Numerical Approximation of a Smoking Dynamics Model Using a Hybrid Deep Neural Network Architecture

Despite the fact that smoking is still a significant global public health concern, current mathematical models of smoking dynamics primarily depend on conventional numerical solvers. A particular five-compartment smoking dynamics model has not yet been solved using deep neural network (DNN) techniques. In order to fill this research gap, this work creates a unique DNN framework that can simulate nonlinear smoking dynamics in a computationally efficient manner. The Levenberg–Marquardt backpropagation technique is used to improve a dual-hidden-layer network consisting of 20 radial basis activation function (RBAF) neurons and 40 log-sigmoid activation function (LSAF) neurons. With a minimum mean squared error (MSE) of $1.865\times {10}^{-6}$ and a coefficient of determination $R^2$ equal to or near unity across all model variables, the trained DNN offers instantaneous predictions while maintaining superior accuracy, in contrast to traditional numerical methods that necessitate the explicit re-solving of differential equations for each parameter change. Crucially, our DNN-based framework is appropriate for automated public health decision-support systems since it functions independently and does not require human intervention during the prediction phase. Key smoking behaviors, such as initiation, quitting efforts, relapse dynamics, and long-term recovery patterns, are successfully replicated by the framework, while relapse dynamics are captured through the recovered-to-potential smoker pathway, consistent with the original model formulation. These findings show that the proposed DNN approach not only closes the methodological gap in the application of deep learning to smoking dynamics but also offers a dependable and computationally effective tool for quick evaluation of intervention scenarios, supporting evidence-based public health decision making without compromising accuracy.