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Stability and Optimal Control Analysis for a Fractional-Order Industrial Virus-Propagation Model Based on SCADA System

Author

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  • Luping Huang

    (College of Mathematics and Information, China West Normal University, Nanchong 637009, China)

  • Dapeng Gao

    (College of Mathematics and Information, China West Normal University, Nanchong 637009, China
    Sichuan Colleges and Universities Key Laboratory of Optimization Theory and Applications, China West Normal University, Nanchong 637009, China
    Institute of Nonlinear Analysis and Applications, China West Normal University, Nanchong 637009, China)

  • Shiqiang Feng

    (College of Mathematics and Information, China West Normal University, Nanchong 637009, China)

  • Jindong Li

    (School of Mathematical Sciences, Chengdu University of Technology, Chengdu 610059, China)

Abstract

The increasing reliance on and remote accessibility of automated industrial systems have shifted SCADA networks from being strictly isolated to becoming highly interconnected systems. The growing interconnectivity among systems enhances operational efficiency and also increases network security threats, especially attacks from industrial viruses. This paper focuses on the stability analysis and optimal control analysis for a fractional-order industrial virus-propagation model based on a SCADA system. Firstly, we prove the existence, uniqueness, non-negativity and boundedness of the solutions for the proposed model. Secondly, the basic reproduction number R 0 α is determined, which suggests the conditions for ensuring the persistence and elimination of the virus. Moreover, we investigate the local and global asymptotic stability of the derived virus-free and virus-present equilibrium points. As is known to all, there is no unified method to establish a Lyapunov function. In this paper, by constructing an appropriate Lyapunov function and applying the method of undetermined coefficients, we prove the global asymptotic stability for all possible equilibrium points. Thirdly, we formulate our system as an optimal control problem by introducing appropriate control variables and derive the corresponding optimality conditions. Lastly, a set of numerical simulations are conducted to validate the findings, followed by a summary of the overall study.

Suggested Citation

  • Luping Huang & Dapeng Gao & Shiqiang Feng & Jindong Li, 2025. "Stability and Optimal Control Analysis for a Fractional-Order Industrial Virus-Propagation Model Based on SCADA System," Mathematics, MDPI, vol. 13(8), pages 1-32, April.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:8:p:1338-:d:1638040
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    References listed on IDEAS

    as
    1. Ali, Hegagi Mohamed & Ameen, Ismail Gad, 2021. "Optimal control strategies of a fractional order model for Zika virus infection involving various transmissions," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    2. Ameen, I. & Baleanu, Dumitru & Ali, Hegagi Mohamed, 2020. "An efficient algorithm for solving the fractional optimal control of SIRV epidemic model with a combination of vaccination and treatment," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
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    4. I. Ameen & M. Hidan & Z. Mostefaoui & H.M. Ali, 2020. "Fractional Optimal Control with Fish Consumption to Prevent the Risk of Coronary Heart Disease," Complexity, Hindawi, vol. 2020, pages 1-13, February.
    5. Ali, Hegagi Mohamed & Ameen, Ismail Gad, 2020. "Save the pine forests of wilt disease using a fractional optimal control strategy," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
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