That's why I really enjoyed reading this 2009 paper recently: "When zombies attack! Mathematical modelling of an outbreak of zombie infection" by Munz et al., published in the book Infectious Disease Modelling Research Progress. The authors used an extended SIR epidemiological model to investigate the dynamics of a zombie apocalypse. Their conclusion:
In summary, a zombie outbreak is likely to lead to the collapse of civilisation, unless it is dealt with quickly. While 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 are dealt with quickly, or else we are all in a great deal of trouble.I liked the paper, but I felt there was one flaw. In their model, all dead humans or zombies were able to re-animate. This left me wondering - what would happen in the model if you could permanently kill zombies, through shots to the head or incineration. Maybe the authors will address that in future papers.
Closer to home, Daniel Farhat from the University of Otago has a recent paper on "The economics of vampires: An agent-based perspective". In his paper, Farhat uses agent-based computational models with heterogeneous agents to investigate the dynamics of human-vampire population interaction. There are a number of interesting results from the simulations, from which I quote selectively:
...where vampires are highly visible, the human population suffers terribly for a short period (building up defences which results in starvation) until the vampire population is driven to extinction. Once they have been eradicated, the human community and their corresponding economy proceeds to grow exponentially. Therefore, one reason why we may not come across vampires in modern times is because they have already died out...
...where vampires are observable but somewhat hidden, they may flourish provided they are easy to destroy in a confrontation. Cycles of fear then emerge. Therefore, if we do not see vampires today it may be because spotting them is rare..
...where vampires are unobservable, their existence persists. Whether they flourish or stagnate depends on their hunger for blood and the speed of human reproduction. If vampires live on the brink of starvation, both vampire and human populations persistently grow despite mild cycles of fear. If humans reproduce easily, both communities languish with extreme cycles of fear keeping both populations in check. The former is more likely given the persistent growth of our planet’s population. If this is the case, we would never encounter vampires (and may even doubt their existence) in reality.Agent-based models are an excellent tool for modelling population dynamics at very disaggregated levels. The vampire model described above is theoretical, but there are more practical applications of these models as well. For instance, I have a Masters student who is developing an agent-based model of local population dynamics for the Hamilton sub-region, to better project small-area population movements over the next 10-15 years. This highlights that these mathematical models are not just useful for developing cool applications in terms of modelling the undead, but also have real-world applicability.