In this paper, we formulate a smoking model with delay and immigration, and the possibility of optimal controls both over the susceptible and heavy problem smoker subjects is assumed. The existence of the optimal control pair is also proved. We derive the optimality condition via the Pontryagin's maximum principle with delay and obtain the existence of the optimal solution. Numerical simulation is given. Numerical simulations are made to support the main results.

中文翻译：

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带移民的延迟吸烟模型的最优控制。

在本文中，我们建立了具有延迟和移民的吸烟模型，并假定了对易感人群和重症吸烟者的最佳控制的可能性。还证明了最优控制对的存在。我们通过Pontryagin的最大原理推导了最优性条件，并得到了最优解的存在性。给出了数值模拟。进行数值模拟以支持主要结果。