Check your stats for diseases after every vampire encounter.
Carry the ability to cure disease. The simplest/easiest thing is just carry some pieces of mandrake root. Eating it is one of the simplest ways to cure disease.
If, after a vampire encounter, you do have the disease and can't cure it right away, then DO NOT sleep. Rather, make your new job #1 getting some sort of cure disease (mandrake root, potion, pray at a chapel, learn a spell, etc).
Save your game routinely so if you mess up, you can reload.