网络节点增减下的潜伏型病毒传播行为建模研究  

Research on Modeling of Latent Virus Propagation Behavior with Increasing or Decreasing Network Nodes

作　　者：王刚[1] 陆世伟 冯云 刘文斌 马润年[1] WANG Gang;LU Shi-wei;FENG Yun;LIU Wen-bin;MA Run-nian(Information and Navigation Institute,Air Force Engineering University,Xi’an,Shaanxi 710077,China;Institute of Computing Technology,Guangzhou University,Guangzhou,Guangdong 510006,China)

机构地区：[1]空军工程大学信息与导航学院,陕西西安710077 [2]广州大学计算科技研究院,广东广州510006

出　　处：《电子学报》2022年第2期273-283,共11页Acta Electronica Sinica

基　　金：国家自然科学基金(No.62072128);国家自然科学基金青年基金(No.61573017,No.61902426)。

摘　　要：研究潜伏型网络病毒的传播行为有助于预先设计合理的防御策略,防止病毒传播对网络造成危害,维护网络的安全.本文以潜伏型病毒传播行为为基础,综合考虑病毒传播存在潜伏期的特点以及网络节点增加与移除的情况,构建了节点增减条件下含时滞项的潜伏型病毒传播模型,用以探索网络节点增减条件下病毒潜伏期τ对病毒传播分岔行为的影响.此外,本文系统分析了病毒传播的平衡点及其稳定性,在此基础上讨论潜伏期时长和节点增减率对病毒传播基本再生数的影响,进而提出了避免潜伏型病毒传播出现分岔行为的方法和控制病毒传播规模的策略.理论分析和数值仿真结果表明:当基本再生数R_(0)≤1时,系统在无病毒平衡点处全局渐进稳定;当R_(0)>1时,如果病毒潜伏时滞τ小于时滞阈值τ_(0),系统在有病毒平衡点处局部渐进稳定;否则,病毒传播会出现Hopf分岔现象,在这种情况下,系统将难以控制.研究发现:在一定范围内调整网络节点的免疫率能够增大病毒在网络中传播的时滞阈值τ_(0),进而避免病毒传播出现分岔行为;在病毒传播不出现分岔行为的情况下,增大网络中易感、潜伏、感染节点的移除率,能够减小病毒在网络中的传播规模.The research on the propagation behavior of the latent network virus is helpful to design reasonable de⁃fense strategy in advance,which can prevent virus propagation from harming the network and maintain the security of the network.In the paper,the propagation behavior of latent virus is analyzed first to find the behavior of the latent virus in its incubation.By considering the increasing and decreasing network nodes,a delayed virus propagation model with the in⁃creasing or decreasing nodes is constructed to explore the influence of the virus latent periodτon the bifurcation behavior of virus propagation under the condition of increasing and removed nodes.Based on the proposed propagation model,the ba⁃sic regeneration number and stability for latent virus propagation are analyzed,and the reasonable control strategy is given to avoid the bifurcating behavior and reduce the scale of the virus propagation.Theoretical analysis and numerical simula⁃tion results show that when the basic regeneration number R_(0)≤1,the system is globally asymptotically stable at the virusfree equilibrium point;When R_(0)>1,if the latent period of virusτis less than the delay thresholdτ0,the system is locally as⁃ymptotically stable at the virus-free equilibrium point;otherwise,the system will appear Hopf bifurcation,and in this case the system will be challenging to control.It is demonstrated that increasing the immune rate of network nodes to the virus within limits can increase the delay threshold,and reduce the possibility of bifurcations in virus propagation;when the virus propagation in the network is stable,increasing the removal rate of susceptible,latent,and infected nodes can reduce the scale of virus propagation in the network.

关 键 词：网络安全 节点增减 网络病毒传播 潜伏时滞 全局稳定性 HOPF分岔 

分 类 号：TP309[自动化与计算机技术—计算机系统结构]