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<p>A fractional order delay SIR model in Mittag–Leffler kernel is proposed. The model initially presented in integer order system and later extended by applying the Atangana-Baleanu derivative. The essential properties of the model are investigated. Equilibrium points of the fractional system are analyzed, and multiple equilibrium points are identified and discussed. The permanence of the model for <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11071_2025_11006_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="54" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathcal {R}_0\le 1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="script">R</mi> <mn>0</mn> </msub> <mo>≤</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> is established. Local stability of the fractional model is examined. For the fractional system, we prove the existence and uniqueness (EUs) result. We obtain the numerical results for fractional delay system by presenting a novel computational procedure, and various sets of numerical values are used to generate graphical results. Different solution behaviors of the model are observed for various numerical values and fractional order parameters.</p>

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Numerical investigation of an SIR fractional order delay epidemic model in the framework of Mittag–Leffler kernel

  • 期刊论文

  • 发表日期：

    2025年3月1日

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  • Bashir Al-Hdaibat,
  • Mahmoud H. DarAssi,
  • Irfan Ahmad,
  • Muhammad Altaf Khan,
  • Reem Algethamie,
  • Ebraheem Alzahrani

摘要

A fractional order delay SIR model in Mittag–Leffler kernel is proposed. The model initially presented in integer order system and later extended by applying the Atangana-Baleanu derivative. The essential properties of the model are investigated. Equilibrium points of the fractional system are analyzed, and multiple equilibrium points are identified and discussed. The permanence of the model for \(\mathcal {R}_0\le 1\) R 0 ≤ 1 is established. Local stability of the fractional model is examined. For the fractional system, we prove the existence and uniqueness (EUs) result. We obtain the numerical results for fractional delay system by presenting a novel computational procedure, and various sets of numerical values are used to generate graphical results. Different solution behaviors of the model are observed for various numerical values and fractional order parameters.