Computational modeling of fractional COVID-19 model by Haar wavelet collocation Methods with real data

Rahat Zarin; Usa Wannasingha Humphries; Amir Khan; Aeshah A. Raezah; Rahat Zarin; Usa Wannasingha Humphries; Amir Khan; Aeshah A. Raezah

doi:10.3934/mbe.2023500

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 6: 11281-11312. doi: 10.3934/mbe.2023500

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Computational modeling of fractional COVID-19 model by Haar wavelet collocation Methods with real data

1.
Department of Mathematics, Faculty of Science, King Mongkut's University of Technology, Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
2.
Department of Mathematics and Statistics, University of Swat, Khyber Pakhtunkhawa, Pakistan
3.
Department of Mathematics, Faculty of Science, King Khalid University, Abha 62529, Saudi Arabia

Academic Editor:Hiroshi Nishiura

Received: 07 February 2023 Revised: 09 April 2023 Accepted: 17 April 2023 Published: 26 April 2023

This study explores the use of numerical simulations to model the spread of the Omicron variant of the SARS-CoV-2 virus using fractional-order COVID-19 models and Haar wavelet collocation methods. The fractional order COVID-19 model considers various factors that affect the virus's transmission, and the Haar wavelet collocation method offers a precise and efficient solution to the fractional derivatives used in the model. The simulation results yield crucial insights into the Omicron variant's spread, providing valuable information to public health policies and strategies designed to mitigate its impact. This study marks a significant advancement in comprehending the COVID-19 pandemic's dynamics and the emergence of its variants. The COVID-19 epidemic model is reworked utilizing fractional derivatives in the Caputo sense, and the model's existence and uniqueness are established by considering fixed point theory results. Sensitivity analysis is conducted on the model to identify the parameter with the highest sensitivity. For numerical treatment and simulations, we apply the Haar wavelet collocation method. Parameter estimation for the recorded COVID-19 cases in India from 13 July 2021 to 25 August 2021 has been presented.
- fractional modeling,
- Haar wavelet,
- COVID-19,
- reproduction number,
- epidemic model,
- parameter estimation
Citation: Rahat Zarin, Usa Wannasingha Humphries, Amir Khan, Aeshah A. Raezah. Computational modeling of fractional COVID-19 model by Haar wavelet collocation Methods with real data[J]. Mathematical Biosciences and Engineering, 2023, 20(6): 11281-11312. doi: 10.3934/mbe.2023500

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Abstract

This study explores the use of numerical simulations to model the spread of the Omicron variant of the SARS-CoV-2 virus using fractional-order COVID-19 models and Haar wavelet collocation methods. The fractional order COVID-19 model considers various factors that affect the virus's transmission, and the Haar wavelet collocation method offers a precise and efficient solution to the fractional derivatives used in the model. The simulation results yield crucial insights into the Omicron variant's spread, providing valuable information to public health policies and strategies designed to mitigate its impact. This study marks a significant advancement in comprehending the COVID-19 pandemic's dynamics and the emergence of its variants. The COVID-19 epidemic model is reworked utilizing fractional derivatives in the Caputo sense, and the model's existence and uniqueness are established by considering fixed point theory results. Sensitivity analysis is conducted on the model to identify the parameter with the highest sensitivity. For numerical treatment and simulations, we apply the Haar wavelet collocation method. Parameter estimation for the recorded COVID-19 cases in India from 13 July 2021 to 25 August 2021 has been presented.

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