Mathematical Modelling of Zombies

Robert Smith

Description

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.

Sujets

• Sciences formelles
• Mathématiques appliquées
• Mathématiques appliquées
• Applied
• Sciences et techniques
• Mathematics

Informations

• Publié par: University of Ottawa Press
• Date de parution: 14 octobre 2014
• Nombre de lectures: 2
• EAN13: 9780776621685
• Langue: English
• Poids de l'ouvrage: 4 Mo

Extrait

Mathematical Modelling of Zombies

Robert Smith? University of Ottawa Press

Mathematical Modelling of Zombies

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Robert Smith?

Mathematical Modelling of Zombies

University of Ottawa Press|2014

The University of Ottawa Press acknowledges with gratitude the support extended to its publishing list by Heritage Canada through the Canada Book Fund, by the Canada Council for the Arts, by the Federation for the Humanities and Social Sciences through the Awards to Scholarly Publications Program and by the University of Ottawa.

Copy editing: Bryn Harris Proofreading: Trish O’Reilly-Brennan Coverdesign:LlamaCommunicationsand É discriptenr.

Library and Archives Canada Cataloguing in Publication

Mathematical modelling of zombies / edited by Robert Smith?

Includes bibliographical references. Issued in print and electronic formats. ISBN 978-0-7766-2210-1 (pbk.).--ISBN 978-0-7766-2168-5 (pdf ).-- ISBN 978-0-7766-2167-8 (epub)

1. Zombies--Mathematical models. I. Smith?, Robert J. (Robert Joseph), 1972–, editor

GR581.M38 2014

©University of Ottawa Press, 2014 Printed in Canada

398.2101'51

C2014-906565-5 C2014-906566-3

To Richard Tongue and Bon Clarke, my high school and undergraduate mathematics teachers. You showed me the beauty of mathematics but, more importantly, also passed on your passion for teaching. This is your opus.

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Contents

Foreword: I Ran with a Zombie Andrew Cartmel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii

Introduction: What can zombies teach us about mathematics? Robert Smith? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii

The Viral Spread of a Zombie Media Story Robert Smith? . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . 1.1.1 A Media Invasion of Zombies . . . . . . . . 1.1.2 The Effects of Media . . . . . . . . . . . . . 1.2 The Model . . . . . . . . . . . . . . . . . . . . . . 1.2.1 The Durability of a Media Story . . . . . . 1.2.2 The Newsworthiness of a Media Story . . . 1.2.3 The Natural Lifespan of a Media Story . . . 1.3 Analysis . . . . . . . . . . . . . . . . . . . . . . . . 1.3.1 Final Size Populations . . . . . . . . . . . . 1.3.2 Stability . . . . . . . . . . . . . . . . . . . . 1.3.3 A Competing Story . . . . . . . . . . . . . 1.4 The Power of a Right Hook . . . . . . . . . . . . . 1.5 Sample Scenarios . . . . . . . . . . . . . . . . . . . 1.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . A Acknowledgements . . . . . . . . . . . . . . B Glossary . . . . . . . . . . . . . . . . . . . .

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The Undead: A Plague on Humanity or a Powerful New Tool for Epidemiological Research? Jane M. Heffernan and Derek J. Wilson . . . . . . . . . . . . . . . . . . . . . 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Creeping up on Us: The Origins of Zombies and the Bubonic Plague 2.3 The Rising Tide: Modelling Epidemics . . . . . . . . . . . . . . . . . 2.4 Living with Vampires: Modelling Endemics . . . . . . . . . . . . . . 2.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

vii

1 1 1 3 5 6 8 9 9 9 10 11 12 12 16 20 20

27 28 28 30 36 40 41

viii

CONTENTS

When Zombies Attack! Alternate Ending Phil Munz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Title Sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 The Story So Far . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 A Behind-the-Scenes Look at the Making of the Alternate Ending . 3.4 The End? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 DVD Extras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A Oscar Speech . . . . . . . . . . . . . . . . . . . . . . . . . . . B IMDB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

