How the Mayor Will Save You in a Zombie Apocalypse (by reminding you to stay at work)

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Hello everyone. Welcome to my first blog post. Today is a silly day, and since it is still zombie awareness month , I’ve decided to present some of my own silly fiction-science research on zombies. Specifically, zombie epidemic mathematics.

Thanks, google image search!

Epidemic Mathematics
Okay, so there are real people out there studying real epidemics using mathematics; and as it happens, modeling an epidemic can be fairly straightforward (you know, like assembling a sky scraper, or running a factory). Let me do a thought experiment with you do demonstrate how it can be done.

Suppose that there are four people moving about randomly (once an hour) inside of a four room house, and one of them has the flu. The odds that a healthy person will meet the sick dude are 1/4. Suppose that, should you get stuck in the same room with the sick dude, the odds of contracting the flu are 1/7. Then the overall odds of catching the flu (by getting caught in the sick room, and then contracting the illness) are 1/(7*4)=1/28. Thus, the number of people who will get sick each hour will be 3/28. Alternatively, I could say that it will take about 10 hours for ONE PERSON to contract the flu. After that, there will be two sick people and two healthy people wandering through the claustrophobic little house.

Follow that?! Then you’ve just taken a baby step toward being able to model an epidemic. Its a helpful and noble field of mathematics. Of course, I’m a physicist, and neither helpful nor noble. So I chose to model a stupid ZOMBIE epidemic.

Why Zombies?
As a brief tangent, I should provide you with a little background to my stupid research in zombies.

I spent about 25 years of my life blissfully unaware of the genre of horror fiction wherein our dead relatives are reanimated and try to eat us. At that time, living in the city of Kingston, Ontario —where autumn shadows are dark and deep— I was introduced to zombie movies. They terrified me. The fundamental elements of the genre spoke to my subconscious and took deep root. Every nightmare I had over the next five years had me wandering amid a post-apocalyptic wasteland, destined to be grabbed by cold fingers.
It's crazy but I think that this is very scary.

As therapy for this crippling phobia (of something which my family was wont to point out does not actually exist), I began to analyze the scenario rationally. The fruit of this analysis is that each autumn for the last three years I have written a “paper” on the mathematics of zombies. Good news! Since I completed this latest batch of research, I have only once had a zombie nightmare (though I had a robot apocalypse the other night…).

Okay Whatever. What’s This Latest Research You’ve Done?
I should mention at the start that Doctor Robert Smith? has recently come to prominence for his research on zombie epidemics. His model is different from mine, and I did my work before reading his paper. I get to meet him next week and I’m excited.

So in my zombie model, I ask two questions. The first is: what if the people who are fighting zombies are also worried about running out of food? Prior zombie discussions haven’t taken into account the fact that a zombie epidemic will grind trade to a halt, and therefore starvation will become an issue. The second question is: is there some strategy which a populace should be encouraged to adopt to increase survivability?

This Next Bit Talks About the Model And It’s Boring  (*skip ift if you want to get to the controversial conclusion*)

This is a model where the human population will become more or less aggressive towards the zombies depending on how the circumstances change. I assume that there are three different human populations: workers who gather food; moles who run and hide and stay hidden; and militia soldiers who patrol the streets in order to cull the undead population. I suppose that, if 100 workers were to randomly meet zombies in the street, A of them (where the parameter A is between 0 and 100 and will be fixed at the start of each simulation) will join the militia, and B (defined similarly) will go into hiding. Alternatively, the workers will (daily) increase the size of the communal food pile, while the soldiers and moles can only reduce it. If the food stored falls too low, some percentage of the soldiers and moles will rejoin the work-force to build them back up again. Finally, if one of the zombies wandering around bites anyone, they’ll become a zombie. I wrote the appropriate equations describing this scenario for a time resolution of 1 day, and after providing some initial values, kept track of how the populations changed day by day.

We can tweak the model so that more workers (after encountering a zombie) are willing to join the militia (we call these cities “brave”), or go into hiding (we call these cities “cowardly”), or keep working at their jobs despite the terror they feel (we call these cities “stoic”). We can model well (or poorly) trained militia members  by appropriately defining a parameter which describes the odds that a soldier will successfully cull a zombie it encounters.

We can also model urban or rural scenarios by setting the initial population density to be either high or low respectively.

We built two models: one where zombies are created only through infection by other zombies (as described by Max Brooks in his rad books, and also in the movies whose titles begin with “28” unit of time “later” ); and one where zombies are the reanimated dead, and anyone who dies can become a zombie (as shown in George Romero’s movies ).

