Math and the apocalypse: Exponential growth in a zombie outbreak

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Amy Odum


Every year, tens of thousands of students gather in universities throughout the country to play Humans vs. Zombies (HvZ). For several weeks, campuses are over run with students in bandanas carrying Nerf-guns. Utah State University is one of the largest games played countrywide. Each game begins with one to three zombies who are tasked with infecting as many humans as possible. If a zombie goes three days without a successful infection, it starves to death and is eliminated from the game. Humans can defend themselves using Nerf-guns, which temporarily stun the zombie. The game is over when all the humans are infected or the game's clock expires. Data was obtained from over 600 games involving over 20,000 participants from the spring of 2012. Participants that signed up but did not play (evident in the data file received from HvZ) were eliminated from the analysis. The human and zombie populations were analyzed over the span of 20 days. The decrease in human population (and conversely the increase in zombie population) followed a one-phase exponential decay model, N(t) = ((N0 - Plateau)e^(-k*X)) + Plateau. The R2 value (indicator of model goodness of fit) for humans was 0.9959 and for zombies 0.9936. This demonstrates that the exponential decay model fit 99% of the data for both zombies and humans. The results reveal dire outcomes for the human population. Half of the human population was infected in a little more than 1.5 days. Analysis of the zombie population did not reveal high rates of starvation, as indicated by the plateau in the population growth. At the 20-day point, the human population decreased to 35 survivors, while the zombie population increased to 22,772, including starvation of a small population of the zombies. Implications are discussed.

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