Math Gets Around: Preventing the Zombie Apocalypse

If pop culture has taught us anything, it is that in the event of a zombie outbreak, we are royally screwed. When faced with an onslaught of classical zombies (of the type first made famous by Romero’s 1968 film Night of the Living Dead), films have shown again and again that we are no match for hordes of cannibalistic undead. With the more recent interpretation of zombies that are faster and smarter, our hopes for survival have diminished even further.

Despite overwhelming odds, however, it is not in our nature to simply roll over in the face of adversity. While the body count is usually high in films chronicling the eventual war between the living and the dead, in most cases there are a few who survive to continue the fight after the credits roll.
But how realistic is this depiction? How prepared are we to defend ourselves from being eaten alive by our deceased ancestors? And what strategies will give us the best chance of survival? You’ll be happy to know that mathematics can answer some of these questions.

Hopefully we are more prepared than Homer Simpson.
Students from the mathematics departments at Carleton University and the University of Ottawa have produced several mathematical models to predict what will happen in the event of a zombie outbreak, and how our response to such an outbreak may affect its outcome. The students, led by Professor Robert J. Smith? (this is not a question, he simply insists on this piece of punctuation after his name) used the theory of differential equations to see what would happen in the event that the dead rise from their graves in search of fresh meat.


As would be expected from a paper with such important pop-culture consequences, this research has already garnered a fair amount of attention. The Globe and Mail ran an article last Friday, as did Wired (and with a much cooler picture, I might add). However, if you really want to get to the heart of the matter, here’s a link to the original paper.

Their model eschews the post-28 Days Later interpretation of zombies, focusing instead on the lumbering, thoughtless monsters that have been the stuff of childhood nightmares for decades. One could argue, however, that the results presented in their work would be even grimmer were we to allow zombies the benefit of intelligence and the ability to run a 6:00 mile.

The underlying ideas are similar to those of the SIR model for the spread of infectious disease, which has been discussed elsewhere on this corner of the internet. One significant difference here, of course, is that when dealing with a zombie infestation, dead people may not necessarily stay dead. This adds complications to the theory, but also allows for a richer analysis.

It’s unclear whether or not the zombies in this model know how to dance.

In the end, their research gives us the following insights into the nature of zombie warfare:

  1. With one exception, human-zombie coexistence is not possible. In order to save humanity from a zombie infestation, we must kill every last one of them.
  2. Often times there is a period of latency from the time a person is bitten until the time they turn into a zombie. Whether or not such latency exists will not have an effect on whether or not the zombie hordes will overwhelm us – the only thing that changes is how long it will take for them to do so.
  3. Quarantining is not an effective way to try and stop a zombie outbreak. All it will do is prolong our extinction.
  4. The only model where coexistence is possible is a model in which a cure exists for zombification. Unfortunately (or fortunately, depending on your preferences), in such a world the zombie population would greatly outnumber the human population. In other words, we would survive, but not by much.
  5. The only way to ensure our survival is to attack with decisive force as frequently as we are able. In particular, the model ignores the impact of birth and death rates, which is fine over a brief period of time, but becomes more significant as the fight continues, since more bodies means more potential zombies. In other words, the longer the fight goes on, the less likely we are to emerge from it.

For the self professed zombie expert, these findings may not be all that surprising. For the rest of us, however, it just goes to show you how far a little mathematics can take you, even when exploring the realms of the highly improbable. You may scoff at this article now, but when World War Z arrives, you’ll be thankful that someone took the time to conduct this preliminary research.

(Hat tip to Patrick for the link to the Globe & Mail article. With a colder climate that no doubt helps to preserve dead bodies, it’s no wonder that Canadians are blazing a trail with this research – they will be on the front lines when the time comes.)

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