Keep in mind the fun level of the game. As a player, it wouldn't be much fun to be doing your thing, making strides in the campaign etc, then suddenly, due to a random dice roll you're dead because you got appendicitis. Or through nothing you did, no decision you made, you're suddenly inflicted with the plague.
Random sicknesses like this wouldn't be fun at all unless they serve a significant plot-point - say you caught the plague - now you and the team are in a race against time to get to the old medical storage facility across the county, or you need to find a proper operating room to take care of the lung clot you got or something. But just inflicting random infliction on players wouldn't be much fun.
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