Mathematical and numerical analysis of a fractional SIQR epidemic model with normalized Caputo–Fabrizio operator and machine learning approaches

Ramsha Shafqat; Ateq Alsaadi; Ramsha Shafqat; Ateq Alsaadi

doi:10.3934/math.2025904

AIMS Mathematics

2025, Volume 10, Issue 9: 20235-20261. doi: 10.3934/math.2025904

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Mathematical and numerical analysis of a fractional SIQR epidemic model with normalized Caputo–Fabrizio operator and machine learning approaches

Ramsha Shafqat ^{1
,
,},
Ateq Alsaadi ²

1.
Department of Mathematics and Statistics, The University of Lahore, Sargodha 40100, Pakistan
2.
Department of Mathematics and Statistics, College of Science, Taif University, P. O. Box 11099, Taif 21944, Saudi Arabia

Received: 13 July 2025 Revised: 17 August 2025 Accepted: 26 August 2025 Published: 04 September 2025
MSC : 34D20, 34K20, 34K60, 92C60, 92D45

This paper introduces, analyzes, and numerically investigates a fractional-order SIQR epidemic model with the normalized Caputo–Fabrizio derivative. The model captures memory effects and the impact of quarantine or isolation interventions, offering a more realistic description of epidemic dynamics. We establish the existence, uniqueness, positivity, and population conservation properties, and then propose a robust numerical scheme. The influence of the memory parameter and kernel normalization is illustrated via simulations, with a discussion on their implications for epidemic forecasting and real-world control strategies. Furthermore, artificial neural networks are applied, with the dataset partitioned into training, validation, and testing subsets. A comprehensive assessment is carried out for each dataset partition.
- fractional differential equation,
- normalized Caputo–Fabrizio,
- SIQR model,
- numerical outcomes,
- machine learning
Citation: Ramsha Shafqat, Ateq Alsaadi. Mathematical and numerical analysis of a fractional SIQR epidemic model with normalized Caputo–Fabrizio operator and machine learning approaches[J]. AIMS Mathematics, 2025, 10(9): 20235-20261. doi: 10.3934/math.2025904

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Abstract

This paper introduces, analyzes, and numerically investigates a fractional-order SIQR epidemic model with the normalized Caputo–Fabrizio derivative. The model captures memory effects and the impact of quarantine or isolation interventions, offering a more realistic description of epidemic dynamics. We establish the existence, uniqueness, positivity, and population conservation properties, and then propose a robust numerical scheme. The influence of the memory parameter and kernel normalization is illustrated via simulations, with a discussion on their implications for epidemic forecasting and real-world control strategies. Furthermore, artificial neural networks are applied, with the dataset partitioned into training, validation, and testing subsets. A comprehensive assessment is carried out for each dataset partition.

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