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<p>This work presents a data-driven fractional-order SEIR model that incorporates a modified Crowley–Martin incidence function to capture nonlinear saturation and behavioral effects in the transmission of COVID-19. By employing the Caputo derivative, the model accounts for memory-dependent infection and recovery processes that cannot be represented in classical integer-order formulations. Fundamental analytical properties of the system, including positivity, boundedness, and the existence and uniqueness of solutions, are rigorously established. The basic reproduction number <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(R_0\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>R</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation> is derived using the next-generation matrix approach, and its threshold behavior is examined through global stability analysis of both disease-free and endemic equilibria. Model parameters are estimated using real COVID-19 data from India via least-squares fitting and Bayesian inference, enabling reliable quantification of uncertainty. An optimal control framework involving time-dependent vaccination and treatment is developed using Pontryagin’s Minimum Principle, and numerical simulations are performed with the Adams–Bashforth–Moulton predictor–corrector scheme. The results demonstrate that fractional-order dynamics slow the progression of the epidemic, while optimal interventions substantially suppress infection levels and reduce control costs. Overall, the study highlights the relevance of memory-driven fractional models and optimized vaccination–treatment policies for realistic epidemic forecasting and effective public health planning.</p>

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Global dynamics of a fractional-order COVID-19 model with modified Crowley–Martin incidence rate and optimal vaccination control using real data analysis

  • 期刊论文

  • 发表日期：

    2026年6月15日

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  • Satyajit Saha,
  • Rakesh Kumar,
  • Purnendu Sardar,
  • Santosh Biswas,
  • Krishna Pada Das

摘要

This work presents a data-driven fractional-order SEIR model that incorporates a modified Crowley–Martin incidence function to capture nonlinear saturation and behavioral effects in the transmission of COVID-19. By employing the Caputo derivative, the model accounts for memory-dependent infection and recovery processes that cannot be represented in classical integer-order formulations. Fundamental analytical properties of the system, including positivity, boundedness, and the existence and uniqueness of solutions, are rigorously established. The basic reproduction number \(R_0\) R 0 is derived using the next-generation matrix approach, and its threshold behavior is examined through global stability analysis of both disease-free and endemic equilibria. Model parameters are estimated using real COVID-19 data from India via least-squares fitting and Bayesian inference, enabling reliable quantification of uncertainty. An optimal control framework involving time-dependent vaccination and treatment is developed using Pontryagin’s Minimum Principle, and numerical simulations are performed with the Adams–Bashforth–Moulton predictor–corrector scheme. The results demonstrate that fractional-order dynamics slow the progression of the epidemic, while optimal interventions substantially suppress infection levels and reduce control costs. Overall, the study highlights the relevance of memory-driven fractional models and optimized vaccination–treatment policies for realistic epidemic forecasting and effective public health planning.