In this paper discusses about the mathematical model the number of smokers with nonlinearincidence rate and the application of fines This model divides the population into four subpopulations,potential smokers, occasional smokers, heavy smokers and quit smokers. The results obtained from theanalysis of models, there is one free smokers equilibrium state and the one smokers endemic equilibriumstate. If the condition are complete, then a free smokers equilibrium state is asymptotically stable and aendemic equilibrium state is asymptotically stable.Keywords: asymptotically stable, equilibrium state, mathematical model the number of smokers
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