Hi,
I'm typing a paper for my history class using Microsoft Word, and I found that this sentence is underlined in green and is considered a fragment: In 1972, smallpox immunization ceased in the United States due to the vaccine’s incredible effectiveness in eliminating smallpox.
Just add a comma as I've shown, and the green will go away. 
In 1972, smallpox immunization ceased in the United States, due to the vaccine’s incredible effectiveness in eliminating smallpox.
For style, I would replace the second word 'smallpox' with the pronoun 'it'.
Best wishes, Clive