<p>COVID-19 has remained a serious global health challenge for over five years, affecting millions of lives and placing immense pressure on healthcare systems worldwide. To better understand its transmission and explore effective control strategies, we developed a discrete-time compartmental model named CoVCom-10, which includes ten key stages of disease progression such as pre-symptomatic (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40435_2025_1781_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">\(E^\chi \)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>E</mi> <mi>χ</mi> </msup> </math></EquationSource> </InlineEquation>), vaccinated (<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40435_2025_1781_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">\(V^\chi \)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>V</mi> <mi>χ</mi> </msup> </math></EquationSource> </InlineEquation>), self-isolated (<InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40435_2025_1781_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">\(F^\chi \)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>F</mi> <mi>χ</mi> </msup> </math></EquationSource> </InlineEquation>) individuals. A central focus of this study is the estimation of the basic reproduction number (<InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40435_2025_1781_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(R_0\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>R</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation>), a fundamental metric that reflects the average number of secondary infections generated by one infected individual. We analyzed both local and global stability of the disease-free equilibrium when <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40435_2025_1781_Article_IEq5.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="51" /> </InlineMediaObject> <EquationSource Format="TEX">\(R_0 &lt; 1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>R</mi> <mn>0</mn> </msub> <mo>&lt;</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> and performed a sensitivity analysis to assess their influence on transmission dynamics. Time-dependent control measures were incorporated to develop an optimal intervention strategy, and a bifurcation analysis, coupled with sensitivity indices (<InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40435_2025_1781_Article_IEq6.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(\phi ^*\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>ϕ</mi> <mo>∗</mo> </msup> </math></EquationSource> </InlineEquation>), was conducted to identify the most influential parameters affecting transmission dynamics The model also indicates that intervention effectiveness increases as the compliance parameter <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40435_2025_1781_Article_IEq7.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\rho \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ρ</mi> </math></EquationSource> </InlineEquation> approaches 1. To enhance predictive accuracy, we integrated a machine learning approach using an artificial neural network (ANN) with 10 neurons, trained on real-world epidemiological data. This study highlights the value of combining mathematical modeling with data-driven machine learning tools to improve our understanding of COVID-19 dynamics. The CoVCom-10 framework, supported by visual performance metrics such as box plots, histograms, and loss curves, demonstrates high accuracy and robustness, with absolute error values ranging from <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40435_2025_1781_Article_IEq8.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="33" /> </InlineMediaObject> <EquationSource Format="TEX">\(10^{-2}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>2</mn> </mrow> </msup> </math></EquationSource> </InlineEquation> to <InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40435_2025_1781_Article_IEq9.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="33" /> </InlineMediaObject> <EquationSource Format="TEX">\(10^{-4}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>4</mn> </mrow> </msup> </math></EquationSource> </InlineEquation>. These findings underscore the potential of this hybrid approach to inform public health policy and mitigate future outbreaks.</p>

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A hybrid mathematical and machine learning approach for COVID-19 dynamics

  • Syeda Alishwa Zanib,
  • Rimsha Tariq,
  • Nadeem Abbas,
  • Aqsa Nazir,
  • Wasfi Shatanawi

摘要

COVID-19 has remained a serious global health challenge for over five years, affecting millions of lives and placing immense pressure on healthcare systems worldwide. To better understand its transmission and explore effective control strategies, we developed a discrete-time compartmental model named CoVCom-10, which includes ten key stages of disease progression such as pre-symptomatic ( \(E^\chi \) E χ ), vaccinated ( \(V^\chi \) V χ ), self-isolated ( \(F^\chi \) F χ ) individuals. A central focus of this study is the estimation of the basic reproduction number ( \(R_0\) R 0 ), a fundamental metric that reflects the average number of secondary infections generated by one infected individual. We analyzed both local and global stability of the disease-free equilibrium when \(R_0 < 1\) R 0 < 1 and performed a sensitivity analysis to assess their influence on transmission dynamics. Time-dependent control measures were incorporated to develop an optimal intervention strategy, and a bifurcation analysis, coupled with sensitivity indices ( \(\phi ^*\) ϕ ), was conducted to identify the most influential parameters affecting transmission dynamics The model also indicates that intervention effectiveness increases as the compliance parameter \(\rho \) ρ approaches 1. To enhance predictive accuracy, we integrated a machine learning approach using an artificial neural network (ANN) with 10 neurons, trained on real-world epidemiological data. This study highlights the value of combining mathematical modeling with data-driven machine learning tools to improve our understanding of COVID-19 dynamics. The CoVCom-10 framework, supported by visual performance metrics such as box plots, histograms, and loss curves, demonstrates high accuracy and robustness, with absolute error values ranging from \(10^{-2}\) 10 - 2 to \(10^{-4}\) 10 - 4 . These findings underscore the potential of this hybrid approach to inform public health policy and mitigate future outbreaks.