Zombie apocalpyse: the math geek edition

Mathematicians at the University of Ottawa, Philip Munz, Ioan Hudea, Joe Imad and Robert J. Smith, have published "When Zombies Attack! Mathematical Modelling of a Zombie Outbreak!" It's a serious look at the mathematical epidemiology of zombiism, published in "Infectious Disease Modelling Research Progress."

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.

PDF: When Zombies Attack! Mathematical Modelling of a Zombie Outbreak! (Thanks, Fipi Lele!)

(Image: Zombies Swarm Apple Store, a Creative Commons Attribution photo from Jayel Aheram's photostream)

Previously:

I write books. My latest is a YA science fiction novel called Homeland (it's the sequel to Little Brother). More books: Rapture of the Nerds (a novel, with Charlie Stross); With a Little Help (short stories); and The Great Big Beautiful Tomorrow (novella and nonfic). I speak all over the place and I tweet and tumble, too.

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Drew from Zhrodague

Math aside, I though that Pittsburgh was the zombie capital of the world, due to Romero’s films.

Nowadays, The It’s Alive Show has taken this a bit further, by doing zombie walks, Deathmobile playing at the Smiling Moose, among other related events.

Wikipedia link
mdh

I wonder what store managers of any stores would think when you see zombies swarming.

I bet they silently curse at the managers of Hot Topic.
Daemon

Actually, if anything, zombie walks are making zombies more dangerous than they otherwise would be.

As I just posted elsewhere regarding zombies, in real life they’d be a lot less of a problem because they are dumb, slow and obvious, and you don’t have to deal with horror tropes like “running away never works”, “the authorities are completely useless”, etc.

A history of zombie walks in your area effectively reduces their obviousness, and thus increases the chances of them getting managing to achieve what amounts to critical mass.

Just to be safe, if you see what you think is a zombie walk going on, assume they’re real and run over them with your truck. It’s the only way to be sure.

(And remember: Zombie dogs aren’t a real threat. Zombie crows are.)
Anonymous

i think commenter #8 is correct. while i loooove seeing zombies in scientific journals, i think the researchers have made a mistake in the model.

as my friend put it:
“they say S+Z+R goes to infinity and that S cannot go to infinity. however, zombies don’t multiiply so how can Z or R go to infinity unless S does. other than that they need PI (their birthrate) to include zombie sex.
I’m impressed zombies and pornography in a technical journal.
Obviously I am in the wrong field.”
Anonymous

I thought zombies couldn’t climb stairs. What gives?
Anonymous

I did my undergrad in math at U of O and I know these mathematicians. Incidentally, Robert J. Smith’s name is legally “Robert J. Smith?” Seriously.
Anonymous

A curious study.

The supplied graph for the base case does not match the calculation results using the supplied parameters. I set up the given equations with the supplied parameters (alpha = 0.005, beta = 0.0095, delta = 0.0001, zeta = 0.0001). Adjusting the size of the time step does not help.

Modifying the base case by adding an equation for unrevivable death inflicted on zombies by susceptibles will not prevent human extinction so long as the rate constant of zombie attack on susceptibles (beta = 0.0095) exceeds the rate constant of susceptibles permanently disabling zombies (alpha = 0.005).

Further modifying the base case by preventing corpses, that have suffered natural death, from becoming zombies will prevent zombies from coming into existence. However, in this case, setting the initial population of zombies above zero and using the values of beta and alpha given above will lead to human extinction. Once again, the ratio of beta to alpha is the key.

In the final analysis, prevention of reanimation combined with the ability of susceptibles to destroy zombies faster than zombies can infect susceptibles will be a successful strategy for human survival – hardly a surprise.

The models would have been more interesting if the birth and death rate terms were included in the susceptibles equation. An extension of that equation to handle the effects of population age distribution on birth rate, death rate, and zombie killing potential would really have been cool.
DUMBOy

Interesting, but I’m not a math geek so this comes across a little dry.
I need to know the logistics of fleeing the greater New York metropolitan area.
Is the an app for that?
Anonymous

yea!! they are covering bad science on Radio 4 in the UK!

won’t the authors respond to our critiques?
(comments #8, 15, 16)
Anonymous

The basic model presented is flawed, in that destroyed/beheaded/debrained zombies are returned to the pool of human dead, allowing them to resurrect back in to zombies. They should be removed from the system entirely.
Furthermore, the rate of resurrection has no dependence on the zombie population and is proportional to the number of corpses. This means that as t->infinity, all corpses->zombies. Since there is a natural death rate in the absence of zombies, it follows that everyone eventually becomes a zombie, even if the scenario begins with zero zombies.
Was this peer-reviewed?
Cicada

“Clearly, this is an unlikely scenario if taken
literally, but possible real-life applications may include allegiance to political parties…”
Righto– can’t quarantine your political opponents, and can’t try to reconvert the converted. The only solution is quick shots to the head. Eesh.
nanuq

“Math aside, I though that Pittsburgh was the zombie capital of the world, due to Romero’s films.”

Considering that Romero now lives in Toronto, I’d like to think that’s changing.
hershmire

It’s been done before, and with graphics to boot:
http://zombies.insertdisc.com/mattcordes/
MattF

Since zombies always win, the obvious conclusion is that we are all zombies. OOHHH… Brains… Yummie…
SednaBoo

I think the problem with the math is that zombies that are killed, with a headshot or something, can not be turned into fresh zombies again. I wish they accounted for that in one of their alternates.

Plus I’d think that the birthrate would be dependent of the amount of humans around, no?
octopussoup

This is just a reworking of the math done to show vampires don’t exist.
Consultant

Haha. Great. I wonder what store managers of any stores would think when you see zombies swarming.
Glossolalia Black

I’d love to see an iPhone app that uses that “bump” tech for Zombie scenario mapping. Take a thousand people, buy ‘em all iPhones, put ‘em in the Mall of America, and see how long it takes for the “infection” to spread in real time. Now that’s hot data.
trippcook

LMAO dudes modeling zombies — the internet is full of interesting and original things that aren’t at all played out.
mrsomuch

Wonderful! They are covering this story on Radio 4 in the UK right now. what a happy thing to have ones breakfast to. Marvelous.