Mathematical Modelling of Zombies

Robert Smith?

• Publisher: University of Ottawa Press
• Year: 2014
• eBook ISBN: 9780776621678
• Topic: Mathematics
• Subtopic: Applied Mathematics
• Index: Mathematics

In this terrible new COVID-19 world, the University of Ottawa is doing its part by offering a 50% discount on this very important book. We decided not to rewrite the witty book description, though we realize it is tone-deaf at the present moment, as we wanted to give readers a sense of the tone of this title. But don't be deceived: while a fun read, this book will help you better understand how epidemiologists, governments and health care planners use mathematical models to figure out how quickly epidemics and pandemics spread, in order to plan appropriately. Reading has perhaps never been as important, and this book should be at the top of your reading list.

You're outnumbered, in fear for your life, surrounded by flesheating zombies. What can save you now? Mathematics, of course.

Mathematical Modelling of Zombies engages the imagination to illustrate the power of mathematical modelling. Using zombies as a "hook, " you'll learn how mathematics can predict the unpredictable. In order to be prepared for the apocalypse, you'll need mathematical models, differential equations, statistical estimations, discretetime models, and adaptive strategies for zombie attacks—as well as baseball bats and Dire Straits records (latter two items not included).

In Mathematical Modelling of Zombies, Robert Smith? brings together a highly skilled team of contributors to fend off a zombie uprising. You'll also learn how modelling can advise government policy, how theoretical results can be communicated to a nonmathematical audience and how models can be formulated with only limited information. A forward by Andrew Cartmel—former script editor of Doctor Who, author, zombie fan and all-round famous person in science-fiction circles—even provides a genealogy of the undead. By understanding how to combat zombies, readers will be introduced to a wide variety of modelling techniques that are applicable to other real-world issues (biology, epidemiology, medicine, public health, etc.).

So if the zombies turn up, reach for this book. The future of the human race may depend on it.

THE ZOMBIE SWARM: EPIDEMICS IN THE PRESENCE OF SOCIAL ATTRACTION AND REPULSION

Evelyn Sander and Chad M. Topaz

Abstract

We develop a spatiotemporal epidemic model incorporating attractive-repulsive social interactions similar to those of swarming biological organisms. The swarming elements of the model describe the ability of distinct classes of individuals to sense each other over finite distances and react accordingly. Our model builds on the 2009 non-spatial SZR model of Munz et al. modelling a zombie attack. This case is interesting from the modelling standpoint, as zombie epidemics are particularly virile, albeit restricted to a theatre near you and certain parts of San Francisco, Washington DC, and other major metropolitan areas [http://www.zombiewalk.com]. Spatial effects not only enhance entertainment value (as a cinematic portrayal of a spatially invariant zombie attack would be somewhat lacking in thrill), but are critical to understanding the epidemic. We show that, in the absence of a cure for zombie-ism, the alert human population will eventually be annihilated, but at a slower rate than in the non-spatial model. The extra time to extinction might allow the development of a cure. We also show that, without any assumption of collusion, the system self-organizes into transient travelling pulse solutions consisting of a swarm of zombies in pursuit of a swarm of alert humans. In the presence of a zombie cure, the travelling solutions exist and are stable for all time.

15.1 Introduction

THE notion of a zombie has its roots in the African Kingdom of Kongo, from whence the African diaspora brought it to Haiti. In Haitian voodoo, a sorcerer (or boko) could force someone (either living or dead) to become a zombie, while the boko maintained control of the soul. In contrast, the more modern view of zombie-ism is that it does not result from a sorcerer’s control, but rather is an uncontrolled and unmodulated epidemiological effect, spread by contact like a disease. This ‘viral’ zombie-ism is depicted the classic 1968 movie Night of the Living Dead, in Michael Jackson’s 1993 music video Thriller, in the computer game Plants versus Zombies and at public events such as zombie walks and the game Humans vs. Zombies played on many college campuses.

On the scientific front, in 2009, Munz et al. [1] first quantified the epidemiological view of zombies. This work (of which we later provide a detailed discussion) adapted classical epidemiological models to predict the course and ultimate outcome of zombie attacks. This important, foundational zombie modelling effort focused on the zombification of a population of healthy alert humans, but did not consider any geographic or spatial information pertaining to zombie attacks. As seen in many previous chapters, spatial information is often critical for understanding how to effectively treat an epidemic. For example, consider the citizens of Copenhagen in 1349, during the bubonic plague. A year later, the epidemic arrived in the city and spread explosively. Knowledge that the epidemic front was moving steadily northwards in an east-west band from the south [2] would have been much more useful for Copenhangen’s citizens than only knowing that the epidemic was adversely effecting the total population of Europe.

In this chapter, we develop an epidemiological model of zombies that addresses the need for spatial information. A previous chapter incorporated spatial movement using spatial diffusion, which assumes that individuals move at random and each interaction with an infected individual results in a potential spread of the infection. Other chapters developed agent-based models (ABM), which ascribes a similarly random component to the movement of zombies. However, random motion is not an appropriate assumption in the case of zombies, who by nature seek out healthy humans as prey. Furthermore, ABMs by their very nature are restricted to computer simulations and cannot be generalized as theoretical models can. Thus our modelling methods will necessarily be different.

One aspect of the standard epidemiological models that we do adopt here is the mean field hypothesis, which says that the behaviour of individuals can be understood by considering a continuous function describing average behaviour. From observations of fluids, one finds it perfectly plausible that their flow and motion can be modelled (for most applications) by such averages, rather than by keeping track of the motion of individual molecules. One might wonder if this is a reasonable modelling assumption to make about the macroscopic behaviour of populations of complex biological organisms. In fact, such an assumption does prove to be quite successful in many situations, and the mean field approach in biology is supported by a sub...

Table of contents

• Cover
• Title Page
• Copyright
• Dedication
• Contents
• Foreword: I Ran with a Zombie
• Introduction: What can zombies teach us about mathematics?
• The Viral Spread of a Zombie Media Story
• The Undead: A Plague on Humanity or a Powerful New Tool for Epidemiological Research?
• When Zombies Attack! Alternate Ending
• When Humans Strike Back! Adaptive Strategies for Zombie Attacks
• Increasing Survivability in a Zombie Epidemic
• How Long Can We Survive?
• Demographics of Zombies in the United States
• Is It Safe to Go Out Yet? Statistical Inference in a Zombie Outbreak Model
• The Social Zombie: Modelling Undead Outbreaks on Social Networks
• Zombie Infection Warning System Based on Fuzzy Decision-Making
• Is There a Zombicidal Maniac Near You? You’d Better Hope So!
• Zombies in the City: A NetLogo Model
• An Evolvable Linear Representation for Simulating Government Policy in Zombie Outbreaks
• Baneling Dynamics in Legend of the Seeker
• The Zombie Swarm: Epidemics in the Presence of Social Attraction and Repulsion
• Conclusion
• Contributors
• Afterword