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Optimal Control Strategy for SLBRS with Two Control Inputs

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  • Xiangqing Zhao

    (Department of Mathematics, Suqian University, Suqian 223800, China)

Abstract

Computer virus attacks result in significant losses each year, drawing considerable attention from enterprises, governments, academic institutions, and various other sectors. Researchers have proposed various approaches to fight against computer viruses, including antivirus software and internet firewalls. In this paper, we focus on investigating computer virus transmission from the perspective of mathematical modeling. Our main contributions in this paper are threefold: (1) we improve the classical SLBRS model by incorporating cure rates, effectively capturing the dynamics of computer network maintenance; (2) we introduce an optimal control system within the SLBRS framework, with the dual objectives of minimizing network detoxification costs and reducing the proportion of broken-out nodes; and (3) by employing Pontryagin’s Maximum Principle, we establish the existence and uniqueness of an optimal control strategy for the proposed control system. Furthermore, we perform numerical simulations to demonstrate the effectiveness of our theoretical analyses.

Suggested Citation

  • Xiangqing Zhao, 2023. "Optimal Control Strategy for SLBRS with Two Control Inputs," Mathematics, MDPI, vol. 11(19), pages 1-10, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:19:p:4036-:d:1245952
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    References listed on IDEAS

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    1. Zhang, Chunming & Huang, Haitao, 2016. "Optimal control strategy for a novel computer virus propagation model on scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 451(C), pages 251-265.
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    Cited by:

    1. Xiangqing Zhao & Wanmei Hou, 2023. "Optimal Control of SLBRS with Recovery Rates," Mathematics, MDPI, vol. 12(1), pages 1-16, December.

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