Not only that, but it also explains why the Native Americans were nearly wiped out by exposure to the European's "native germs", but not vice versa.
A chapter or two in "Guns, Germs, and Steel", by Jared Diamond, is devoted to that issue.
The reason is that most of mankind's epidemics have been acquired from our domesticated animals -- they are pathogens which, during thousands of years of close assocation between men and their domestic animals, had the opportunity to "jump species" and begin to specialize in infecting humans (much as the SIV virus recently jumped from chimps to humans, becoming the HIV virus causing AIDS).
People in the "old world" (Europe and Asia) had domestic animals for thousands of years, and many diseases (including smallpox which was originally cowpox, etc.) had adapted to infecting humans. Also during those thousands of years, the humans, through constant exposure to the diseases, had developed innate resistances to them (via evolution, you'll note, since the more susceptible humans died out early, while the less suscpetible ones survived and passed on their resistant genes to future generations).
So the Europeans arrived in the Americas carrying many diseases, and they were diseases which the Native Americans had absolutely no inborn resistance to. The results of that were predictable -- the diseases ran rampant through their populations, killing large percentages of them.
Conversely though, the Native Americans had far fewer domestic animals of any sort, and had had them for shorter periods of time. If they had any native diseases acquired from animals at all, and they may have had none, they must have been mild ones. Another factor which would have limited the acquisition and spread of any "New World" diseases is the fact that the Native Americans lived in smaller groups and were more widely spaced than the Europeans (many of whom had been living crowded together in huge cities and nation-states for many centuries). Any virulent diseases originating in the Americas had a good chance of dying out after killing only the tribe which first contracted it. The Americas were never the home of any far-spreading disease like the Black Plague of Europe -- the Americas never had the large, close-packed populations necessary to sustain the spread of such epidemics.