In a question on the RPG stack exchange that I tried to answer I attempted to work out the ratio of humans to vampires in a game setting based on what I know of a handful of settings. I was wondering if my rationale for the percieved ratios holds up in general, and if an expert could give a comparison of the most common human:vampire ratios seen, and the differences in vampires required for this to be sustainable?
As was mentioned in comments, this varies quite widely depending upon the type of vampire.
Some vampires don't actually require human blood, and can survive exclusively on other sources of mammalian blood. Anne Rice's vampire Louis, for example, survived off of rats for a period of time. This implies that the actual blood requirements are fairly low (although it did imply that he drained quite a few rats, with mention of a trail of rat corpses, iirc).
Vampires that must feed off of human blood range from needing to feed daily (well, nightly), to once every several weeks. Even within a specific universe, the length between feedings can vary due to a number of factors including physical exertion or injuries (which often necessitate more frequent feedings, as the blood is used to heal/rejuvenate the vampire), types of feedings (some feedings may drain the victim completely, while others might only drain enough to make the victim slightly woozy) or personal preference (some vampires maintain some semblance of human morality, and attempt to limit their feedings, while others... indulge).
Very few universes seem to require that vampires completely drain their victims. Most allow for vampires to feed repeatedly upon the same victim, in many cases night after night. However, quite a few universes indicate that repeated feedings can be very... ah, draining on the victim, leaving them in rapidly deteriorating states of health after repeated feedings (for example, in the movie Bram Stoker's Dracula).
Therefore, if we are looking for long-term viability, 2 victims per vampire, alternated each night, would seem like a conservative minimum number in any universe where the vampire doesn't have to drain the victim completely, yet feeds daily. Three victims per vampire would perhaps be safer, but again, this number varies per universe. In True Blood we see repeated examples where a single victim can comfortably sustain a vampire indefinitely. In Bram Stoker's Dracula we see Lucy succumb rather rapidly after a few days of consecutive feedings.
Other universes may require the vampire to either kill or turn their victims. However, these typically involve much less frequent feedings (otherwise they would be unsustainable). In this type of scenario, the time in between feedings seems to depend more upon individual restraint in the vampire, as well. Those who wish to can typically go several weeks to a month in between feedings. Those without restraint may feed weekly, or even go on rampages feeding daily. Daily feedings that kill/turn daily seem to be the exception, and the sign of a "rogue" vampire, however (due to the aforementioned lack of sustainability).
Assuming an average of 1 feeding every 2 weeks, this means that the vampire will consume roughly 26 humans a year. While I won't touch on the subject of population growth of humans-as-livestock, this does give a rough indication of how many humans would be required to support a vampire population: enough to produce 26 healthy new adult individuals each year, for each vampire.
However, these examples assume stable vampire populations. A vampire nest actively trying to grow by converting every victim increases at an exponential rate, and can take over even major population centers in just a few months (in Stephen King's Salem's Lot, for example, almost the entire town was converted within a few weeks). This rarely happens, as it results in both too much attention, and too much competition for food, but it is a possibility in any universe where vampires can create new vampires simply by draining them/sharing their blood.
An additional factor to consider is visibility. The closer to the "maximum" ratio of vampire:human, the more likely that the humans will be aware of the vampire predation. Vampires seeking to avoid alerting their prey to the danger will generally consciously maintain populations far, far smaller than the human population would allow.
From America's Blood Centers:
A vampire would do well to establish an effective blood bank. Working with the numbers from below. A donor can give once every 8 weeks (56 days). Assume a full person (~10 pints) per night? That's 560 people... at an absolute minumum. (You'd want more, esp. if you wanted anonymity).
Stats from below suggest 43,000 * 365.25 = 15705750 pints are donated each year in North America. 10 pints a day * 365 days = 3650 units a year / vampire. 15705750 / 3650 is about 4300 vampires in North America, if the whole blood supply went to feeding them.
However, in this case, you'd have consider...
- tool-using, sentient prey that may (not) be aware of the threat
- Malthusianism in both predator and prey populations
- ability of vampires to husband us as cattle
- prey may becomes predator
- predator doesn't need to kill prey
But don't let scientific method get in the way of a good yarn...