Social distancing as a form of nonpharmaceutical intervention has been enacted in many countries as a form of mitigating the spread of COVID-19. There has been a large interest in mathematical modeling to aid in the prediction of both the total infected population and virus-related deaths, as well as to aid government agencies in decision making. As the virus continues to spread, there are both economic and sociological incentives to minimize time spent with strict distancing mandates enforced, and/or to adopt periodically relaxed distancing protocols, which allow for scheduled economic activity. The main objective of this study is to reduce the disease burden in a population, here measured as the peak of the infected population, while simultaneously minimizing the length of time the population is socially distanced, utilizing both a single period of social distancing as well as periodic relaxation. We derive a linear relationship among the optimal start time and duration of a single interval of social distancing from an approximation of the classic epidemic SIR model. Furthermore, we see a sharp phase transition region in start times for a single pulse of distancing, where the peak of the infected population changes rapidly; notably, this transition occurs well before one would intuitively expect. By numerical investigation of more sophisticated epidemiological models designed specifically to describe the COVID-19 pandemic, we see that all share remarkably similar dynamic characteristics when contact rates are subject to periodic or one-shot changes, and hence lead us to conclude that these features are universal in epidemic models. On the other hand, the nonlinearity of epidemic models leads to non-monotone behavior of the peak of infected population under periodic relaxation of social distancing policies. This observation led us to hypothesize that an additional single interval social distancing at a proper time can significantly decrease the infected peak of periodic policies, and we verified this improvement numerically. While synchronous quarantine and social distancing mandates across populations effectively minimize the spread of an epidemic over the world, relaxation decisions should not be enacted at the same time for different populations.

社交距离作为一种非药物干预形式已在许多国家/地区实施，作为减轻 COVID-19 传播的一种形式。人们对数学建模非常感兴趣，以帮助预测总感染人口和与病毒相关的死亡人数，并帮助政府机构做出决策。随着病毒的继续传播，存在经济和社会激励措施，以最大程度地减少执行严格的距离命令所花费的时间，和/或采用定期放宽的距离协议，从而允许按计划进行经济活动。这项研究的主要目的是减少人口的疾病负担，这里以感染人口的高峰来衡量，同时最大限度地减少人口与社会保持距离的时间长度，利用一段时期的社交距离和周期性放松。我们从经典流行病的近似值中推导出最佳开始时间和单个社会距离间隔的持续时间之间的线性关系先生模型。此外，我们在单个距离脉冲的开始时间看到一个尖锐的相变区域，其中受感染人口的峰值变化迅速；值得注意的是，这种转变发生的时间早于人们的直觉预期。通过对专门为描述 COVID-19 大流行而设计的更复杂的流行病学模型进行数值研究，我们发现当接触率发生周期性或一次性变化时，所有模型都具有非常相似的动态特征，因此我们得出结论，这些特征是普遍的在流行病模型中。另一方面，流行病模型的非线性导致在社会隔离政策周期性放松的情况下感染人口峰值的非单调行为。这一观察使我们假设，在适当的时间增加一个单一的社会距离间隔可以显着降低周期性政策的感染高峰，我们通过数字验证了这种改进。虽然跨人群的同步隔离和社会疏远任务有效地减少了流行病在世界范围内的传播，但不应同时针对不同人群制定放宽决定。