具有ICU状态约束的时滞SIR流行病的生存性与控制
Viability and control of a delayed SIR epidemic with an ICU state constraint
AI总结：
针对含常数潜伏期的时滞SIR模型，研究在ICU容量约束下利用泛函生存性理论综合反馈控制，并比较连续与Lipschitz初始条件下的策略及延迟影响。
摘要：
本文研究了时滞SIR流行病的生存性与控制综合。该模型整合了表示潜伏/潜伏期时间的常数时滞。控制输入用于建模非药物干预措施，同时引入重症监护病房（ICU）状态约束以反映医疗系统的容量。所产生的时滞控制系统通过泛函生存性工具进行分析，为通过反馈控制映射满足ICU约束提供了见解。具体而言，我们考虑两种情形：首先，考虑一般连续初始条件的情形。随后，作为分析的进一步细化，我们假设初始条件满足Lipschitz连续性，这与所考虑的模型相一致。本研究将所得的（通常为次优的）控制策略与无延迟情形下的最优策略进行比较，强调了延迟参数的影响。所得结果在结论部分通过数值示例得到支持和说明。
英文摘要：
This paper studies viability and control synthesis for a delayed SIR epidemic. The model integrates a constant delay representing an incubation/latency time. The control inputs model non-pharmaceutical interventions, while an intensive care unit (ICU) state-constraint is introduced to reflect the healthcare system's capacity. The arising delayed control system is analyzed via functional viability tools, providing insights into fulfilling the ICU constraint through feedback control maps. In particular, we consider two scenarios: first, we consider the case of general continuous initial conditions. Then, as a further refinement of our analysis, we assume that the initial conditions satisfy a Lipschitz continuity property, consistent with the considered model. The study compares the (in general, sub-optimal) obtained control policies with the optimal ones for the delay-free case, emphasizing the impact of the delay parameter. The obtained results are supported and illustrated, in a concluding section, by numerical examples.
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