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Optimal control of a delayed SLBS computer virus model

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  • Chen, Lijuan
  • Hattaf, Khalid
  • Sun, Jitao

Abstract

In this paper, a delayed SLBS computer virus model is firstly proposed. To the best of our knowledge, this is the first time to discuss the optimal control of the SLBS model. By using the optimal control strategy, we present an optimal strategy to minimize the total number of the breakingout computers and the cost associated with toxication or detoxication. We show that an optimal control solution exists for the control problem. Some examples are presented to show the efficiency of this optimal control.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:427:y:2015:i:c:p:244-250
    DOI: 10.1016/j.physa.2015.02.048
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Yang, Lu-Xing & Yang, Xiaofan, 2013. "The effect of infected external computers on the spread of viruses: A compartment modeling study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(24), pages 6523-6535.
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    Citations

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    2. 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.
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    4. Liliana Eva Donath & Gabriela Mircea & Mihaela Neamțu & Grațiela Georgiana Noja & Nicoleta Sîrghi, 2024. "The Effect of Network Delay and Contagion on Mobile Banking Users: A Dynamical Analysis," Mathematics, MDPI, vol. 12(22), pages 1-22, November.
    5. 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.
    6. 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.
    7. Xiangqing Zhao & Wanmei Hou, 2023. "Optimal Control of SLBRS with Recovery Rates," Mathematics, MDPI, vol. 12(1), pages 1-16, December.
    8. Yang, Wenbin & Li, Danqing & Chang, Xin, 2024. "Analysis and numerical simulation of computer virus propagation model based on limited resources," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 223(C), pages 494-508.
    9. Sun, Ruoyan, 2016. "Optimal weight based on energy imbalance and utility maximization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 442(C), pages 429-435.
    10. Zizhen Zhang & Limin Song, 2017. "Dynamics of a Computer Virus Propagation Model with Delays and Graded Infection Rate," Advances in Mathematical Physics, John Wiley & Sons, vol. 2017(1).
    11. Guiyun Liu & Zhimin Peng & Zhongwei Liang & Xiaojing Zhong & Xinhai Xia, 2022. "Analysis and Control of Malware Mutation Model in Wireless Rechargeable Sensor Network with Charging Delay," Mathematics, MDPI, vol. 10(14), pages 1-28, July.
    12. Wu, Yingbo & Li, Pengdeng & Yang, Lu-Xing & Yang, Xiaofan & Tang, Yuan Yan, 2017. "A theoretical method for assessing disruptive computer viruses," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 325-336.

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