Exploring COVID-19 model with general fractional derivatives‎: ‎novel Physics-Informed-Neural-Networks approach for dynamics and order estimation

Volume 36, Issue 2, pp 142--162 https://dx.doi.org/10.22436/jmcs.036.02.01

Publication Date: July 02, 2024 Submission Date: March 19, 2024 Revision Date: May 09, 2024 Accteptance Date: May 27, 2024

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Authors

H‎. ‎ Aghdaoui - MAIS Laboratory‎, ‎MAMCS Group‎, ‎FST Errachidia, ‎Moulay Ismail University of Meknes, ‎P.O‎. ‎Box 509, ‎Errachidia 52000, ‎Morocco. A. A‎. ‎ Raezah - Department of Mathematics‎, ‎Faculty of Science, ‎King Khalid University, ‎Abha 62529, ‎Saudi‎ ‎Arabia. M. Tilioua - MAIS Laboratory‎, ‎MAMCS Group‎, ‎FST Errachidia, ‎Moulay Ismail University of Meknes, ‎P.O‎. ‎Box 509, ‎Errachidia 52000, ‎Morocco. Y. Sabbar - MAIS Laboratory‎, ‎MAMCS Group‎, ‎FST Errachidia, ‎Moulay Ismail University of Meknes, ‎P.O‎. ‎Box 509, ‎Errachidia 52000, ‎Morocco.

Abstract

‎In this paper‎, ‎a fractional coronavirus disease model including unreported cases is suggested‎. ‎The considered model includes a general fractional derivative incorporating well-known types‎, ‎specifically Caputo-Fabrizio‎, ‎Atangana-Baleanu and Weighted Atangana-Baleanu‎. ‎Our theoretical results are two-fold‎. ‎First‎, ‎under suitable assumptions‎, ‎the existence of a solution for the considered system is proven‎. ‎Moreover‎, ‎the local stability of the free-disease and endemic equilibrium points is addressed in terms of \(R_{0}\)‎. ‎Secondly‎, ‎a particular example is considered where the fractional derivative has two varying parameters‎, ‎and an approach allowing for their estimation is proposed‎, ‎with the aim of providing the best approximation of the real COVID-19 dynamics‎. ‎The main novelty of our proposed approach is its use of physics-informed-neural-networks (PINNs) for estimating the fractional orders‎. ‎On the other hand‎, ‎to validate our results‎, ‎a numerical simulations are conducted to illustrate the local stability of the disease dynamics‎, ‎as well as the effectiveness of our proposed method in providing the best approximation of the two fractional derivative parameters‎.

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Keywords

• Epidemic model
• incidence rate
• equilibrium points
• optimal control
• numerical analysis

MSC

•  92B05
•  93D20

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