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<p>The classical integer-order epidemic models often struggle to reproduce the memory effects and complicated temporal patterns seen in real infectious disease data. In this work, we study a fractional-order SEIRVA model for COVID-19 in which each compartment has its own fractional derivative, enabling distinct memory behaviors among epidemiological classes. The model tracks susceptible, exposed, infected, recovered, vaccinated, and adverse-effect populations, and we examine its basic mathematical properties, including positivity of solutions and stability of the relevant equilibria. For the numerical solution of the fractional system, we use the Gorenflo–Mainardi–Moretti–Paradisi (GMMP) scheme and estimate the parameters through the Modified Grid Approximation Method (MGAM). We further embed the model in a hybrid machine-learning framework that produces time-dependent parameter functions, making it more adaptable to real-world COVID-19 data. Our simulations show that the resulting multi-order fractional model fits the observed COVID-19 data, as reflected by a significantly lower root mean squared relative error (RMSRE) than the integer-order model. In particular, assigning distinct fractional orders to the different compartments yields the best predictive performance, highlighting the importance of heterogeneous memory effects in epidemic dynamics.</p>

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Stability, numerical solution and parameter estimation of SEIRVA fractional order model

  • 期刊论文

  • 发表日期：

    2026年6月29日

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  • Arjun Prakash,
  • Syed Abbas,
  • Amel Touati,
  • Khaled A. Aldwoah

摘要

The classical integer-order epidemic models often struggle to reproduce the memory effects and complicated temporal patterns seen in real infectious disease data. In this work, we study a fractional-order SEIRVA model for COVID-19 in which each compartment has its own fractional derivative, enabling distinct memory behaviors among epidemiological classes. The model tracks susceptible, exposed, infected, recovered, vaccinated, and adverse-effect populations, and we examine its basic mathematical properties, including positivity of solutions and stability of the relevant equilibria. For the numerical solution of the fractional system, we use the Gorenflo–Mainardi–Moretti–Paradisi (GMMP) scheme and estimate the parameters through the Modified Grid Approximation Method (MGAM). We further embed the model in a hybrid machine-learning framework that produces time-dependent parameter functions, making it more adaptable to real-world COVID-19 data. Our simulations show that the resulting multi-order fractional model fits the observed COVID-19 data, as reflected by a significantly lower root mean squared relative error (RMSRE) than the integer-order model. In particular, assigning distinct fractional orders to the different compartments yields the best predictive performance, highlighting the importance of heterogeneous memory effects in epidemic dynamics.