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.

中文翻译：

---

不仅仅是“拉平曲线”：通过纯粹的非药物干预措施对流行病进行最佳控制。


当无法提供有效的医疗和疫苗接种时，保持社交距离、家庭隔离和广泛关闭公共生活等非药物干预措施是防止流行病传播的唯一可用策略。基于扩展的SEIR（易感-暴露-感染-恢复）模型和连续时间最优控制理论，我们计算了在从未找到疫苗并完全遏制（消灭疫情）的情况下的最优非药物干预策略是不可能的。在这种情况下，最佳控制必须满足相互竞争的要求：首先，最大限度地减少与疾病相关的死亡；其次，在措施结束时建立足够程度的自然免疫力，以排除第二波疫情。此外，干预措施的社会经济成本应保持在最低限度。数值计算的最优控制策略是一种单次干预场景，超越了启发式干预和简单的“曲线压平”。然而，对计算的控制策略的仔细分析表明，所获得的解决方案实际上是接近系统稳定边界的走钢丝，必须不断平衡社会经济成本和新疫情爆发的风险。该模型系统经过校准，可重现德国 COVID-19 大流行的初始指数增长阶段。