Did a virus outright kill some; zombify others either immediately, upon their death, or upon their being bitten; and the few were immune (Jenner's secret)? If a bite is required, then how did the first zombie originate? If the virus caused zombify action directly, then all would likely be carriers, right?
Actually this could work. The virus was airborne and spreading really, really fast pandemic-style. It immediately killed some of the people in the world with high fever and infection, zombified others and then it just mutated into what we are seeing now. If the virus was transmitted through bites all the way in the beginning... that really doesn't hold up.