The success of the program to eradicate smallpox has stimulated experts to pursue
what they had not previously considered possible−better control, if not eradication, of the other infections such as measles and yaws.
Option elimination -
(A)
what they had not previously considered possible−better control, if not eradication, of (correct usage - usage of what to introduce a relative clause to modify the noun experts) the other infections such as - the problem is "the" The means only limited to "the other infections." What are those specific other infections - measles and yaws?. The sentence actually means other infections such as measles, yaws bla bla ....
(B) what they had not previously considered a possibility−better control, if not eradication, of such infections like - easy one. Like is wrong.
(C) something they had not previously considered possible−better control, if not eradication, of such infections as - the is gone, even other is gone. Better.
(D) something not considered a previous possibility−better control and perhaps eradication, of other infections such as - "a" is a problem. "and" is a problem. The actual meaning is better control (if not eradication). Here it says: better control and eradication - either we control or eradicate ....how do we do control and eradication simultaneously? Wrong. Comma before "of" not required.
(E) the possibility of what they had not previously considered possible−better control and possibly eradication of infections like - same "and". Like is wrong.