Let us assume that a vampire need feed only once a month. This is certainly a highly conservative assumption, given any Hollywood vampire film. Now, two things happen when a vampire feeds. The human population decreases by one and the vampire population increases by one. Let us suppose that the first vampire appeared in 1600 c.e. ...[when] the global population was 536,870,911. In our argument, we had at the same time one vampire.Two very obvious points, apparent in almost all depictions of vampires in film and fiction, are ignored by this argument:
We will ignore the human mortality and birth rate for the time being and only concentrate on the effects of vampire feeding. On February 1, 1600, one human will have died and a new vampire will have been born. This gives two vampires and 536,870,911–1 humans. The next month, there are two vampires feeding, thus two humans die and two new vampires are born. This gives four vampires and 536,870,911–3 humans. ... The vampire population increases geometrically and the human population decreases geometrically. … We conclude that if the first vampire appeared on January 1, 1600, humanity would have been wiped out by June of 1602, two and a half years later.
1. Vampires can feed without creating new vampires. There is usually some rule like “the vampire must feed from the same victim three times” or “the victim must also feed from the vampire.” Or in the words of Buffy Summers, “To make you a vampire, they have to suck your blood, then you have to suck their blood. It’s like a whole big sucking thing.”
2. Sometimes vampires die, perhaps through starvation, perhaps by getting staked or decapitated or doused with holy water.
(And before anybody asks... no, I don’t believe in vampires, this article notwithstanding.)