A physics-informed neural network approach to analyze the dynamics of SIR epidemic model with Hattaf fractional derivative

Résumé

This paper presents a susceptible-infected-removed (SIR) model with the gen-
eralized Hattaf fractional derivative involving a non-singular kernel, integrated
in a physics-informed neural networks (PINNs), as a means of comprehending
the temporal evolution dynamics of infectious diseases. The proof demonstrates
the existence, uniqueness, positivity and boundedness of the solution. This study
establishes the stability of the disease-free equilibrium in the Mittag-Leer sense.
Another signicant contribution of this work is the integration of PINNs approach
to analyze the SIR model. We propose this approach as an alternative to classi-
cal numerical methods for solving the SIR model. Our results demonstrate that
PINNs are a promising solution, not only for solving this type of system, but also
for studying the dynamics of infectious diseases.