Battling with bugs, a farmer grew bananas (4,7)

I believe the answer is:

germ warfare

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'battling with bugs' is the definition.
I can't tell whether this definition defines the answer.

'a farmer grew bananas' is the wordplay.
'bananas' is an anagram indicator (bananas can informally mean crazy).
'a'+'farmer'+'grew'='afarmergrew'
'afarmergrew' is an anagram of 'GERM WARFARE'.

Can you help me to learn more?

(Another definition for germ warfare that I've seen is " threatening use of biology".)

I've seen this clue in The Times and The Sunday Times.

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