关键词: 网络安全, 蠕虫, 机器更换率, 平衡态, 稳定性, 动力系统

Abstract: The updating of computers has great impact on the dynamics of worms. To contain the propagation of worms, it is necessary to characterize this factor. A model was proposed in this paper, which took account of the influence of computer updating. Furthermore, the model's equilibria and their stability conditions were obtained mathematically and then verified by simulations. The analytical and simulated results show that the updating of computers can lead to the persistence of worms, which will die out otherwise. The simulation results also show that the updating rate has bi-effects on the spreading of worms. Under the guidance of basic reproduction number, the negative effect can be alleviated and worms can be terminated by introducing a anti-virus system of high initial installation rate.

Key words: network security, worm, updating rate of computer, equilibrium, stability, dynamical system