Out of curiosity, I had a quick look at epidemics around the world. After a quick look at Wikipedia, I was a bit surprised. Let's say that a "great epidemic" has a mortality rate of at least 10-20%, and is geographically widespread. Then the only mentioned occurences of such phenomena are the Justinian plague, the Black Death, and, if we stretch a bit the meaning of epidemics, the outbreaks of plague, measles, smallpox, etc. in the Americas following the colonisation by Europeans.
There does not seem to be other great epidemics : none in the pre-Colombian Americas, none in Africa, Asia is barely mentioned even for the plagues (I don't know what actual effects the plagues have had there, by the way). And none in the Antiquity or earlier.
What good reason is there for that? Is there something special about Europe, which catalysed these outbreaks? Or is there a lack of sources (or good historiography) about these other areas?
There were massive outbreaks of plague in india, north Africa and the middle east in the C19th. (mainly facilitated by the hajj)
Bombay had awful problems with cholera and plague (as did many port cities in the empire)
There was a global outbreak of plague in 1885 that had cases reported in New York. Iirc that killed around 200,000 people. 60k in egypt.
In terms of massive outbreaks on par with the black death I think a lot of it can be put down to record taking (or lack thereof)