Vampirism is a spiritual disorder in which a person's spiritual body cannot produce or otherwise supply enough energy for the person to thrive. They do not typically die, just have extremely poor health, when cut off from their feeding source.
It is neither a virus nor genetic. It seems to be something you are born with, though most people report "awakening" to it near puberty. There also does not appear to be any sort of genetic factor in that vampiric parents do not typically produce vampiric off-spring.
Or at least that's how things are according to the vampiric community.