Optimal existence of fractional order computer virus epidemic model and numerical simulations. (19th April 2021)

• Record Type: Journal Article
• Authors: Akgül, Ali; Sajid Iqbal, Muhammad; Fatima, Umbreen; Ahmed, Nauman; Iqbal, Zafar; Raza, Ali; Rafiq, Muhammad; Rehman, Muhammad Aziz‐ur
• Is Part Of: Mathematical methods in the applied sciences. Volume 44:Number 13(2021)
• Page Start: 10673
• Page End: 10685
• Publication Date: 2021-04-19
• Subjects: epidemic models -- fractional derivatives -- Mittag–Leffler kernel -- numerical simulations; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.7437
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : Aim of this article is to analyze the fractional order computer epidemic model. To this end, a classical computer epidemic model is extended to the fractional order model by using the Atangana–Baleanu fractional differential operator in Caputo sense. The regularity condition for the solution to the considered system is described. Existence of the solution in the Banach space is investigated and some benchmark results are presented. Steady states of the system is described and stability of the model at these states is also studied, with the help of Jacobian matrix method. Some results for the local stability at disease free equilibrium point and endemic equilibrium point are presented. The basic reproduction number is mentioned and its role on stability analysis is also highlighted. The numerical design is formulated by applying the Atangana–Baleanu integral operator. The graphical solutions are also presented by computer simulations at both the equilibrium points.