WordNet sense 1 (a disease that is constantly present to a greater or lesser degree in people of a certain class or in people living in a particular location):

endemic disease

WordNet sense 2 (of or relating to a disease (or anything resembling a disease) constantly present to greater or lesser extent in a particular locality):

endemical

WordNet sense 3 (originating where it is found):

indigenous, autochthonal, autochthonic, autochthonous

WordNet sense 4 (characteristic of or existing by virtue of geographic origin):

native