The impact of travel and timing in eliminating COVID-19

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. Large-scale containment measures that reduce the spread of COVID-19 have proven to have too large an impact on both the economy and our mental health to be sustainable in the long term. Here, the authors show that travel reductions between geographical regions and timely local control measures can reduce the region-to-region reproduction number below one, thus eliminating the epidemic and preventing recurrent waves without the need for long-term lockdown measures.