This study presents a mathematical model utilizing fractal fractional-order Mittag-Leffler (FFM) operators to investigate the transmission dynamics of the mumps virus. The model was assessed both qualitatively and quantitatively, focusing on the existence and uniqueness of solutions, Ulam-Hyers stability, well-posedness, and treatment sensitivity analysis related to the Paramyxoviridae family. Fixed-point theory was used to establish solution constraints for modeling fractional dynamics. A comparative analysis revealed that the fractional-order model outperforms traditional integer-order approaches, offering a more robust and realistic framework for studying mumps virus epidemiology. Synthetic data generated from the two-step Newton solver with a Mittag-Leffler kernel was analyzed using supervised learning techniques and artificial neural networks. The neural network predictions closely matched the numerical results, showing minimal errors, and were validated through convergence metrics and regression analysis. This integrated framework offers a strong method for understanding the transmission dynamics of the mumps virus.
Citation: I-Hung Lee, Sanaullah Saqib, Qin Sheng, Yin-Tzer Shih. An epidemiological model of the mumps virus via Mittag-Leffler Kernel: Stability analysis and artificial neural network solutions[J]. AIMS Mathematics, 2025, 10(10): 24923-24957. doi: 10.3934/math.20251103
This study presents a mathematical model utilizing fractal fractional-order Mittag-Leffler (FFM) operators to investigate the transmission dynamics of the mumps virus. The model was assessed both qualitatively and quantitatively, focusing on the existence and uniqueness of solutions, Ulam-Hyers stability, well-posedness, and treatment sensitivity analysis related to the Paramyxoviridae family. Fixed-point theory was used to establish solution constraints for modeling fractional dynamics. A comparative analysis revealed that the fractional-order model outperforms traditional integer-order approaches, offering a more robust and realistic framework for studying mumps virus epidemiology. Synthetic data generated from the two-step Newton solver with a Mittag-Leffler kernel was analyzed using supervised learning techniques and artificial neural networks. The neural network predictions closely matched the numerical results, showing minimal errors, and were validated through convergence metrics and regression analysis. This integrated framework offers a strong method for understanding the transmission dynamics of the mumps virus.
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I-Hung Lee, Sanaullah Saqib, Qin Sheng, Yin-Tzer Shih. An epidemiological model of the mumps virus via Mittag-Leffler Kernel: Stability analysis and artificial neural network solutions[J]. AIMS Mathematics, 2025, 10(10): 24923-24957. doi: 10.3934/math.20251103
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