Surviving a Zombie Apocalypse: Just Do the Math


Math tackles the hordes

Analyzing zombies adds a couple of new wrinkles to traditional disease modeling, Smith said: Dead people can be resurrected as zombies, and humans will attack the infected. "Usually, the dead aren't a dynamic variable," Smith said. "And people don't try to kill the people who have an infection."

Those elements -- infections and attacks on zombies -- made the model more complicated, because they introduce two nonlinear factors, or factors that don't change at a constant rate, said Smith, who has modeled outbreaks of HIV, malaria and West Nile virus. Most disease models include only one nonlinear element: disease transmission. Having two nonlinear factors makes zombie math extremely sensitive to small changes to parameters, Smith said.

The most important parameter, however, was the infectivity of the zombie disease. In zombie movies, the affliction spreads fast, Mackay said. In "World War Z," for instance, Pitt's character counts out the seconds from bite to zombification, whereas most infections take days, months or even years in the case of HIV to manifest.

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That high infectivity makes the zombie epidemic unstoppable in most cases, according to Smith's model. "Because it only takes one zombie to overtake a city," neither quarantine nor a slower disease progression could stop the Zombie Apocalypse -- only delay it, Smith said. Only frequent, increasingly effective attacks against humanity's transformed brethren would win an actual zombie war, he said. (End of the World? Top 10 Doomsday Fears)

To model that kind of human-zombie tangling, Smith used a relatively new mathematical technique called "impulsive differential equations," which show how abrupt shocks affect systems. Commonly used to model satellite orbits, the technique didn't appear until the 1990s, whereas most mathematical tools date back centuries, Smith said.

Zombies IRL

Applying such techniques to the flesh-devouring masses provides more than geeky entertainment, Smith said. It also serves an educational purpose, with a number of colleges and even high schools using the paper to introduce mathematical modeling to students, he said. "Teachers say it's the first time they've gotten their kids interested in math."

Tara Smith, an infectious disease professor at the University of Iowa, uses the paper to show how math models can predict the effects of quarantines, vaccines and other public health measures.

The zombie model's methods have already proved useful in at least one real-life analysis. While working on a model of HPV (human papillomavirus), Robert Smith's team noted that transmission via both gay and straight sex introduced two nonlinear variables to the equation. Fortunately, the zombie model had already blazed this path, demonstrating how to handle multiple nonlinear factors.

That real-world relevance in part explains the pop-culture resurgence of zombies over the last few years, Mogk said. As epidemics and emerging diseases like SARS and swine flu have grabbed the headlines, zombie fictions like "Walking Dead" and "28 Days Later" have brought the undead a new cultural cachet, he said.

"With increasing urbanization, you're getting all these new diseases," he said. "It's almost a disease of the week or disease of the month now." And those flesh-hungry viruses-with-teeth are poised to reflect the public's pandemic-related anxieties.

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