The abstract says it all:
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.
They use the mathematical models applied to outbreaks of infectious diseases to show that -- absent a cure or concerted eradication of large proportions of zombies simultaneously -- we are well and truly screwed. This realization should in no way detract from the observation that MATH IS COOL. It will be a damn shame when the zombies eat it out of our brains.
Hat-tip: Marginal Revolution
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Of course, this ALSO assumes that zombies do not need to feed constantly to maintain animation. Most zombie scenarios assume this, but is it actually the case? Perhaps there would be a way of "starving" a zombie to death. We know that brains maintain them, and we know that zombies expend energy, therefore a zombie in possession of brains must eventually be in want of more brains (as phrased so excellently in Pride and Prejudice and Zombies). I want to see that model...
the zombie flick "28 days later" looked into the energy requirements of zombies. i don't remember how many days it took for their energy reserves to be exhausted though.
perhaps i'm in the minority, but i happen to think that humans are often more dangerous than zombies. the comic book "the walking dead" does a good job of explaining that.
Fantastic! Thanks for posting this. This could go a long way towards improving my nephew's attitude toward math.
Muhr,
Most zombie films I know of hammer that point home.
A normal human is almost always more evil than a zombie.
From that final scene in Night of the Living Dead to the military rape camp in 28 Days Later a normal human is always worse.
That is actually a lesson that pervades through a lot of horror and sci fi.
It is one of my faves.
It is in Alien and the early works of Clive Barker as well
Yeah, I know I need to get out more...
Totally AWESOME! Now we just need to engineer a virus (assuming it would be viral, don't know why, just feels right) to make people zombies to see if the model holds true.
(assuming it would be viral, don't know why, just feels right)
'Cause bacteria are (more classically) alive! Awesome.
Their model is wrong! Dead zombies can't come back to life.
jim,
very true, humans are often portrayed as the main danger. incidentally, the walking dead looks like it will be made into a tv series on amc.
I am really getting tired of hearing about zombies.
Just to be sure I understand, in all models, members of the removed class can become zombies? But killed zombies and humans by natural death go to the same removed class?
I'm kind of thinking the model is built wrong if it intends to match film accounts (and the Brooks account) of zombies, where they are only made from the susceptible group, and shifted to the infected group. Natural death cases don't become zombies in most films. For that matter, a susceptible "losing" an encounter to a zombie ONLY results in infection, never in removal, in spite of the greater likelihood of dismemberment (and thus removal, rather than infection) in a losing encounter.
I think this is the best thing I've ever seen in a paper:
"This is, perhaps unsurprisingly, the first mathematical analysis of an outbreak of zombie infection."