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

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.