网络节点增减下的潜伏型病毒传播行为建模研究

doi:10.12263/DZXB.20200489

电子学报 ›› 2022, Vol. 50 ›› Issue (2): 273-283.DOI: 10.12263/DZXB.20200489

网络节点增减下的潜伏型病毒传播行为建模研究

王刚¹, 陆世伟¹, 冯云¹, 刘文斌², 马润年¹

^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

收稿日期:2020-05-22 修回日期:2021-06-22 出版日期:2022-02-25
- 作者简介:
- 王刚男，1976年生，湖北黄冈人.中国空军工程大学信息导航学院教授.分别于1998和2001获空军工程大学学士学位和硕士学位.2005于国防科技大学获博士学位.主要研究方向包括网络空间安全和复杂网络. E-mail: wglxl@nudt.edu.cn
  陆世伟男，1995年生，陕西汉中人.中国空军工程大学博士研究生.于2017获浙江大学计算机科学与技术学士学位，2019年获空军工程大学网络空间安全专业硕士学位.主要研究方向包括网络空间安全，病毒传播机理与防御. E-mail: 3130104597@zju.edu.cn
  冯云男，1996年生，山西长治人.空军工程大学信息导航学院的硕士研究生.于2018获北京航空航天大学计算机科学与技术学士学位.主要研究方向包括网络空间安全和计算机科学. E-mail: 13520346937@163.com
  刘文斌男，1969年生.中国广州大学计算科技研究院教授，于2004年获华中科技大学控制科学与工程专业博士学位.主要研究方向包括计算生物学、数据挖掘、模式识别、DNA计算和进化算法. E-mail: wbliu6910@126.com
  马润年男，1963年生，陕西绥德人.中国空军工程大学教授.获山东大学运筹学和控制论硕士学位，西安电子科技大学电路与系统专业博士学位.研究方向包括数学、运筹学、控制理论. E-mail: mrn314@163.com
- 基金资助:
- 国家自然科学基金 (62072128); 国家自然科学基金青年基金 (61573017)

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

WANG Gang¹, LU Shi-wei¹, FENG Yun¹, LIU Wen-bin², MA Run-nian¹

^1.Information and Navigation Institute, Air Force Engineering University, Xi’an, Shaanxi 710077, China
^2.Institute of Computing Technology, Guangzhou University, Guangzhou, Guangdong 510006, China

Received:2020-05-22 Revised:2021-06-22 Online:2022-02-25 Published:2022-02-25
- Supported by:
- National Natural Science Foundation of China (62072128); Youth Fund of National Natural Science Foundation of China (61573017)

摘要/Abstract

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.

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

Abstract:

The research on the propagation behavior of the latent network virus is helpful to design reasonable defense 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 increasing or decreasing nodes is constructed to explore the influence of the virus latent period $τ$ on the bifurcation behavior of virus propagation under the condition of increasing and removed nodes. Based on the proposed propagation model, the basic 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 simulation results show that when the basic regeneration number $R 0 ≤ 1$ , the system is globally asymptotically stable at the virus-free equilibrium point; When $R 0 > 1$ , if the latent period of virus $τ$ is less than the delay threshold $τ 0$ , the system is locally asymptotically 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.

Key words: network security, increasing and decreasing node, network virus propagation, latency delay, global stability, Hopf bifurcation

中图分类号:

TP309

王刚, 陆世伟, 冯云, 等. 网络节点增减下的潜伏型病毒传播行为建模研究[J]. 电子学报, 2022, 50(2): 273-283.

Gang WANG, Shi-wei LU, Yun FENG, et al. Research on Modeling of Latent Virus Propagation Behavior with Increasing or Decreasing Network Nodes[J]. Acta Electronica Sinica, 2022, 50(2): 273-283.

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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

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