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<p>This study presents a comprehensive analysis of infectious disease dynamics through mathematical modeling and optimal control strategies. The primary objective is to derive insights into disease transmission by employing a model structured on integer and Caputo fractional order derivatives (CFOD). Initially, we establish the feasible region and confirm the boundedness of the model. Subsequently, the disease-free equilibrium (DFE) points and the basic reproduction number (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40808_2025_2394_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathcal {R}_{0}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">R</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation>) are analytically determined. Using fixed point theory, we rigorously prove theoretical results relevant to the model. To approximate solutions, we apply the Modified Euler’s Method (MEM), which demonstrates the model’s capacity to simulate disease dynamics with increased realism. Finally, optimal control analysis reveals that an integrated application of all four control strategies significantly reduces the infected population, thus enhancing the recovery rate.</p>

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A fractional derivative approach to infectious disease dynamics: modeling and optimal control strategies

  • 期刊论文

  • 发表日期：

    2025年4月24日

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  • Sayooj Aby Jose,
  • Raja Ramachandran,
  • Jirawattanapanit Anuwat,
  • Jinde Cao,
  • Ravi P. Agarwal

摘要

This study presents a comprehensive analysis of infectious disease dynamics through mathematical modeling and optimal control strategies. The primary objective is to derive insights into disease transmission by employing a model structured on integer and Caputo fractional order derivatives (CFOD). Initially, we establish the feasible region and confirm the boundedness of the model. Subsequently, the disease-free equilibrium (DFE) points and the basic reproduction number ( \(\mathcal {R}_{0}\) R 0 ) are analytically determined. Using fixed point theory, we rigorously prove theoretical results relevant to the model. To approximate solutions, we apply the Modified Euler’s Method (MEM), which demonstrates the model’s capacity to simulate disease dynamics with increased realism. Finally, optimal control analysis reveals that an integrated application of all four control strategies significantly reduces the infected population, thus enhancing the recovery rate.