Mathematical modeling of smoking habits in the society

Abstract In this study, we formulate and analyze a non-linear mathematical model to study the dynamics of smoking and its impact on society. This is a compartment model which has four compartments, namely, potential smoker, occasional smoker, smoker and quitters. As per WHO, each year there is a significant number of smoking-related deaths. Keeping this in view, we have incorporated smoking-related death in our proposed model. Further, we investigate the model for possible equilibria, compute the basic reproduction number and investigate the stability of obtained equilibria. Later we extend this model to stochastic model and perform numerical simulation for both the deterministic and the stochastic model. The results of stochastic model are almost similar to the results obtained for deterministic model. We have also explored the impact of the parameters related to quitting smoking habits on the equilibrium level of occasional smokers. We also perform sensitivity analysis to find the key parameters which make significant change in the reproduction numbers.