Zebras have been found to be immune to the bite of the tsetse fly which can spread a disease called Nagana, also called nagana pest or Animal African Trypanosomiasis.
There are many types of immunoglobulin within the body. They are part of the immune response which the body activates when a pathogen/bacteria/virus enters the body. The body responds by initiating...
If you buy the idea that a vampire is a revivified corpse in search of blood, then, in being undead, there would be no real reason why it should succumb to illnesses.