Science tackles zombie attacks
My apologies for the prolonged radio silence - it turns out the real world is a rather busy place. I have a sneaking suspicion that this may have something to do with the fact that I am working at a Centre for Disease Control IN THE MIDDLE OF A PANDEMIC, but I haven't got a control job in place so cannot reliably confirm whether my hypothesis holds true with any measure of statistical confidence.
I can, however, confirm that working in the realm of infectious disease research is tremendously interesting. Global surveillance is constantly turning up cases of the usual assortment of gnarly human ailments, from anthrax to rabies to pneumonic plague, and the animal kingdom is verily rife with exotic zoonoses. In the last two weeks, for example, I have received reports on Ecuadorian penguins with malaria, herpetic horses, a tuberculotic cow, and a bunch of vampire bats with SARS.
All the rabid humans, coughing cows and sneezing febrile bats of the world, however, cannot even come close to the most interesting bit of infectious disease research I've come across lately - the mathematical modelling of the potential outcomes for humanity should zombies attack.
I came across the paper a couple of weeks ago, when I was giving a workshop on practical conference-going skills to a group of students about to attend the Annual Meeting of the Society for Mathematical Biology. The pre-conference meeting also featured introductory lectures from many of the conference session chairs, 45-minute cheat sheets introducing the students to the different areas the conference plenary sessions would cover. I arrived early to the check out the session before mine - an introduction to mathematical modelling of infectious disease - and discovered Robert Smith?'s (yes, that is a question mark) zombie model.
Now I am certain that most readers will agree with me when I say that mathematical modelling does not sound like the most compelling of subjects. Partial differential equations, eigen decomposition and matrix diagonalization are all very important concepts that the advanced undergraduate in physics, engineering, or math ought to be familiar with, but when one is being taught the aforementioned concepts through examples that include latent semantic analysis and pharmacokinetic cumulation processes, the material can get a little, uh, dry.
When you use zombies as your example process, however, students sit up and take notice.
There is no nerd on the face of this earth who hasn't at least idly considered what they'd do in the event of a zombie attack, and there are a good many more of us who have actually thought through our specific plans and debated their various benefits and pitfalls with others (my solar-powered-chainsaw-studded fence, for example, while brutally effective in the short term, would likely soon enough result in the build-up of a ramp of zombie carcasses in front of the fence, blocking the chainsaw blades. See, it's good to think of these things now.)
Smith? and his colleagues decided to apply the basic principles of mathematical modelling to a zombie outbreak situation. They define a series of classes to which people can belong (susceptible, zombie, or removed) and a set of parameters modelling the transition between classes (the rate at which susceptible become zombies, for example). From this they can construct a basic epidemiological model that predicts how quickly zombies will take over the world. The model can be successively refined by adding new parameters, like the effect of quarantine, treatment, or what the authors politely refer to as "impulsive eradication" (nuking the $#!% of the zombies, in other words).
By explaining a highly technical scientific method using a flat-out cool pop-culture example, the authors manage to make concepts like Jacobians, unstable equilibria, and mass-action transmissions infinitely more palatable and memorable to students and researchers alike. The approach is one more and more profs are adopting - at UBC, for example, a second-year physics course in instrument design is taught as a Robot Wars-eqsue competition, where the students build robots to carry out a specified task and then battle it out of at the end of term to see whose robot emerges triumphant. In my own work, a colleague and I recently jazzed up a textbook chapter on the computational analysis of immunology data by using an exotic and disgusting case of purulent smallpox as our example dataset.
Using a catchy example is a fantastic way to engage students with your subject matter. For proof, you need to look no further than the fact that you, dear reader, kept reading past matrix diagonalizations and mass-action transmissions to find out what happens to humanity in the event of a zombie outbreak. The bad news is that in most cases - the basic model, the latent infection model, the small-scale quarantine model - the disease-free equilibria are unstable and zombies take over the world. Treatment doesn't do a fat lot of good either, as humanity continues to exist but at much lower population numbers than before the outbreak. The good news, however, is that under the model of impulsive eradication, in which large-scale assaults on the zombie population take place as resources permit, humanity survives. So stock up on nukes, folks - the ordinary differential equations don't lie.
Tagged with
mathematical,
teaching,
zombies,
modelling
| 
JENNIFER GARDY 
Comments
Hilarious Ms. Gardy!! Thank you for the continuing articles and allowing me to laugh at my overeducated self! Please don't stay quiet too long!!
BBBRRRAAAIIINNNSSSS!!!!!
You might find this amusing now... But extensive research by Max Brooks (The Zombie Survival Guide, ISBN: 1400049628) has shown us that medications will be of no use...
The only way to stop a Zombie is to destroy his brain. A head shot been the best way to do it.
Unfortunatly for us, the rules and regulations imposed on Canadians over the last decade... have lead to many people now been defenceless...
Nice. I have a pet theory about zombie movies that says they appeal to us not because the dead rise, but because we have an innate fascination about what happens when your neighbours turn on you and become butchers. Just like they did during the Terror in France, China's cultural revolution, the killing fields of Cambodia and then again in Rwanda, lately in Darfur and any other genocide perpetrated largely by civilians. They are allegories for revolutions from the perspective of the incumbent. Zombies are good for explaining pretty much anything from hidden markov models and nash equilibria to campy critical theory.
I spoke with Smith? prior to the publication of his work. There are some zombie and non-zombie problems with the paper. For a better mathematical exploration of zombies you should check out a manuscript from Dr. Troy Day at Queens University. I don't think it is online, but it uses 28 Days later to determine R0 (see wikipedia) for zombies.
What I meant to say was, we need a Zombie Colloquia Series where people can present foundational ideas from their fields in terms of what they mean during a zombie attack. Economists, neuro surgeons, engineers and computer scientists can present findings from modelling zombie mayhem.
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So - is it ordinary or partial differential equations which govern the dynamics of a zombie outbreak? You mention both.
I just finished reading Max Brooks' other book, World War Z... Obviously Z is for Zombie. He even touches on the topic of scientific modeling and how the results changed each countries approach to the war.
As for my strategy I'm a firm believer in breaking into medieval times for plate mail and lots and lots of swords and axes.
Oh man, Zombies are so yesterday. The REAL threat is ROBOTS!!!!
http://www.amazon.com/How-Survive-Robot-Uprising-Defending/dp/1582345929/ref=cm_syf_dtl_pl_2/181-2874208-9300812/181-2874208-9300812
From editor: This comment has been removed because it does not conform with our comment policies.
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Must have been a Zombie who removed it. LOL.
World War Z by Max Brooks is an original, eye-opening zombie-read. The socio-political forces that influence how each country responds to the outbreak is interesting (including some thought-provoking actions from South Africa). Thanks for the article - a good reminder to start stocking up my zombie survival kit (if you have that, any other natural disaster is child`s play), and remember, to avoid zombies, get up high and take out the stairs!
@Zachary: Both! PDEs and ODEs are both used in modelling in different scenarios.
@Mike: I'd love to find that paper - Smith? did the classical zombies - would be cool to see R0 for the 21st century speedy zombie.
@Fellow Brooks-readers: I just finished WWZ a couple of months ago - it's being adapted into a film, and zombie movies are the only films I show up to on opening day!
Does it have anything to do with complex eigenvectors when you talk about matrices and PDE's?
P.S. I think I love you.
I mean because of the property of complex eigen vector when you solve PDE I recall from my differential equations course (math 215 in UBC) can you use complex eigenvectors to model zombie behavior?
More please: Jen you are my new fav in the G&M;, brains, beauty and funny, an unbeatable combo. Illumination of the thinking mans feminine ideal presented through literate entertainment, long overdue and rare in newspapers, if not already, you really should be syndicated. Kudo's.
Turn up the Specials and pass me a Cricket Bat.
It's funny, I am reading this as I study for my ODE exam tomorrow.
I'll be taking PDEs this coming term. Perhaps I'll suggest to the prof that he put a zombie-outbreak scenario on a problem set.
Jennifer Gardy,
I think it might help you to look into NP-complete algorithm properties. Zombie behavior might resemble those.
P.S. I visited your website. My question has been answered.
I think the problem with modelling disease outbreaks based on a zombie attack is that the zombie disease causes significant behavioural changes. Rather than staying at home in bed and washing their hands, zombies will actively form mobs and seek out new prey to infect. The only way to stop the outbreak is with guns and blades, not hand-washing and hospitals.
Actually, from decision-making point of view I don't think Zombie behavior would be that unpredictable/complicated. I am no expert on Zombies but from what I know they resemble "mindless automatons" no? So their decision-making pattern is really very basic. When talking about chess or some very deep decision making algorithms then NP-complete problems will apply I think but in this case I think it's much simpler and hence the resulting mathematical model. Maybe you are over-analyzing the problem?
Being a scientist myself and having attended said conference, it is hard for me to think of a more obvious waste of public (i.e. taxpayer's) money than this kind of research.
Wait, I found one: Giving a workshop on "practical conference-going skills".
Peter: Just so you can rest easy, no taxpayer dollars were spent during this research. It might surprise you, but we didn't actually go out and collect field data or travel to the exotic locations to study zombies in the wild.
I have to give thanks to everyone associated with this blog - Jennifer, your subject matter is brilliant! And your style of writing is even more hilarious than some of the other posters (Chamale, -edan, Victor Skovorodnikov - keep 'em coming!) I also love the pop-culture references to zombies - Cricket Bats, Max Brooks as required reading (World War Z - I laughed, I cried...) and 28 Days Later. Awesome film! And so, Miss Gardy, please keep up the good work!
while snowshoeing last winter I had a zombie encounter of a kind... two guys were filming a zombie short. The scene they were filming was part of the escape. Our hero headed out into the frozen north, because as we all know, zombies are exothermic, so here in the great white north we will survive!
Thanks for the mid-afternoon sanity break! Now back to being a mindless automaton...
This awesome. I'm going to remember this article and tell all my friends about it. As sad as it is, our fall back dinner conversation is our competing zombie contingency plans. Hey, it's problem solving, aren't we supposed to learn about that in university? They're getting surprisingly complex and detailed though... oh well, I guess we're ready for anything!
This is all nice and fun but how about trying to find a cure for the recent flu epidemic or cancer research? Are you working on these things Jennifer Gardy?
Victor: Don't worry, we're working on those things as well. In fact, you can read about the link between zombie modelling and swine flu at National Geographic:
http://blogs.ngm.com/blog_central/2009/08/what-can-zombies-teach-us-about-swine-flu.html
Also, as the original paper itself notes, it is instructive to research problems that don't necessarily have immediate applications. If, God forbid, a disease with a very fast and aggressive infection rate did suddenly surface - and it's not beyond the realms of possibility - wouldn't it be helpful if research into treatment and containment methods had already been done? Equally, this is quite clearly to be used as a teaching tool and anything that will help get the potential next generation of mathematical disease modellers interested and involved (in what must be something of a niche subject area, one may assume) may well be instrumental in solving any of the major diseases that afflict humanity in the future. This is clearly neither a waste of time nor money; it's just extremely effective futures planning.
I'm a long-serving math prof who has attempted to teach a couple of generations of engineers the elements of ODEs. The Zombie paper is a pretty good example, accessible, I should think, to most sharp undergrads who have gotten the idea for 2x2 systems and are ready to tackle a 3x3 example. The chief point at issue is what a linearization of the vector field looks like, qualitatively, at an equilibrium point, and how that is determined by the Jacobean, so that one may say what kind of (in)stability is exhibited. Thus, the point that with an eigenvalue of real positive part one either has a flow line emanating from the equilibrium (a straight line in a linear change of co-ordinates)when the eigenvalue is real or an outward-flowing spiral when it is complex. Likewise, when all eigenvalues have negative real part, the equilibrium is a sink.
What the paper seems to omit is that there are no limit cycles, so that all initial values apart from the unstable equilibrium flow to the sink. But you can repair that by finding a function whose gradient dotted with the field is always non-zero away from equilibria, ruling out a limit cycle.
A little differential topology is helpful here--but too much to ask of undergrads. Nonetheless, see Milnor, "Topology from the Differential Viewpoint" to see how these ideas can be built into lovely mathematics apart from grubbing about with epidemiology.
A paper modeling a disease epidemic, written by a man named "Robert Smith?" GOLD.
Er - I've just found out that it was neither a clever pseudonym nor actually referring to the singer from The Cure.
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