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April 26, 2011 11:34 PM   Subscribe

Infectious Disease Modeling: Zombie Edition (PDF)
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.

For those who want to get to the end and skip the epidemiological modeling.
An outbreak of zombies infecting humans is likely to be disastrous, unless extremely aggressive tactics are employed against the undead. While aggressive quarantine may eradicate the infection, this is unlikely to happen in practice. A cure would only result in some humans surviving the outbreak, although they will still coexist with zombies. Only sufficiently frequent attacks, with increasing force, will result in eradication, assuming the available resources can be mustered in time.

Furthermore, these results assumed that the timescale of the outbreak was short, so that the natural birth and death rates could be ignored. If the timescale of the outbreak increases, then the result is the doomsday scenario: an outbreak of zombies will result in the collapse of civilisation, with every human infected, or dead. This is because human births and deaths will provide the undead with a limitless supply of new bodies to infect, resurrect and convert. Thus, if zombies arrive, we must act quickly and decisively to eradicate them before they eradicate us.

The key difference between the models presented here and other models of infectious disease is that the dead can come back to life. Clearly, this is an unlikely scenario if taken literally, but possible real-life applications may include allegiance to political parties, or diseases with a dormant infection.

This is, perhaps unsurprisingly, the first mathematical analysis of an outbreak of zombie infection. While the scenarios considered are obviously not realistic, it is nevertheless instructive to develop mathematical models for an unusual outbreak. This demonstrates the flexibility of mathematical modeling and shows how modelling can respond to a wide variety of challenges in ‘biology’.

In summary, a zombie outbreak is likely to lead to the collapse of civilisation, unless it is dealt with quickly. While aggressive quarantine may contain the epidemic, or a cure may lead to coexistence of humans and zombies, the most effective way to contain the rise of the undead is to hit hard and hit often. As seen in the movies, it is imperative that zombies are dealt with quickly, or else we are all in a great deal of trouble.
posted by Weebot (22 comments total)

This post was deleted for the following reason: Sorry but this is a zombie post -- vacapinta



 
I remember reading this a while ago. Then, as now, I felt a key flaw in the analysis was the fact that dead zombies could return to hideous, shambling undeath.
posted by pengu at 11:42 PM on April 26, 2011


Night of the Living Wonks: Toward an international relations theory of zombies.

There are many sources of fear in world politics -- terrorist attacks, natural disasters, climate change, financial panic, nuclear proliferation, ethnic conflict, and so forth. Surveying the cultural zeitgeist, however, it is striking how an unnatural problem has become one of the fastest-growing concerns in international relations. I speak, of course, of zombies.
posted by Blazecock Pileon at 11:43 PM on April 26, 2011


So World War Z is pretty accurate then?
posted by Ghidorah at 11:44 PM on April 26, 2011


seems a bit light on the research there...

One thing they don't resolve in their modeling is an accurate rate of growth for zombie infection that takes into account zombie metabolism and consumption of human flesh. Assuming they're referring to biological zombies and not necromanced zombies animated by dark magic, one has to take into account the possibility that a pack of zombies will consume enough of a human being so as to render it incapable of turning into a zombie (only scraps of flesh left), or that they'll consume the human host's legs which result in a zombie lacking any significant degree of mobility and a vastly limited potential to further spreading the infection.

I'm kind of stumped as to why this would be included in a $90 textbook. It seems like more of the thing you'd do in your spare time for fun, rather than something you could present in an academic forum.
posted by lemuring at 11:58 PM on April 26, 2011


Eh, I'm more concerned about creepers.
posted by darkstar at 11:58 PM on April 26, 2011 [1 favorite]


Nonsense. The truth is that no-one knows what will happen after a zombie outbreak. It's all just models and simulations. By calling for quick and aggressive attacks on zombies, we put developing nations at a huge disadvantage, requiring them to invest in shotguns and chainsaw hands when they could be combating malaria and providing fresh water.

If a zombie outbreak does become a problem, it will be a self-correcting one. As canned food and ammunition grow scarcer, prices will rise, and the motivation for entrepreneurs to eliminate all the zombies and return the world to its pristine state will increase. We may not be able to imagine a way for one man to triumph over literally billions of unstoppable monsters, but the free market will provide — it always has, and always will.

The role of the government here is solely to provide police and soldiers to guard the bunkers of the rich for the duration of the outbreak, so that desperate throngs of less fortunate people cannot violate their property rights and thereby distort the market incentives inherent in the collapse of civilization into a gore-drenched waking nightmare from which there can never be any escape, ever, ever, ever.
posted by No-sword at 12:03 AM on April 27, 2011 [9 favorites]


"Mr. President, we must not allow a MineCraft gap!"

