So in real life if someone told you "there's plague in Genoa", it meant they probably had come from Genoa, which meant they could carry the plague. Even if they didn't, other travelers from Genoa were probably not far. You only had a small window to close the gates before it was probably too late.
But in the game with instant diplomatic communication, you'll probably be able to see the plague spread and be prepared to close the gates when it comes too close. Don't you worry that this might either lessen the spread of the epidemics or make quarantines way less effective than they should be?