The epidemic diseases that the Europeans brought with them to the Americas were the result of large scale animal domestication. Disease like Measles for example originated in cattle and mutated to effect humans. The waste generated by the animal domestication attracts vermin like rats (carriers the black plague) and fleas and ticks (carriers of the bubonic plague).

Also the food surplus generated by animal domestication and the subsequent trade between nations with ships and roads created vectors for disease.

Native Americans subsisted on small scale agriculture and hunting and gathering and thus did not conditions conducive to the creation and spread of epidemic diseases.

There was Malaria in climates like Florida though.

This is my first answer I hope that helped.