Like many infectious diseases, mathematical models can be used to understand the spread of smoking and to
predict the impact of smokers on the community in order to help reducing the number of smokers. Castillo-Garsow
et al. [3] presented a general epidemiological model to describe the dynamics of Tobacco use and they considered
the effect of peer presure, relapse, counselling and treetment. In their model the population was devided into nonsmokers,
smokers and smokers who quit smoking. Later, this mathematical model was refined by Sharomi and Gumel
[4], they introduced a new class Qt of smokers who temporarily quit smoking. They concluded that the smokingfree
equilibrium is globally-asymptotically stable whenever a certain threshold, known as the smokers-generation
number, is less than unity, and unstable if this threshold is greater than unity. The public health implication of this
result is that the number of smokers in the community will be effectively controlled (or eliminated) at equilibrium