Yes, apparently there is such a thing.
A surprisingly large number of academic studies—as in, more than one—have applied mathematical modeling to the concept of human-vampire co-existence. Using the depiction of bloodsuckers in various forms of media, from Bram Stoker’s Dracula to True Blood, these papers look at whether Earth’s vampire population would inevitably annihilate humanity, and, if so, how long it would take.
Darrell J. Pursiful 
Assuming your vampires don’t automatically turn every human they bite, there would be plenty of humans to continue to sustain a small vampire population.
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Alas, that seems to be a fairly rare assumption in these studies, as best I can tell.
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This problem has been addressed by writers of modern vampire fiction as noted toward the end of the article. One that wasn’t mentioned was the explicit sustainability solution provided in one of the Blade movies. In the movie, vampires had built blood banks. These warehouses of brain dead humans, whose bodies were kept alive for the express purpose of solving the sustainability problem, provided blood for vampire consumers.
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Too many variables. Unlike a zombie apocalypse and vampire apocalypse is not that easy to model.
Do they have to kill? If so how long does it take (vampires in folklore seem to be blamed for lingering illnesses more than sudden death). Are they even contagious? If so is it just from being drained or is blood transfer needed (or as was claimed in the Arnold Paole case can you become a vampire if you ate the meat from a cow that was attacked by a vampire?) Is there a cure? Can they be warded against?
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