A Google search indicates that "generalized disease" is likely to be correct. It seems to be an actual medical term, and is used in context in the title of a medical journal article.
A search for "generalized illness" (which was my first guess) did not yield as good results, that seems to be a less well-defined term (and gets fewer search hits).
I don't think there's good reason to search for a less literal translation, "generalized disease" seems to fit neatly.