Moriarty, that really sounds like a cheesy remake of Resident Evil and some Left 4 Dead elements, but with vampires.
To be honest, it probably wouldn't be a very good game. By the sounds of it, it would be no more than you killing one thing, to kill 20 other things. How would that work?
Would it just be somewhat rare to see an enemy, and when you do, have a nice fight? Or would it be a few enemies in a room, and the follow-up enemies would be little mobs that charge at you, and die with one hit?
It just doesn't sound like a very fun concept, imo.