What Did You Conclude?
In brief, I concluded three things. First off, the worst thing that people can do in a zombie epidemic is to have everyone pick up a gun and fight. Secondly, you’re better off living in a CITY than the countryside during a zombie epidemic. Thirdly, the rural areas are DOOMED when the dead begin to walk.

ugh... no

That’s The Opposite Of Every Damn Thing I’ve Ever Been Told! Justify Your Statements with Some Damn Graphs, Dammit!

The worst thing that people can do in a zombie epidemic is to pick up a gun and fight.

As we see in this totally awesome graph of human and zombie populations: there is an enthusiastic enlistment in the militia every time the zombie population grows (click on this link to see a bigger verion).

So uh, this graph probably applies to swinging your government wildly between republican and democrat. but no one reads the alt text.
As we also see, the human population is dwindling. The second graph tells the story: too many people in the militia means not enough people finding supplies. Before too long, supplies dwindle and everyone has to go back to work. Further analysis shows that a small (sustainable) and well trained militia is far more efficient at culling the zombie population.

You’re better off in the city than the countryside during a zombie epidemic

Let me show you 2 graphs.

the dotted region is the region where that strategy WORKED at killing off zombies.
This graph represents the parameter space (where the side axis represents the odds that a worker will join the militia, and the bottom axis represents the odds that a soldier will successfully cull a zombie) of a stoic, urban scenario where the zombies have been completely culled within 3 years.
the dotted regions are the EFFECTIVE strategies.

This graph represents the parameter space of a stoic, rural scenario where the zombies have been culled within 6 years. Notice that the area is much smaller (and thus more difficult to achieve) and that a successful cull takes much LONGER in the rural scenario. This is because the zombie “war” will burn much SLOWER in the countryside than in the city.

Incidentally, it’s also clear from these graphs that the efficiency of the militia is much more important than the population of the militia.

The Countryside is DOOMED if the zombies are undead

If zombies are really the reanimated dead, rather than just being diseased cannibals, then the dynamics of the model change in a frightening way. In this scenario, any person who dies will turn into a zombie, even someone who gets killed in an accident. You know what kills people accidentally a LOT? Having a bunch of people roaming around with orders to shoot anyone acting suspiciously. In other words, the militia becomes a double edged sword, where the accidents they cause can ADD to the zombie population.

In a rural environment, the slow pace of the cull means that zombies will become endemic to the countryside. “BUT!” you say, “WHAT IF WE SEND IN A MASSIVE ARMY TO WIPE THEM OUT?” Well, miss smarty shoes, I DID THAT SIMULATION! Suppose that the military is as large as the working population will allow, and it’s in a rural setting.
aaah! everyone died!

This graph represents the parameter space where the undead zombies have killed off EVERYONE. Have you noticed how LARGE IT IS?

Superman help us! Here is my radical paper in its FULL GRAPHY GLORY.

Feel free to post your opinion below or write to me at ben[AT]sciencesortof.com

Keep science in your hearts! Next week I’ll talk about the TWIN PARADOX.

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7 Responses to How the Mayor Will Save You in a Zombie Apocalypse (by reminding you to stay at work)

  1. ClaveNo Gravatar 27 May, 2010 at 7:50 am #

    Excellent work! Very enthralling! I’d love to hear more!

  2. CaveDwellerNo Gravatar 27 May, 2010 at 11:32 am #

    Two words. Love it.

    Three words. I want more!!

  3. BenNo Gravatar 28 May, 2010 at 7:27 pm #

    Fascinating ideas. You should look into the novels “World War Z” and “The Zombie Survival Guide” by Max Brooks: excellent zombie books, and outstanding literature by any standard.

    • benNo Gravatar 29 May, 2010 at 9:41 pm #

      they’re rad and TERRIFYING!

  4. Amy BiznessNo Gravatar 7 June, 2010 at 11:03 pm #

    while i agree with most of your work, one
    varible is that people change.
    maybe i get tired of hiding. or i’m an obese person and live off my fat.
    great work though!

  5. dkNo Gravatar 1 September, 2010 at 6:27 am #

    The creation of an army of anti-zombie ninjas (ie, soldiers trained NOT to accidentally create more zombies) might turn the tide. I’d imagine that over the course of a month, or two, or a year, that tactics would improve. Any chance, at least for the undead cannibals, that we could poison them with baited corpses? Or some kind of time-release white phosphorus or something?

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