Zombies are a popular figure in pop culture/entertainment and they are usually portrayed as being brought about through an outbreak or epidemic. Consequently, we model a zombie attack, using biological assumptions based on popular zombie movies. We introduce a basic model for zombie infection, determine equilibria and their stability, and illustrate the outcome with numerical solutions. We then refine the model to introduce a latent period of zombification, whereby humans are infected, but not infectious, before becoming undead. We then modify the model to include the effects of possible quarantine or a cure. Finally, we examine the impact of regular, impulsive reductions in the number of zombies and derive conditions under which eradication can occur. We show that only quick, aggressive attacks can stave off the doomsday scenario: the collapse of society as zombies overtake us all.They model the spread of infection a number of ways, based on zombie features from classic film (and ignoring nouveau-zombies, such as the fast moving, more aware monsters from 28 Days Later), and playing with variables such as latency of infection and the effects of quarantine or cure development.
Of course a zombie outbreak is far-fetched, and nit-pickers now have another tool in their arsenal when tearing apart the believability of movies ("There's no way that quarantine would be effective!"), but it does demonstrate a neat use of math in modeling disease spread - even fictitious ones. As the authors note in their discussion:
This is, perhaps unsurprisingly, the first mathematical analysis of an outbreak of zombie infection. While the scenarios considered are obviously not realistic, it is nevertheless instructive to develop mathematical models for an unusual outbreak. This demonstrates the flexibility of mathematical modelling and shows how modelling can respond to a wide variety of challenges in ‘biology’.Of course the real bottom line is when the zombie uprising happens, we're all screwed.
Read the full paper here [pdf].