Abstract:In this paper we propose smoking epidemic model which analyzes the spread of smoking in a population. The model consists of five compartments corresponding to five population classes, namely, potential-moderate-heavy-temporarily recoveredpermanently recovered class. The basic reproduction number R 0 has been derived, and then the dynamical behaviors of both smoking free equilibrium and smoking persistent equilibrium are analyzed by the theory of differential equation, and Numerical simulation has been carried out and the results have confirmed the verification of analytical results. Sensitivity analysis of R 0 identifies β 1 , the transmission coefficient from potential smokers to moderate smokers and β 2 , the transmission coefficient from potential smokers to heavy smokers, as the most useful parameters to target for the reduction of R 0 .