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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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    Citations

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    Cited by:

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    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.
    3. 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.
    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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