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Optimal control strategy for a novel computer virus propagation model on scale-free networks

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  • Zhang, Chunming
  • Huang, Haitao

Abstract

This paper aims to study the combined impact of reinstalling system and network topology on the spread of computer viruses over the Internet. Based on scale-free network, this paper proposes a novel computer viruses propagation model—SLBOSmodel. A systematic analysis of this new model shows that the virus-free equilibrium is globally asymptotically stable when its spreading threshold is less than one; nevertheless, it is proved that the viral equilibrium is permanent if the spreading threshold is greater than one. Then, the impacts of different model parameters on spreading threshold are analyzed. Next, an optimally controlled SLBOS epidemic model on complex networks is also studied. We prove that there is an optimal control existing for the control problem. Some numerical simulations are finally given to illustrate the main results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:451:y:2016:i:c:p:251-265
    DOI: 10.1016/j.physa.2016.01.028
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    References listed on IDEAS

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    1. Shi, Hongjing & Duan, Zhisheng & Chen, Guanrong, 2008. "An SIS model with infective medium on complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(8), pages 2133-2144.
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    3. 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.
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    Cited by:

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    2. Chen, Shanshan & Jiang, Haijun & Li, Liang & Li, Jiarong, 2020. "Dynamical behaviors and optimal control of rumor propagation model with saturation incidence on heterogeneous networks," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    3. Linhe Zhu & Hongyong Zhao, 2017. "Dynamical behaviours and control measures of rumour-spreading model with consideration of network topology," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(10), pages 2064-2078, July.
    4. Xiangqing Zhao, 2023. "Optimal Control Strategy for SLBRS with Two Control Inputs," Mathematics, MDPI, vol. 11(19), pages 1-10, September.
    5. 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.
    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 1-17, December.
    8. Yi, Yinxue & Zhang, Zufan & Gan, Chenquan, 2018. "The effect of social tie on information diffusion in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 783-794.
    9. Zhou, Jiaying & Zhao, Yi & Ye, Yong, 2022. "Complex dynamics and control strategies of SEIR heterogeneous network model with saturated treatment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 608(P2).

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