¡La Esquina de la Gramática! Rule 19
Illnesses with a lower case letter
The nouns that refer to illnesses are common nouns so they should be written with an initial lower case letter: acromegalia, cáncer, diabetes, espina bífida, gripe, sida.
They will start with a capital letter if they are part of a denominative expression that requires to start with a capital letter (the name of an institution, an organization or a congress): Federación Española de Asociaciones de Espina Bífida e Hidrocefalia.
For the names of illnesses and syndromes that include a prepositional complement that includes the proper noun of the investigator or discoverer, you have to keep the first capital letter of the anthroponym, but the generic noun should be written with a lower case: enfermedad de Alzheimer, enfermedad de Parkinson.
Only when the proper noun designates by itself the illness, it becomes a common name that should be written with an initial lower case letter, and follow the correspondent Spanish grammar rules: Su padre tenía párkinson.