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Science, Maths & Technology

What are your chances during a zombie apocalypse?

Updated Thursday 18th May 2017

According to mathematics we'd all die in a zombie apocalypse but nature and computer science offer us more optimistic outcomes. 

Two women dressed as zombies taking part in the Toronto Zombie Walk 2008. Creative commons image Icon Sam Javanrouh under CC BY-NC 2.0 licence under Creative-Commons license

The seminal paper When Zombies Attack: Mathematical Modelling of an Outbreak of Zombie Infection published in 2009 uses traditional epidemiological techniques (the patterns, causes, and effects of health and disease conditions in defined populations) to model a zombie outbreak. Their result is that we're all doomed in the event on a zombie outbreak, as dead people (including dead zombies) won't stay dead and will rise to eat more brains. Our only hope is to rapidly and overwhelmingly eradicate any zombie outbreak as soon as it occurs, which would probably involve large amounts of military firepower.

There are a couple of problems with this approach, however. One, pointed out by National Wildlife Federation naturalist David Mizejewski is that wildlife will quickly make short work of the zombie hordes, whether it being flocks of crows gorging themselves on conveniently walking stacks of carrion, or all manner of decomposing organisms reducing the zombies to little more than stacks of bones in a few days to a few weeks. This means that if zombies are deprived of new victims (either through quarantining an outbreak or by survivors holing up somewhere safe), the zombie outbreak will eventually burn itself out.

The other problem is the mathematical model assumes that people and zombies are in an undifferentiated mass with infections spread evenly across the population. While this is a reasonable assumption if you're thinking about large-scale epidemics across countries, it misses the effects you see with smaller numbers of people, from a few dozen to a few thousand. This is the territory of most zombie-based stories, so we need a different tool to understand what happens in these situations.

As a computer scientist, my first thought was to create a virtual world filled with people (and a few zombies) and "run" this world for a few weeks to see how the zombie outbreak played out. The world has a few rules that reflect how a zombie outbreak would play out.

  • When a zombie encounters a person, there's a chance that the zombie will infect that person and turn them into another zombie.
  • Zombies are only active for a while before they succumb to wild animals or decay.
  • Zombies can spot nearby people and will chase them for the brains. If there's no-one nearby, the zombie will move at random.
  • People like to be near other people and will move towards them.
  • People in a group can defend each other from zombie attacks, reducing their chances of being infected by a zombie.

"Infectiousness" represents two factors: how likely you are to turn into a zombie if it bites you, and how likely you are to beat off a zombie attacker before it can bite you in the first place.

The simulation proceeds by chance: people start in different places, there's a chance that a person will escape a zombie encounter unharmed, and people might move towards other people or they might move randomly. This means that different runs of the virtual world will produce different outcomes, even if the starting conditions are the same. To work out the expected outcomes for different situations, you have to run the model several times for each starting condition and this allows you to see the range of likely outcomes. In this case, I ran the virtual world 100 times and looked at the aggregate results of how many people survived the outbreak.

Repeated runs of the same world is good, but it doesn't tell you anything about how different types of zombie outbreaks will play out. For instance, we (luckily) don't have good real-world evidence for how likely you'll be infected if you encounter a zombie. For that, we need to set up the virtual world differently and run it a few times to see how the outbreak develops.

For this investigation, I changed four variables in world:

  • how likely a zombie is to infect a person they meet
  • how much people seek out other non-zombie people
  • how much better groups are at defending each other than lone individuals
  • how dense the initial population is

Each variable changed over a range, and I set up a virtual world for each of the 3000 or so combinations of starting conditions. With 100 runs for each combination, I had the results from over 300,000 worlds to look at.

What are the outcomes?

First, a zombie outbreak won't necessarily doom everyone. It depends a lot on the nature of the zombie attack. The plot below shows the percentage of survivors (averaged over all the runs) with different rates of zombie infectiousness and group defence, if the people have a medium tendency to flock together and there was a low initial population density. 

Graphical outputs from a computer simulation depicting what would happen if there was a zombie apocalypse. Copyrighted image Icon Copyright: The Open University

As you would expect, when the zombies are better at turning people into more zombies (high infection), fewer people survive the outbreak. When groups of people are better able to defend each other (high group defence), more survive. However, unless you have both inept zombies and good group defence, very few people survive, shown by the large blue region at the bottom of the plot.

Interestingly, the degree of "flocking" behaviour, where people seek out each other for mutual defence, doesn't have a large effect on survival rates. Even more interestingly, groups of people are bad for survival! What seems to happen is that groups of people can survive for a while until one or two zombies get lucky and infect someone. Then the group has a few zombies in its midst, the effect of mutual defence drops, and those zombies very soon infect the whole group. The chart below shows that more people survive if they don't seek each other out. 

Graphical outputs from a computer simulation depicting what would happen if there was a zombie apocalypse. Copyrighted image Icon Copyright: The Open University

Increasing the population density makes things worse. With a lot of people around, the zombies can easily find and infect humans when the outbreak starts, so the number of zombies rises quickly and soon overwhelm the remaining humans. With a lot of people clustered into large clumps, the zombies have a field day:

Graphical outputs from a computer simulation depicting what would happen if there was a zombie apocalypse. Copyrighted image Icon Copyright: The Open University

How to survive

What does this modelling say about how to survive a zombie attack? The most important criterion for survival is to pick your zombie outbreak properly. If you can, ensure the outbreak is by zombies that either aren't very infectious or who you can beat off easily.

But whatever the zombies are like, your best chance for survival is to avoid the zombies, and other people! Large groups will tend to attract zombies eager for brains; they may survive for a while, but once someone in the group turns, the rest will be infected before they have a chance to flee. Stay away from people and zombies and wait out the outbreak until the scavengers and decomposers have destroyed the zombies for you.


  • Mizejewski, D. (2013) "Zombies vs. animals? The living dead wouldn't stand a chance", Boing Boing, published 12:30pm, Mon 14th Oct 2013. 
  • Munz, P., Hudea, I., Imad, J., & Smith, R. J. (2009) "When zombies attack!: mathematical modelling of an outbreak of zombie infection", Infectious Disease Modelling Research Progress, 4, pp.133–150.
  • Wilensky, U. (1999) NetLogo, Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

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