Asymptotic stability of an epidemiological fractional reaction-diffusion model

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Abstract: The aim of this article is to study the known susceptible-infectious (SI) epidemic model using fractional order reaction-diffusion fractional partial differential equations [FPDEs] in order to better describe the dynamics of a reaction-diffusion SI with a nonlinear incidence rate describing the infection dynamics of the HIV/AIDS virus. We initially examined the nonnegativity, global existence, and boundedness for solutions of the proposed system. After determining that the proposed model has two steady states, we derived sufficient conditions for the global and local asymptotic stability of the equilibrium of the proposed system and their relationship to basic reproduction in the case of fractional ordinary differential equations and FPDEs by analyzing the eigenvalues and using the appropriately chosen Lyapunov function. Finally, we used numerical examples to illustrate our theoretical results.

Location: Deutsche Nationalbibliothek Frankfurt am Main

Extent: Online-Ressource

Language: Englisch

Bibliographic citation: Asymptotic stability of an epidemiological fractional reaction-diffusion model ; volume:56 ; number:1 ; year:2023 ; extent:27
Demonstratio mathematica ; 56, Heft 1 (2023) (gesamt 27)

Creator: Djebara, Lamia
Abdelmalek, Salem
Bendoukha, Samir

DOI: 10.1515/dema-2022-0224

URN: urn:nbn:de:101:1-2023061514080910933779

Rights: Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.

Last update: 14.08.2025, 10:48 AM CEST

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Djebara, Lamia
Abdelmalek, Salem
Bendoukha, Samir

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Asymptotic stability of an epidemiological fractional reaction-diffusion model

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