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Keywords
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Fractal-fractional operator, Mathematical model, Numerical algorithm, Caputo fractional derivative, Operational matrix method
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Abstract
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SARS-CoV-2 is a strain of the large coronavirus family that has led to COVID-19 disease. The virus has been one of the deadliest
known viruses in the world to date. Rapid mutations and the creation of new strains cause researchers to focus on the dynamic
behaviors of the virus and to analyze it accurately through clinical research and mathematical models. In this paper, from the
point of view of mathematical modeling, we intend to focus on the dynamic behavior of the system and examine its analytical
and numerical aspects in two different structures. In other words, by recalling newly formulated hybrid fractional-fractal
operators, we present a fractal-fractional probability-based model of SARS-CoV-2 virus for the first time and extract its
equivalent compact fractal-fractional IVP to investigate its existence and stability criteria. A type of special admissible
contractions will help us in this regard. Moreover, based on the source data, we simulate our system according to algorithms derived by Adams-Bashforth method and explain the effects of variation of the dimension of fractal and fractional order on
dynamics of solutions. Finally, we transform our fractal-fractional model into a Caputo probability-based model of SARS-CoV-2 to derive solutions via the operational matrix method under Taylor’s basis. The numerical simulations show close behaviors for both of models.
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