Abstract

We analyze the spread of COVID-19 by considering the transmission of the disease among individuals both within and between communities. A set of communities can be defined as any partition of a population such that travel/social contact within each community far exceeds that between them (e.g. the U.S. could be partitioned by state or commuting zone boundaries). COVID-19 can be eliminated if the community-to-community reproductive number—i.e. the expected/average number of other communities to which a single infected community will transmit the virus—is reduced to less than one. We find that this community-to-community reproductive number is proportional to the travel rate between communities and exponential in the length of the time-delay before community-level action is taken. Thus, reductions in travel and the speed at which communities take action can play decisive roles in stopping the outbreak. The analysis suggests that for the coronavirus to be eliminated, it is not necessary to impose aggressive social distancing measures all over the world at once, but rather only in communities in which active spreading is detected. The sooner such measures are imposed, the shorter the duration they must remain in place. If infected communities (including those that become re-infected in the future) are quick enough to act, the number of actively infected communities (and thus the number of communities in which such measures are required) will exponentially decrease over time.