Qualitative analysis of fractal-fractional order COVID-19 mathematical model with case study of Wuhan
| Autor: | Touraj Khodadadi, Kamal Shah, Zeeshan Ali, Faranak Rabiei |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Fractal-fractional derivative
020209 energy 34A08 02 engineering and technology Fixed point Type (model theory) 01 natural sciences Fractal dimension Article 010305 fluids & plasmas symbols.namesake Fractional Adams-Bashforth (AB) method Fractal Operator (computer programming) 0103 physical sciences Numerical simulations 0202 electrical engineering electronic engineering information engineering Nonlinear functional analysis Applied mathematics Coronavirus disease model Uniqueness Mathematics Fixed point theorem General Engineering Lagrange polynomial Engineering (General). Civil engineering (General) 93A30 symbols TA1-2040 26A33 Ulam’s stability |
| Zdroj: | Alexandria Engineering Journal Alexandria Engineering Journal, Vol 60, Iss 1, Pp 477-489 (2021) |
| ISSN: | 1110-0168 |
| DOI: | 10.1016/j.aej.2020.09.020 |
| Popis: | In this manuscript, a qualitative analysis of the mathematical model of novel coronavirus ( COVID -19) involving anew devised fractal-fractional operator in the Caputo sense having the fractional-order q and the fractal dimension p is considered. The concerned model is composed of eight compartments: susceptible, exposed, infected, super-spreaders, asymptomatic, hospitalized, recovery and fatality. When, choosing the fractal order one we obtain fractional order, and when choosing the fractional order one a fractal system is obtained. Considering both the operators together we present a model with fractal-fractional. Under the new derivative the existence and uniqueness of the solution for considered model are proved using Schaefer’s and Banach type fixed point approaches. Additionally, with the help of nonlinear functional analysis, the condition for Ulam’s type of stability of the solution to the considered model is established. For numerical simulation of proposed model, a fractional type of two-step Lagrange polynomial known as fractional Adams-Bashforth ( AB ) method is applied to simulate the results. At last, the results are tested with real data from COVID -19 outbreak in Wuhan City, Hubei Province of China from 4 January to 9 March 2020, taken from a source (Ndairou, 2020). The Numerical results are presented in terms of graphs for different fractional-order q and fractal dimensions p to describe the transmission dynamics of disease infection. |
| Databáze: | OpenAIRE |
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