The Math of Zombie Outbreaks

Setting the differential equations equal to zero gives braaaaaaaaiiiiiiins

By Seth Freilich | Posted Under Miscellaneous | Comments (20)

I don’t know anything about Carleton University or The University of Ottawa except that they’re in Canada (eh). And that they employ awesome faculty members in their math departments. And four of said faculty members recently published an 18-page paper called “When Zombies Attack!: Mathematical Modeling of an Outbreak of Zombie Infection.”

As the article’s abstract explains, they looked at three zombie scenarios:

Zombies are a popular ﬁgure in pop culture/entertainment and they are usually portrayed as being brought about through an outbreak or epidemic. Consequently, we model a zombie attack, using biological assumptions based on popular zombie movies. We introduce a basic model for zombie infection, determine equilibria and their stability, and illustrate the outcome with numerical solutions. We then reﬁne the model to introduce a latent period of zombiﬁcation, whereby humans are infected, but not infectious, before becoming undead. We then modify the model to include the effects of possible quarantine or a cure. Finally, we examine the impact of regular, impulsive reductions in the number of zombies and derive conditions under which eradication can occur. We show that only quick, aggressive attacks can stave off the doomsday scenario: the collapse of society as zombies overtake us all.

The biggest problem with this paper is a practical one. They decided to focus on your more dumb slow-and-steady zombies, rather than your smarter ragey-lickety-split zombies, and they don’t offer a particularly compelling reason why:

The zombie that we chose to model was characterised best by the popular-culture zombie. The basic assumptions help to form some guidelines as to the speciﬁc type of zombie we seek to model (which will be presented in the next section). The model zombie is of the classical pop-culture zombie: slow moving, cannibalistic and undead. There are other ‘types’ of zombies, characterized by some movies like 28 Days Later and the 2004 re-make of Dawn of the Dead. These ‘zombies’ can move faster, are more independent and much smarter than their classical counterparts. While we are trying to be as broad as possible in modeling zombies - especially since there are many varieties - we have decided not to consider these individuals.

See, but the problem is, I’m of the mindset that when the zombies come, they’re much more likely to be of the run-and-grab variety, so that’s what I want as the basis of my nerdtastic scholarly papers, damn it. I need practical application!

In any event, you can snag a PDF of the paper from this link, with a hat tip to io9. And in the meantime, for your entertainment:

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Comments

Carleton University?

Is that like the Correspondence College of Tampa?

Posted by: BarbadoSlim at August 17, 2009 7:25 PM

Fuck you Slim, Canada's edumicational system is awesomer.

Posted by: admin at August 17, 2009 7:33 PM

Exactly.

Posted by: laredo at August 17, 2009 7:45 PM

I dont know I feel it's way more proper to consider the slow moving zombie like they did. after all if you consider actual living dead who just come to a brainless, yet brain centered, life I can see how the movement would be slower (also considering the clearly fast decomposition of the body, which I always assumed was also somehow connected to the mysterious alien virus that caused the epidemic in the first place and not only by the needs of cool make-up). After all "28 days later" was more of a homage cause the people were never really shown as dead coming back to life (Jim parents kill themselves with pills and just stay dead), but only as infected poor schmucks so they could still run they asses off. So I buy the scientific specifics of the study. or maybe the lazy student in the class could have totally made the 28 days later study which would have consisted in 3 words "we are doomed" and that, despite what inspirational movies with michelle pfeiffer and Robin williams tell us , never grants you an A.
and now I hust pictured a zombie-like Usain Bolt, well at least we would go fast.

Posted by: rio at August 17, 2009 7:50 PM

You know, I've never been good at math, but I can figure out one equation:

Shotgun + Zombie + Ax = Dead Zombie

As far as I'm concerned, that's all the math I'll need when the Zombie Apocalypse comes.

Posted by: Genny (actually Rusty now) at August 17, 2009 7:51 PM

See, but the problem is, I’m of the mindset that when the zombies come, they’re much more likely to be of the run-and-grab variety, so that’s what I want as the basis of my nerdtastic scholarly papers, damn it.

Give me your basis for fast zombies...that's what I want to know. They're dead...ummm...dead. So they would be re-animated. Look at dead people. Rigamortis anyone? Plus, why would you want them to be fast, if they were fast, we'd all be fucked.

Posted by: Deistbrawler at August 17, 2009 8:37 PM

See, I know why they used the slow zombies. It's because it's probably the only scenario we survive. I mean, look there:

We show that only quick, aggressive attacks can stave off the doomsday scenario: the collapse of society as zombies overtake us all.

And that's the optimistic scenario with slow zombies. With fast zombies, we'd like the fat kid in dodgeball. Dead under any every conceivable scenario.

