Wednesday, March 10, 2010

Agent-Based Computational Model of Humanity’s Prospects for Post Zombie Outbreak Survival

Last summer, a team of researchers led by Robert Smith? at the University of Ottawa (don't ask about the question mark) published a chapter in a book on biological modeling entitled "When Zombies Attack!: Mathematical Modeling of an Outbreak of Zombie Infection."

The article's publication caused an outbreak of its own, earning attention from what seemed like the entire blogosphere -- Slashdot, Ars, BoingBoing, Wired... even NPR found it newsworthy.

Admittedly, your run-of-the-mill infectious disease model's abstract probably isn't quite as stimulating as the Ottawa team's:
...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 show that only quick, aggressive attacks can stave off the doomsday scenario: the collapse of society as zombies overtake us all.
A divergence from much of the nonacademic literature, their finding shows that if we can't keep the outbreak from spreading initially, then the equilibrium solution is human extinction.

Headlines should have read: "Canadian Researchers Have Very Little Faith In Humanity."

The concept might be novel, but the implementation is far from air tight. The Ottawa team's model sacrifices too much alongside its simplifying assumptions. First, the model allows dead zombies to reanimate after being killed. Second, the risk of death and zombification for a given 'Susceptible' (the Ottawa team's term for humans) is a fixed constant in their model.

The latter problem may be less intuitive so I'll explain my reasoning: Humans who survive the initial outbreak survive for a reason. Disproportionately, they were faster, smarter, and stronger to begin with than their fallen peers. Even if they weren't, they were luckier and have probably been able to, at least, find a more defensible location than where they started at round zero of the outbreak, increasing their chances of survival simply by virtue of having survived the early rounds of the outbreak.

So, I constructed a computational agent-based zombie outbreak model to test how my assumptions might alter the solution.

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). This is a typical simulation where the outbreak ends in human extinction:

More or less, this mimics the Ottawa team's solutions. A couple of runs with the same parameters are plotted on the left graph below. The graph on the right is one of the Ottawa team's solutions:

The results can be changed dramatically just by changing the concentration of resources from the initial plot:

Granted, this model probably has some shortfalls in terms of scientific rigor. Every parameter was wonkishly assumed; and so, it should be unsurprising that I can churn out the corner solutions just by shifting parameters around. After all, several of the parameters affect the odds of a human surviving a given encounter with a zombie. (By the way, if anyone can find any empirical data on this I'll gladly plug them in).

If you ask me, though, the Ottawa team's model leaves something more profound out the equation: human capacity for ex-post organization and response. When accounting for these things, I can show 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!

And finally, here's a video I made of some MATLAB "movie" runs of the simulation. I suggest skipping to 2m45s:

EDITS: Embedded the video and corrected for some grammar after reading quotes of myself on other blogs.