. . . . . . . . great improvement in . . . . . . . . patients condition was brought about by . . . . . . . . use of . . . . . . . . newly developed antibiotic.

The first blank shall take 'a' as 'great improvement' is an expression of quantity. The second and third blank shall take 'the' as the sentence talks about a particular set of patients taking a particular antibiotic. The fourth blank shall take 'a' as 'newly developed antibiotic' represents a singular countable noun and is followed by a word starting with the consonant sound.