Guess How Many People Will Survive A Zombie Apocalypse

Suppose a zombie apocalypse really happened. Do you think you’d survive? A team of students in the Department of Physics and Astronomy at the University of Leicester took this question seriously. You’re not going to like the answer.

The students published a pair of papers in Leicester’s undergraduate Journal of Physics Special Topics based on an epidemiological model called SIR (Susceptible, Infected and Recovered or Removed) that is often used to model the spread of infectious diseases throughout a population. They adapted SIR to model a zombie apocalypse.

In their first version of the model they assumed that zombies could infect, but not kill, people who were uninfected. They also assumed that there was a 90% probability that an uninfected person who met a zombie would be infected, and that zombies died after 20 days if they did not feed. They set the population of the world at 7.5 billion which is very close to current real-world estimates. The model was started with one zombie at day zero.

Nothing much happens for about 3 weeks as the number of zombies slowly multiplies. And then the fecal matter hits the whirling cooling device. On or about day 20 the zombie population begins a meteoric exponential increase that is mirrored in a decline in the uninfected population. Most of the world’s population is wiped out over the next three weeks. On day 100 there are 181 uninfected survivors on the planet. You’re probably not one of them.

This grim version of the model assumes that there are no geographic boundaries like oceans or mountain ranges that might slow the zombie apocalypse down. The students modified the model to see what would happen if geography separated people into three zones. They assumed that zombies could not cross a boundary until there were at least 500,000 zombies in an infected zone. The zones were arranged so that Zone A was connected to Zone B and B was connected to C. The zombies couldn’t spread directly from Zone A to C.

Once again, the model started with one zombie in Zone A. The uninfected did a little better in this scenario but not by much. Again, nothing much happens for about three weeks and then the zombies increase exponentially. About a week later the zombie population decreases slightly as they try to make their way into Zone B. The respite is brief and the zombies quickly resume their exponential march (stagger?) to dominance. The pattern is repeated when the zombies move from Zone B to C. After 100 days, there are 273 uninfected people in the world.

But wait. There are a number of things missing from these models. People aren’t going to sit around waiting to be infected; they’re going to fight back. They’re also going to get better at avoiding zombies as time goes on – although they’re going to have to learn to do this quickly. Finally, if they can survive long enough, people can replace some of their losses by having babies.

The students published a second paper in the Journal of Physics Special Topics that took all of these factors into account. They added a parameter to the model that gives each person a 10% chance of killing a zombie when they meet. They modeled people’s increasing sophistication at avoiding zombies by replacing the 90% probability of infection when an encounter takes place with a parameter that decreases the chance of infection as the number of uninfected declines.

Births were modeled by assuming that the uninfected are equally divided between males and females, that half the uninfected are in a position to make a baby at any given time, and that half of the females are capable of having a baby. They also assumed that females could have one baby every three years.

Not all of the new factors benefit the uninfected; the zombies were also given some love. Their lifespan without feeding was increased from 20 days to one year.

The uninfected do much better in this scenario. The exponential increase in the number of zombies is delayed by about 10 days but then it rises exponentially as before. However, at 100 days there are still roughly 200 million uninfected left alive. This is a drastic decline from the 7.5 billion that were alive when the scenario began but it is orders of magnitude better than the few hundred people that were left in the earlier scenarios.

The number of uninfected continues to decline but they manage to survive until day 1,000. At this time there are roughly 67 million uninfected left. This may sound like a lot but it’s approximately 88 survivors out of every 10,000 people who were alive on day 0.

On day 1,000 things look bad for the uninfected but they look worse for the zombies. Most of the zombies have died because there aren't very many uninfected left to feed on and the ones who are still alive have gotten very good at avoiding zombies. The zombies disappear completely over the next six years. About three years after that, the human population begins to slowly but noticeably grow.

So there you have it. If you quickly learn to avoid the zombies, fight back when you can’t avoid them and make babies when you’re not avoiding or fighting, you have a .0088 probability of surviving for 1,000 days. Think you can make it?

One thing that the models didn’t consider that you should be aware of is that zombies are always more dangerous at night. So, if you're planning on surviving for 1,000 days . . .  good night and good luck.

Note. The population numbers and survival probabilities given in this article for the final scenario were not directly reported in the student's paper. They were calculated based on measurements from a graph presented in the paper that showed how zombie and uninfected populations change over time.