Dynamical analysis of nonlinear smoking mathematical model: Levenberg- Marquardt backpropagated intelligent networks

Abstract

Abstract The purpose of this study is to explain the design and analysis of a differential system representing a non-linear smoking mathematical (NSM) model by leveraging the strength of the stochastic method via an artificial Neural Network with Levenberg Marquardt technique (NNs-LMBT), which allows for a more accurate, reliable, and efficient calculation procedure of the dynamics. The NSM model is developed along with experiments that use integer and nonlinear mathematical forms to assign five classes of differential operators to potential smokers, occasional smokers, smokers, smokers who temporarily quit smoking, and smokers who permanently quit smoking. The NSM system is numerically computed using Adams methods, and the results are input into the proposed NNs-LMBT to determine the approximated solution of five distinct examples by incorporating 15% of the data for testing and validation and 85% for training. The given NNs-LMBTs accuracy is demonstrated by comparing the findings from the Adam method's obtained dataset for various scenarios indicating variations in Natural Death frequency. An index of relationships between potential and occasional smokers Index of the relationship between light and heavy smokers, an Index of smoking cessation, The fraction of smokers who effectively quit, and the relationship between smokers and those who temporarily quit but then relapse. In numerical replications of the NNs-LMBTs, the usage of state transitions, error histograms, regression, mean square error, and correlation is also investigated to check their capacity, validity, consistency, correctness, and competence.