Zombies are usually portrayed as being brought about through an outbreak or epidemic. Consequently, we model a zombie attack using biological assumptions based on zombie movies. We introduce a basic model for zombie infection, determine equilibriums and their stability, and illustrate the outcome with numerical solutions. We then refine the model to introduce a latent period of zombification, wherein humans are infected, but not infectious, before they become 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. The key difference between the models presented here and other models of infectious disease is that the dead can come back to life. Clearly, this is an unlikely scenario if taken literally, but possible real-life applications may include allegiances to political parties or diseases with a dormant infection. A zombie outbreak is likely to lead to the collapse of a civilization unless it is dealt with quickly. Although aggressive quarantine may contain the epidemic or a cure may lead to coexistence of humans and zombies, the most effective way to contain the rise of the undead is to hit hard and hit often. As seen in the movies, it is imperative that zombies be dealt with quickly, or else we are all in a great deal of trouble.
Philip Munz, Ioan Hudea, Joe Imad and Robert J. Smith
When Zombies Attack!: Mathematical Modeling of an Outbreak of Zombie Infection
Infectious Disease Modelling Research Progress (2011)
Illustration by Ralph Steadman: Reagan’s Latest Close-Up (1980)