Mathematical modeling of smoking habits in the society

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.

Automated summary

In this study, a nonlinear mathematical model is formulated and analyzed to study the dynamics of smoking and its societal impact. The model considers different compartments representing potential smokers, occasional smokers, smokers, and quitters. The inclusion of smoking-related deaths and exploration of parameter impacts on equilibrium levels provide insights into understanding and addressing smoking habits.