While the spread of communicable diseases such as coronavirus disease 2019 (COVID-19) is often analyzed assuming a well-mixed population, more realistic models distinguish between transmission within and between geographic regions. A disease can be eliminated if the region-to-region reproductive number—i.e., the average number of other regions to which a single infected region will transmit the disease—is reduced to less than one. Here we show that this region-to-region reproductive number is proportional to the travel rate between regions and exponential in the length of the time-delay before region-level control measures are imposed. If, on average, infected regions (including those that become re-infected in the future) impose social distancing measures shortly after experiencing community transmission, the number of infected regions, and thus the number of regions in which such measures are required, will exponentially decrease over time. Elimination will in this case be a stable fixed point even after the social distancing measures have been lifted from most of the regions.

虽然经常在假设人口充分混合的情况下分析诸如冠状病毒病2019（COVID-19）之类的传染病的传播，但更实际的模型可以区分地理区域内和地理区域之间的传播。如果区域间的生殖数可以消除疾病也就是说，单个感染区域将疾病传播到的其他区域的平均数量减少到少于一个。在这里，我们表明，该区域间的繁殖数量与区域之间的传播速度成比例，并且在实施区域级控制措施之前的时间延迟长度呈指数形式。如果平均而言，在经历社区传播后不久，受感染地区（包括将来会再次感染的地区）采取社会疏离措施，则受感染地区的数量以及需要采取此类措施的地区数量将成倍增长。随时间减少。在这种情况下，即使在大多数地区取消了社会隔离措施之后，消除也将是一个稳定的固定点。