Stability Analysis of a Smoking Behavior Model

Abstract

This research discussed the mathematical model of smoking behavior. The model will be analogous to an epidemic model which will be divided into several compartments/groups. This research aimed to explain the formation of a mathematical model of smoking behavior, to investigate the equilibrium point, the value of the basic reproduction number, to analyze the stability of the model, then to determine and interpret the numerical solutions using the fourthorder Runge-Kutta method. By the results of this research, a mathematical model of smoking behavior which consists of three compartments, namely the population of non-smokers, smokers and ex-smokers, was obtained. Based on the model formed the smoke-free equilibrium point and the smoker equilibrium point, then the basic reproduction number was also obtained using the next generation matrix. Furthermore, the result of the stability analysis of the smoker-free population was asymptotically stable provided that the basic reproduction number is less than one, while the population was asymptotically stable provided that the basic reproduction number is greater than one. The simulation of the model was presented to support the explanation of the stability analysis of the model using the fourth-order Runge-Kutta method based on the parameters that met the requirements of the stability analysis.