In this article, we consider an age-structured SIR endemic model. The model is formulated from the available literature while adding some new assumptions. In order to control the infection, we consider vaccination as a control variable and a control problem is presented for further analysis. The method of weak derivatives and minimizing sequence argument are used for deriving necessary conditions and existence results. The desired criterion is achieved and sample simulations were presented which shows the effectiveness of the control.

中文翻译：

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年龄结构SIR流行模型的最优控制策略

在本文中，我们考虑了一个年龄结构的 SIR 流行模型。该模型是根据现有文献制定的，同时添加了一些新假设。为了控制感染，我们将疫苗接种视为控制变量，并提出控制问题以供进一步分析。弱导数和最小化序列自变量的方法用于推导必要条件和存在结果。达到了所需的标准，并提供了示例模拟，显示了控制的有效性。