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Mathematical analysis of the effectiveness of control strategies to prevent the autorun virus transmission propagation

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  • Kim, Kwang Su
  • Ibrahim, Malik Muhammad
  • Jung, Il Hyo
  • Kim, Sangil

Abstract

In this work, a deterministic model for autorun computer virus propagation is presented and discussed. Two new control parameters; vaccination rate and perfect recovery rate are introduced to validate the existence of computer virus infection via external devices likewise USBs. The model is comprehensively analyzed with and without control parameter for verification of proposed model and strategy. The recovery population of the infected computers has been divided into perfectly recovered with probability ‘p’ and partially recovered with probability ‘1 − p’. The results show that as vaccination rate is increased reproductive number and number of infected computers decreased. Since reproductive number does not depend upon p, change in the value of p does not affect the basic reproductive number. However, as value of p is increased, a reduction in steady state of infected computer is observed. Local and global stability analysis of virus-free equilibrium has been investigated through basic reproductive number. The endemic equilibrium has also been determined under certain conditions.

Suggested Citation

  • Kim, Kwang Su & Ibrahim, Malik Muhammad & Jung, Il Hyo & Kim, Sangil, 2020. "Mathematical analysis of the effectiveness of control strategies to prevent the autorun virus transmission propagation," Applied Mathematics and Computation, Elsevier, vol. 371(C).
    • Handle: RePEc:eee:apmaco:v:371:y:2020:i:c:s0096300319309476
    DOI: 10.1016/j.amc.2019.124955
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    References listed on IDEAS

    as
    1. Chenquan Gan & Maobin Yang & Zufan Zhang & Wanping Liu, 2017. "Global Dynamics and Optimal Control of a Viral Infection Model with Generic Nonlinear Infection Rate," Discrete Dynamics in Nature and Society, Hindawi, vol. 2017, pages 1-9, February.
    2. Chunming Zhang & Yun Zhao & Yingjiang Wu, 2012. "An Impulse Model for Computer Viruses," Discrete Dynamics in Nature and Society, Hindawi, vol. 2012, pages 1-13, July.
    3. Lu-Xing Yang & Xiaofan Yang, 2015. "A Novel Virus-Patch Dynamic Model," PLOS ONE, Public Library of Science, vol. 10(9), pages 1-16, September.
    4. Hu, Zhixing & Wang, Hongwei & Liao, Fucheng & Ma, Wanbiao, 2015. "Stability analysis of a computer virus model in latent period," Chaos, Solitons & Fractals, Elsevier, vol. 75(C), pages 20-28.
    5. Kwang Sung Lee & Abid Ali Lashari, 2014. "Global Stability of a Host-Vector Model for Pine Wilt Disease with Nonlinear Incidence Rate," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-11, January.
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