Intelligent forecasting of monkeypox spread using fractional epidemiological models and machine learning

Saeed M. Alamry; Saeed M. Alamry

doi:10.3934/math.20251006

AIMS Mathematics

2025, Volume 10, Issue 9: 22598-22621. doi: 10.3934/math.20251006

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Intelligent forecasting of monkeypox spread using fractional epidemiological models and machine learning

Saeed M. Alamry ^,

Department of Mathematics and Statistics, College of Science, Taif University, P. O. Box 11099, Taif 21944, Saudi Arabia

Received: 05 August 2025 Revised: 09 September 2025 Accepted: 12 September 2025 Published: 29 September 2025
MSC : 34D20, 34K20, 34K60, 92C60, 92D45

This study develops a fractal-fractional epidemiological model to investigate the transmission dynamics of monkeypox. The existence, uniqueness, and stability of the model are established using fixed-point and Ulam-Hyers frameworks. A fractional Adams-Bashforth scheme is implemented for a numerical approximation, and simulations illustrate the role of memory and fractal effects in the disease spread. To enhance the predictive capability, the model is integrated with an Artificial Neural Network (ANN) and evaluated using publicly available datasets of outbreaks. Benchmarking against Caputo-derivative-based models demonstrates that the proposed approach achieves a superior goodness-of-fit, parameter identifiability, and short-term forecasting accuracy. These results highlight the potential of fractal-fractional modeling combined with machine learning to improve forecasting and inform control strategies for emerging epidemics.
Citation: Saeed M. Alamry. Intelligent forecasting of monkeypox spread using fractional epidemiological models and machine learning[J]. AIMS Mathematics, 2025, 10(9): 22598-22621. doi: 10.3934/math.20251006

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Abstract

This study develops a fractal-fractional epidemiological model to investigate the transmission dynamics of monkeypox. The existence, uniqueness, and stability of the model are established using fixed-point and Ulam-Hyers frameworks. A fractional Adams-Bashforth scheme is implemented for a numerical approximation, and simulations illustrate the role of memory and fractal effects in the disease spread. To enhance the predictive capability, the model is integrated with an Artificial Neural Network (ANN) and evaluated using publicly available datasets of outbreaks. Benchmarking against Caputo-derivative-based models demonstrates that the proposed approach achieves a superior goodness-of-fit, parameter identifiability, and short-term forecasting accuracy. These results highlight the potential of fractal-fractional modeling combined with machine learning to improve forecasting and inform control strategies for emerging epidemics.

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