Table of 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
1.1 Introduction 1
1.1.1 A Media Invasion of Zombies 1
1.1.2 The Effects of Media 3
1.2 The Model 5
1.2.1 The Durability of a Media Story 6
1.2.2 The Newsworthiness of a Media Story 8
1.2.3 The Natural Lifespan of a Media Story 9
1.3 Analysis 9
1.3.1 Final Size Populations 9
1.3.2 Stability 10
1.3.3 A Competing Story 11
1.4 The Power of a Right Hook 12
1.5 Sample Scenarios 12
1.6 Discussion 16
A Acknowledgements 20
B Glossary 20
The Undead: A Plague on Humanity or a Powerful New Tool for Epidemiological Research? Jane M. Heffernan Derek J. Wilson 27
2.1 Introduction 28
2.2 Creeping up on Us: The Origins of Zombies and the Bubonic Plague 28
2.3 The Rising Tide: Modelling Epidemics 30
2.4 Living with Vampires: Modelling Endemics 36
2.5 Conclusions 40
A Glossary 41
When Zombies Attack! Alternate Ending Phil Munz 45
3.1 Title Sequence 45
3.2 The Story So Far 46
3.3 A Behind-the-Scenes Look at the Making of the Alternate Ending 48
3.4 The End? 51
3.5 DVD Extras 53
A Oscar Speech 54
B IMDB 54
When Humans Strike Back! Adaptive Strategies for Zombie Attacks Bard Ennentrout 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 71
5.1 Introduction 71
5.2 The Model 72
5.2.1 Interaction Rates Assuming a Uniform Population Density 72
5.2.2 Zombie Population Dynamics 73
5.2.3 Worker Population Dynamics 73
5.2.4 Militia Population Dynamics 74
5.2.5 Mole Population Dynamics 75
5.2.6 Supply Stockpile Dynamics 75
5.2.7 Comments 76
5.3 Modelling Specific Scenarios 76
5.3.1 Humanity Is Exterminated Outright 78
5.3.2 The Zombie Population Is Culled 78
5.3.3 Humans Nearly Starve 79
5.4 How Public Policy Affects Survivability During a Zombie Epidemic 81
5.4.1 Managing a Zombie Epidemic in an Urban Scenario 81
5.4.2 The Countryside 83
5.5 The Romero Scenario 85
5.5.1 Altered Transmission Equations 85
5.5.2 Simulation Results 86
5.6 Discussion 90
A Acknowledgements 91
B Glossary 91
How Long Can We Survive? Thomas E. Woolley Ruth E. Baker Eamorm A. Gaffney Philip K. Maim 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 117
7.1 Introduction 117
7.2 Data Sources 118
7.3 Demographic Variables Examined 119
7.4 Univariate Results 122
7.5 Multivariate Analyses 125
7.6 Conclusion 126
A Glossary 127
Is It Safe to Go Out Yet? Statistical Inference in a Zombie Outbreak Model Ben Calderhead Mark Girolami 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
The Social Zombie: Modelling Undead Outbreaks on Social Networks Laurent Hébert-Dufresne Vincent Marccau Pierre-André Noël Antoine Allard Louis J. Dubé 149
9.1 Introduction 150
9.2 Modelling a Zombie Invasion: A Practical Guide 150
9.2.1 Contact Networks 101 151
9.2.2 Building a Contact Network 151
9.2.3 The Rules of the Game 152
9.2.4 Monte Carlo Simulations 153
9.3 Mathematical Zombies: A Theory of the Undead 154
9.3.1 The Variables of the System 154
9.3.2 Moment-Closure Approximation 155
9.3.3 Writing the Dynamical System 157
9.4 Results: Does Humanity Have the Slightest Chance? 158
9.4.1 Choosing the Victims 158
9.4.2 Body Count 159
9.5 The Social Zombie: Adapting for Realism 162
9.5.1 The New Rules of the Game 162
9.5.2 Hope Is the Last Thing to Die, Isn't It? 164
