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<p>Mathematical epidemic models increasingly incorporate fractional calculus to better capture memory effects and heterogeneous transmission dynamics. In this study, we formulate a conformable fractional SEIR model incorporating vaccination as a time-dependent control strategy. Unlike classical integer-order formulations, the conformable derivative introduces temporal memory behavior without losing essential differential properties. Stability analysis of the disease-free equilibrium demonstrates that vaccination intensity significantly contributes to reducing the effective reproduction number. A modified fractional Runge–Kutta numerical method is developed and implemented to approximate solutions with improved stability and accuracy over traditional schemes. Numerical simulations demonstrate how the fractional order and vaccination rate jointly govern epidemic peaks, persistence, and eradication timelines. The results confirm that fractional dynamics and adaptive vaccination policies yield more realistic epidemic trajectories than classical models. The proposed framework provides an efficient tool for assessing public-health vaccination strategies under memory-dependent epidemic evolution.</p>

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Optimal vaccination control in a conformable fractional COVID-19 model: A numerical simulation approach using fractional Runge–Kutta method

  • 期刊论文

  • 发表日期：

    2026年5月5日

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  • Jaydev Patel,
  • Kunjan Shah,
  • Himanshu Patel

摘要

Mathematical epidemic models increasingly incorporate fractional calculus to better capture memory effects and heterogeneous transmission dynamics. In this study, we formulate a conformable fractional SEIR model incorporating vaccination as a time-dependent control strategy. Unlike classical integer-order formulations, the conformable derivative introduces temporal memory behavior without losing essential differential properties. Stability analysis of the disease-free equilibrium demonstrates that vaccination intensity significantly contributes to reducing the effective reproduction number. A modified fractional Runge–Kutta numerical method is developed and implemented to approximate solutions with improved stability and accuracy over traditional schemes. Numerical simulations demonstrate how the fractional order and vaccination rate jointly govern epidemic peaks, persistence, and eradication timelines. The results confirm that fractional dynamics and adaptive vaccination policies yield more realistic epidemic trajectories than classical models. The proposed framework provides an efficient tool for assessing public-health vaccination strategies under memory-dependent epidemic evolution.