论文标题
不仅仅是“平坦曲线”：纯粹的非药物干预措施对流行病的最佳控制
Beyond just "flattening the curve": Optimal control of epidemics with purely non-pharmaceutical interventions
论文作者
论文摘要
如果没有有效的医疗治疗和疫苗接种，则唯一可以防止流行病的传播的唯一可用策略，例如社会疏远，家庭隔离和公共生活的深远关闭措施，例如社会疏远，家庭隔离和深远的关闭。基于扩展的SEIR（易感性侵袭性的反射）模型和持续的最佳控制理论，我们计算了永远无法找到疫苗并且完全遏制（消除流行病）的最佳非药物干预策略是不可能的。在这种情况下，最佳控制必须满足竞争要求：首先，与疾病相关的死亡的最小化，其次，在措施结束时建立足够的自然免疫力，以排除第二波。此外，干预的社会经济成本应至少保留。数值计算的最佳控制策略是一种单干性的场景，它超出了启发式动机的干预措施和简单的“曲线平坦”。然而，对计算控制策略的仔细分析表明，所获得的解决方案实际上是靠近系统稳定性边界的绳索步行，在这种情况下，社会经济成本和新爆发的风险必须不断与彼此保持平衡。对模型系统进行了校准，以重现德国Covid-19大流行的初始指数生长阶段。
When effective medical treatment and vaccination are not available, non-pharmaceutical interventions such as social distancing, home quarantine and far-reaching shutdown of public life are the only available strategies to prevent the spread of epidemics. Based on an extended SEIR (susceptible-exposed-infectious-recovered) model and continuous-time optimal control theory, we compute the optimal non-pharmaceutical intervention strategy for the case that a vaccine is never found and complete containment (eradication of the epidemic) is impossible. In this case, the optimal control must meet competing requirements: First, the minimization of disease-related deaths, and, second, the establishment of a sufficient degree of natural immunity at the end of the measures, in order to exclude a second wave. Moreover, the socio-economic costs of the intervention shall be kept at a minimum. The numerically computed optimal control strategy is a single-intervention scenario that goes beyond heuristically motivated interventions and simple "flattening of the curve." Careful analysis of the computed control strategy reveals, however, that the obtained solution is in fact a tightrope walk close to the stability boundary of the system, where socio-economic costs and the risk of a new outbreak must be constantly balanced against one another. The model system is calibrated to reproduce the initial exponential growth phase of the COVID-19 pandemic in Germany.
