You might like to check out our Frequently Asked Questions section on introduced infectious disease in the Americas, as well as this post I made in /r/badhistory on the common popular myth of death by disease alone in the Americas.

Briefly, disease was simply one of many factors influencing Native American population dynamics after contact. While disease alone has been stressed as the prime mover of change during colonization, recent research is showing how the full cocktail of colonialism (including but not limited to the slave trade, warfare, territory displacement, intentional resource deprivation, identity erasure, etc) resulted in Native American population decline at different rates, and at different times, across the Americas and those same factors influenced population rebound after epidemics in various ways. There is no one story of demography following contact, and the assumption of complete devastation due to disease is now seen as an overly simplistic interpretation of a highly complex time.

The best book to learn more about this topic is Beyond Germs: Native Depopulation in North America if you are interested.