Mathematics of a Zombie Attack

by on August 16, 2009 at 7:01 am in Science | Permalink

Here is the abstract of a new paper 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.

Hat tip to Cory Doctorow at Boing Boing.

1 MostlyAPragmatist August 16, 2009 at 7:28 am

I’ve been worried about this scenario since I was about five years old. It’s nice to see someone’s finally taking the threat seriously.

But I think I see a flaw in their system of equations. They are modelling that there is a chance of all removed (i.e. deceased humans and zombies) coming back to life-including the destroyed zombies, but in all the zombie epidemics they cite, destroyed zombies stay dead. I’d like to see how dire their predicitions are after accounting for this.

Also, I’ve always thought the assumption that zombies don’t attack each other a little far-fetched. How do the dynamics of an epidemic change if zombies can’t distinguish between live human flesh and the flesh of a zombie deceased within the last 24 hours?

2 Harkins August 16, 2009 at 8:32 am

Not absurd, but hardly news either. All this has been empirically known for years.

3 Tomasz Wegrzanowski August 16, 2009 at 11:20 am

Dead humans and especially destroyed zombies don’t spontaneously become zombiefied. This mode of transmission disagrees with all fictional evidence. There’s always some starting zombie population, and then the only way people can become zombiefied is by an existing zombie.

4 Kat August 16, 2009 at 11:54 am

See also a slightly different model, in time-wasting game format: http://www.hardcorepawn.com/zombie3/

5 David August 16, 2009 at 2:59 pm

I’d like to place a request for a “My Favorite Things Zombie.” Book, film, setting, method of transmission, author, director, method of destruction, etc.

6 Gil August 17, 2009 at 1:53 am

Uh huh . . . Does anyone here know that under traditional zombie lore if a zombie ingest salt he becomes aware he’s dead and dies shortly thereafter? If you reply “well we’re not talking about those types of zombies but our versions of zombies” then you might as well be arguing over what would happen in an alien attack. Will be like:

1. 1953 War of the Worlds – aliens use some sort of crescent formation to almost take over of the world (if it weren’t for them dang microbes).

2. 1996 Independence Day – aliens use a top down approach to get a decent way through an invasion (if it weren’t for a dang computer virus).

3. 2007 War of the Worlds – aliens engage in a random blastarama but don’t get a great deal done though they had a lot of fun (and were still culled by microbes).

7 Travis August 17, 2009 at 10:35 am

I can picture it now.

A real life zombie epidemic breaks out, and the military, with complete ignorance of what the outbreak will look like, show up at the authors’ of this paper’s houses, bringing them in for duty as the civilian experts who save the day. Of course, the civilians will will have to have a major disagreement with an admistrative type, and be proved right in the end.

Great hollywood script.

8 charlie dank August 17, 2009 at 1:00 pm

My friends and myself have been talking about the zombie doomsday for sometime now and what I’m seeing here is that no one is counting on a fast zombie, and I also didn’t hear anything about mass populated areas, like Chicago, that are part of a state that does not allow guns legally. We think an infection in a big city is gonna be the major downfall, but we are happy that educated people are talking about this subject. The seventh horn has been sounded.

9 Tricky August 17, 2009 at 3:19 pm

Hm, this comes down to weather or not a zombie actually needs it’s head. Since it’s dead anyway, lopping off it’s head really shouldn’t do much (although they would be blind, unless they go by smell, in which case they still wouldn’t be able to). I think the most efficient way is simply beating it until it can no longer function.

10 Richard August 17, 2009 at 4:59 pm

The best line in the paper is near the end: “Clearly, this is an unlikely scenario if taken literally, but possible real-life applications may include allegiance to political parties …” <insert obvious comparisons here>

11 Vote For David August 17, 2009 at 11:38 pm

The question I have is, can zombies go under water?

If you take refuge on an island, and they try a human (zombie?) wave attack all around your perimeter, and pop up on the shore, you’re screwed.

12 gullydj September 10, 2009 at 8:17 am

zombies are already dead so technically they don’t breathe so they should be able to survive indefinitely underwater. I dont think that they could swim because they lack the agility and gross motor skills to be able to do this.

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