Cigarettes are one of the addictive tobacco products because they contain nicotine, which is transmitted between smokers and non-smokers. Prevention is done by not making contact with smokers and giving one type of nicotine replacement therapy. The purpose of this study was to find out the form of the spread of smoking habits that occurs among the community when given nicotine replacement therapy as an effort to prevent this spread. The method in this research is literature. The results of the analysis show that the smoking free fixed point always exists. If then the smoking habit free fixed point is asymptotically stable. The smoking habit endemic fixed point will exist if it fulfills several conditions. Under certain conditions, the endemic fixed point is asymptotically stable and the smoking free fixed point is unstable so that smoking will endemic in the population
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