What question did this study set out to answer?

The aim is to analyze a fractional-order norovirus transmission model considering vaccination and environmental factors.

May 27, 2026Open Access

AI-Driven Analysis of Fractal Scaling in Fractional-Order Norovirus Transmission Models with L-BFGS-B Parameter Calibration

Key Points

The aim is to analyze a fractional-order norovirus transmission model considering vaccination and environmental factors.
Developed a fractional-order model with multiple infection stages and a memory effect using Atangana-Baleanu derivative.
Employed L-BFGS-B optimization for parameter calibration, split data for training and testing at 80%-20%.
Used RMSE, MAE, and fitted analyses for evaluating model accuracy across compartments.
For fractional orders below 0.9, the model demonstrated near-perfect agreement with test data.
Parameter estimation for fractional orders 0.9 and 1.0 showed disturbances leading to negative values in some compartments.
The findings suggest fractional calculus enhances the accuracy of epidemiological models for norovirus.

Abstract

Norovirus is a leading cause of acute gastroenteritis worldwide, characterized by high transmissibility, environmental persistence, and limited lasting immunity. We propose and analyse a fractional-order norovirus transmission model with vaccination, environmental contamination, and multiple infection stages including pathogen. The model is constructed with the Atangana-Baleanu fractional derivative to capture memory effects in epidemiological dynamics. We establish the well-posedness of the system: positivity, boundedness, and invariance of solutions are proved, and existence and uniqueness of solutions are analyzed via fixed-point theory. The disease-free equilibrium is computed and the basic reproduction number Formula: see text is derived using the next-generation matrix approach, followed by a sensitivity analysis (PRCC) to identify key parameters. A numerical scheme based on Lagrange interpolation is developed, and Ulam-Hyers stability is verified. Synthetic data are generated for fractional orders Formula: see text and the integer case Formula: see text. The unknown transmission parameters Formula: see text (from quarantine) and Formula: see text (recovery rate from quarantine) are estimated by nonlinear least squares (L-BFGS-B optimisation) using 80% of the data for training and the remaining 20% for testing, with a detailed algorithm and flowchart provided. The fitted model is analyzed through RMSE, MAE, and Formula: see text for all eight compartments. Results show that for Formula: see text the model achieves near-perfect agreement with test data Formula: see text, while for Formula: see text and 1.0 parameter estimation shows disturbance, leading to negative Formula: see text values for some compartments. These findings demonstrate that fractional orders below 0.9 provide a more robust description of norovirus dynamics and facilitate parameter recovery. The study highlights the value of combining fractional calculus with rigorous theoretical analysis and modern optimisation for epidemiological modelling.

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Cite This Study

Bouhnik et al. (Mon,) studied this question.

synapsesocial.com/papers/6a168a340c924ddd1bd58dc0 https://doi.org/https://doi.org/10.1142/s0218348x27400081

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