This is one of the areas, where gameplay should imho trumph historicality.
A natural disaster of any relevant size will screw the player over, while being dependent on factors completely outside the players control. I'm sure it is a recipe for a thousand rage-quits and save/reloads. Of course flavour events are always nice for the uhm.. flavor.
But imagine playing the Aztecs and having 90 % (I think that was the historical figure?) of your population wiped out by smallpox. You really upped your game, perhaps you got a bit lucky, you made sure you had tribal alliances in place, so Spain found no eager allies, when they landed in meso-america, and consequently the whole story ended with you mounting Cortéz head on a spike outside the gates of Tenochtitlan. But what is this? The Europeans brought smallpox with them, and there's nothing you can do to fight it, and nothing you could have done to prevent it. 90% of your population is now dead. YOU LOSE.
This would litteraly make the game unplayable for such a nation, and become and "auto-loss" outside of player control, almost as bad as the event-annexations of earlier version of Vicky2 (Hawaii and Madagascar). I know it's historical, and small events (like a temporary drop in support limits or something) is all fine, but implementing real nation-shattering epidemics would simply be a bad experience.
You could of course answer that you don't support deterministic epidemics and natural disaster, but would have them happen at random. But this just encourages save/reload-cheating and rage-quitting.
You can take a look at the plague in CKII as far as I know it is seriously watered down. Precisely because a plague that left a third of Europe dead would have ruined the gameplay experience.
I'm sorry, other than flavor events I think this is a bad idea.
EDIT: Okay, so in all fairness I noticed you wrote this:
And you should also be able to quarantine a province or entire regions to decrease the chance of infecting other provinces (which would still happen half of the times).
This is player influence on the event, making the idea more viable BUT:
1) Was a real epidemic ever succesfully contained in this period? And even if quarantine measures were put up they should "fail half the time" (and surely a higher succesrate would be unrealistic)
2) Would quarantining diseased provinces be a no-brainer? - if so this is a choice, where in reality you have no reason to choose option 2: Do nothing, and therefore not adding any depth to the game. Of course you could make the cost of quarantining so prohibitive that it represented a real choice, but then an epidemic would remain a nation-shattering event (either economically if you quarantine or because of population decline if you don't) which is esentially out of the players control, which is bad.