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Stability analysis and control strategies for worm attack in mobile networks via a VEIQS propagation model

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  • Gao, Qingwu
  • Zhuang, Jun

Abstract

Mobile devices are considerably pervasive in society, but also increase their vulnerability to worm attacks from mobile networks. In this paper, we propose a new Vulnerable-Exposed-Infectious-Quarantined-Secured worm propagation model with saturated incidence and strategies of both vaccination and quarantine. We obtain that the basic reproduction number R0 is a sharp threshold parameter such that the worm-free equilibrium is asymptotically stable for R0 ≤ 1, implying that the worm dies out eventually and its attack remains under control; the worm-existence equilibrium is asymptotically stable when R0 > 1, namely, the worm is always persistent and spreading within a population. This paper provides some novel insights to cyber security by that (a) the stability of worm-free equilibrium establishes the control strategies to reduce the intensity of worm attacks, and the optimal control strategy is proposed by using Pontryagins Minimum Principle; (b) the stability of worm-existence equilibrium predicts the tendency of worm propagation in a long run and assesses the level of the worm popularity by the final scale of infected devices. Numerical simulations are implemented to illustrate the feasibility of the theoretical results and the effectiveness of the control strategies.

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  • Gao, Qingwu & Zhuang, Jun, 2020. "Stability analysis and control strategies for worm attack in mobile networks via a VEIQS propagation model," Applied Mathematics and Computation, Elsevier, vol. 368(C).
    • Handle: RePEc:eee:apmaco:v:368:y:2020:i:c:s0096300319305764
    DOI: 10.1016/j.amc.2019.124584
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    References listed on IDEAS

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    1. Sun, Chengjun & Lin, Yiping & Tang, Shoupeng, 2007. "Global stability for an special SEIR epidemic model with nonlinear incidence rates," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 290-297.
    2. Hernández Guillén, J.D. & Martín del Rey, A. & Hernández Encinas, L., 2017. "Study of the stability of a SEIRS model for computer worm propagation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 479(C), pages 411-421.
    3. Wang, Lianwen & Liu, Zhijun & Zhang, Xingan, 2016. "Global dynamics of an SVEIR epidemic model with distributed delay and nonlinear incidence," Applied Mathematics and Computation, Elsevier, vol. 284(C), pages 47-65.
    4. Chung‐Min Liao & Chao‐Fang Chang & Huang‐Min Liang, 2005. "A Probabilistic Transmission Dynamic Model to Assess Indoor Airborne Infection Risks," Risk Analysis, John Wiley & Sons, vol. 25(5), pages 1097-1107, October.
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    Cited by:

    1. Piqueira, José Roberto C. & Cabrera, Manuel A.M. & Batistela, Cristiane M., 2021. "Malware propagation in clustered computer networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 573(C).
    2. Jiang, Jiehui & Ma, Jie, 2023. "Dynamic analysis of pandemic cross-regional transmission considering quarantine strategies in the context of limited medical resources," Applied Mathematics and Computation, Elsevier, vol. 450(C).
    3. Rajeev Kumar Shakya & Tadesse Hailu Ayane & Feyissa Debo Diba & Pushpa Mamoria, 2022. "SEIRS model with spatial correlation for analyzing dynamic of virus spreading in event-driven wireless sensor networks," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 13(2), pages 752-760, April.

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