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An optimal feedback control that minimizes the epidemic peak in the SIR model under a budget constraint
Automatica ( IF 6.4 ) Pub Date : 2022-09-10 , DOI: 10.1016/j.automatica.2022.110596
Emilio Molina, Alain Rapaport

We give the explicit solution of the optimal control problem which consists in minimizing the epidemic peak in the SIR model when the control is an attenuation factor of the infectious rate, subject to a L1 constraint on the control which represents a budget constraint. The optimal strategy is given as a feedback control which consists in a singular arc maintaining the infected population at a constant level until the immunity threshold is reached, and no intervention outside the singular arc. We discuss and compare this strategy with the one that minimizes the peak when fixing the duration of a single intervention, as already proposed in the literature. Numerical simulations illustrate the benefits of the proposed control.



中文翻译:

在预算约束下最小化 SIR 模型中的流行峰值的最优反馈控制

我们给出了最优控制问题的显式解决方案,该问题包括当控制是传染率的衰减因子时最小化 SIR 模型中的流行峰值,受大号1对表示预算约束的控制的约束。最优策略是作为反馈控制给出的,其包括将感染群体维持在恒定水平直到达到免疫阈值的奇异弧,并且在奇异弧之外没有干预。正如文献中已经提出的那样,我们讨论并将这一策略与在确定单一干预持续时间时最小化峰值的策略进行比较。数值模拟说明了所提出的控制的好处。

更新日期:2022-09-12
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