Semi-analytical method for solving a model of the evolution of smoking habit using global rational approximants

The evolution of the smoking habit represents a complicated issue that requires a deep understanding in order to formulate effective public health strategies. Mathematical models have proved to be useful tools for studying and predicting the spread of social habits, including the dynamics of the smoking habit. However, finding exact solutions for such models is usually difficult and requires the development of accurate approximate solutions. In this paper, we provide an efficient semi-analytical method for finding global rational approximants of a model of the evolution of smoking habit with less computational effort. These global rational approximants are obtained as numerical analytical solutions to the model using a few coefficients from the series expansions for small and large values. They are derived in terms of two-point Padé approximants. To demonstrate the effectiveness of our study, some plots have been provided and compared with the results obtained via the one-point Padé approximants and the numerical Runge–Kutta–Fehlberg method. Furthermore, a numerical comparison between our method and the Laplace–Padé series method is also included. Moreover, the results obtained in this study show high accuracy without using long computation.