Mathematical Modelling of Zombies
181 pages
English

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181 pages
English

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Description

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.


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Informations

Publié par
Date de parution 14 octobre 2014
Nombre de lectures 5
EAN13 9780776621678
Langue English
Poids de l'ouvrage 3 Mo

Informations légales : prix de location à la page 0,1200€. Cette information est donnée uniquement à titre indicatif conformément à la législation en vigueur.

Extrait

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
Cover design: Llama Communications and discript enr.
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
398.2101 51
C2014-906565-5 C2014-906566-3
University of Ottawa Press, 2014
Printed in Canada
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.
Contents
Foreword: I Ran with a Zombie
Andrew Cartmel
Introduction: What can zombies teach us about mathematics?
Robert Smith?
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
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
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
When Humans Strike Back! Adaptive Strategies for Zombie Attacks
Bard Ermentrout and Kyle Ermentrout
4.1 Introduction
4.2 Multiple Zombies
4.3 Adaptive Strategies for Humans
4.4 Discussion
A Glossary
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
How Long Can We Survive?
Thomas E. Woolley, Ruth E. Baker, Eamonn A. Gaffney and Philip K. Maini
6.1 Introduction
6.2 Random Walks and Diffusion
6.3 A Mathematical Description of Diffusion
6.4 Solution to the Diffusion Equation
6.5 Time of First Interaction
6.5.1 Diffusive Time Scale
6.6 Slowing the Infection
6.6.1 Interaction Kinetics
6.6.2 Is It Possible to Survive?
6.6.3 Infection Wave
6.7 Conclusion
A Diffusion Solution Details
B Approximating First Interaction Time
C Changing Coordinates
D Acknowledgements
E Glossary
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
Is It Safe to Go Out Yet? Statistical Inference in a Zombie Outbreak Model
Ben Calderhead, Mark Girolami and Desmond J. Higham
8.1 Mathematical Modelling with Ordinary Differential Equations
8.2 Simple Model
8.3 More Realistic Model
8.4 Model Selection
8.5 Is It Safe to Go Out Yet?
8.6 Discussion
A Glossary
The Social Zombie: Modelling Undead Outbreaks on Social Networks
Laurent H bert-Dufresne, Vincent Marceau, Pierre-Andr No l, Antoine Allard and Louis J. Dub
9.1 Introduction
9.2 Modelling a Zombie Invasion: A Practical Guide
9.2.1 Contact Networks 101
9.2.2 Building a Contact Network
9.2.3 The Rules of the Game
9.2.4 Monte Carlo Simulations
9.3 Mathematical Zombies: A Theory of the Undead
9.3.1 The Variables of the System
9.3.2 Moment-Closure Approximation
9.3.3 Writing the Dynamical System
9.4 Results: Does Humanity Have the Slightest Chance?
9.4.1 Choosing the Victims
9.4.2 Body Count
9.5 The Social Zombie: Adapting for Realism
9.5.1 The New Rules of the Game
9.5.2 Hope Is the Last Thing to Die, Isn t It?
9.6 A Conclusion on Networks
9.7 and Zombies
A Numerical Integration
B Glossary
Zombie Infection Warning System Based on Fuzzy Decision-Making
Micael S. Couceiro, Carlos M. Figueiredo, J. Miguel A. Luz and Michael J. Delorme
10.1 Introduction
10.2 Zombie Mathematical Models
10.2.1 The Base Model
10.2.2 Incorporating Latent Infection
10.2.3 Zombie Outbreak with Quarantine of Zombies and Infected Individuals
10.2.4 Medical Treatment for Zombies
10.3 Introduction to Fuzzy Systems
10.3.1 Zombie Infection Warning System
10.3.2 Decision-Making System Using Fuzzy Logic
10.4 Experimental Results
10.5 Conclusions
A Acknowledgements
B Glossary
Is There a Zombicidal Maniac Near You? You d Better Hope So!
Nick Beeton, Alex Hoare and Brody Walker
11.1 Introduction
11.2 Data Collection
