In this study, we used a mathematical model of the smoking epidemic which was divided into three sub-classes. In this model we provide four optimal controls, namely education campaign about cigarettes, vaccines, treatment and rehabilitation. To solve the problem of optimal control, we use the principle of maximum pontryagin, where the objective function is set to increase the population of individuals who quit smoking and reduce the number of smokers. In the solution, we use the numerical method namely Runge Kutta forward-backward sweep order4 and simulated using MATLAB with the values of initial parameters and conditions are given based on the results of a survey that conducted on high school students in several schools in Lamongan. The control provided in this study shows a decrease in the number of individual population of potential smokers and active smokers, as well as an increase in the number of individual ex-smokers. These results also indicate that the system gets the optimal solution according to certain values of the control level.
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