Excerpt from Chapter 6, by Kyle William Bishop, David Tufte, and Mary Jo Tufte
To model the unspoken endgame of an apocalyptic zombie narrative, we need a model with comparative dynamics. In fact, such a model already exists.2 Munz, Hudea, Imad, and Smith (2009) created a mathematical model of a zombie outbreak in a paper that has been heavily cited in both the scholarly literature and over a hundred blog posts. What they did was use comparative dynamics to figure out how many possible endgames exist for narratives with typical zombie behavior. However, their model is hobbled by untenable assumptions about both zombie and human behavior, and these assumptions lead directly to their dire conclusion: that once zombies appear, doomsday is the only plausible endgame. Using insights from economics and biology, we will argue that Munz and his colleagues’ conclusion is incomplete, and that other endgames are also possible—including both stalemate and total victory over the zombies.
COMPARATIVE DYNAMICS OF THE ZOMBIE APOCALYPSE
Munz, Hudea, Imad, and Smith model the comparative dynamics of an infectious agent, an infectible host, and perhaps an infected but uncompromised carrier. In their view of the narratives, zombies are the infectious agent, humans can be infected and become zombies, and the carriers are corpses that may reanimate. They come to a startling conclusion: if there are any zombies at all, humans will eventually lose. They show there are only two steady states: an unstable zombie-free one with only humans and a stable one with only zombies that they call “doomsday.” A word of caution is in order about terminology. In comparative dynamics, unstable doesn’t mean impossible, but rather possible unless disturbed. So a zombie-free society (like our own) is sustainable, and it is one possible endgame. But the advent of zombies disturbs us away from that steady state, and because it wasn’t stable, we eventually make our way to the other stable steady state—doomsday.
The contribution of Munz, Hudea, Imad, and Smith has two related weaknesses: one related to epidemiology and the other related to the absence of economic decision making. Both of these weaknesses serve to strengthen their conclusion that only the doomsday outcome is stable. The epidemiological issue is the assumption that corpses never stop reanimating: in their model, there’s a chance any corpse will reanimate at any time. This view is consistent with films such as Night of the Living Dead, in which radiation reanimates the recently deceased; Zombie, in which vintage corpses also reanimate; Dawn of the Dead, in which corpses reanimate because “there’s no more room in hell”; or AMC’s The Walking Dead, in which living humans are already infected with the zombie virus. However, not all zombienarratives support this assumption; in World War Z, for example, zombies only arise from dead and infected humans. But the difficulty runs even deeper: Munz, Hudea, Imad, and Smith also assume that all deanimations are transitory, meaning that even a killed zombie will arise again. This strange assumption leads straight to their forecast of doom. The usual “rules” say a zombie can be deanimated “by a shot to the head or a heavy blow to the skull. . . . Kill the brain, and you kill the ghoul.”3This insight occurs commonly across a variety of narratives,4 and when Munz’s model is corrected so that properly dispatched zombies remain dead, it turns out other endgames are possible, including both total victory over the zombies and stable coexistence of humans and zombies—depending on the parameters.
Furthermore, most zombie narratives focus on humans’ ability to change their behavior in ways economists find sensible. They learn to avoid attacks in which death and reanimation are likely. They hide and fortify—in a farmhouse, a shopping mall, a bunker, a pub,5 or even in a reality show’s house (as in the miniseries Dead Set). Those in Land of the Dead and World War Z use military equipment to limit direct contact and avoid being overwhelmed by hordes of zombies. For others, the zombie threat is mitigated by imprisonment, as in The Walking Dead or World War Z. Furthermore, to ensure zombies will “stay down” when deanimated, special care must be taken (as in the “double tap” from Zombieland). Introducing these possibilities into the comparative dynamics allows yet another endgame: one with cyclical movements in both zombie and human populations.
2. Philip Munz, Ioan Hudea, Joe Imad, and Robert J. Smith, “When Zombies Attack! Mathematical Modelling of an Outbreak of Zombie Infection,” in Infectious Disease Modelling Research Progress (Hauppage, NY: Nova Science Publishers, 2009), 133–50.
3. Night of the Living Dead, directed by George A. Romero (Continental Distributing, 1968).
4. Such as Romero’s other films, as well as Shaun of the Dead and The Walking Dead.
5. Respectively Night of the Living Dead, Dawn of the Dead, Day of the Dead, and Shaun of the Dead.
Economics of the Undead 