A Numerical Prediction on the Smoking Habits

The goal of this study is to predict the smoking habits of individuals that belong to different kinds of groups, namely: potential smokers/non-smokers, light smokers, heavy smokers, and smokers who temporarily and permanently quit smoking. The interactions between these groups are modeled by five ordinary differential equations representing each group. The governing system of differential equations is solved by using the Gegenbauer polynomials. Since the model does not have an analytical solution, numerical results are compared by the fourth order Runge Kutta method and Mathematica default solver to validate the accuracy and efficiency of the method. We simulate the long-term behavior of these individuals and show the interaction among the groups.