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Optimal existence of fractional order computer virus epidemic model and numerical simulations
Author(s) -
Akgül Ali,
Sajid Iqbal Muhammad,
Fatima Umbreen,
Ahmed Nauman,
Iqbal Zafar,
Raza Ali,
Rafiq Muhammad,
Rehman Muhammad Azizur
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7437
Subject(s) - mathematics , equilibrium point , jacobian matrix and determinant , stability (learning theory) , epidemic model , operator (biology) , fixed point theorem , fractional calculus , order (exchange) , differential equation , mathematical analysis , computer science , population , biochemistry , chemistry , demography , finance , repressor , machine learning , sociology , transcription factor , economics , gene
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.