# New Math Suggests Zombies Won't Kill Us All

What can zombie films teach us about real life epidemics?
##### Scene from Night of the Living Dead. Still via Wikipedia

If physics is for understanding the mechanics of the TARDIS, apparently math is for understanding the zombie apocalypse.

In a paper published on the arXiv pre-print server, Caitlyn Witkowski of Bryant University and Brian Blais of Brown University attempt to mathematically model the zombie plague as it appears in movies. Their work expands on that of Philip Munz of Carleton University, who in 2009 drafted a similar paper called “When Zombies Attack!: Mathematical Modeling of an Outbreak of Zombie Infection.”

Munz relied on the traditional SIR model of infectious disease, where SIR refers to three subpopulations of people during an epidemic: susceptible and infected individuals, and those removed from the susceptible group. However, Witkowski and Blais argue that Munz's modeling of the removed group (R) was incorrect. Instead, they developed a new model for groups removed from infection, one at least partially based on—what else?—zombie movies.

##### This graph from the paper, based off of the team's Night of the Living Dead model, shows that as an epidemic progresses, the infected grow while eventually those susceptible to infection  disappear. But not everyone who's susceptible ends up infected.

“One serious consequence of this term [R] is that there is no permanently removed subpopulation,” they write. “In their model, zombies never truly die.” But as anyone who has watched a zombie movie can attest, zombies can and do die. Chop off their heads or axe their brains, they remain “mortal,” though obviously not in the conventional sense.

This is key, the authors write, because Munz's model suggests humans can never win. "The assumption that the removed population will inevitably recycle into the zombie subpopulation implies that the zombie subpopulation will always win, while the other two subpopulations will always be diminished, regardless of parameters," they write. "We have found that this assumption does not match any depiction of zombies in the popular culture, so the conclusions from models with this assumption should be suspect."

Essentially, they're arguing that people (or zombies) can be removed from the equation. Not every zombie comes back to life to infect more people, a conclusion supported by real-world evidence. "Further, there is no analog to this 'recycling' terms in real-world diseases, thus limiting the application of the Munz et. al. (2009) model to only entertainment purposes," they write.

Witkowski and Blais' new equations are based on hours of meticulous film viewing, during which they catalogued the zombies on screen. Based on this binge-watching, they claim there are two basic modes of zombie infection, represented respectively by the films Night of the Living Dead and Shaun of the Dead. In the former, everyone who dies becomes a zombie, whether or not they’ve been in physical contact with the undead. In the latter, death doesn’t necessarily lead to zombification. Rather, only those who have been infected become brain-eaters.

Academic studies of zombies are more common than you might think. In fact, on a personal note, I took a class in 2009 about zombies as part of my undergraduate degree—it involved lots of Wednesday evenings spent watching Romero films and writing papers on The Walking Dead. But Witkowski and Blais suggest their paper is not just an intellectual exercise, but that this has some real world value as well.

The importance of the paper, they say, is twofold. One, by using an “entertaining example” to lure people in, Witkowski and Blais can teach readers about certain complicated mathematical topics. Second, and perhaps more important, is the idea that studying fictional representations of epidemics can assist in analyzing and planning for real world illness as well.

Using the SIR model and Google-supplied influenza data, they confirm that the same processes they underwent to study zombies—Bayesian parameter estimation, Markov chain Monte Carlo methods—can be used to illuminate the spread of the flu or other real afflictions.

So on your next repeat viewing of Night of the Living Dead, just remember: it’s not just a stark and disturbing movie about the rising of the undead, but perhaps a learning experience regarding how disease works.

@heyiamlex