madness vs rabidity

madness and rabidity both are nouns.

Word	Noun	Adjective	Verb	Adverb
madness	Yes	No	No	No
rabidity	Yes	No	No	No

As nouns, madness and rabidity are synonyms defined as:

Other synonyms of madness include rabidness.

madness (noun)	rabidity (noun)
unrestrained excitement or enthusiasm	unrestrained excitement or enthusiasm
the quality of being rash and foolish	The property of being very extreme, unreasonable, or fanatical in opinion; excessively zealous; comparable to one with rabies.
a feeling of intense anger
obsolete terms for legal insanity
an acute viral disease of the nervous system of warm-blooded animals (usually transmitted by the bite of a rabid animal); rabies is fatal if the virus reaches the brain