A fractal fractional model for computer virus dynamics. (June 2021)

• Record Type: Journal Article
• Authors: Akgül, Ali; Fatima, Umbreen; Iqbal, Muhammad Sajid; Ahmed, Nauman; Raza, Ali; Iqbal, Zafar; Rafiq, Muhammad
• Is Part Of: Chaos, solitons and fractals. Volume 147(2021)
• Publication Date: 2021-06
• Subjects: Fractal fractional derivatives -- Computer model -- Stability analysis -- Numerical technique; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2021.110947
• Languages: English
• ISSNs: 0960-0779

Abstract

Highlights: We investigate the computer model in details. We use the Mittag-Leffler kernel in the model. We present the stability analysis. We construct very effective numerical technique. We demonstrate the numerical simulations. 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 R 0 is also brought into lime light for stability analysis. Sensitivity analysis of R 0 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.