论文标题
与社会结构隔室流行模型的不确定数据的控制
Control with uncertain data of socially structured compartmental epidemic models
论文作者
论文摘要
采用遏制措施来减少流行峰的幅度是解决流行病的迅速传播的关键方面。必须修改和研究经典的隔间模型，以正确描述强迫外部作用减少疾病影响的影响。必须考虑社会结构的重要性，例如在最近的Covid-19大流行中证明的年龄依赖性，而且还必须考虑，此外，可用数据通常是不完整和异质的，因此必须从一开始就将高度的不确定性纳入模型中。在这项工作中，我们通过在存在不确定数据的情况下对社会结构化流行模型的最佳控制表述来解决这些方面。在引入最佳控制问题之后，我们制定了对控制的瞬时近似，这使我们能够得出能够描述流行峰值降低的新反馈控制的隔间模型。对长期干预措施的需求表明，基于系统的社会结构的替代行动可能与更昂贵的全球战略一样有效。然而，对于实际受感染人数不确定的参数，干预措施的时间和强度尤其重要。介绍并讨论了与最近Covid-19-19-19的第一波潮流中的数据相关的模拟。
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.