45 45 46 48 51 53 54 54

When Humans Strike Back! Adaptive Strategies for Zombie Attacks Bard Ermentrout and Kyle Ermentrout . . . . . . . . . . . . . . . . . . . . . 57 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 4.2 Multiple Zombies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 4.3 Adaptive Strategies for Humans . . . . . . . . . . . . . . . . . . . . . 62 4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 A Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

Increasing Survivability in a Zombie Epidemic Ben Tippett . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1 Interaction Rates Assuming a Uniform Population Density . 5.2.2 Zombie Population Dynamics . . . . . . . . . . . . . . . . . . 5.2.3 Worker Population Dynamics . . . . . . . . . . . . . . . . . . 5.2.4 Militia Population Dynamics . . . . . . . . . . . . . . . . . . 5.2.5 Mole Population Dynamics . . . . . . . . . . . . . . . . . . . 5.2.6 Supply Stockpile Dynamics . . . . . . . . . . . . . . . . . . . 5.2.7 Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Modelling Specific Scenarios . . . . . . . . . . . . . . . . . . . . . . 5.3.1 Humanity Is Exterminated Outright . . . . . . . . . . . . . . 5.3.2 The Zombie Population Is Culled . . . . . . . . . . . . . . . . 5.3.3 Humans Nearly Starve . . . . . . . . . . . . . . . . . . . . . . 5.4 How Public Policy Affects Survivability During a Zombie Epidemic 5.4.1 Managing a Zombie Epidemic in an Urban Scenario . . . . . 5.4.2 The Countryside . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 The Romero Scenario . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5.1 Altered Transmission Equations . . . . . . . . . . . . . . . . 5.5.2 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . 5.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . B Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

71 71 72 72 73 73 74 75 75 76 76 78 78 79 81 81 83 85 85 86 90 91 91

CONTENTS

ix

How Long Can We Survive? Thomas E. Woolley, Ruth E. Baker, Eamonn A. Gaffney and Philip K. Maini 93 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 6.2 Random Walks and Diffusion . . . . . . . . . . . . . . . . . . . . . . 94 6.3 A Mathematical Description of Diffusion . . . . . . . . . . . . . . . . 95 6.4 Solution to the Diffusion Equation . . . . . . . . . . . . . . . . . . . 97 6.5 Time of First Interaction . . . . . . . . . . . . . . . . . . . . . . . . . 99 6.5.1 Diffusive Time Scale . . . . . . . . . . . . . . . . . . . . . . . 99 6.6 Slowing the Infection . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 6.6.1 Interaction Kinetics . . . . . . . . . . . . . . . . . . . . . . . 101 6.6.2 Is It Possible to Survive? . . . . . . . . . . . . . . . . . . . . 102 6.6.3 Infection Wave . . . . . . . . . . . . . . . . . . . . . . . . . . 104 6.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 A Diffusion Solution Details . . . . . . . . . . . . . . . . . . . . 107 B Approximating First Interaction Time . . . . . . . . . . . . . 110 C Changing Coordinates . . . . . . . . . . . . . . . . . . . . . . 111 D Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . 113 E Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

Demographics of Zombies in the United States Daniel Zelterman . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Data Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3 Demographic Variables Examined . . . . . . . . . . . . . . . . . . . . 7.4 Univariate Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.5 Multivariate Analyses . . . . . . . . . . . . . . . . . . . . . . . . . . 7.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

117 117 118 119 122 125 126 127

Is It Safe to Go Out Yet? Statistical Inference in a Zombie Outbreak Model Ben Calderhead, Mark Girolami and Desmond J. Higham . . . . . . . . . . . 129 8.1 Mathematical Modelling with Ordinary Differential Equations . . . . 129 8.2 Simple Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 8.3 More Realistic Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 8.4 Model Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 8.5 Is It Safe to Go Out Yet? . . . . . . . . . . . . . . . . . . . . . . . . 144 8.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 A Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147