Fascinating. The 1334 date caught my eye, and I wonder where you got it, and if it might possibly be accurate.
You are accurately quoting the first regular Star Trek episode called Requiem for Methuslah
https://m.facebook.com/permalink.php?story_fbid=1533344353361419&id=297107380318462
I never knew that Star Trek dealt with the plague, let alone Constantinople. That said, for some reason Star Trek has the dates off.
The Plague rolled spread from Constantinople throughout the Mediterranean in 1347—it didn’t arrive there any earlier than 1346, and everything that I find (outside of Star Trek) points to 1347 being the arrival time.
https://www.ncbi.nlm.nih.gov/pubmed/22037442
No: Season 3, Episode 19.
Regards,