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Global attractivity and optimal dynamic countermeasure of a virus propagation model in complex networks

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  • Zhang, Xulong
  • Gan, Chenquan

Abstract

This paper aims to study the combined impact of countermeasure and network topology on virus diffusion and optimal dynamic countermeasure. A novel heterogenous propagation model and its optimal control problem are proposed and analyzed. Qualitative analysis shows that the unique equilibrium of the proposed model is globally attractive and the optimal control problem has an optimal control. Some simulation experiments are also performed. Specifically, it is found that our obtained results are contrary to some previous results and countermeasure dissemination to higher-degree nodes is more effective than that to lower-degree nodes. The related explanations are also made. This indicates that countermeasures and network topology play an important role in suppressing viral spread.

Suggested Citation

  • Zhang, Xulong & Gan, Chenquan, 2018. "Global attractivity and optimal dynamic countermeasure of a virus propagation model in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 1004-1018.
    • Handle: RePEc:eee:phsmap:v:490:y:2018:i:c:p:1004-1018
    DOI: 10.1016/j.physa.2017.08.085
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    References listed on IDEAS

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    1. Yang, Lu-Xing & Draief, Moez & Yang, Xiaofan, 2016. "The optimal dynamic immunization under a controlled heterogeneous node-based SIRS model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 403-415.
    2. Chen, Lijuan & Hattaf, Khalid & Sun, Jitao, 2015. "Optimal control of a delayed SLBS computer virus model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 427(C), pages 244-250.
    3. Ren, Jianguo & Xu, Yonghong & Liu, Jiming, 2015. "Investigation of dynamics of a virus–antivirus model in complex network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 533-540.
    4. Zhang, Chunming & Huang, Haitao, 2016. "Optimal control strategy for a novel computer virus propagation model on scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 451(C), pages 251-265.
    5. Yang, Lu-Xing & Yang, Xiaofan, 2013. "The effect of infected external computers on the spread of viruses: A compartment modeling study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(24), pages 6523-6535.
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    Cited by:

    1. Chorozoglou, D. & Kugiumtzis, D. & Papadimitriou, E., 2018. "Testing the structure of earthquake networks from multivariate time series of successive main shocks in Greece," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 499(C), pages 28-39.
    2. Liao, Shi-Gen & Yi, Shu-Ping, 2021. "Modeling and analysis knowledge transmission process in complex networks by considering internalization mechanism," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).

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