Without widespread immunization, the road to recovery from the current COVID-19 lockdowns will optimally follow a path that finds the difficult balance between the social and economic benefits of liberty and the toll from the disease. We provide an approach that combines epidemiology and economic models, taking as given that the maximum capacity of the healthcare system imposes a constraint that must not be exceeded. Treating the transmission rate as a decreasing function of the severity of the lockdown, we first determine the minimal lockdown that satisfies this constraint using an epidemiology model with a homogeneous population to predict future demand for healthcare. Allowing for a heterogeneous population, we then derive the optimal lockdown policy under the assumption of homogeneous mixing and show that it is characterized by a bang–bang solution. Possibilities such as the capacity of the healthcare system increasing or a vaccine arriving at some point in the future do not substantively impact the dynamically optimal policy until such an event actually occurs.

如果没有广泛的免疫接种，从目前的 COVID-19 封锁中恢复的最佳途径将是在自由的社会和经济利益与疾病造成的损失之间找到艰难的平衡。我们提供了一种结合流行病学和经济模型的方法，假设医疗保健系统的最大容量施加了一个不能超过的约束。将传播率视为锁定严重程度的递减函数，我们首先使用具有同质人口的流行病学模型来确定满足此约束的最小锁定，以预测未来对医疗保健的需求。允许异质人口，然后，我们在均匀混合的假设下推导出最优锁定策略，并表明它具有 bang-bang 解决方案的特征。在此类事件实际发生之前，医疗保健系统容量增加或疫苗在未来某个时间到达等可能性不会对动态最优策略产生实质性影响。