rapid
slow
dental (esp. BrE), tooth
industrial (esp. BrE), urban
moral, physical, social

cause
Bacteria stick to food debris in the teeth, causing decay.

stop
Without a lot of money, the mayor won't be able to stop urban decay.

reverse
This government promises to reverse industrial decay.

prevent
The wood is treated with preservative to prevent decay.

fall into
old buildings that had fallen into decay

in decay
The derelict buildings are the signs of a town in decay.

decay in
Smoking accelerates decay in the heart and arteries.

decay of
the slow decay of the castle and the surrounding buildings

the process of decay
signs of decay
My dentist could not find any signs of decay.

an odour/odor of decay, a smell of decay, a stench of decay
A smell of decay pervaded the air.

a state of decay

Decay is used with these nouns as the subject:
rubbish, timber