When zombies attack: Students predict the outcome of apocalypse

Penn State students use mathematical equations in unique scenario

Mechanical engineering students conducted high-level mathematical calculations to determine who would prevail in a hypothetical zombie attack—the humans or zombies. Based on the results of their "zombie math," the equation (bN)(S/N)Z=bSZ could spell doom for the human population during a zombie apocalypse. Credit: Tom FlachAll Rights Reserved.

UNIVERSITY PARK, Pa. — Last semester, mechanical engineering students in Alok Sinha’s M E 450 Modeling of Dynamic Systems course conducted high-level mathematical calculations to determine who would prevail in a hypothetical zombie attack — the humans or zombies. Based on the results of their “zombie math,” the equation (bN)(S/N)Z=bSZ proves the zombies will likely always win. That's because the calculation shows that in a zombie apocalypse, the rate at which humans would be infected by the walking dead is insurmountable.

“Brainz, brainzz!” cried the zombies.Matt Sherman heard them, while briefly catching his breath behind a large elm tree on campus. Sherman, who had two plastic Nerf blasters strapped to his chest and an arsenal of rolled-up socks and marshmallows stuffed in a drawstring bag dangling from his waist, had been running from the zombie horde all day.  The groaning sounds intensified as the zombies swarmed around him. “Brainz, Graagh, Brainzzz, Graaaagh!!”

"Oh no," he thought to himself, "Am I going to make it out of this alive?"Probably not, according to some Penn State mechanical engineering students.Sherman, a junior in the College of Information Sciences and Technology, was taking part in a Humans vs. Zombies (HvZ) event hosted by the Penn State Urban Gaming Club (UGC), a student-run organization that coordinates such campus-wide Urban Gaming events as Capture the Flag, Assassins and HvZ, where participants gather to play a huge game of tag. All HvZ events take place in pre-defined areas within campus, where the play space is on a large, human scale using Nerf blasters, rolled-up socks and marshmallows as common “weapons” against the zombies.And that means Sherman’s sock bullets, no matter how he uses them, will be no match for those brain-hungry zombies.Sinha's 400-level course focuses on modeling and analysis of dynamic interactions in engineering systems and helps mechanical engineering students gain a better understanding of complex mathematical concepts used in predicting system outcomes. Tanmay Mathur, a graduate student majoring in mechanical engineering and a teaching assistant for the course, presented the zombie assignment as a fun way to get students interested in learning the mathematical tools they’ll need to use in real life.“If they are building an engine control unit, which controls a series of actuators on an internal combustion engine, they need to know how to go about modeling different state variables and algorithms that would help them design the controller,” said Mathur.The equation the students used to determine the outcome of a zombie attack was originally created by a mathematics professor at the University of Ottawa to model the rate at which humans would become zombies if they were infected by the living dead. Mathur refined the model using different scenarios. As part of the assignment, the students used biological assumptions based on popular zombie movies and SIMULINK — a graphical programming language tool for designing, simulating and analyzing dynamic systems — to model a zombie infection and illustrate the outcomes with numerical solutions. Most of the time the zombies were the victors.“The assignment basically used the state-space framework for modelling an infectious disease,” said Mathur. “But what made it effective for the students, I think, was the coolness quotient associated with using zombies.”The Urban Gamers would be wise to study their results. With this model, the students could predict an apocalypse by controlling and deciding the factors that affect the populations of zombies and healthy humans. Fortunately, for the humans, the outcome wasn’t always doom and gloom. Mathur says that in one scenario, the students were able to wipe out the zombies by introducing 10 zombie slayers into a population of 1,000 zombies (whereas the model with only five zombie slayers had the doomsday scenario). However, the models ultimately show that only quick and aggressive attacks by the zombie slayers could stave off the doomsday scenario in each application of the equation.Mathur says that some of the students were familiar with SIMULINK before coming into the course. But for most, the program and the zombie assignment were something new. “The students were flabbergasted at first because they weren’t expecting to be modelling a zombie apocalypse in a 400-level engineering course,” Mathur laughed. “But as the assignment progressed and they were able to make sense of it, they were quite receptive and excited to see the results of the mathematical model.”Once the students had a mental picture of the diagrammatic relationship between variables and how things relate to each other in a dynamic system, the SIMULINK program enabled them to draw block diagrams and define parameters to plot the variations of different human and zombie populations with time. Mathur says that unless humans take the time to protect the population in an enclosure or build quarantine zones and bring in more zombie slayers, the models always show that the doomsday scenario would dominate as the most plausible outcome.But the computerized results don’t resonate much with Sherman and other students taking part in UGC HvZ events on campus. “I think humans would definitely win in a real-world scenario because of our military prowess and advanced weaponry. The Department of Defense actually has a full-fledged fictional zombie apocalypse response plan, which it uses to teach military mass disaster planning to trainees, so I think the threat would get stomped out hard before it ever really got as big as in the movies,” says Sherman, who’s been participating in UGC events since his freshman year.As UGC secretary, Megan Lamb has seen her share of zombie missions. “Without limitations and having more resources, humans can definitely get crafty and I think that even if a ‘patient zero’ had some sense left, the zombies still would not be able to be as innovative. Humans can team up and strategize while zombies are just... zombies. Not to say that's a label to take lightly. I'm just saying you don't see zombies winning any of those extreme marathons.”Fellow UGC administrator and senior criminology major Nicole Solano agrees that humans could win in a hypothetical zombie apocalypse. But only if there were certain variables brought into the equation. “If the attack happened on a Penn State campus, I’m sure our club would be able to rally the students together to handle the situation,” Solano grins.Rallying to survive was not the case for Sherman as the zombie horde closed in on him. But, according to the mission details, if he could hold them off long enough for one of the human players stranded nearby to be escorted back to the starting point at Chambers Building untagged, the humans would win. With that in mind, he darted out from behind the elm tree and heroically sacrificed himself by rushing into the horde while firing darts from both Nerf blasters. He and most of the nearby human group were zombified in the mad scramble that lasted mere minutes. But two human survivors managed to get away. As they reached the steps of Chambers Building they were swarmed by zombies and tagged at the threshold of their victory.Just as the mathematical models predicted, Sherman didn’t survive the game but he had a fair hand in ending it. He plans to try his luck again in the next Penn State UGC HvZ event taking place on Nov. 1.For more IT stories at Penn State, visit

Last Updated October 24, 2014