You can deal with disease a number of ways. Having a reliable source of healing is one, for example getting a heart symbol on a reroll face or just having one symbol being a large amount of healing like 3 or so hearts on a chain or something. Another is to simply replace disease faces as soon as you get them to keep them from spreading. This one can be tricky since it requires a lot of gold, but you should really be upgrading often anyways since that's a major source of xp. Try to get a good source of gold early so that you can always afford to upgrade faces (even if the face is not great, it's still better than letting disease spread). A third way, is to utilize your class/relics/abilities to either avoid getting diseased in the first place or to cure it. So, if you're the demonologist, capturing frogs instead of killing them. If you're the cleric, picking up the ability that removes debuffs from 2 faces. Taking the multivitamin relic, so that if it spreads too much you start curing it. Ultimately, as with many aspects of this game, a lot of it is rng dependent, so you won't always be able to efficiently deal with disease. The most you can do is mitigate it as much as possible and hope for the best.