9.6 A Conclusion on Networks 165
9.7 …and Zombies 166
A Numerical Integration 167
B Glossary 169
Zombie Infection Warning System Based on Fuzzy Decision-Making Micael S. Couceiro Carlos M. Figueiredo J. Miguel A. Luz Michael J. Delorme 171
10.1 Introduction 171
10.2 Zombie Mathematical Models 173
10.2.1 The Base Model 173
10.2.2 Incorporating Latent Infection 173
10.2.3 Zombie Outbreak with Quarantine of Zombies and Infected Individuals 174
10.2.4 Medical Treatment for Zombies 174
10.3 Introduction to Fuzzy Systems 175
10.3.1 Zombie Infection Warning System 179
10.3.2 Decision-Making System Using Fuzzy Logic 181
10.4 Experimental Results 182
10.5 Conclusions 185
A Acknowledgements 187
B Glossary 187
Is There a Zombicidal Maniac Near You? You'd Better Hope So! Nick Beeton Alex Hoare Brody Walker 191
11.1 Introduction 191
11.2 Data Collection 193
11.3 Agent-Based Model 193
11.4 Stochastic Model 195
11.5 Transmission Dynamics 19(3
11.6 Zombie Management
11.7 Observations on Behaviour 202
11.8 Discussion 202
A Acknowledgements 204
B Glossary 205
Zombies in the City: A NetLogo Model Jennifer Badham Judy-anne Osborn 209
12.1 Introduction 209
12.2 Methodology 211
12.2.1 Why Use ABMs and NetLogo? 211
1.2.2.2 Our NetLogo Model 212
12.2.3 Experimental Design 214
12.3 Generic Behaviours Exhibited by the Model 216
12.3.1 Zombies Win 216
12.3.2 Humans Win 217
12.3.3 Stalemate 217
12.4 Effects of Speed and Skill 218
12.4.1 Humans Slow and Unskilled 218
12.4.2 Humans Fast and Unskilled 221
12.4.3 Humans Skilled and Slow 221
12.4.4 Humans Faster Than Zombies and Skilled 224
12.5 Implications for Education and Research Training 229
12.6 Conclusion 230
A Acknowledgements 230
B Glossary 231
An Evolvable Linear Representation for Simulating Government Policy in Zombie Outbreaks Daniel Ashlock Joseph Alexander Brown Clinton limes 233
1.3.1 Introduction 233
13.2 The Discrete-Time Model 235
13.3 Representation of Government Policies 237
13.3.1 Overview of Policies 237
13.3.2 Public Response to Government Policies 238
13.4 The Evolutionary Algorithm 239
13.5 Experiments 241
13.6 Results and Discussion 242
13.7 Conclusions and Future Directions 245
A Glossary 245
Baneling Dynamics in Legend of the Seeker Gergely Röst 249
14.1 Introduction 249
14.2 Model Derivation 251
14.3 Analysis of a Simplified Baneling Model 253
14.4 Intervention 1: Wizard's Fire 256
14.5 Intervention 2: Treatment by Shadow Water 256
14.6 The Time-Delay Baneling Model 258
14.7 Numerical Simulations 259
14.8 Summary and Conclusions 260
A Acknowledgements 263
B Glossary 263
The Zombie Swarm: Epidemics in the Presence of Social Attraction and Repulsion Evelyn Sander Chad M. Topaz 265
15.1 Introduction 266
15.2 Model Construction 269
15.3 Basic Model Properties 274
15.4 Numerical Simulations and Dissipating Travelling Pulses 276
15.5 Epidemics with Treatment 277
1.5.6 Numerical Simulations and Persistent Travelling Pulses 281
15.7 Conclusion 286
A Nondimensionalization 288
B Conservation of Population 289
C Centre of Mass 290
D Mass-Balanced States 292
E Steady States 293
F Linear Stability 293
G Glossary 298
Conclusion Robert Smith? 301
Contributors The Undead 303
Afterword Robert Smith? 313
