Neural network-based analysis of heroin epidemic models with modified fractional operators

Source abstract

Heroin and synthetic narcotic abuse have become a major global concern, posing challenges to individuals, families, and communities. Their widespread availability and low cost have intensified the crisis. This study investigates a heroin transmission model using the modified Atangana--Baleanu--Caputo (mABC) fractional operator, with emphasis on non-zero solutions. Series solutions are derived by combining the Laplace transform with the Adomian decomposition method to address nonlinear components. Qualitative analysis is conducted through fixed-point theory, while stability is assessed using the T-Picard method. Numerical simulations explore the effects of different fractional orders and transmission parameters on the system. The study incorporates a deep neural network with two hidden layers: the first employs a hyperbolic tangent (\textit{tanh}) activation function, and the second uses a linear activation function. The dataset is divided into training, testing, and validation sets.