The black death came from fleas. Rats in China had these fleas, and they found their way to Europe. The black death spread so easily because a) there was no proper hygiene, b) cities were often crowded and animals would walk around the streets with humans, c) the 'treatments' that doctors had really didn't have anything to do with the black death. In the end, the black death ended up killing 1/3 of Europe's population and was actually one of the reasons why the feudal system ended.
The capital of Constantinople gave the Byzantine Empire significant strategic advantage, as it was right on the trade routes between Europe and Asia as well as the Mediterranean and Black Seas.
