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The optimal dynamic immunization under a controlled heterogeneous node-based SIRS model

Author

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  • Yang, Lu-Xing
  • Draief, Moez
  • Yang, Xiaofan

Abstract

Dynamic immunizations, under which the state of the propagation network of electronic viruses can be changed by adjusting the control measures, are regarded as an alternative to static immunizations. This paper addresses the optimal dynamical immunization under the widely accepted SIRS assumption. First, based on a controlled heterogeneous node-based SIRS model, an optimal control problem capturing the optimal dynamical immunization is formulated. Second, the existence of an optimal dynamical immunization scheme is shown, and the corresponding optimality system is derived. Next, some numerical examples are given to show that an optimal immunization strategy can be worked out by numerically solving the optimality system, from which it is found that the network topology has a complex impact on the optimal immunization strategy. Finally, the difference between a payoff and the minimum payoff is estimated in terms of the deviation of the corresponding immunization strategy from the optimal immunization strategy. The proposed optimal immunization scheme is justified, because it can achieve a low level of infections at a low cost.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:450:y:2016:i:c:p:403-415
    DOI: 10.1016/j.physa.2016.01.026
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    References listed on IDEAS

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    1. Ren, Jianguo & Yang, Xiaofan & Yang, Lu-Xing & Xu, Yonghong & Yang, Fanzhou, 2012. "A delayed computer virus propagation model and its dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 45(1), pages 74-79.
    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.
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    Citations

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    Cited by:

    1. Yonghong Xu & Jianguo Ren, 2016. "Propagation Effect of a Virus Outbreak on a Network with Limited Anti-Virus Ability," PLOS ONE, Public Library of Science, vol. 11(10), pages 1-15, October.
    2. Jichao Bi & Lu-Xing Yang & Xiaofan Yang & Yingbo Wu & Yuan Yan Tang, 2018. "A tradeoff between the losses caused by computer viruses and the risk of the manpower shortage," PLOS ONE, Public Library of Science, vol. 13(1), pages 1-12, January.
    3. 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.
    4. 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.
    5. Rodrigo Matos Carnier & Yue Li & Yasutaka Fujimoto & Junji Shikata, 2024. "Deriving Exact Mathematical Models of Malware Based on Random Propagation," Mathematics, MDPI, vol. 12(6), pages 1-28, March.
    6. Ren, Jianguo & Xu, Yonghong, 2017. "A compartmental model for computer virus propagation with kill signals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 446-454.
    7. Pan, Cheng & Yang, Lu-Xing & Yang, Xiaofan & Wu, Yingbo & Tang, Yuan Yan, 2018. "An effective rumor-containing strategy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 500(C), pages 80-91.
    8. Li, Pengdeng & Yang, Xiaofan & Yang, Lu-Xing & Xiong, Qingyu & Wu, Yingbo & Tang, Yuan Yan, 2018. "The modeling and analysis of the word-of-mouth marketing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 493(C), pages 1-16.
    9. Yang, Dingda & Liao, Xiangwen & Shen, Huawei & Cheng, Xueqi & Chen, Guolong, 2018. "Dynamic node immunization for restraint of harmful information diffusion in social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 640-649.
    10. Piqueira, José Roberto C. & Cabrera, Manuel A.M. & Batistela, Cristiane M., 2021. "Malware propagation in clustered computer networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 573(C).
    11. Li, Pengdeng & Yang, Xiaofan & Wu, Yingbo & He, Weiyi & Zhao, Pengpeng, 2018. "Discount pricing in word-of-mouth marketing: An optimal control approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 512-522.
    12. Kar, T.K. & Nandi, Swapan Kumar & Jana, Soovoojeet & Mandal, Manotosh, 2019. "Stability and bifurcation analysis of an epidemic model with the effect of media," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 188-199.

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