AI 中文总结
研究在社会经济目标冲突下疫情动态的最优控制，提出经济模型预测控制框架应用于扩展模型，通过敏感性分析等得出预测时域N = 35天成本最小，“锤击与舞蹈”策略是最优解，建立最优运行点稳定性为疫情政策提供决策支持。
AI 中文摘要
本文探讨了在相互冲突的社会经济目标下疫情动态的最优控制问题。我们提出了一个经济模型预测控制（MPC）框架，应用于扩展的SEIR - V（易感 - 暴露 - 感染 - 康复 - 接种）分区模型来控制传染病传播，同时最小化经济干扰。控制问题被表述为一个约束非线性优化问题，控制器动态调整社会互动水平（传播率β）和疫苗接种力度，以最小化一个综合成本函数，该函数惩罚死亡、医疗能力违规和经济损失。我们对预测时域N进行了严格的敏感性分析，表明闭环对时域选择具有鲁棒性，且N = 35天可使实际成本最小化。此外，闭环解决方案和跨不同初始条件的开环大道分析表明，著名的“锤击与舞蹈”缓解策略自然地作为数学最优解出现：最优轨迹锚定到唯一的抑制大道（最大封锁），将住院人数推向无病平衡点，然后逐步重新开放经济。通过基于大道理论的论证，我们建立了最优运行点的实际渐近稳定性，为疫情政策提供了一个有数学依据的决策支持工具。
英文摘要
This paper addresses the optimal control of epidemic dynamics under conflicting socio-economic objectives. We propose an economic Model Predictive Control (MPC) framework, applied to an extended SEIR-V (Susceptible-Exposed-Infected-Recovered-Vaccinated) compartmental model to govern the spread of an infectious disease while minimizing economic disruption. The control problem is formulated as a constrained nonlinear optimization problem, in which the controller dynamically adjusts social interaction levels (transmission rate beta) and vaccination efforts to minimize a composite cost function that penalizes fatalities, healthcare capacity violations, and economic losses. We conduct a rigorous sensitivity analysis of the prediction horizon N, demonstrating that the closed loop is robust to the horizon choice and that N = 35 days minimizes the realized cost. Furthermore, both the closed-loop solution and an open-loop turnpike analysis across diverse initial conditions reveal that the celebrated "Hammer and Dance" mitigation strategy emerges naturally as the mathematical optimum: the optimal trajectories anchor to a unique suppression turnpike (maximum lockdown) to drive hospitalizations toward the disease-free equilibrium before progressively reopening the economy. Through a turnpike-based argument we establish practical asymptotic stability of the optimal operating point, providing a mathematically grounded decision-support tool for pandemic policy.
Comments17 pages, 4 figures. Companion papers: arXiv:2606.07413 (model calibration and identification) and arXiv:2606.16305 (EKF state estimation)
