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

Gang WANG; Shi-wei LU; Yun FENG; Wen-bin LIU; Run-nian MA

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

更新时间：2022-02-08

- Research on Modeling of Latent Virus Propagation Behavior with Increasing or Decreasing Network Nodes
- ACTA ELECTRONICA SINICA Pages: 1-11(2022)
- 作者机构：
  
  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
- 作者简介：
- 基金信息：
- DOI：
  CLC： TP309;
- Received：22 May 2020，
  
  Revised：2021-06-22，
  
  Published Online：08 February 2022，
- 稿件说明：
移动端阅览
Gang WANG, Shi-wei LU, Yun FENG, et al. Research on Modeling of Latent Virus Propagation Behavior with Increasing or Decreasing Network Nodes[J/OL]. ACTA ELECTRONICA SINICA, 2022, 1-11.
DOI：

Gang WANG, Shi-wei LU, Yun FENG, et al. Research on Modeling of Latent Virus Propagation Behavior with Increasing or Decreasing Network Nodes[J/OL]. ACTA ELECTRONICA SINICA, 2022, 1-11. DOI：

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.论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

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对病毒传播分岔行为的影响.此外，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

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时，系统在无病毒平衡点处全局渐进稳定；当

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时，如果病毒潜伏时滞

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小于时滞阈值

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，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

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，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.

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

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on the bifurcation behavior of virus propagation under the condition of increase or removal 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 of virus propagation and reduce the scale of the virus propagation. Theoretical analysis and numerical simulation results show that when the basic regeneration number

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the system is globally asymptotically stable at the virus-free equilibrium point; When

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if the latency of virus

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is less than the delay threshold

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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.

关键词

Keywords

references

张恒巍 , 李涛 , 黄世锐 . 基于攻防微分博弈的网络安全防御决策方法 [J]. 电子学报 , 2018 , 46 ( 6 ): 1428 - 1435 .

ZHANG H W , LI T , HUANG S R . Network defense decision-making method based on attack-defense differential game [J]. Acta Electronica Sinica , 2018 , 46 ( 6 ): 1428 - 1435 . (in Chinese)

黄健明 , 张恒巍 . 基于随机演化博弈模型的网络防御策略选取方法 [J]. 电子学报 , 2018 , 46 ( 9 ): 2222 - 2228 .

HUANG J M , ZHANG H W . A method for selecting defense strategies based on stochastic evolutionary game Model [J]. Acta Electronica Sinica , 2018 , 46 ( 9 ): 2222 - 2228 . (in Chinese)

YANG X Q , WEI K J , MA H Q , et al . Trojan horse attacks on counterfactual quantum key distribution [J]. Physics Letters A , 2016 , 380 ( 18-19 ): 1589 - 1592 .

DABAROV A , SHARIPOV M , DADLANI A , et al . Heterogeneous projection of disruptive malware prevalence in mobile social networks [J]. IEEE Communications Letters , 2020 , 24 ( 8 ): 1673 - 1677 .

LI H J , DANIELS J J . Social significance of community structure: Statistical view [J]. Physical Review E , 2015 , 91 ( 1 ): 012801 .

LI H J , WANG Q , LIU S F , et al . Exploring the trust management mechanism in self-organizing complex network based on game theory [J]. Physica A: Statistical Mechanics and its Applications , 2020 , 542 : 123514 .

KEPHART J O , WHITE S R . Directed-graph epidemiological models of computer viruses [C]// Proceedings of fourth annual computer virus and security conference . New York : IEEE , 1991 , 66 - 87 .

LIU L J , WEI X D , ZHANG N M . Global stability of a network-based SIRS epidemic model with nonmonotone incidence rate [J]. Physica A: Statistical Mechanics and its Applications , 2018 , 515 : 587 - 599 .

CAI Y L , KANG Y , WANG W M . A stochastic SIRS epidemic model with nonlinear incidence rate [J]. Applied Mathematics and Computation , 2017 , 305 : 221 - 240 .

李黎 , 张瑞芳 , 杜娜娜 , 柳寰宇 . 基于有限临时删边的病毒传播控制策略 [J]. 南京大学学报(自然科学) , 2019 , 55 ( 4 ): 651 - 659 .

LI L , ZHANG R F , DU N N , LIU H Y . Virus propagation control strategy based on limited temporary links removed [J]. Journal of Nanjing University (Natural Sciences) , 2019 , 55 ( 4 ): 651 - 659 . (in Chinese)

UPADHYAY R K , KUMARI S , MISRA A K . Modeling the virus dynamics in computer network with SVEIR model and nonlinear incident rate [J]. Journal of Applied Mathematics and Computing , 2016 , 54 ( 1 ): 485 - 509 .

LANZ A , ROGERS D , ALFORD T L . An epidemic model of malware virus with quarantine [J]. Journal of Advances in Mathematics and Computer Science , 2019 , 33 ( 4 ): 1 - 10 .

王亚奇 , 蒋国平 . 考虑网络流量的无标度网络病毒免疫策略研究 [J]. 物理学报 , 2011 , 60 ( 6 ): 060202(1-8 .

