Mathematical Ecology Research Group, Department of Zoology, University of Oxford, Oxford, United Kingdom.
UK Centre for Ecology and Hydrology, Wallingford, United Kingdom.
Front Public Health. 2020 Jun 10;8:262. doi: 10.3389/fpubh.2020.00262. eCollection 2020.
Countries around the world are in a state of lockdown to help limit the spread of SARS-CoV-2. However, as the number of new daily confirmed cases begins to decrease, governments must decide how to release their populations from quarantine as efficiently as possible without overwhelming their health services. We applied an optimal control framework to an adapted Susceptible-Exposure-Infection-Recovery (SEIR) model framework to investigate the efficacy of two potential lockdown release strategies, focusing on the UK population as a test case. To limit recurrent spread, we find that ending quarantine for the entire population simultaneously is a high-risk strategy, and that a gradual re-integration approach would be more reliable. Furthermore, to increase the number of people that can be first released, lockdown should not be ended until the number of new daily confirmed cases reaches a sufficiently low threshold. We model a gradual release strategy by allowing different fractions of those in lockdown to re-enter the working non-quarantined population. Mathematical optimization methods, combined with our adapted SEIR model, determine how to maximize those working while preventing the health service from being overwhelmed. The optimal strategy is broadly found to be to release approximately half the population 2-4 weeks from the end of an initial infection peak, then wait another 3-4 months to allow for a second peak before releasing everyone else. We also modeled an "on-off" strategy, of releasing everyone, but re-establishing lockdown if infections become too high. We conclude that the worst-case scenario of a gradual release is more manageable than the worst-case scenario of an on-off strategy, and caution against lockdown-release strategies based on a threshold-dependent on-off mechanism. The two quantities most critical in determining the optimal solution are transmission rate and the recovery rate, where the latter is defined as the fraction of infected people in any given day that then become classed as recovered. We suggest that the accurate identification of these values is of particular importance to the ongoing monitoring of the pandemic.
世界各地的国家都处于封锁状态，以帮助限制 SARS-CoV-2 的传播。然而，随着每日新增确诊病例数开始减少，政府必须决定如何以最高效的方式让民众从隔离中释放出来，同时又不会使医疗系统不堪重负。我们将最优控制框架应用于适应性易感-暴露-感染-恢复（SEIR）模型框架中，以研究两种潜在的封锁释放策略的效果，重点关注英国作为测试案例的人口。为了限制反复传播，我们发现同时结束所有人口的隔离是一种高风险策略，而渐进式重新整合的方法则更为可靠。此外，为了增加可以首先释放的人数，在新的每日新增确诊病例数达到足够低的阈值之前，不应结束封锁。我们通过允许不同比例的隔离人群重新进入工作非隔离人群，来模拟渐进式的释放策略。数学优化方法与我们的适应性 SEIR 模型相结合，确定如何在防止医疗系统过载的同时最大化工作人数。研究发现，最优策略是在最初感染高峰结束后 2-4 周内释放大约一半的人口，然后再等待 3-4 个月，以便在释放其他人之前允许出现第二次高峰。我们还模拟了一种“开-关”策略，即释放所有人，但如果感染率过高则重新实施封锁。我们得出结论，渐进式释放的最坏情况比开-关策略的最坏情况更易于管理，并警告不要基于依赖于阈值的开-关机制的封锁释放策略。在确定最优解方面最关键的两个数量是传播率和恢复率，后者定义为每天任何给定的感染人数中随后被归类为已恢复的人数比例。我们建议，准确识别这些值对于对大流行的持续监测特别重要。
