 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 .
<clarity>  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 community-to-community reproductive number is proportional to the travel rate between regions and exponential in the length of the time-delay before community-level action is taken .