From a MP game with players in France and HRE, we had hospital ranging from level 1 to max level.The black plague came and the max level were not touched.The level 5 were 50/50 and where holding quite a long time before getting the disease (so started later for those who got it and thus ended later for them). It allow a bit more strategic option as the plague will reduce your forces, thus allow to spread the reduction overtime.The level 4, I think 1 province was able to avoid it out of more than 10.And lower level got it, just a smal delay compared to those without.After it really depends on the disease : https://ck2.paradoxwikis.com/Disease#List_of_epidemic_diseases Here you can see the disease and their Contagiousness. I'm pretty sure that with a medium level hospital, you can fend of most of the 30-50% disease. For the plague, it's mostly luck considering how high its cotagiousness is.