In the show, Tony catches a mutated and incurable form of the plague from a woman who thinks she's exacting revenge on the Navy for the mishandling of her daughter's case (the daughter's case was actually not mishandled and was actually a false report, and the woman herself had a brain tumor that interfered with her reasoning, and none of that had anything to do with Tony anyway, but yeah). Because it's a mutated strain, he's given the same chances as anyone in the Middle Ages would have had. Of course, he survives but not until it looks dramatically grim. It's referenced multiple times in later episodes.

And I guess for the purposes of OP's secret, Gibbs at one point orders Tony not to die, which is as warm and fuzzy as Gibbs gets.