I thought I heard something once about a massive loss of lives in the native populations before the wars between natives and whites. But, I remember them saying it wasn't on purpose, i.e not the blankets. (Sorry if this is confusing, wrote this on 4 hours of sleep)
There's always room for discussion but perhaps the section Disease in the Americas in our FAQ will answer your inquiry.
By all accounts, there was a plague that drastically depopulated the land inhabited by the Eastern Algonquin tribes roughly from present day Portland, Maine, to Providence, RI, and as far inland as the Connecticut River valley. The onset seems to have been between 1610-17.
This is covered in volume I of The History of New England by John Gorham Palfrey (1858), pp 99, 176.
Between 1620-30, both Pilgrims and the Puritans also reported very high mortality from sickness in their first few years. This is usually attributed to the weather and poor nutrition but it may be that the English settlers were only somewhat less susceptible to the same disease that devastated the Algonquins.