https://doi.org/10.1140/epjs/s11734-024-01267-3
Regular Article
Analysis of a fractional endemic SEIR model with vaccination and time delay
1
Department of Mathematics, LabSIPE laboratory, Chouaib Doukkali University of El Jadida, Faculty of Sciences, El Jadida, Morocco
2
National School of Applied Sciences, Science Engineer Lab Energy, Chouaib Doukkali University of El Jadida, El Jadida, Morocco
3
Department of Mathematical Sciences, College of Science, UAE University, 15551, Al-Ain, United Arab Emirates
Received:
4
May
2024
Accepted:
17
July
2024
Published online:
30
July
2024
This article analyzes a fractional-order SEIR infection epidemic model, including time delays and vaccination strategies. Four differential equations describe the infection dynamics with non-integer derivative orders, which account for memory effects and non-local interactions in disease spread. The paper first establishes the existence and uniqueness of the solution and presents equilibrium points based on the basic reproduction number, 
. Using the Lyapunov direct method, the global stability of each equilibrium is proven to depend primarily on . Theoretical findings are validated through numerical simulations, exploring the impact of vaccination and fractional derivatives on the epidemic dynamics.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