11.3 Agent-Based Model
11.4 Stochastic Model
11.5 Transmission Dynamics
11.6 Zombie Management
11.7 Observations on Behaviour
11.8 Discussion
A Acknowledgements
B Glossary
Zombies in the City: A NetLogo Model
Jennifer Badham and Judy-anne Osborn
12.1 Introduction
12.2 Methodology
12.2.1 Why Use ABMs and NetLogo?
12.2.2 Our NetLogo Model
12.2.3 Experimental Design
12.3 Generic Behaviours Exhibited by the Model
12.3.1 Zombies Win
12.3.2 Humans Win
12.3.3 Stalemate
12.4 Effects of Speed and Skill
12.4.1 Humans Slow and Unskilled
12.4.2 Humans Fast and Unskilled
12.4.3 Humans Skilled and Slow
12.4.4 Humans Faster Than Zombies and Skilled
12.5 Implications for Education and Research Training
12.6 Conclusion
A Acknowledgements
B Glossary
An Evolvable Linear Representation for Simulating Government Policy in Zombie Outbreaks
Daniel Ashlock, Joseph Alexander Brown and Clinton Innes
13.1 Introduction
13.2 The Discrete-Time Model
13.3 Representation of Government Policies
13.3.1 Overview of Policies
13.3.2 Public Response to Government Policies
13.4 The Evolutionary Algorithm
13.5 Experiments
13.6 Results and Discussion
13.7 Conclusions and Future Directions
A Glossary
Baneling Dynamics in Legend of the Seeker
Gergely R st
14.1 Introduction
14.2 Model Derivation
14.3 Analysis of a Simplified Baneling Model
14.4 Intervention 1: Wizard s Fire
14.5 Intervention 2: Treatment by Shadow Water
14.6 The Time-Delay Baneling Model
14.7 Numerical Simulations
14.8 Summary and Conclusions
A Acknowledgements
B Glossary
The Zombie Swarm: Epidemics in the Presence of Social Attraction and Repulsion
Evelyn Sander and Chad M. Topaz
15.1 Introduction
15.2 Model Construction
15.3 Basic Model Properties
15.4 Numerical Simulations and Dissipating Travelling Pulses
15.5 Epidemics with Treatment
15.6 Numerical Simulations and Persistent Travelling Pulses
15.7 Conclusion
A Nondimensionalization
B Conservation of Population
C Centre of Mass
D Mass-Balanced States
E Steady States
F Linear Stability
G Glossary
Conclusion
Robert Smith?
Contributors
The Undead
Afterword
Robert Smith?
FOREWORD: I RAN WITH A ZOMBIE
Andrew Cartmel
O NE of the hallmarks of a good horror film is that you leave the cinema retaining a residual sense of unease. Suddenly, there seems to be a chill to the sunlight and the world becomes an oddly-less-comfortable place. Then you pinch yourself and remember that you aren t actually living in a society beleaguered by perpetual onslaughts from hordes of the undead. Cue an embarrassed rush of relief.
And the only time such a sense of unease, perhaps blossoming into full-blown terror, is likely to recur is in your dreams. Or nightmares. I ve personally lost count of the number of times that zombies, vampires (and, in the interests of full disclosure, occasional Nazi battle groups) have troubled my own sleep.
But there was always one source of comfort in zombie scenarios. As established by films-from the earliest efforts such as Val Lewton, Curt Siodmak and Jacques Tourneur s 1943 I Walked with a Zombie right through to George Romero s tipping-point classic Night of the Living Dead -the zombie has not been depicted as the most nimble or fleet of creatures. In fact, the lumbering, shambling, clumsy gait of the inadequately reanimated became their hallmark. Consequently, even in the most effective of films or the most personal of nightmares, there has always been a ray of hope. Escape is possible.
Ever since Romero s 1968 debut feature, zombies have gone hand in (cadaverous, rotting) hand with the destruction of the broader social order. This specific trope of a collapsed human society under siege by fiends actually goes back further still, to Richard Matheson s brilliant 1955 novel I Am Legend, which depicted a world of the vampiric undead where the last human scrabbles f

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