--Zombie Zbigniew Brzezinski, Year 3 of The Great Pandemic
posted by darkstar at 12:06 AM on April 27, 2011 [1 favorite]


The worries addressed in the scenario become much clearer if you replace the term "zombie" with the term "non-white “.
posted by happyroach at 12:13 AM on April 27, 2011 [1 favorite]


Hard as it is to imagine, the University of Florida's Zombie Attack Disaster Preparedness Simulation Exercise does not seem to have been previously posted to MeFi.
posted by Slithy_Tove at 12:23 AM on April 27, 2011


The worries addressed in the scenario become much clearer if you replace the term "zombie" with the term "non-white “.

BRAINSJERBS!!!
posted by darkstar at 12:26 AM on April 27, 2011


The worries addressed in the scenario become much clearer if you replace the term "zombie" with the term "non-white “.

Huh? I think even the worst, stupidest racists realize that there exists no group of humans that reproduce via biting.
posted by nathan v at 12:27 AM on April 27, 2011


Huh? I think even the worst, stupidest racists realize that there exists no group of humans that reproduce via biting.

You've never spent much time in Appalachia, have ya?

(I kid, I KID!)
posted by darkstar at 12:29 AM on April 27, 2011 [1 favorite]


Relevant

7 reasons a zombie attack would fail

Sorry for all those who hate cracked...
posted by psycho-alchemy at 12:29 AM on April 27, 2011 [1 favorite]


Weebot: "An outbreak of zombies infecting humans is likely to be disastrous, unless extremely aggressive tactics are employed against the undead. While aggressive quarantine may eradicate the infection, this is unlikely to happen in practice. A cure would only result in some humans surviving the outbreak, although they will still coexist with zombies. Only sufficiently frequent attacks, with increasing force, will result in eradication, assuming the available resources can be mustered in time."

Sounds harsh, but it's viscerally borne out in this simple zombie simulator, which allows you to drop small bombs that destroy people and buildings. The only way to prevent a total pandemic is to hammer the initial outbreaks with explosions until everything in the area is dead; even a few seconds of hesitation leads to irreversible seeding of infection throughout the city as panicked people spread the disease in all directions.
posted by Rhaomi at 12:30 AM on April 27, 2011


In all seriousness, just today I was thinking about the epidemiology of how propaganda is spread. It seems just as pernicious as zombie epidemic, in a way.

The article that catalyzed this thinking was the recent one in NYT that showed something like 47% of a certain political party continue to believe that a particular political figure wasn't "something-something". Now, I REALLY don't want to open up that particular political argument here, but it struck me how belief in conspiracy theories requires "carriers" of misinformation, including some who are particularly virulent, as well as vectors of administration. And how you hope to be able to achieve a kind of "herd immunity" to misinformation by inoculation with real info and healthy conditions.

If the zombie simulator that was linked upthread is any indicator, the way to deal with virulent propaganda is rapid-response carpet bombing of truth to combat the spread of the rumor/lie, otherwise, you can pretty much just count on losing a whole chunk of your population to the eventual infection.
posted by darkstar at 12:52 AM on April 27, 2011


Nuke 'em all and let God sort 'em out.
posted by WalterMitty at 1:26 AM on April 27, 2011


I'm kind of stumped as to why this would be included in a $90 textbook. It seems like more of the thing you'd do in your spare time for fun, rather than something you could present in an academic forum.

Sir, may I point you to the Ig Nobel Prize? A particular favourite of mine would be 2010's Peace Prize winner:
Richard Stephens, John Atkins, and Andrew Kingston of Keele University, UK, for confirming the widely held belief that swearing relieves pain.
Here is the abstract.
posted by WalterMitty at 1:31 AM on April 27, 2011


eh, the "human births = limitless zombie fodder" fails to account for the confounding factor of me being an outright machete wielding badass zombie killer.


Try to replenish your numbers with me around, goddamn Z's!
posted by Panjandrum at 2:00 AM on April 27, 2011


Apologies for the self-link, but a student of mine recently had a paper accepted in which he describes the process of converting this model from a set of equations to an agent-based simulation - the PDF is here (top paper).
posted by gene_machine at 2:16 AM on April 27, 2011


Double.
posted by Bangaioh at 2:25 AM on April 27, 2011 [1 favorite]


"An outbreak of zombies republicans infecting humans is likely to be disastrous, unless extremely aggressive tactics are employed against the undead. "

ftfy
posted by tomswift at 3:17 AM on April 27, 2011


If only ideas were as easy to kill as zombies
posted by Redhush at 3:58 AM on April 27, 2011


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