Pandemic

Vampires have become a big business in popular culture. Books, comics, movies: they're everywhere! Well, fictional ones are, at any rate. Nonfictional examples are harder to come by. So hard, in fact, that it's worth asking: do vampires actually exist?

There are a lot of conflicting stories about vampire behavior in pop culture, so before we can answer this question, let's first agree on some ground rules:

  1. If you're bitten by a vampire, you become a vampire.
  2. Vampires need to drink human blood.
  3. Vampires need to feed once a week.

For the sake of argument, let's say there's a vampire out there who plays by these rules. What would that mean for the future of mankind?

After one week, this bloodsucker would have bitten one person, creating one new vampire. In the second week, both vampires will feed, bringing their total number up to four. And so on:

Week 0 1 2 3 4 w
Number of Vampires 1 2 4 8 16 2w

If this doubling continues, then after w weeks we'd expect 2w vampires roaming the earth. 16 vampires in a month may not seem all that concerning for a human population that's 7 billion strong, but the situation gets dire awfully quickly. In fact, it would only take 33 weeks for vampires to wipe us out:

Scary stuff, right? And our assumptions — like vampires feasting just once a week — may be conservative. If vampires fed twice a week, for instance, it'd only take them 21 weeks to devour us all. On the other hand, even if vampires only fed once a year, it'd still take just 33 years for mankind to go extinct. Basically, if any vampires existed, we'd all be vampires by now.

But we're not. And since we're not all vampires, this means there must not have been a first vampire to begin with. So chill out on the vampire hysteria, people: we can all relax.

Or can we? Before you decide to go wandering through the Transylvanian countryside, consider that there's a shortcoming in our model. Namely, we assumed that the vampire population would have grown without any opposition. But if you've ever seen any vampire movie ever, you know that this is unlikely: we humans love vampire-hunting, and won't go down without a fight.

So what happens if we try to factor in the percent of vampires that get slain each week?

If we don't put up a fight, then things progress exactly as they did before. But if we're aggressive in our fight against vampires, we can slow their exponential growth, and in some cases, eliminate it entirely. For instance, if vampires feed once per week, but we're able to slay 50% of all vampires every week, then the population will never grow above a single vampire!

Of course, eliminating half the vampire population is easier when there are 2 vampires than when there are 2 million. So in order for this strategy to be successful, we need to strike early. If we can do this, then we might be able to keep any future vampire outbreak at bay.

That's the good news. The bad news is that, if we factor in vampire death, we can no longer say that it's impossible for vampires to exist. Though the risks are pretty low, we wouldn't judge you if you took some garlic and a wooden stake along with your trick-or-treat bag.

Happy Halloween, everybody.  And sleep tight.

Teachers: want to talk about vampires with your students?  Check out this week's featured lesson, Pandemic.


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