model, we obtain the basic reproduction number for determining whether the worm dies out completely. The global stabilities of worm-free equilibrium and endemic equilibrium are proved, and determined by the basic reproduction number. The impact of different parameters of this model is studied. Simulation results show that the number of susceptible and infected hosts are consistent with theoretical analysis. The model provides a theoretical foundation for control and forecasting for Internet worms.