There's a zillion sane ways to handle that problem: for the not obviously infected, confine them for 21+ days of being nonsymptomatic. That would have caught our current index case (AKA Patient Zero). For the infected, send them straight to a hospital equipped for this, we've got 4 of them, our military is building one in Liberia right now, we could make more, and more beds in the ones we have, here and over there.

This could be remedied by allowing 'new entries' after a certain time to exit with proper screening, couldn't it?