Smoking is a large problem in the entire world. Despite overwhelming facts about
the risks, smoking is still a bad habit widely spread and socially accepted. Many people
start smoking during their gymnasium period. The main purpose of this paper is to
determine the asymptotic behavior of a mathematical model using for giving up smoking.
Our interest here is to derive and analysis the model taking into account the occasional
smokers compartment in the giving up smoking model. Analysis of this model reveals that
there are four equilibria, one of them is the smoking-free and the other three correspond
to presence of smoking. We also present the global stability and parameter estimates that
characterize the natural history of this disease with numerical simulations.