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

M. Ait Ichou; Z.  Hajhouji; K.  Hattaf

doi:10.5269/bspm.76771

M. Ait Ichou EMA Team, LRST Laboratory, ESEFA, Ibnou Zohr University of Agadir, Morocco.
Z. Hajhouji
K. Hattaf

Abstract

This paper presents a susceptible-infected-removed (SIR) model with the generalized 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-Leffler sense. Another significant contribution of this work is the integration of PINNs approach to analyze the SIR model. We propose this approach as an alternative to classical 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.

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