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

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.