Halloween Math: The Zombie Apocalypse

Here’s a classic bit of Halloween math from the Playful Math Archive, featuring Thomas Woolley and James Grime:

Getting Down to Details

The zombie attack spreads like an infection — similar to an outbreak of flu or measles — as the zombies shamble about, with their movement modeled as a random walk.

“We can calculate that anyone within 100 metres would have at most 28 minutes before they encounter their first zombie. Now, if we were able to slow down the zombies by half then the time to an encounter is doubled. But, as we double the distance between us and them the time is quadrupled!

“The number of zombies depend on the rate at which they can infect us compared to the rate at which we can kill them. If we can kill them faster than they can infect us then our survival just comes down to a race of who becomes extinct first. We need a large population more deadly than they are. Either way, we are going to suffer heavy losses.

“Another way we can slow down the infection is by removing the human population. If they can’t infect us then their numbers can’t grow. This could mean killing our fellow humans – but we do not recommend it. We don’t need to help them speed up our extinction!

“So, to survive you need to run. In the long term we need a fortified society, but if the barricades fall we need to reduce the speed of infection, slow them down, and be more deadly than they are.”

—James Grime and Thomas Woolley
28 Minutes Later – The Maths of Zombies

For Further Study

Will you survive the apocalypse? Read Mathematical Modelling of Zombies to find out.

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