How To Survive The Zombie Apocalypse (According To Math)


Dr. Katie Spalding

Katie has a PhD in maths, specializing in the intersection of dynamical systems and number theory.

Freelance Writer


Run, you idiot - haven't you ever heard of Fick's Laws of Diffusion?! Image: fotogestoeber/Shutterstock

Listen, the way things have been going lately, you probably wouldn't be alone in thinking it’s only a matter of time until there’s a full-blown zombie outbreak. And if (or when) the uprising begins, you’re going to need a plan – assuming, that is, you don’t already have one.

Luckily, zombie apocalypses (apocalti?) are one of many areas where the answer all boils down to math. A new video by the inimitable Numberphile explains exactly how Z-Day would go – and how you can best protect yourself.


It turns out that, as anyone who has watched a horror movie knows, zombies are quite like viral particles when you consider them on a population-wide scale: they move around randomly, diffuse throughout a population, and either kill or infect whoever they come into contact with.

So, using a type of math called a partial differential equation, or PDE, it’s possible to work out your best course of action – and unlike the suspiciously-well-groomed survivors in Hollywood zombie films, it definitely doesn’t involve fighting back.

“It’s much better to run away from a zombie than it is to try to slow them down,” explains mathematical biologist Thomas Woolley, whose big brain would probably make him a delicacy for his undead pursuers.

“I won’t judge you,” he adds. “I will be at the head of the people [running].”


So what does the math say about defeating a zombie invasion? It’s fairly self-explanatory actually: we just need to kill zombies at a faster rate than they infect other humans.

Since the zombies invade at a rate that’s proportional to their distance from us and their speed of travel, that means the best course of action is to get as far away as possible from the horde of undead. Previous mathematical models of zombie outbreaks – and there have been quite a few – have placed the northern Rockies as your best bet for sanctuary, though rural areas in general would likely stay safe for weeks after major cities got completely zombified.

You might want to stay there for a while, too: one study from 2017 found that within 100 days of patient zero, zombies would outnumber humans a million to one. It would take a long period of breeding and fighting before humans managed to reclaim the planet.

Of course, since your fellow humans are basically zombies in potentia, there is another option: pre-emptive attack. Right now.


But Woolley doesn’t recommend that. Definitely not.

He promises.


  • tag
  • math,

  • humans