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A fractal fractional model for computer virus dynamics

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  • Akgül, Ali
  • Fatima, Umbreen
  • Iqbal, Muhammad Sajid
  • Ahmed, Nauman
  • Raza, Ali
  • Iqbal, Zafar
  • Rafiq, Muhammad

Abstract

The gist behind this study is to extend the classical computer virus model into fractal fractional model and subsequently to solve the model by Atangana-Toufik method. This method solve nonlinear model under consideration very efficiently. We use the Mittag-Leffler kernels on the proposed model. Atangana-Baleanu integral operator is used to solve the set of fractal-fractional expressions. In this model, three types of equilibrium points are described i.e trivial, virus free and virus existing points. These fixed points are used to establish some standard results to discuss the stability of the system by calculating the Jacobian matrices at these points. Routh-Hurwitz criteria is used to verify that the system is locally asymptotically stable at all the steady states. The emphatic role of the basic reproduction number R0 is also brought into lime light for stability analysis. Sensitivity analysis of R0 is also discussed. Optimal existence and uniqueness of the solution is the nucleus of this study. Computer simulations and patterns and graphical patterns illustrate reliability and productiveness of the proposed method.

Suggested Citation

  • Akgül, Ali & Fatima, Umbreen & Iqbal, Muhammad Sajid & Ahmed, Nauman & Raza, Ali & Iqbal, Zafar & Rafiq, Muhammad, 2021. "A fractal fractional model for computer virus dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    • Handle: RePEc:eee:chsofr:v:147:y:2021:i:c:s0960077921003015
    DOI: 10.1016/j.chaos.2021.110947
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. Al-Raeei, Marwan, 2021. "Applying fractional quantum mechanics to systems with electrical screening effects," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    3. Avcı, İbrahim & Hussain, Azhar & Kanwal, Tanzeela, 2023. "Investigating the impact of memory effects on computer virus population dynamics: A fractal–fractional approach with numerical analysis," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).

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