## When models scorn data.

A while back there was a splash on the internet over the publication of a book titled, Infectious Disease Modelling Research Progress. The reason, aside from the snappy name, was that it included a chapter discussing an agent-based model of a zombie outbreak. As you might guess, this kind of outbreak was judged to be a very bad thing:

“Only sufficiently frequent attacks, with increasing force, will result in eradication, assuming the available resources can be mustered in time,” they concluded.

“If the timescale of the outbreak increases, then the result is the doomsday scenario: an outbreak of zombies will result in the collapse of civilization, with every human infected, or dead,” they wrote. “This is because human births and deaths will provide the undead with a limitless supply of new bodies to infect, resurrect and convert.”

How fast do we need to deal with the outbreak? If an infection breaks out in a city of 500,000 people, the zombies will outnumber the susceptibles in about three days.

The story is getting more interesting, however, because now we don’t just have an article discussing an outbreak of a fictional plague that is more or less physically impossible. No, now we have an academic argument over the quality of said modeling.

I’m referring to Blake Messer’s rebuttal of the chapter’s conclusions. In short, he alters the assumptions used by the researchers in the original paper and finds that human survival in the face of an undead horror is, indeed, quite possible:

In my version, there is a ‘continent’ consisting of a two dimensional surface with some gradient distribution of a defensive resource scattered across it.

Call this resource what you want. It might reflect terrain that humans find highly defensible or zombies find particularly hostile. It might reflect concentration of ammunition stores or access to some sort of defense resource. Mathematically, if a human is closer to the centers of the orange circles, he or she is more likely to survive a zombie attack.

At round 0, humans are randomly distributed across the plot and the first zombie appears in the middle of the map. In each round, each human seeks a more defensible position than his current location and each zombie attacks the human closest to him (or wanders randomly if he can’t find a human).

When accounting for these things, I can find scenarios of large initial zombie outbreaks that, when followed by quick adoption of strong anti-zombie defense policies may help pockets, or even large fractions of civilization to ward off the impending doom of mass zombie infection! How exciting!

Leaving aside my natural pleasure that the new field of zombie studies is growing, it’s fair to ask why I’m mentioning this on Permutations. Is it just because it’s a fun example of mathematical modeling that we could all use in class to get talented students interested?

Maybe…

But it’s also because it’s a good example of the necessity of empiricism even in abstract mathematical models. The thing that strikes me about this “debate” is that there is no way to adjudicate between what is a reasonable modeling strategy and what is not. Messer objects, for example, to the choice in the original paper to allow dead zombies reanimate after being killed. So, in other words, he objects to semi-immortal zombies. I’m forced to agree with him, but given that there’s not actually any such thing as a zombie, who are we to argue? Without some kind of hard referent- an empirical anchor against which we can judge our models and upon which we can base their assumptions and dynamics- it all just turns into a sort of abstract mathematical game.

This is not to say that I object to the use of abstraction and generalization in formal models- far from it- but it does draw attention to the basic empirical roots of even the most abstract of models. We need abstraction, we need generalization, but we must balance those needs against a basic necessity for some sort of empirical grounding- if only in terms of defining the subject matter!

Mathematical models are powerful tools and have an important, and growing, place in the social sciences. It’s just nice to not wake up one day and wonder if this whole time you’ve been studying the shambling dead by accident.