WANG Y Q , JIANG G P . Epidemic immunization on scale-free networks with traffic flow [J]. Acta Physica Sinica , 2011 , 60 ( 6 ): 060202(1-8 ) . (in Chinese)

张晓潘 , 袁凌云 . 具有时滞－扩散作用的无线传感网络病毒传播模型的振荡动力学研究 [J]. 计算机科学 , 2017 , 44 ( 6 ): 400 - 404 .

ZHANG X P , YUAN L Y . Oscillatory behaviors of malware propagation model in wireless sensor networks with time delays and reaction-diffusion terms [J]. Computer Science , 2017 , 44 ( 6 ): 400 - 404 . (in Chinese)

王昕炜 , 彭海军 , 钟万勰 . 具有潜伏期时滞的时变SEIR模型的最优疫苗接种策略 [J]. 应用数学和力学 , 2019 , 40 ( 7 ): 701 - 712 .

WANG X W , PENG H J , ZHONG W X . Optimal vaccination strategies for a time-varying SEIR epidemic model with latent delay [J]. Applied Mathematics and Mechanics , 2019 , 40 ( 7 ): 701 - 712 . (in Chinese)

SONG H T , LIU S Q , JIANG W H . Global dynamics of a multistage SIR model with distributed delays and nonlinear incidence rate [J]. Mathematical Methods in the Applied Sciences , 2017 , 40 ( 6 ): 2153 - 2164 .

ZHU LIN H , GUAN G , LI Y M . Nonlinear dynamical analysis and control strategies of a network-based SIS epidemic model with time delay [J]. Applied Mathematical Modelling , 2019 , 70 : 512 - 531 .

关治洪 , 亓玉娟 , 姜晓伟 , 等 . 基于复杂网络的病毒传播模型及其稳定性 [J]. 华中科技大学学报(自然科学版) , 2011 , 39 ( 1 ): 114 - 119 .

GUAN Z H , QI Y J , JIANG X W , et al . Virus propagation dynamic model and stability on complex networks [J]. Journal of Huazhong University of science and Technology (Natural Science) , 2011 , 39 ( 1 ): 114 - 119 . (in Chinese)

王刚 , 陆世伟 , 胡鑫 , 等 . “去二存一”混合机制下的病毒扩散模型及稳定性分析 [J]. 电子与信息学报 , 2019 , 41 ( 3 ): 709 - 716 .

WANG G , LU S W , HU X , et al . Virus propagation model and stability under the hybrid mechanism of "two-go and one-live " [J]. Journal of Electronics & Information Technology , 2019 , 41 ( 3 ): 709 - 716 . (in Chinese)

王刚 , 陆世伟 , 胡鑫 , 等 . 潜伏机制下网络病毒传播SEIQRS模型及稳定性分析 [J]. 哈尔滨工业大学学报 , 2019 , 51 ( 5 ): 131 - 137 .

WANG G , LU S W , HU X , et al . Network virus spreading SEIQRS model and its stability under escape mechanism [J]. Journal of Harbin Institute of Technology , 2019 , 51 ( 5 ): 131 - 137 . (in Chinese)

LI C , LIAO X F . The impact of hybrid quarantine strategies and delay factor on viral prevalence in computer networks [J]. Mathematical Modelling of Natural Phenomena , 2016 , 11 ( 4 ): 105 - 119 .

OMATA K . Nonequilibrium statistical mechanics of a susceptible-infected-recovered epidemic model [J]. Physical Review E , 2017 , 96 ( 2 ): 022404(1-5 .

王克 , 范猛 . 泛函微分方程的相空间理论及应用 [M]. 北京 : 科学出版社 , 2009 : 237 .

YUAN Y , BÉLAIR J . Stability and hopf bifurcation analysis for functional differential equation with distributed delay [J]. SIAM Journal on Applied Dynamical Systems , 2011 , 10 ( 2 ): 551 - 581 .

张子振 , 储煜桂 , KUMARI S. , 等 . 一类具有非线性发生率的无线传感网络蠕虫传播模型的延迟动力学行为 [J]. 浙江大学学报(理学版) , 2019 , 46 ( 02 ): 168 - 186 .

ZHANG Z Z , CHU Y G , KUMARI S , et al . Delay dynamics of worm propagation model with non-linear incidence rates in wireless sensor network . Journal of Zhejiang University (Science Edition) , 2019 , 46 ( 2 ): 168 - 186 . (in Chinese)

LESKOVEC J , KLEINBERG J , FALOUTSOS C . SNAP Datasets: Stanford Large Network Dataset Collection . [OL]. 2007 [ 2021-12-10 ]. http://snap.stanford.edu/data/p2p-Gnutella05.html http://snap.stanford.edu/data/p2p-Gnutella05.html .

WANG F W , HUANG W Y , SHEN Y L , et al . Analysis of SVEIR worm attack model with saturated incidence and partial immunization [J]. Journal of Communications and Information Networks , 2016 , 1 ( 4 ): 105 - 115 .

DAI Y X , LIN Y P , ZHAO H T , et al . Global stability and Hopf bifurcation of a delayed computer virus propagation model with saturation incidence rate and temporary immunity [J]. International Journal of Modern Physics B , 2016 , 30 ( 28 ): 1640009(1-24 .

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