Optimal existence of fractional order computer virus epidemic model and numerical simulations

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...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2021-09, Vol.44 (13), p.10673-10685
Main Authors: Akgül, Ali, Sajid Iqbal, Muhammad, Fatima, Umbreen, Ahmed, Nauman, Iqbal, Zafar, Raza, Ali, Rafiq, Muhammad, Rehman, Muhammad Aziz‐ur
Format: Article
Language:English
Subjects:
Banach spaces
Computer viruses
Differential equations
epidemic models
Epidemics
Equilibrium
fractional derivatives
Jacobi matrix method
Jacobian matrix
Mathematical models
Mittag–Leffler kernel
numerical simulations
Operators (mathematics)
Stability analysis
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Summary: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.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.7437