As evidenced by recent outbreaks, given the drop in childhood immunization rates in certain parts of the country, we're not as protected against vaccine-preventable diseases as we have been in the past. Compared to many parts of the world, our vaccination rates are high and we do not see as many cases as are seen in other countries. Assuming our rates do not change, the most likely reason for future outbreaks will be related to travel by someone who is not vaccinated, a citizen becoming infected with something like measles or polio and bringing it back home (often returning before even having symptoms).
We can further prevent this by requiring the same up-to-date vaccination records (with strict, objective medical exceptions only) that we do for those applying (e.g., visas) to move here.