The narrative of a universal catastrophic epidemic of Old World diseases is not supported by the current best archaeological, anthropological, and historical data. Please see this post for more about the complexity behind the "death by disease alone" narrative. You might also enjoy this deep dive into the history of the U.S. Southeast as a specific example of the complexity of interpreting population history when disease, warfare, slaving raids, and territorial displacement interact over centuries.

To the larger question, paleodemography examines human population history, but it will always be difficult to determine exact numbers of those who perished in the excess mortality following contact. See this answer for a brief rant on how estimates were constructed in the past, and the current different perspectives. As I wrote in a previous answer, Native American history is richer and deeper than estimates of population size, or the percentage who died from epidemic disease, can ever encapsulate. I highly recommend diving into a specific time or place of interest to help understand how contact influenced different populations at different times. We are always happy to provide suggestions for further reading!

I'm wondering why it didn't work the other way, new world diseases killing old world people. Was it due to diversity of the old world having built up immunity?