Posted by: alphawhiskey at August 17, 2009 9:05 PM

Posted by: Deistbrawler at August 17, 2009 8:37 PM

One of my best friends is one of the chief medical examiners in New York City. (He performed Heath Ledger's autopsy.) And he's a zombie enthusiast. He's our canary in the coal mine. He calls, gives the word, I run.

Anyway, he posits that zombies would, indeed, be "fast" zombies up until decay started to set in. At that point they would start to lose cohesion and things would begin to fall apart. So, fresh zombie = fast zombie and rotten zombie = slow zombie.

Posted by: ForbiddenDonut at August 17, 2009 10:05 PM

I knew there was a reason I went to this school...

Posted by: Amanda at August 17, 2009 10:22 PM

High Five Amanda! At least WE'RE TRYING TO HELP! Which is more than you lot ever do. Wah wah wah. The strategy is RIGHT THERE. We give and give, I swear.

Posted by: replica at August 17, 2009 11:38 PM

Shotgun + Zombie + Ax = Dead Zombie

As far as I'm concerned, that's all the math I'll need when the Zombie Apocalypse comes.

Posted by: Genny (actually Rusty now) at August 17, 2009 7:51 PM
---
I don't see a banjo in your equation.

*stoked for "Zombieland"*

Posted by: , (the commenter formerly known as bucdaddy) at August 17, 2009 11:39 PM

Can someone sum up what all this math is saying? It's not English to me.
And I really hope that they're slow. I'm a pretty good shot but I'm not in the shape I used to be.

Posted by: Optimus Rhyme at August 18, 2009 1:12 AM

Speaking of the wandering dead, I participated in a Zombie Walk this weekend in Vancouver. It was fleshtastic. If there's one in your city, I highly recommend getting your ghoul on.

Also, if you need an idea for Halloween, the zombie clown walking ahead of me was much appreciated by passers-by.

Um, I took Math Alternate, so this is the most I can do:

Zombie clown > regular zombie
or
zombie + clown = extra scary

Posted by: Lauren at August 18, 2009 2:27 AM

ForbiddenDonut
So you're saying initial outbreak we're fucked. If we last long enough we have a chance?

Posted by: Deistbrawler at August 18, 2009 3:58 AM

The advantage of the infection model in 28 days later is that the "zombies" were still alive, and thus could die from normal mortal injuries. So instead of having to kill them via headshots, or waiting until they rot into the ground, you can kill them conventionally or wait until they succumb to exposure/dehydration/etc. So the 28 days later epidemic is fast & furious, but if you can stay hidden for a month or so, you face a much smaller population of zombies waiting for you when you surface.

Wow, I need to get a life.

Posted by: saartjie at August 18, 2009 6:06 AM

WOW! I actually saw the Zombies open for Cheap Trick...

yes, I am that frickin' old

Posted by: dammitjanet at August 18, 2009 9:23 AM

ForbiddenDonut,

Is your friend single? Cause, damn...

Posted by: dammitjanet at August 18, 2009 9:28 AM

See, but the problem is, I’m of the mindset that when the zombies come, they’re much more likely to be of the run-and-grab variety, so that’s what I want as the basis of my nerdtastic scholarly papers, damn it. I need practical application!

What is it going to take to convince you radicals that zombies are decaying, slow moving menaces? Do I have to hire a team of biologists, kill half of them, split that half into a control group (not coming back thanks to bullet in the head) and a test group (crank up the radiation, we've got zombies to study), and then have the remaining living biologists study their mobility and rate of decay to prove that the human body won't be running when brain dead and falling apart? And none of this embalming nonsense - those zombies are going to stink to high heaven and fall apart faster. I'll then hire more biologists, kill off the original batch, then control with non-embalmed and test the embalmed. Will that finally do it? Cause I'm not afraid to whore myself out to fund this study.

Posted by: Robert at August 18, 2009 11:53 AM

ForbiddenDonut, before you make a run for it, will you post an alert on pajiba?

We should establish a coded phrase so we know when it's for real. Something no one would ever say on pajiba, like "I'm tired of the internet. I think I'll go for a hike."

Posted by: marya at August 18, 2009 6:02 PM

Zombies, zombies, zombies!!! Oh, how I love zombies! I think I believe in the slow zombie theory, but I would want to have a primary plan in place for the fast ones. Once you learn the skills to defeat the fast zombie, the slow ones will be a piece of cake! Dead, rotting, stinky cake.

Posted by: Mistress Violet at August 19, 2009 1:12 AM

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Setting the differential equations equal to zero gives braaaaaaaaiiiiiiins

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