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Mathematics of a Zombie Attack
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.
Posted by Alex Tabarrok on August 16, 2009 at 07:01 AM in Science | Permalink
Comments
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?
Posted by: MostlyAPragmatist at Aug 16, 2009 7:28:56 AM
Relative to some of the remarkable silly "serious" econ papers I've read by prominent economists, this actually doesn't sound that absurd :\
Posted by: William at Aug 16, 2009 8:19:53 AM
Not absurd, but hardly news either. All this has been empirically known for years.
Posted by: Harkins at Aug 16, 2009 8:32:35 AM
Dinosaur Comics covered this almost two years ago!
Posted by: Jason (the commenter) at Aug 16, 2009 10:25:08 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.
Posted by: Tomasz Wegrzanowski at Aug 16, 2009 11:20:29 AM
but which came first, zombification or the zombie?
Posted by: anony at Aug 16, 2009 11:36:47 AM
See also a slightly different model, in time-wasting game format: http://www.hardcorepawn.com/zombie3/
Posted by: Kat at Aug 16, 2009 11:54:33 AM
Anything in it about the banks?
Posted by: Yancey Ward at Aug 16, 2009 12:30:29 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.
Posted by: David at Aug 16, 2009 2:59:25 PM
Tomasz--
You are right about destroyed zombies, but familiarize yourself with the literature. Dead humans do spontaneously become zombies in Romero's original film.
Posted by: MostlyAPragmatist at Aug 16, 2009 10:25:34 PM
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).
Posted by: Gil at Aug 17, 2009 1:53:44 AM
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Posted by: sevda sohbet at Aug 17, 2009 2:32:06 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.
Posted by: Travis at Aug 17, 2009 10:35:00 AM
Traditional zombies are not very bright and not very fast-moving. Given that our distant ancestors managed to hunt woolly mammoths with spears, how hard could it be to bring down zombies?
Using our superior agility, smarts, speed, and rapid communication and teamwork, it should be a piece of cake. The key, I think, is to tumble them over: zombies crawl even more slowly than they can walk, their infectious teeth are now at ground level and more easily avoided, and their head and brains are also at ground level, so a gravity-assisted vertical head-bashing will kill them with less effort and fatigue and less risk than a horizontal baseball swing.
Something as simple as stringing up tripwires at knee level should be quite effective against a creature that moves by shuffling. Or, using golf balls and pantyhose and rope, you could easily fashion bolas like South American gauchos use, throwing them at the zombie's feet to entangle their legs and trip them up. Digging short but extensive trenches would also be very helpful. When they're down, use pointy sticks to pin them motionless before administering the coup de grâce.
Flamethrowers and shotguns will be more emotionally satisfying and cinematic, but fuel and bullets will undoubtedly be in limited supply in a crisis, not to mention the weapons themselves, so a purely mechanical human-powered extermination methodology seems preferable.
Posted by: anonymous at Aug 17, 2009 11:42:22 AM
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.
Posted by: charlie dank at Aug 17, 2009 1:00:29 PM
FYI never set zombies on fire. A flaming zombie is harder to kill, i.e. you can't get in close for the decapitation and are required to kill the brain from a distance.
Posted by: zombie killer at Aug 17, 2009 2:28:13 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.
Posted by: Tricky at Aug 17, 2009 3:19:50 PM
I'm thinking dessication is an under-appreciated tactic. Again, drawing upon the oft-mentioned lack of planning ability of zombies, it would seem effective to simply hole up in the desert (with supplies of course) and let any zombies that find their way out there dry up and either fall apart or turn to undead jerky in the sun.
There might be some opportunity for mold or fungus-based antizombie methods in particularly wet climates, what with zombie hygiene lacking, but dessication seems like a great tactic if you can just get to the Sonora or Mojave deserts ahead of the undead hoard with a couple weeks of water to wait them out.
Posted by: Li'l Miss Muffet at Aug 17, 2009 3:45:51 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>
Posted by: Richard at Aug 17, 2009 4:59:28 PM
I myself am not much familiar with the zombie literature, so excuse me if I ask a simple question. What incentives drive zombie behavior? Answering that question seems fundamental to any economic analysis of zombies, not to mention being helpful in designing anti-zombie tactics.
Posted by: Bernard Yomtov at Aug 17, 2009 9:34:34 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.
Posted by: Vote For David at Aug 17, 2009 11:38:49 PM
its possible it just depends on when
Posted by: zach at Aug 26, 2009 9:52:36 PM
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.
Posted by: gullydj at Sep 10, 2009 8:17:43 AM
