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Optimal control strategies in a quitting smoking model with age structure

In this paper, we propose a kind of quitting smoking model with age structure, in which we consider two control measures, i,e., propaganda and education for the public and treatment for the smokers, in order to achieve the desired effect of smoking cessation. We calculated the threshold of smoking, and put forward an objective function. Based on Pontryagin Maximum Principle(PMP), we discuss issues related with control to get the optimal control expressions. The results of this paper have certain theoretical reference values for the relevant policy makers and individuals.