incompetence vs disease

incompetence and disease both are nouns.

Word	Noun	Adjective	Verb	Adverb
incompetence	Yes	No	No	No
disease	Yes	No	No	No

As nouns, disease is a hypernym of incompetence; that is, disease is a word with a broader meaning than incompetence:

incompetence (noun)	disease (noun)
lack of physical or intellectual ability or qualifications	an impairment of health or a condition of abnormal functioning
inability of a part or organ to function properly