The abstract says it all:
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 use the mathematical models applied to outbreaks of infectious diseases to show that -- absent a cure or concerted eradication of large proportions of zombies simultaneously -- we are well and truly screwed. This realization should in no way detract from the observation that MATH IS COOL. It will be a damn shame when the zombies eat it out of our brains.
Hat-tip: Marginal Revolution