Sunday, February 6, 2011

Why a Zombie Outbreak should scare you

In light of me taking Linear Algebra and Differential Equations, I decided to find a real life example that could have real results instead of bunnies or bacteria: zombies. I realize that exponential growth and decay are not the most amazing or challenging concepts, but it still very much applies to a zombie outbreak.

So anyway, I was in class and thinking "Just how long would it take for a zombie outbreak to take over the world? Or even just the US? Well, the US population at this exact moment is 310,768,791 according to the US & World Population Clock. Now let's say that, being extremely greedy, Patient Zero only bites 2 people in the first day before escaping into the night or what have you. Let's just start with that, and then assume some other things that make no sense in the real world, but make it fun to attempt to find mathematical models.
  1. The human population remains the same besides those turned to zombies, i.e., none are lost to accidents and any that die are replaced by newborns.
  2. No zombies are killed. (I know, crazy, right? Because if you're interested in this post at all, it's because you want to kill some zombies, if the day ever prevents itself. But roll with me on this for now.
  3. It's not airborne. Bites and fluids only.
Now given our initial conditions,
2 = e k → k = ln 2
To find what point there would be the amount of zombies = the world population,

310768791 = eln 2 * t  →  ln 310768791 = ln 2 * t  →  t = (ln 310768791)/(ln 2)  →  t = 28.2
So that means that on a 2 bites a day per zombie, it would only take 28.2 days -a little less than a month- to infect the entire United States. If we bump it up to 3 bites, it would only take 17.8 days.

That is why you should be afraid of a Zombie outbreak.

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