plague vs epidemic disease

plague and epidemic disease both are nouns.

Word	Noun	Adjective	Verb	Adverb
plague	Yes	No	Yes	No
epidemic disease	Yes	No	No	No

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

plague: a serious (sometimes fatal) infection of rodents caused by Yersinia pestis and accidentally transmitted to humans by the bite of a flea that has bitten an infected animal
epidemic disease: any infectious disease that develops and spreads rapidly to many people

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

plague: any epidemic disease with a high death rate
epidemic disease: any infectious disease that develops and spreads rapidly to many people

plague (noun)	epidemic disease (noun)
an annoyance	any infectious disease that develops and spreads rapidly to many people
any large scale calamity (especially when thought to be sent by God)
a swarm of insects that attack plants
a serious (sometimes fatal) infection of rodents caused by Yersinia pestis and accidentally transmitted to humans by the bite of a flea that has bitten an infected animal
any epidemic disease with a high death rate

plague (verb)	epidemic disease (verb)
annoy continually or chronically
cause to suffer a blight