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Investigation of dynamics of a virus–antivirus model in complex network

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  • Ren, Jianguo
  • Xu, Yonghong
  • Liu, Jiming

Abstract

In this paper, a new model of computer virus–antivirus propagation dynamics based on the topology nature of the Internet is established. We analyze theoretically the complex dynamics of the model and it is found that, unlike the existing models, the model admits two virus-free equilibria and possesses possibly two virus equilibria: one being antivirus-independent and the other being antivirus-dependent. Furthermore, the stability of virus-free equilibria is analyzed via a threshold value associated with the topology of the Internet and the model parameters. It is established that, if the threshold value is less than or equal to the unity, the virus-free equilibria are alternatively globally attractive, resulting in virus eradication, while if the threshold value is greater than unity, the antivirus-independent virus equilibrium is globally asymptotically stable, leading to virus diffusion, while the antivirus-dependent virus equilibrium also is globally asymptotically stable. Some numerical examples are presented to illustrate the analytical results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:421:y:2015:i:c:p:533-540
    DOI: 10.1016/j.physa.2014.11.019
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    Citations

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    Cited by:

    1. Zhang, Tianrui & Yang, Lu-Xing & Yang, Xiaofan & Wu, Yingbo & Tang, Yuan Yan, 2017. "Dynamic malware containment under an epidemic model with alert," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 470(C), pages 249-260.
    2. 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.
    3. 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.

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