Smallpox, influenza, and measles spread rapidly in the americas because of

Prior to the arrival of European colonists and explorers, indigenous American populations had had no exposure to these diseases. As such, they not no inherited immunity, and once the diseases arrived, they spread quickly throughout the native populations, inflicting massive damage and causing tremendous loss of life.

The main reason as to why small pox, influenza, and measles spread rapidly in the America was because of the fact that there was a lack of previous exposure in which would have been responsible of having to build a natural immunity.