Computational analysis of COVID-19 model outbreak with singular and nonlocal operator

Maryam Amin; Muhammad Farman; Ali Akgül; Mohammad Partohaghighi; Fahd Jarad; Maryam Amin; Muhammad Farman; Ali Akgül; Mohammad Partohaghighi; Fahd Jarad

doi:10.3934/math.2022919

AIMS Mathematics

2022, Volume 7, Issue 9: 16741-16759. doi: 10.3934/math.2022919

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Computational analysis of COVID-19 model outbreak with singular and nonlocal operator

1.
Department of Mathematics and Statistics, University of Lahore, Lahore-54590, Pakistan
2.
Department of Mathematics, Khawaja Fareed University of Engineering and Information Technology, Rahim Yar Khan, Pakistan
3.
Art and Science Faculty, Department of Mathematics, Siirt University, 56100 Siirt, Turkey
4.
Department of Mathematics, Clarkson University, Potsdam, NY 13699, USA
5.
Department of Mathematics, Cankaya University, Etimesgut, Ankara, Turkey
6.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan

Received: 30 March 2022 Revised: 10 June 2022 Accepted: 14 June 2022 Published: 13 July 2022
MSC : 37C75, 65L07, 93B05

The SARS-CoV-2 virus pandemic remains a pressing issue with its unpredictable nature, and it spreads worldwide through human interaction. Current research focuses on the investigation and analysis of fractional epidemic models that discuss the temporal dynamics of the SARS-CoV-2 virus in the community. In this work, we choose a fractional-order mathematical model to examine the transmissibility in the community of several symptoms of COVID-19 in the sense of the Caputo operator. Sensitivity analysis of $ R_{0} $ and disease-free local stability of the system are checked. Also, with the assistance of fixed point theory, we demonstrate the existence and uniqueness of the system. In addition, numerically we solve the fractional model and presented some simulation results via actual estimation parameters. Graphically we displayed the effects of numerous model parameters and memory indexes. The numerical outcomes show the reliability, validation, and accuracy of the scheme.
- COVID-19 model,
- Caputo operator,
- stability analysis,
- numerical simulations
Citation: Maryam Amin, Muhammad Farman, Ali Akgül, Mohammad Partohaghighi, Fahd Jarad. Computational analysis of COVID-19 model outbreak with singular and nonlocal operator[J]. AIMS Mathematics, 2022, 7(9): 16741-16759. doi: 10.3934/math.2022919

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Abstract

The SARS-CoV-2 virus pandemic remains a pressing issue with its unpredictable nature, and it spreads worldwide through human interaction. Current research focuses on the investigation and analysis of fractional epidemic models that discuss the temporal dynamics of the SARS-CoV-2 virus in the community. In this work, we choose a fractional-order mathematical model to examine the transmissibility in the community of several symptoms of COVID-19 in the sense of the Caputo operator. Sensitivity analysis of $ R_{0} $ and disease-free local stability of the system are checked. Also, with the assistance of fixed point theory, we demonstrate the existence and uniqueness of the system. In addition, numerically we solve the fractional model and presented some simulation results via actual estimation parameters. Graphically we displayed the effects of numerous model parameters and memory indexes. The numerical outcomes show the reliability, validation, and accuracy of the scheme.

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