Castillo et al. (2000) proposed a simple mathematical model for giving up smoking in which the population was divided into three classes: Potential smokers, i.e. people who do not smoke yet but might become smokers in the future (P),Smokers (S) and smokers who have quit smoking permanently (Qp). We adopt in this paper the mathematical model developed by Shoromi and Gumel (2008). In their work, they introduced a new class QT of smokers who temporarily quit smoking and they described the dynamics of smoking by the following four non-linear differential equations: