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A Mathematical Model For a Spreading Zombie Infestation 121

Posted by Soulskill
from the integrating-by-parts dept.
cloude-pottier writes "What do you do when zombies attack? Turn to a mathematician to come up with a model for the spread of a zombie infestation, of course! Students at Carleton University and the University of Ottawa have published a paper in a book titled Infectious Disease Modelling Research Progress detailing how to model the spread of a zombie population and various complications in managing the spread of the infestation. They even give humans a fighting chance in some cases! The original paper (PDF) can be found at their professor's website."
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A Mathematical Model For a Spreading Zombie Infestation

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  • by The_mad_linguist (1019680) on Friday August 14, 2009 @10:06PM (#29073293)
    • by Jurily (900488)

      It's hard to find a geekier programming topic than zombies. Maybe Star Trek. Or the Babylon 5 space fights (you know, the one where you obey Newton's laws).

      • by exploder (196936)

        It was done already by one of the groups in a mathematical modeling course I took, too. And I'm sure they weren't the first to consider the problem. I suspect there's a ton of prior art here.

    • Perhaps the parent comment should have been rated funny, the zombie simulator at kevan.org is a model of a city where humans are getting infected. However, the work by Kephart and White [ibm.com] is prior art which wasn't cited. However, the models used in this paper are pretty standard fare for population dynamics and epidemiological modeling, and use the classical simplifying modeling by treating the population as continuous (i.e. they aren't using a discrete individual based modeling approach). Additionally, th
      • by Spacelem (189863)

        Heterogenity and stochasticity are very important in modelling. Diseases are far less likely to die out in a deterministic model, and you end up modelling infinitesimally small individuals which can still affect the disease, such as "atto-foxes" allowing the persistence of rabies (Mollison, 1991).

        Space is important too, as predator prey cycles seen in deterministic simulations (which are fairly similar to an SI model) don't occur in a stochastic model, unless you include space, and then you only get localis

    • by iggymanz (596061)

      be more fun if some of the humans could get to tool sheds with chainsaws

    • by kybur (1002682)
      I don't like how in that simulation, there is a 0% chance of a survivor killing a zombie. How about some hope!
  • by lyinhart (1352173) on Friday August 14, 2009 @10:10PM (#29073309)
    I am officially sick of the concept of zombies. Yes, they used to be cool and frightening, but nowadays, they're everywhere. In video games (Left 4 Dead, Dead Rising, Plants vs. Zombies (what the heck?), etc.), lots of movies (movies about Nazi zombies, Woody Harrelson versus zombies, even another Romero movie), comics books (Marvel Zombies), and even classic literature (Pride and Prejudice and Zombies?). Now they're in math too?

    It's time that someone called for a moratorium (no pun intended) on zombies in the media.
    • Re: (Score:3, Insightful)

      by digitalunity (19107)

      But its on digg, and therefore Slashdot is required to post it...

      Maybe I'm trolling here, but it seems like a voluminous number of articles these days are already on diggs front page. Not sure whats so hard about finding new and interesting things to post.

      • by osu-neko (2604)

        But its on digg, and therefore Slashdot is required to post it...

        Maybe I'm trolling here, but it seems like a voluminous number of articles these days are already on diggs front page. Not sure whats so hard about finding new and interesting things to post.

        That's the point. It's not hard at all. Just check digg. :p

    • by FlyingSquidStudios (1031284) on Friday August 14, 2009 @10:30PM (#29073413) Homepage
      You're just jealous because none of them think your brain is worthy of eating.
      • Actually, it's the other way around - we're saving the tastiest brains for the dessert.

      • You're just jealous because none of them think your brain is worthy of eating.

        Come on! How can you condone a creature for trying to survive? After all arenÂt they out the just after their next meal? They are not evil per se. Why all this talk about extermination and all... in ten year time (http://news.bbc.co.uk/2/hi/technology/8164060.stm) weÂll be able to lice in harmony! WeÂll just feed them these artificial brains! Imagine what cooperation can achieve! Imagine how the zombies can help us in case of disasters or helping in hazardous invironments!

    • Re: (Score:1, Interesting)

      by Anonymous Coward
      Don't worry, the Decade of the Zombie is nearly over (also, I think it's clear that 2009 is the Year of the Twat).

      Except in this scenario: people obsess so much over how to protect themselves from zombie infestation that scientists, possibly working for the military or NIH, start working on serious protections from zombie-like scenarios. In order to realistically simulate cures and containment tactics, of course, one will need working models... But these tests will all be safely under the control of expe
    • Re:Sick of zombies (Score:5, Interesting)

      by Lord Kano (13027) on Friday August 14, 2009 @10:42PM (#29073461) Homepage Journal

      Outside of entertainment, Zombies are a metaphor for social unrest. When I was house shopping, my girlfriend asked me what criteria I was using to evaluate properties. I explained that there was price, location, condition, number of bedrooms, yard space, parking, garage space, and defensibility in the event of a zombie holocaust. She thought that I was joking with that last one. Then I explained that I wasn't talking about movie zombies. I was talking about small to medium sized groups of attackers in the event of widespread social unrest. If the economy goes south and we have people robbing and looting, how well can I defend this property? The house that I eventually chose wasn't the highest on the zombie defense mark, but it was in the top third.

      LK

      • Sounds like the train of thought the Militia type in Michigan go through.
        • Re: (Score:3, Insightful)

          by Lord Kano (13027)

          Sounds like the train of thought the Militia type in Michigan go through.

          Or shopkeepers in Los Angeles.

          Or anyone who's aware of events that took place in the 1960s.

          LK

      • Defense against zombies is actually trivial if you know what you're doing. All you need to do is put out bowls of potato chips, popcorn, pork rinds and other salty snacks. Once they eat them and taste the salt, they'll remember that they're dead and go back to their graves forever.
        • by bogjobber (880402)
          I prefer tall nuts, gatling peas, and flame bushes. Of course you have to strategically place some magnets to defend against football players and diggers, but you should be able to last 12-13 levels at least.
      • by Vahokif (1292866)
        Zombies don't have guns, or ladders, but rioters do.
      • by ultranova (717540)

        I was talking about small to medium sized groups of attackers in the event of widespread social unrest. If the economy goes south and we have people robbing and looting, how well can I defend this property?

        Well, in that case, get a house that's in the middle of a thick forest, as far from any civilization as possible. You can't defend a house in urban areas, not only because there's too many attackers and widespread fires but also because there's no source of food or water in the case of social meltdown. O

        • by Lord Kano (13027)

          Well, in that case, get a house that's in the middle of a thick forest, as far from any civilization as possible. You can't defend a house in urban areas,

          Compromise my friend. Suburbs. My neighbors are far enough away that a fire at one of their houses will not easily spread to mine. I live in an area that could be defended by a handful of motivated individuals. Rioters or looters would simply move on to easier prey.

        • Not too thick a forest. You need to be able to see people approaching, and not provide assailants with cover within range. As ultranova points out, a typical residential house in an urban or suburban area is not defensible over the long term. My emergency plan involves a little place in the North Ga. mountains - limited approaches, fresh water, good hunting and arable land adjacent, and you can't find it unless you know how. Google Maps and Mapquest will both get you totally lost.
          • by bhiestand (157373)

            Not too thick a forest. You need to be able to see people approaching, and not provide assailants with cover within range. As ultranova points out, a typical residential house in an urban or suburban area is not defensible over the long term. My emergency plan involves a little place in the North Ga. mountains - limited approaches, fresh water, good hunting and arable land adjacent, and you can't find it unless you know how. Google Maps and Mapquest will both get you totally lost.

            Funny, my survival plan involves following somebody like you to his survival house and killing him once he shows me where everything is hidden. :)

            • <quote>
              <p>Funny, my survival plan involves following somebody like you to his survival house and killing him once he shows me where everything is hidden. :)</p></quote>

              Good luck finding someone smart enough to have a good contingency plan, yet dumb enough to show all his secret holdouts to a stranger. That's a fine line. :)
              • by bhiestand (157373)

                Funny, my survival plan involves following somebody like you to his survival house and killing him once he shows me where everything is hidden. :)

                Good luck finding someone smart enough to have a good contingency plan, yet dumb enough to show all his secret holdouts to a stranger. That's a fine line. :)

                You're right, I'm going to need breasts and a sex change...

      • by Trogre (513942) on Saturday August 15, 2009 @08:05AM (#29075343) Homepage

        FREE O.J.

        Where? And do we need to bring our own cups?

        • by EdIII (1114411) *

          It took me about a minute to get that.... and then a few more to get the ice tea off my monitors :)

      • I second your usage of 'zombies' but I think there is a darker side to it... I wind up on various libertarian/survivalist/gun-related forums every now and then trying to find obscure information (how to remove front post sight from AK-47, for example. Innocent little things). Something I noticed, and it took me a while, is that 'zombies', for them, is a euphemism for minorities.

        Now, there is a distinction here- You and I using it as a euphemism for civil unrest and they using it for civil unrest of dark peo

        • by Lord Kano (13027)

          This must be a recent phenomenon, I spend a fair amount of time on survivalist forums back in the mid 90s. The thing that stands out most in my mind was the advice I gave some people on avoiding lice. The reason it stands out is that there was a typo in my post and for some reason it was copied and mirrored all over the place. If I'm really inclinedBeing that I am a member of a minority group, I'm sure that I would have noticed such usage.

          I see "Urban" as being an accurate representation of a certain segmen

      • You might be the best realtor in the world, but you'd probably never guess that the homebuyer was looking for zombie attach defensibility. Probably would never ask.
    • by Hellhog (1617707)
      If I had mod points, I'd be giving them. Amen to everything you said. Zombies are abso-fucking-lutely played the hell OUT. Sadly, it seems we're going to be back on overusing vampires very soon. This stuff's cyclical, you know.
    • by Artifakt (700173)

      Zombies and Vampires, and maybe some others. But one thing that makes zombies the most overused cliche evah is that ALL these zombies are just a subset of Night of the Living Dead's zombies. The whole sudden lunges, eat brains, massively multiplying zombies trend ignores Zombies as they used to be in film and print fiction before Romero. The only films I can think of offhand that portrayed old fashioned Zombies after NotLD is the two Phil Lovecraft Private Eye movies made for HBO - "Cast a Deadly Spell" and

    • by Eudial (590661)

      Fortunately, a silly concept like "zombies" is not the only application for this theory. As far as I understand things, it should work perfectly well to simulate the much more realistic spread of an infection of Borg nanoprobes in a society as well.

  • Somebady got too much time on their hands....
  • Oblig. (Score:3, Funny)

    by dln385 (1451209) on Friday August 14, 2009 @10:21PM (#29073351)
  • This is just posturing - when the zombies come the mathematicians will be the first to go - the human race will be repopulated by whoever can run the fastest
  • Zombie Modelling (Score:2, Insightful)

    by BrightSpark (1578977)
    Many of today's top models look like zombies. :-p I have had many zombies on my unix systems and Wikipedia here shows how to kill them.. http://en.wikipedia.org/wiki/Zombie_process [wikipedia.org] Not as satisfying as Left 4 Dead, but it does the job.
  • by russotto (537200) on Friday August 14, 2009 @10:39PM (#29073451) Journal
    Until we manage to create real zombies and release them on the population, we'll never be able to test the model.
    • Re: (Score:2, Troll)

      by Tumbleweed (3706) *

      Until we manage to create real zombies and release them on the population, we'll never be able to test the model.

      There are already three different test cases that have been released into the populace: teabaggers, birthers and deathers.

      In all cases, mental activity is absolutely zero, yet they keep moving around, menacing the living, going after anyone who looks like they have a brain. The teabagger test case flamed out fairly quickly, the birthers took quit a bit longer, and the deathers are still going.

      The

    • by mapkinase (958129)

      Rabid animals are probably the closest subjects in the real world for candidates of such testing.

    • by selven (1556643)
      Zombies aren't the threat people make them out to be. Under the rules in the Zombie Survival Guide (if you get bitten, you feel symptoms in 4h, fall unconscious in 16h, become a zombie in 24h; zombies move at 1.5 feet per second (45cm/s) and their gait makes it easy to tell them apart; zombies have the brain of an insect, so they can't use guns or even knives; the zombie's brain (the only way to kill a zombie is by taking out the brain) is located in the frontal lobe), even if 5% of the population instantly
    • by Sulphur (1548251)
      Wes Craven's Serpent and the Rainbow http://www.imdb.com/title/tt096071 [imdb.com]
  • by gmuslera (3436) on Friday August 14, 2009 @10:49PM (#29073489) Homepage Journal
    It grow fast but always is limited by the absolute numbers of installed windows PC.
    • Re: (Score:3, Interesting)

      Oh, good! It's nice to see that I wasn't the only slashdotter to read the summary and think it referred to zombified PCs.
  • Similar work has been done previously with vampires: See http://www.hphomeview.com/Tips/Vampire%20Ecology%20in%20the%20Jossverse.pdf [hphomeview.com] which uses vampires functioning in the Buffyverse.
    • by pwagle (13408)
      Something may be odd with this pdf. My debian system freaked (load average spike, failed attempt to make network connection) when I opened it with evince.
  • by Anonymous Coward

    ...it should make zombie movies more interesting, not to mention more scary. Human brains (at least the ones not eaten by zombies) are usually fairly good at determining when something is logically consistent.

  • They're wrong... (Score:1, Informative)

    by Anonymous Coward

    If Shaun of the Dead (movie) is any indication, being aggressive and fast isn't the way to go about defeating hordes of zombies.

    1) Relax, ignore them at first. Be completely oblivious, not knowing they're even around is useful.

    2) Once they can't be ignored anymore, stand back a little and have a pleasant conversation with a friend about it if you have any left. Maybe throw a few vinyl records.

    3) Don't try to survive by staying somewhere safe like a hi-rise flat, head to the nearest pub with easy to break wi

  • 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.

    Hummm so the moral we should all take from this is if you are in an area with a zombie outbreak you should get the fuck out before the nukes start falling...

    Good to know...

    • 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.

      Did anyone else RTFA? Note the bold part... I always knew there was more to political fandom than met the eye. Apparently it involves your brain being consumed...

    • ...and go out and smash up the corpsicles.

      (Okay, yeah, tropical zones, waves of reinfection, etc. But there's a reason zombie movies always take place in the summer.)

      • by Jarlsberg (643324)
        The new norwegian zombie movies takes place in the winter, with nazi zombies crawling out of the snow.
  • Once we get done reforming healthcare, perhaps someone could pass this up to Obama and get a plan for a zombie infestation drawn up. Never a bad idea to have one of those...
    • by maxume (22995)

      I prefer it if the government were drawing up a plan for dealing with zombie infestations.

  • by Dahamma (304068) on Friday August 14, 2009 @11:29PM (#29073649)

    Unfortunately, after reading this study there seem to be several missing elements:

    1. zombie speed and effectiveness. Are these 28 Days Later psycho zombies or Shaun of the Dead shambling loser zombies? And sure, they modeled an "encounter" but it's a simple one-on-one winner takes all. Any good zombistician knows most zombie encounters are between a small band of survivors and a horde. It needs to be modeled!

    2. It appears that any individual can transition between the "Zombie" and "Removed" state. There needs to be a 4th (end) state: "Brains Splattered By Shotgun".

    3. Bruce Campbell.

    • by Cramit (609487)
      3. Bruce Campbell...and his boom stick!
    • 1.) 'Shaun of the dead'-style, page 2 second to last sentence.

      2.) Already there. Zombies can be 'killed' and then enter the Removed group, final defeat is modelled by the parameter alpha (page 3).

      3.) Touché.
    • by Scrab (573004)
      Not to mention, what damage does it take to kill a zombie? Headshots only, or just a savage beating, possibly with a frying pan? Details, people!
  • by Archfeld (6757) *

    Do you have your Redeker Plan ?

  • Senior author (Score:2, Informative)

    by plasmidmap (1435389)

    The senior author is a professor at the university I attend--he is a super nice guy and does very interesting non-zombie related research too.

  • Let us (Score:4, Funny)

    by Anonymous Coward on Saturday August 15, 2009 @12:06AM (#29073807)

    Consider a spherical zombie in simple harmonic motion...

  • There is a great book called The Lucifer Effect: How Good People Turn Evil by Philip Zimbardo. The author was the guy who conducted the Standford Prison Experiment [wikipedia.org] a few decades ago. The book discusses that experiment and how it relates to other well-known acts of evil that have occurred, such as massacres during war, genocides, and abuse of prisoners at Abu Ghraib.

    In the book, the author argues against the idea that some people are intrinsically good and other people are intrinsically evil. Instead, the ev

  • by Spacelem (189863) on Saturday August 15, 2009 @07:43AM (#29075277)

    Modelling a zombie outbreak?

    That's entirely similar to the work I've been doing for the last year, modelling the spread of a disease among an animal population. I've been trying to work out under what situations culling will lead to an increase in the number of infecteds.

    So, if I name the particular species I've been working on "zombies", and adjust some of the parameters, I've got an SI model that is not only very similar to this, but also includes spatial structure and stochasticity, which is crucial for describing the stability of the disease, and modelling the spread when the population size is low.

    • That's because the model they use is pretty much the stock standard SRI (Succeptible-Recovered-Infected) infection model. They even say so themselves (while showing that their model contains an extra non-linear term, included via Mass-Action - another pretty common modelling "law").

      Still, a fun application of stability analysis.

  • ...from computer simulation, that this year is going to be the year of Zombies on the Desktop !
  • Nothing scientifically interesting here. This is just basic 101 mathematical modeling, straight from the text book. They start with the most basic SIR model, building it from the elementary reactions and do the basic analysis: solve the equilibria and determine their stability with eigenvalues. They have just renamed the generic "infected" as "zombies". We did these calculations for dozens of different models as part of course exercises. For some reason, they don't do phase plane analysis, which is a very b

  • One of the best scene in the film 'The Thing' (1982) was when the scientist realizes that they are dealing with an alien foe who can replicate and imitate other species. He rapidly writes a computer program and creates his own equations within it to accurately calculate, based his cellular observations of the alien organism, the best projection of how quickly the alien could take over earth's population should it reach mainland (they are stranded on an arctic base with the alien creature).

    Below is the IMDB

  • Okay, I know the first rule of slashdot is that you don't read TFA. But I did, and they messed up. On p. 135 they describe a process that occurs at rate alpha where normal humans decapitate or destroy the brains of zombies. This reduces the population Z of zombies, and increases the population R of "removed" individuals. But they also have a process that occurs at rate zeta, where "removed" individuals are resurrected and become zombies. No way! Once you decapitate the zombie or destroy its brain, it can't
  • Meh. Zombies are mostly a problem due to horror movie tropes like "running away never works", "the authorities are useless when it comes to anything important" and "nobody in the movie has ever seen a zombie movie". Chances are it wouldn't get beyond a small initial outbreak.

    Even if they get established in a city, once the military gets called in, tanks and other armored vehicles will make short work of the milling throngs - if the "zombies are attracted to noise" rule is in effect, you could get them all b

  • What do you do when zombies attack?

    Most people buy popcorn.

Facts are stubborn, but statistics are more pliable.

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