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<p>In this manuscript, we introduce an SEIVR model for COVID-19 and conduct a stability and numerical analysis. The stability of the integral-order system is examined using the Routh-Hurwitz criterion for local stability and the Lyapunov function for global stability. The basic reproduction number <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40819_2025_1914_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="33" /> </InlineMediaObject> <EquationSource Format="TEX">\((R_0)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <msub> <mi>R</mi> <mn>0</mn> </msub> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> is derived using the next-generation matrix approach. Additionally, a sensitivity analysis is performed to identify the most influential parameters affecting disease dynamics. To enhance the model’s accuracy, the integer-order system is extended to a fractional-order framework using fractional derivatives. Numerical simulations are carried out using the non-standard finite difference scheme for the integral-order model and the RK2 method for the fractional-order system. Finally, a comparative analysis of both numerical methods are presented in the last diagrams.</p>

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Stability and Numerical Analysis of SEIVR COVID-19 Fractional and Integral Order Model under Saturated Incidence Rate

  • 期刊论文

  • 发表日期：

    2025年5月15日

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  • Shahid Ullah,
  • Muhammad Shoaib Arif,
  • Rahim Ud Din,
  • Ikram Ullah

摘要

In this manuscript, we introduce an SEIVR model for COVID-19 and conduct a stability and numerical analysis. The stability of the integral-order system is examined using the Routh-Hurwitz criterion for local stability and the Lyapunov function for global stability. The basic reproduction number \((R_0)\) ( R 0 ) is derived using the next-generation matrix approach. Additionally, a sensitivity analysis is performed to identify the most influential parameters affecting disease dynamics. To enhance the model’s accuracy, the integer-order system is extended to a fractional-order framework using fractional derivatives. Numerical simulations are carried out using the non-standard finite difference scheme for the integral-order model and the RK2 method for the fractional-order system. Finally, a comparative analysis of both numerical methods are presented in the last diagrams.