# Page 3 model: When zombies attack

Every issue we feature another great model on page 3 of our magazine. This time we look at what to do when zombies attack.

Run? Kill? Ask nicely? (Source: flickr.com/joelf)

Every issue we feature another great model on page 3 of our magazine. This issue it’s this:

\begin{align*}
S’ &= \Pi – \beta S Z – \delta S,\\
Z’ &= \beta S Z + \zeta R – \alpha S Z ,\\
R’ &= \delta S + \alpha S Z – \zeta R.
\end{align*}

This is a model of a zombie outbreak as proposed in When Zombies Attack! by Philip Munz, Ioan Hudea, Joe Imad and Robert J. Smith? (the question mark is not a typo; it is part of his name).

The model features three populations: S, the susceptible or living humans; Z, the zombies; and R, the removed or dead humans. Humans can move between these three groups. The rates of movement are modelled by the following parameters:

α, the rate at which humans can kill zombies,
β, the rate at which live humans are infected and become zombies,
δ, the rate of non-zombie related death in the live humans,
ζ, the rate at which the dead rise again as zombies,
Π, the human birth rate (assumed to be constant).

The terms in the model can be nicely shown in the following diagram:

See how the number of susceptibles feeds the number of zombies, etc.

Munz, Hudea, Imad and Smith? showed that unless a zombie outbreak could be ended quickly by a swift killing of zombies then the human population will eventually become entirely zombie.

• ### How to make: a Möbius Surprise

Surprise yourself by making this thing
• ### Read Issue 08 now!

Swing on a magnetic pendulum into our latest issue. Topological tic-tac-toe, maths, cake, categories, plus all your favourite regulars.
• ### Prize crossnumber, Issue 08

Win £100 of Maths Gear goodies by solving our famously fiendish crossnumber
• ### Black Mathematician Month

See what we're doing this October to promote and celebrate diversity in mathematics
• ### Which number are you?

Are you perfect or imaginary? Are you a square?
• ### Dear Dirichlet, Issue 08

Village fetes, Brexit and flowers are among the topics of discussion in this issue's Dear Dirichlet advice column