Asymptotic stability of an epidemiological fractional reaction-diffusion model

• Autorzy: Djebara Lamia , Abdelmalek Salem , Bendoukha Samir

Identyfikatory

DOI

10.1515/dema-2022-0224

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

asymptotic stability; fractional calculus; basic reproduction number; fractional Lyapunov method; Lyapunov functional

PL

stabilność asymptotyczna; rachunek ułamkowy; podstawowy współczynnik reprodukcji; metoda Lapunowa; funkcja Lapunowa

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2023
• Tom: Vol. 56, nr 1
• Strony: art. no. 20220224
• Opis fizyczny: Bibliogr. 35 poz., rys., tab.

Twórcy

autor

Djebara Lamia

• Laboratory (LAMIS), Abbes Laghrour University Khenchela, Khenchela, Algeria

autor

Abdelmalek Salem

• Laboratory (LAMIS), Larbi Tebessi University, Tebessa, Algeria

autor

Bendoukha Samir

• Department of Electrical Engineering, College of Engineering, Taibah University, Yanbu, Saudi Arabia

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).