A FRACTIONAL SARS-COV-2 MODEL WITH ATANGANA–BALEANU DERIVATIVE: APPLICATION TO FOURTH WAVE

Yu-Ming Chu, Mansour F. Yassen, Irshad Ahmad (), Pongsakorn Sunthrayuth and Muhammad Altaf Khan
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Yu-Ming Chu: College of Science, Hunan City University, Yiyang, Hunan 413000, P. R. China†Department of Mathematics, Huzhou University, Huzhou, Zhejiang 313000, P. R. China‡Institute for Advanced Study Honoring Chen Jian Gong, Hangzhou Normal University, Hangzhou, Zhejiang 311121, P. R. China
Mansour F. Yassen: �Department of Mathematics, College of Science and Humanities in Al-Aflaj, Prince Sattam Bin Abdulaziz University, Al-Aflaj 11912, Saudi Arabia¶Department of Mathematics, Faculty of Science, Damietta University, New Damietta 34517, Damietta, Egypt
Irshad Ahmad: ��Department of Medical Rehabilitation Sciences, College of Applied Medical Sciences, King Khalid University, Abha, Saudi Arabia
Pongsakorn Sunthrayuth: *Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi (RMUTT), Thanyaburi, Pathumthani 12110, Thailand
Muhammad Altaf Khan: ��†Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein Campus, Bloemfontein, South Africa‡‡Department of Mathematics, Faculty of Science and Technology, Universitas Airlangga, Surabaya 60115, Indonesia

FRACTALS (fractals), 2022, vol. 30, issue 08, 1-24

Abstract: A dynamical model of SARS-CoV-2 in fractional derivative using the cases of coronavirus of the fourth wave is presented. We construct basically the model in an integer case, and later it is extended to a fractional-order system by applying the Atangana–Baleanu operator definition. We give some background definitions and results for the fractional-order model. We present for the disease-free case that the model is locally asymptotically stable when ℛ0 < 1. The global dynamics of the fractional model are given when ℛ0 ≤ 1 for the disease-free case. The model is further extended to fractional stochastic piecewise equations in the Atangana–Baleanu case. The reported cases from the fourth wave in Pakistan starting from July 1 up to November 16, 2021 are considered for the estimation of the parameters. We fitted our model to the suggested data and obtained the numerical value of the basic reproduction number ℛ0 ≈ 0.9775 for fractional order. We give the data fitting to both the fractional and piecewise stochastic differential equations, and show them both as having a good fitting to the data. We use further the numerical values of the model parameters and present its numerical results graphically using the effective numerical approaches. Some sensitive parameters that are reasonable for disease eliminations are used to obtain the graphical results.

Keywords: Fourth Wave Cases; COVID-19 Fractional Model; Estimations of Parameters; Results and Discussions (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22402101

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