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.
Recommended Citation
El-Shorbagy, M. A.; Pak, Sedat; Rahman, Mati Ur; and Nabwey, Hossam A.
(2026)
"Neural network-based analysis of heroin epidemic models with modified fractional operators,"
Mathematical Modelling and Numerical Simulation with Applications: Vol. 6:
Iss.
3, Article 5.
DOI: https://doi.org/10.53391/2791-8564.1037
Available at:
https://mmnsa.researchcommons.org/journal/vol6/iss3/5
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Artificial Intelligence and Robotics Commons, Dynamic Systems Commons, Numerical Analysis and Computation Commons