In this paper we propose a macro-dynamic age-structured set-up for the analysis of epidemics/economic dynamics in continuous time. The resulting optimal control problem is reformulated in an infinite dimensional Hilbert space framework where we perform the basic steps of dynamic programming approach. Our main result is a verification theorem which allows to guess the feedback form of optimal strategies. This will be a departure point to discuss the behavior of the models of the family we introduce and their policy implications.

中文翻译：

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经济流行动态的年龄结构模型验证结果

在本文中，我们提出了一种宏观动态的年龄结构设置，用于分析连续时间的流行病/经济动态。由此产生的最优控制问题在无限维希尔伯特空间框架中重新表述，我们在其中执行动态规划方法的基本步骤。我们的主要结果是一个验证定理，它允许猜测最优策略的反馈形式。这将是讨论我们引入的家庭模型的行为及其政策含义的出发点。