I can't think of any disease that's an infection that isn't also contagious. (It may spread some other way than person to person, but it's still spread.) It may be more appropriate to think of an environmental illness such as poisoning.

Not that that matters at all. The only thing it could possibly tell a person is that if Bernie the Monk has a red dot and Eddie the monk both has one too, and you were at the same poker game and drank the same spiked holy Koolaid, and nobody that was NOT there has a red dot, you might want to consider your options.