【摘要】 针对经典SIRS(易感-感染-免疫-易感)模型中没有考虑到网络拓扑结构发生变化的情况,提出了一种网络拓扑结构发生变化的SIRS改进模型,其利用李雅普诺夫稳定性分析方法分析得到传播阈值以及拓扑结构变化与传播过程的相关性。在传播过程中当系统满足阈值条件时,计算机病毒最终消失,从而证明了系统不满足阈值条件时地方病平衡点的存在性与唯一性,并得出了满足地方病平衡点稳定的限制条件。对比仿真实验的结果验证了上述理论结果,并表明带有网络拓扑结构发生变化的SIRS模型比已有的SIRS模型更加逼近现实生活中计算机病毒的传播过程。更多还原

【Abstract】 This paper proposed an improved model to tackle the problem that the network topology changes is not considered in the classic SIRS(Susceptible-infected-recovered-susceptible) model.The threshold and the correlation between the topology and transmission process are deduced by Lyapunov stability theory.In the spread process of virus,computer virus will disappear ultimately when the system meets the threshold condition,which proves that there exists an equilibrium point of local virus when the system does not meet the threshold condition,and from which the limiting conditions for stability of the equilibrium point is also reached.Simulated experiment results indicate that the theoretical conclusions are valid and the SIRS model with network topology changes can simulate the spread process of actual computer virus better than the existing SIRS model.更多还原