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<p>Mathematical models of infectious diseases are traditionally formulated using integer-order differential equations; however, such models often fail to capture the memory-dependent and non-local characteristics observed in real epidemic dynamics. To address this limitation, this study proposes a Fractional-Order Physics-Informed Neural Network (FPINN) framework for solving inverse parameter estimation problems in both fractional SIR and augmented SEIR epidemiological models. The proposed approach incorporates Caputo fractional derivatives into the neural network architecture, enabling the integration of epidemiological data with the underlying fractional governing equations. For several prescribed fractional orders, the FPINN framework is employed to estimate key epidemiological parameters, including transmission, incubation, recovery, and vaccination-related rates, while ensuring consistency with the biological dynamics of disease propagation. The framework eliminates the need for traditional mesh-based discretization and provides a unified data-driven and physics-informed strategy for parameter identification. Numerical results demonstrate that the proposed method accurately reconstructs epidemic trajectories and captures the influence of memory effects on disease evolution. The findings highlight the potential of FPINNs as an effective computational tool for parameter estimation, epidemic forecasting, and the analysis of intervention strategies in fractional-order epidemiological systems.</p>

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Fractional physics-informed neural network approach to inverse problems in epidemiological modeling

  • 期刊论文

  • 发表日期：

    2026年7月9日

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  • S. Naveen,
  • V. Parthiban

摘要

Mathematical models of infectious diseases are traditionally formulated using integer-order differential equations; however, such models often fail to capture the memory-dependent and non-local characteristics observed in real epidemic dynamics. To address this limitation, this study proposes a Fractional-Order Physics-Informed Neural Network (FPINN) framework for solving inverse parameter estimation problems in both fractional SIR and augmented SEIR epidemiological models. The proposed approach incorporates Caputo fractional derivatives into the neural network architecture, enabling the integration of epidemiological data with the underlying fractional governing equations. For several prescribed fractional orders, the FPINN framework is employed to estimate key epidemiological parameters, including transmission, incubation, recovery, and vaccination-related rates, while ensuring consistency with the biological dynamics of disease propagation. The framework eliminates the need for traditional mesh-based discretization and provides a unified data-driven and physics-informed strategy for parameter identification. Numerical results demonstrate that the proposed method accurately reconstructs epidemic trajectories and captures the influence of memory effects on disease evolution. The findings highlight the potential of FPINNs as an effective computational tool for parameter estimation, epidemic forecasting, and the analysis of intervention strategies in fractional-order epidemiological systems.