Mathematical model of changes in smoking behavior which involves smokers who temporarily and permanently quit smoking

In this paper, we discuss a mathematical model of changes in smoking behavior, in which the population is classified into five classes as follow: potential smokers, light smokers, heavy smokers, smokers who temporarily quit smoking and smokers who permanently quit smoking. In this model, the crude death rate of each classes are set apart. The density-dependent death rates are also considered in this model. From this model, we find the smoking-free equilibrium point and analyze the stability by using reproduction number. Then, we analyze the sensitivity of reproduction numbers to determine the parameters that influence the dissemination of changes in smoking behavior. After that, we perform numerical simulations to illustrate the analytic conclusions and to know how far the influence of some parameters on the dissemination of changes in smoking behavior so that we can predict the ways to overcome the dissemination of smoking behavior.