A Hybrid Approach for Approximating a Smoking Epidemic Model via Caputo’s Derivative, a Novel Integral Transform, and Artificial NeuralNetworks

Abstract

This work focuses on obtaining approximate analytical solutions for a fractional-order smoking epidemic model formulated with the Caputo derivative. The model divides the population into five compartments—potential smokers, current smokers, occasional smokers, permanent smokers, and temporary quitters—allowing the fractional framework to capture the long-term memory effects in smoking dynamics. Transition rates between these compartments are described by a set of parameters that reflect realistic behavioral changes. To solve the non linear fractional differential system efficiently, we propose a new hybrid computational strategy that combines the Junaid integral transform TN G with the Adomian Decomposition Method (ADM) and an Artificial Neural Network (ANN). The combined TN G–ADM stage ensures rapid convergence and accurate series solutions, while the ANN improves predictive performance by learning directly from the system dynamics. Numerical simulations validate the effectiveness and computational efficiency of the proposed approach, demonstrating its suitability for modelling memory-dependent epidemiological processes.