Smoking model with cravings to smoke

Among smokers, often the desire to quit smoking arise. A large number of smokers attempt to quit, but only a fraction of them are successful. While the health and monetary benefits are inarguable. The huge amount of stress associated with smoking, a combination of powerful cravings, sleep and mood disturbances and cognitive changes often stymie even the most motivated of individuals. In this paper, a mathematical model is proposed and analyzed in which the temporary quitters turn back to smoking by powerful cravings for smoking. We have discussed the qualitative behavior of the model and numerical simulations are carried out to support the analytical results.