# Defeating a Zombie Attack with Mathematics

/**Have you ever wondered what would happen in a real-life zombie outbreak? Researchers believe maths could hold the answer, Patrick Doolan explains.**

Trying to predict the outcome of a zombie plague is nothing new. There are many movies and books that explore what could happen if the dead rose and developed a hunger for human flesh. Mathematicians from Carleton University and the University of Ottawa, in Canada, ** **found a different way to imagine life with zombies. By applying real-world mathematics techniques, they were able to determine how humans would fare in a war against the undead and figure out strategies to increase our chances of survival.

**Why maths?**

Maths might seem like an odd choice for fending off zombies, but it is often used to understand similar real-world problems in epidemiology.

Epidemiology is the study of how, why and where diseases occur. Epidemiologists use this information to control the spread of diseases, particularly infectious ones. Infectious diseases are caused by tiny organisms, such as bacteria and viruses. They are spread by contact with the source of the organism, which is often animals, humans or contaminated food. Common examples of infectious diseases are measles and chickenpox. The sudden and uncontrollable spread of infectious disease is called an epidemic. A famous example is the Spanish flu epidemic of the early 20th century, which is estimated to have killed up to 50 million people.

Maths is used in epidemiology to create models of epidemics. A mathematical model is a simplified version of a real system or event, and helps us understand them. Mathematicians use models of epidemics to predict how a disease will spread, including how many people will become infected and how long this will take.

The researchers at the Canadian universities realised that zombie epidemics are similar to real epidemics. By biting humans, zombies spread a ‘zombie virus’ just as a person with the common cold infects others by sneezing. This means maths can also be used to study zombie epidemics.

**How do mathematical models work?**

The SIR model is one example of how maths is used in epidemiology. The acronym SIR represents the three groups in a population threatened by disease:

- S stands for ‘susceptible’ – people who don’t have the disease, but could get it
- I stands for ‘infected’ – the people who have the disease and can infect others
- R stands for ‘removed’ – the people that recovered from the disease or died

The model works by estimating the probability that a human will move between the S, I and R categories. For example, a human might have a 50% chance of becoming infected, represented by moving from S to I. Once mathematicians know how the number of people in each group changes over time, they can use maths to estimate the size of each group at different points during the epidemic.

The researchers used a similar approach to model a zombie epidemic. They replaced the usual infected category of the population with a zombie category. The way humans move between categories was also changed. With real diseases, susceptible humans can only become infected. However, if a human is attacked by a zombie they could be bitten (moved to the zombie group) or killed (placed in the removed category). The scientists also assumed that people in the removed group could spontaneously rise from the dead and enter the zombie group.

By estimating how people would move between the different groups (susceptible, zombie, removed) the scientists were able to predict the sizes of the zombie and human populations during a zombie epidemic.

**What do mathematical models tell us?**

Being able to predict the spread of a disease is useful, but stopping an epidemic is more important. Changing parts of a mathematical model allow mathematicians to forecast how different factors – for example, a cure for the disease – would influence the epidemic. After testing many preventative measures, the best one can be selected.

A common real-world method of fighting epidemics is vaccination. Administering a vaccine makes a person immune to the disease. This corresponds to moving that person from the susceptible group to the removed group. The SIR model predicts that once enough of the population is vaccinated, no epidemic occurs. Interestingly, it also predicts that we do not have to vaccinate everyone to achieve this outcome. This is called the herd immunity effect.

Using their models for a zombie epidemic, the mathematicians found that unless humans take drastic measures, zombies will overrun them. They also found that a cure for ‘zombieism’ would probably prove ineffective, but a small population of humans could coexist with zombies in such a case. They concluded that the best chance humans have of surviving a zombie attack is launching several coordinated attacks against the undeath.

Unfortunately, maths indicates the outlook is bleak if zombies do rise from the dead. It also tells us what we should do to survive, which is vital information. So next time you study maths, pay attention – it could save you from becoming a zombie.