The adoption of containment measures to reduce the amplitude of the epidemic peak is a key aspect in tackling the rapid spread of an epidemic. Classical compartmental models must be modified and studied to correctly describe the effects of forced external actions to reduce the impact of the disease. The importance of social structure, such as the age dependence that proved essential in the recent COVID-19 pandemic, must be considered, and in addition, the available data are often incomplete and heterogeneous, so a high degree of uncertainty must be incorporated into the model from the beginning. In this work we address these aspects, through an optimal control formulation of a socially structured epidemic model in presence of uncertain data. After the introduction of the optimal control problem, we formulate an instantaneous approximation of the control that allows us to derive new feedback controlled compartmental models capable of describing the epidemic peak reduction. The need for long-term interventions shows that alternative actions based on the social structure of the system can be as effective as the more expensive global strategy. The timing and intensity of interventions, however, is particularly relevant in the case of uncertain parameters on the actual number of infected people. Simulations related to data from the first wave of the recent COVID-19 outbreak in Italy are presented and discussed.

采取遏制措施以减少流行病高峰的幅度是应对流行病迅速蔓延的关键方面。必须修改和研究经典的隔室模型，以正确描述强迫性外部作用的影响，以减少疾病的影响。必须考虑社会结构的重要性，例如在最近的COVID-19大流行中被证明必不可少的年龄依赖性，此外，可用的数据通常不完整且异质，因此必须将高度不确定性纳入研究范围。从一开始就是模特。在这项工作中，我们通过存在不确定数据的社会结构流行病模型的最优控制公式来解决这些问题。引入最优控制问题后，我们制定了控制的瞬时近似值，该近似值使我们能够导出能够描述流行病高峰减少的新的反馈控制隔室模型。对长期干预的需求表明，基于系统社会结构的替代行动可以与成本更高的全球战略一样有效。但是，在实际感染人数参数不确定的情况下，干预的时机和强度尤其重要。提出并讨论了与来自意大利最近一次COVID-19爆发的第一波数据有关的模拟。对长期干预的需求表明，基于系统社会结构的替代行动可以与成本更高的全球战略一样有效。但是，在实际感染人数参数不确定的情况下，干预的时机和强度尤其重要。提出并讨论了与来自意大利最近一次COVID-19爆发的第一波数据有关的模拟。对长期干预的需求表明，基于系统社会结构的替代行动可以与成本更高的全球战略一样有效。但是，在实际感染人数参数不确定的情况下，干预的时机和强度尤其重要。提出并讨论了与来自意大利最近一次COVID-19爆发的第一波数据有关的模拟。