Bloke gets half the dogs' disease (5)
I believe the answer is:
mange
'disease' is the definition.
(mange is a kind of disease)
'bloke gets half the dogs'' is the wordplay.
'bloke' becomes 'man' (informal term for a man).
'half' means to take half the letters.
'the dogs'' means one lot of letters go next to another (dogs can mean follows or chases).
'gets' halved is 'ge'.
'man'+'ge'='MANGE'
(Other definitions for mange that I've seen before include "Skin disease of mammals" , "Skin disease of cats and dogs" , "Skin disease affecting hairy animals" , "Animal's skin disease causing loss of hair" , "Disease in dogs causing hair loss" .)