Kisses can oddly spread illness (8)
I believe the answer is:
sickness
'illness' is the definition.
(sickness is a kind of health problem)
'kisses can oddly spread' is the wordplay.
'oddly' indicates alternate letters.
'spread' indicates an anagram.
The alternating letters of 'can' are 'cn'.
'kisses'+'cn'='kissescn'
'kissescn' anagrammed gives 'SICKNESS'.
(Other definitions for sickness that I've seen before include "It's not looking good" , "Illness, malady" , "State of being ill" , "Ailment" , "Infirmity" .)