Right now around 2000 inmates are infected. If doubling time is 1 day in prison population then there were only 2 infected prisoners 10 days ago.
Could be you had one person that infected 200 fellow prisoners over a couple of days. After that you only need a week to infect everyone.
Strikes me we probably I was well need to be really careful drawing naive inferences from epidemiological numbers. That said suspect limiting group contact sizes is really important because of stuff like this. In order to keep random highly infectious people from infecting large numbers of people in one setting.
E.g. if you put 1 infected person in a crowded bus for a day long trip, the R0 within that group would probably be close to number of passengers.