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

摘要： 对机器的更新换代对蠕虫传播、演化等动力学行为的影响进行了研究,给出了一个蠕虫传播模型,运用动力学分析方法得到了模型的平衡态及其稳定性条件,并进行了仿真验证。理论分析与仿真结果均表明,机器更新会导致蠕虫的持续。仿真结果还表明,机器更换率对蠕虫的传播具有双重影响。在基本再生数的指导下,通过提高防病毒系统预装率,能减弱机器更新带来的负面影响,并能有效抑制蠕虫的传播。

关键词: 网络安全, 蠕虫, 机器更换率, 平衡态, 稳定性, 动力系统