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Dynamics of SIR mathematical model for COVID-19 outbreak in Pakistan under Fractal-fractional derivative

There are still mathematical predictions in the fight against epidemics. Speedy expansion, ways and procedures for the pandemic control require early understanding when solutions with better computer-based mathematical modeling and prognosis are developed. Despite high uncertainty in each of these m...

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Main Authors: Ali, Zeeshan, Rabiei, Faranak, Shah, Kamal, Abdul Majid, Zanariah
Format: Article
Language:English
Published: World Scientific Publishing 2021
Online Access:http://psasir.upm.edu.my/id/eprint/96819/1/ABSTRACT.pdf
http://psasir.upm.edu.my/id/eprint/96819/
https://www.worldscientific.com/doi/epdf/10.1142/S0218348X21501206
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spelling my.upm.eprints.968192022-12-01T02:21:55Z http://psasir.upm.edu.my/id/eprint/96819/ Dynamics of SIR mathematical model for COVID-19 outbreak in Pakistan under Fractal-fractional derivative Ali, Zeeshan Rabiei, Faranak Shah, Kamal Abdul Majid, Zanariah There are still mathematical predictions in the fight against epidemics. Speedy expansion, ways and procedures for the pandemic control require early understanding when solutions with better computer-based mathematical modeling and prognosis are developed. Despite high uncertainty in each of these models, one of the important tools for public health management system is epidemiology models. The fractional order is shown to be more effective in modeling epidemic diseases, in relation to the memory effects. Notably, recently founded calculus tools, called fractal-fractional calculus, having a fractional order and fractal dimension, enable us to study the behavior of a real-world problem under both fractal and fractional tools. This paper is about the dynamical behavior of a new mathematical model of novel corona disease (COVID-19) under the fractal-fractional Atangana–Baleanu derivative. The considered model has three compartments, namely, susceptible, infected and recovered or removed (SIR). The existence and uniqueness of the model’s solution will be proved via Krasnoselskii’s and Banach’s fixed point theorems, respectively. The stability of the solution in the sense of Hyers–Ulam (HU) will be built up by nonlinear functional analysis. Moreover, the numerical simulations for different values of isolation parameters corresponding to various fractal-fractional orders are analyzed using fractional Adams–Bashforth (AB) method with two-step Lagrange polynomial. Finally, the obtained simulation results are applied to the real data of disease spread from Pakistan. The graphical interpretations demonstrate that increasing the isolation parameters which is caused by strict precautionary measures will reduce the disease infection transmission in society. World Scientific Publishing 2021 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/96819/1/ABSTRACT.pdf Ali, Zeeshan and Rabiei, Faranak and Shah, Kamal and Abdul Majid, Zanariah (2021) Dynamics of SIR mathematical model for COVID-19 outbreak in Pakistan under Fractal-fractional derivative. Fractals-Complex Geometry, Patterns, and Scaling in Nature and Society, 29 (5). pp. 1-16. ISSN 0218-348X; ESSN: 1793-6543 https://www.worldscientific.com/doi/epdf/10.1142/S0218348X21501206 10.1142/S0218348X21501206
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
language English
description There are still mathematical predictions in the fight against epidemics. Speedy expansion, ways and procedures for the pandemic control require early understanding when solutions with better computer-based mathematical modeling and prognosis are developed. Despite high uncertainty in each of these models, one of the important tools for public health management system is epidemiology models. The fractional order is shown to be more effective in modeling epidemic diseases, in relation to the memory effects. Notably, recently founded calculus tools, called fractal-fractional calculus, having a fractional order and fractal dimension, enable us to study the behavior of a real-world problem under both fractal and fractional tools. This paper is about the dynamical behavior of a new mathematical model of novel corona disease (COVID-19) under the fractal-fractional Atangana–Baleanu derivative. The considered model has three compartments, namely, susceptible, infected and recovered or removed (SIR). The existence and uniqueness of the model’s solution will be proved via Krasnoselskii’s and Banach’s fixed point theorems, respectively. The stability of the solution in the sense of Hyers–Ulam (HU) will be built up by nonlinear functional analysis. Moreover, the numerical simulations for different values of isolation parameters corresponding to various fractal-fractional orders are analyzed using fractional Adams–Bashforth (AB) method with two-step Lagrange polynomial. Finally, the obtained simulation results are applied to the real data of disease spread from Pakistan. The graphical interpretations demonstrate that increasing the isolation parameters which is caused by strict precautionary measures will reduce the disease infection transmission in society.
format Article
author Ali, Zeeshan
Rabiei, Faranak
Shah, Kamal
Abdul Majid, Zanariah
spellingShingle Ali, Zeeshan
Rabiei, Faranak
Shah, Kamal
Abdul Majid, Zanariah
Dynamics of SIR mathematical model for COVID-19 outbreak in Pakistan under Fractal-fractional derivative
author_facet Ali, Zeeshan
Rabiei, Faranak
Shah, Kamal
Abdul Majid, Zanariah
author_sort Ali, Zeeshan
title Dynamics of SIR mathematical model for COVID-19 outbreak in Pakistan under Fractal-fractional derivative
title_short Dynamics of SIR mathematical model for COVID-19 outbreak in Pakistan under Fractal-fractional derivative
title_full Dynamics of SIR mathematical model for COVID-19 outbreak in Pakistan under Fractal-fractional derivative
title_fullStr Dynamics of SIR mathematical model for COVID-19 outbreak in Pakistan under Fractal-fractional derivative
title_full_unstemmed Dynamics of SIR mathematical model for COVID-19 outbreak in Pakistan under Fractal-fractional derivative
title_sort dynamics of sir mathematical model for covid-19 outbreak in pakistan under fractal-fractional derivative
publisher World Scientific Publishing
publishDate 2021
url http://psasir.upm.edu.my/id/eprint/96819/1/ABSTRACT.pdf
http://psasir.upm.edu.my/id/eprint/96819/
https://www.worldscientific.com/doi/epdf/10.1142/S0218348X21501206
_version_ 1751538259283935232
score 13.211869

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