It's probably not an accident that the most pervasive use of them is in the zombie apocalypse -- that is, an SF veneer to a magical notion. (More medieval European vampire than Haitian zombie, but still definitely magic.)
And I say this despite using it as a device myself. A Diabolic Bargain features the white sickness early in the book, for many consequences in the plot, but not the main event. It begins with the villain deciding to exploit it as a cover for his plans, and ties in other things later.
More extensive is Connie Willis's Doomsday Book, where, despite the time-travel and associated issues that naturally tie into such plots, is heavily about day-to-day life in an epidemic. A slice-of-life in epidemic is a kind of genre, however necessarily limited in scope.
It's also big in Illuminae by Amie Kaufman and Jay Kristoff. The plot of "fleeing a dangerous enemy" is greatly complicated by the disease and the issues of dealing with it when in a few spaceships. Quarantine is a big part -- another plot device, though requiring a certain level of tech/magic to make it a reasonable plot.
It can feature in a smaller role, of course. Plagues, as well as floods and famine, can be an excellent disaster to motivate a quest for the magical MacGuffin that can stop them. It produces changes when the refugees come from a disease-laden area, although not quite so much as it might seem at first, because even those coming from war, fire, earthquake, famine, or flood may be a dangerous burden to the place where they arrive. The All-Of-A-Kind family had a background of a polio epidemic when one character got polio. There is a Conan the Barbarian story where the villain's evil wizard produces a plague culminating in the death of the king and all his sons, characterized by rumor as divine retribution, and Tanith Lee wrote a sword and sorcery tale where the plague, killing the king among others, was divine retribution, from a fairly demoniac god, but in both plots the chief effect is to kill the king and so allow someone else to claim the throne.
