This [Thomas' assumptions] results in an equilibrium population of 36,346 humans and 18 vampires. Thomas then notes that interestingly enough the established population of Sunnydale on the show is 38,500 humans, pretty damn close to the equation result. Maybe Buffy needs to cut back on the slaying in order to let the vampires weed out that extra 2100 people, we wouldn’t want human overpopulation to lead to starvation.
But is this equilibrium stable? Will natural fluctuations in the vampire population prevent the equilibrium state from ever existing? Thomas then ran the model using several different initial population sizes and seeing whether they eventually moved to equilibrium, or spiraled off into an abyss where everybody died. Turns out the model is stable and the vampires and humans can co-exist forever! Hooray!
Twilight-style sparkly vampires don't work out that well.