 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 .
<meaning-changed>  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 .
 We find that this region-to-region 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 .