For laughs, I did a google-search to see whether there was any band with that name, The Disease. There are lots of bands with the word disease in their name:
Sweet New Disease,
Faith & Disease,
The Cassandra Disease,
Legionaire's Disease Band,
Finnish death/thrash band Spirit Disease,
Swedish death metal band Terminal Spirit Disease,
Canadian black metal band Spread The Disease (acron: STD!)
punk rock band Mad Crowd Disease,
another punk band called Mad Kid Disease...
alternative rock band Mad Cow Disease
but I could not find a band that was simply called "The Disease", though I did find "Thy Disease".
Though (unfortunately) not a band name, one of the wildest finds was... Ballet's Disease! http://www.whonamedit.com/synd.cfm/612.html.
Musicians apparently feel the need to specify the Disease, but not The Cure...