By the sound of it, viral disease went quickly (4)
I believe the answer is:
flew
'went quickly' is the definition.
(I've seen this before)
'by the sound of it viral disease' is the wordplay.
'by the sound of it' indicates a 'sounds like' (homophone) clue.
'viral disease' becomes 'flu' (I've seen this before).
'flu' sounds like 'FLEW'.
(Other definitions for flew that I've seen before include "Fled" , "Rushed (by air?)" , "Rushed < from local flat" , "Took off" , "Dashed" .)