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Dynamic malware containment under an epidemic model with alert

Author

Listed:
  • Zhang, Tianrui
  • Yang, Lu-Xing
  • Yang, Xiaofan
  • Wu, Yingbo
  • Tang, Yuan Yan

Abstract

Alerting at the early stage of malware invasion turns out to be an important complement to malware detection and elimination. This paper addresses the issue of how to dynamically contain the prevalence of malware at a lower cost, provided alerting is feasible. A controlled epidemic model with alert is established, and an optimal control problem based on the epidemic model is formulated. The optimality system for the optimal control problem is derived. The structure of an optimal control for the proposed optimal control problem is characterized under some conditions. Numerical examples show that the cost-efficiency of an optimal control strategy can be enhanced by adjusting the upper and lower bounds on admissible controls.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:470:y:2017:i:c:p:249-260
    DOI: 10.1016/j.physa.2016.11.143
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    References listed on IDEAS

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    1. Yang, Meng & Chen, Guanrong & Fu, Xinchu, 2011. "A modified SIS model with an infective medium on complex networks and its global stability," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(12), pages 2408-2413.
    2. Amador, Julia, 2014. "The stochastic SIRA model for computer viruses," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 1112-1124.
    3. 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.
    4. 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.
    5. Yang, Lu-Xing & Yang, Xiaofan, 2014. "The spread of computer viruses over a reduced scale-free network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 396(C), pages 173-184.
    6. 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.
    7. Liu, Yang & Wei, Bo & Du, Yuxian & Xiao, Fuyuan & Deng, Yong, 2016. "Identifying influential spreaders by weight degree centrality in complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 86(C), pages 1-7.
    8. Hu, Jiantao & Du, Yuxian & Mo, Hongming & Wei, Daijun & Deng, Yong, 2016. "A modified weighted TOPSIS to identify influential nodes in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 73-85.
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    Cited by:

    1. 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).
    2. Xiaoyang Liu & Chao Liu & Xiaoping Zeng, 2017. "Online Social Network Emergency Public Event Information Propagation and Nonlinear Mathematical Modeling," Complexity, Hindawi, vol. 2017, pages 1-7, June.
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    4. Jose Diamantino Hernández Guillén & Ángel Martín del Rey & Roberto Casado Vara, 2020. "On the Optimal Control of a Malware Propagation Model," Mathematics, MDPI, vol. 8(9), pages 1-16, September.
    5. 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.
    6. 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.

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