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


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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ISRP Style

H‎. ‎ Aghdaoui, A. A‎. ‎ Raezah, M. Tilioua, Y. Sabbar, Exploring COVID-19 model with general fractional derivatives‎: ‎novel Physics-Informed-Neural-Networks approach for dynamics and order estimation, Journal of Mathematics and Computer Science, 36 (2025), no. 2, 142--162

AMA Style

Aghdaoui H‎. ‎, Raezah A. A‎. ‎, Tilioua M., Sabbar Y., Exploring COVID-19 model with general fractional derivatives‎: ‎novel Physics-Informed-Neural-Networks approach for dynamics and order estimation. J Math Comput SCI-JM. (2025); 36(2):142--162

Chicago/Turabian Style

Aghdaoui, H‎. ‎, Raezah, A. A‎. ‎, Tilioua, M., Sabbar, Y.. "Exploring COVID-19 model with general fractional derivatives‎: ‎novel Physics-Informed-Neural-Networks approach for dynamics and order estimation." Journal of Mathematics and Computer Science, 36, no. 2 (2025): 142--162


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