As I recall from reading early accounts, settlers in Jamestown Virginia suffered a lot from malaria and typhoid fever. http://www.u-s-history.com/pages/h519.html
Malaria was a given almost anywhere on the East Coast ~ it was even "seasonal" ~ and populations had been known to grow and prosper in the face of it whether in India or Africa, or China!. All you needed to do was drain the swamps and clear the area of large animals (so the mosquitos had fewer targets).
Philadelphia had malaria pretty bad right up into the 1800s when they finally built a covered over sewer system.
Now, typhoid ~ there's this crowd with an inherent immunity to typhoid, diptheria, black plague, AIDS and cholera. In any European population their percentage is going to grow as those diseases kill the part that isn't immune.
All of those diseases taken together do not equal the carnage at Jamestown.
NOTE: Latin settlement of the South American and North American mainlands was delayed substantially and the focus turned to settling the offshore islands first. Same with Virginia ~ Bermuda and other British "possessions" offshore were well developed long before the East Coast.
Having lived on Maryland's Eastern Shore for 18 years, I testify that the mosquitoes are as big as humming birds, and a bulldozer is needed to cut through the humidity.