The choice of region size depends on the spatial granularity at which policy makers are willing and able to control disease transmission. Regions could be cities, counties, states, or any other partition of a population such that the disease transmission occurs predominantly within (as opposed to between) regions. Understanding the dynamics of disease transmission both within and between regions 3, 4, 5, 6, 7, 8, 9, 10 can provide insight into how to eliminate the outbreak by imposing restrictive measures only where the virus is locally spreading, thus minimizing larger-scale economic impacts 11, 12, 13, 14. The outbreak of coronavirus disease 2019 (COVID-19), caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), emerged in Wuhan, China, reportedly in December 2019 1 and has since become a severe pandemic 2.

Elimination will in this case be a stable fixed point even after the social distancing measures have been lifted from most of the regions. 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. 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. 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.

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.

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