I did think of Annatar, and Frodo's answer regarding the orcs (and whether they eat and drink): 'the shadow that made them can only mock; it cannot make.'
Not as eloquently as Pitchwife, though.
Could the disease be the unwholesomeness that Sauron brought to two different places when, after his fall, he took up residence there? Mirkwood, due to his proximity (in Dol Guldur - is that right - ie is it near Mirkwood?) and then in Mordor. (I'm not sure Mordor was particularly a health-spa before he went back there, though).