Fantastic, yeah Black Death makes sense.
I doubt we're set in that period however (not that it makes any difference), because it wouldn't be called black death then.
So, considering we're right about black death, what I feel is, after the plague broke in the city, one person (or 2?) out of the 7 remaining were affected, and they are now supposed to / inadvertently spread the virus to the rest of us.
We might have a doctor/medic who can diagnose who's infected (sort of the cop).
Now, the thing we don't know is, do the infected person(s) know they're infected, and are doing it on purpose, or it's random. I think it is the former, so that's the anti-town for us.
It would also make sense to kill Simon because he was the first to suggest a plague, which is an important breakthrough.