The approach of artificial neural network backpropagation with Levenberg Marquardt algorithm (LMA) and Bayesian Regularization algorithm (BRA) is used to analyze the smoking model in this study. We start by looking at a delayed smoking model wherein potential smokers be supposed to meet the logistic equation. As in manner of Delayed Differential Equations (DDEs), we analyze the dynamic characteristics of the developed framework and provide criteria regarding asymptotic stability of the system in steady condition. The model's Hopf bifurcation study is also addressed. The Adam numerical approach is used to build the reference dataset in Mathematica. The numerical and graphical results to the smoking problem is then interpreted using this dataset in MATLAB. The validity of applied techniques is validated using regression plots, MSE curves, and error histogram.