My wife and I were reminded of this while watching The West yesterday evening and immediately wondered if there was a mutual exchange of harmful contagions.
Not to discourage further answers, but /u/anthropology_nerd's answer in the thread "One of the main reasons Europeans were so utterly victorious against Native Americans was the introduction of diseases, that decimated the population. Why did the Norsemen of Vinland not bring diseases that carried the same effect? answered a similar question fantastically well.