Most epidemic diseases originated as zoonoses, i.e. came from animals. In particular, most came from domesticated animals, where there was a large amount of contact between man and beast. [No, that's not what I mean, get your mind out of the gutter.
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There's a REASON why the Columbian exchange was so massively weighted against the New World.
Smallpox, or equivalent, is really highly unlikely to get established in the New World unless 1) you have lots of domestic livestock for a millennium or more and 2) you have large enough populations in easy communication distances of each other to keep the disease going.
Measles, for instance, seems to need 5 million people in easy contact, or it burns out.
There are, of course, exceptions. Several of the tropical diseases (like malaria) have been with humanity since before humans existed (e.g. one strain split when humans and chimps split). Again, the New World doesn't have that million years of co-evolution.
There are many, many threads on this board trying to even the Columbian exchange, and they all boil down to the same basics, really.