Motivated by the current COVID-19 epidemic, this work introduces an epidemiological model in which separate compartments are used for susceptible and asymptomatic “socially distant” populations. Distancing directives are represented by rates of flow into these compartments, as well as by a reduction in contacts that lessens disease transmission. The dynamical behavior of this system is analyzed, under various different rate control strategies, and the sensitivity of the basic reproduction number to various parameters is studied. One of the striking features of this model is the existence of a critical implementation delay (CID) in issuing distancing mandates: while a delay of about two weeks does not have an appreciable effect on the peak number of infections, issuing mandates even slightly after this critical time results in a far greater incidence of infection. Thus, there is a nontrivial but tight “window of opportunity” for commencing social distancing in order to meet the capacity of healthcare resources. However, if one wants to also delay the timing of peak infections – so as to take advantage of potential new therapies and vaccines – action must be taken much faster than the CID. Different relaxation strategies are also simulated, with surprising results. Periodic relaxation policies suggest a schedule which may significantly inhibit peak infective load, but that this schedule is very sensitive to parameter values and the schedule’s frequency. Furthermore, we considered the impact of steadily reducing social distancing measures over time. We find that a too-sudden reopening of society may negate the progress achieved under initial distancing guidelines, but the negative effects can be mitigated if the relaxation strategy is carefully designed.

受当前 COVID-19 疫情的推动，这项工作引入了一种流行病学模型，其中针对易感人群和无症状的“社交距离较远”人群使用单独的隔间。保持距离的指令是通过进入这些隔间的流量以及减少接触来减少疾病传播来表示的。分析了该系统在各种不同速率控制策略下的动态行为，并研究了基本再生数对各种参数的敏感性。该模型的显着特征之一是在发布疏远命令时存在严重的执行延迟（CID）：虽然大约两周的延迟对感染峰值数量没有明显影响，但即使在稍晚一些的情况下也可以发布命令关键时期导致感染发生率更高。因此，为了满足医疗资源的容量，开始保持社交距离有一个重要但紧迫的“机会之窗”。然而，如果人们还想推迟感染高峰的时间 — — 以便利用潜在的新疗法和疫苗 — — 采取行动的速度必须比 CID 快得多。还模拟了不同的放松策略，取得了令人惊讶的结果。周期性放松政策建议采用可以显着抑制峰值感染负荷的时间表，但该时间表对参数值和时间表的频率非常敏感。此外，我们还考虑了随着时间的推移稳步减少社交距离措施的影响。我们发现，过于突然的社会重新开放可能会抵消最初的疏远准则下取得的进展，但如果仔细设计放松策略，负面影响是可以减轻的。