The quick population decay in a lot of native groups in different parts of the Americas are attributed among other things to diseases brought over by Europeans. but I haven't seen or heard much about American diseases affecting Europeans. Were there no rapidly spreading diseases in the Americas at the time? Or maybe it was related to advances in Western medicine?
There is always more to be said, but check out the impact of indigenous pathogens on Europeans section of our FAQ for previous answers to similar questions related to disease spread after contact.