Article history: Received 16 April 2015 Accepted 12 June 2015 Available online 10 July 2015 Keywords: Mathematical model, Education Campaign, Stability analysis, Smoking
In this study, we are proposed and analyzed a deterministic mathematical model for the epidemic model of smoking. The effect of education campaign is taken into account. Our model is analyzed using standard stability method. We investigated the basic properties of the model and the equilibrium points. The smoking free equilibrium and smoking present equilibrium are investigated and the stabilities of the model are determined by Routh-Hurwitz criteria. Smoker reproductive number is determined using the next generation method. If the smoker reproductive number is less than one, the smoking free equilibrium is local asymptotically stable. If smoker reproductive number is greater than one, the smoking present equilibrium point is local asymptotically stable. The graphical results shown that when the value of the effective of education campaign between the potential smoker and the smoker increase, the number of smoker decreases and if the cost of treatment is decrease, the number of smokers increase. Numerical simulations are also presented to support the analytic results of the model.
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