Mathematical modelling of zombies / [edited by] Robert Smith?

Format:

Book

Contributor:

Smith?, Stacey, 1972- editor.

Language:

English

Subjects (All):

Zombies--Mathematical models.

Zombies.

Epidemics--Mathematical models--Humor.

Epidemics.

Epidemics--Mathematical models.

Mathematical models.

Genre:

Humor.

Physical Description:

xix, 314 pages : illustrations ; 26 cm

Place of Publication:

Ottawa : University of Ottawa Press, 2014.

Summary:

You're outnumbered, in tear for your life, surrounded by flesh-eating 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, discrete-time 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 non-mathematical audience and how models can be formulated with only limited information. A foreword 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. Book jacket.

Contents:

The Viral Spread of a Zombie Media Story / Robert Smith? Smith?, Robert 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 Heffernan, Jane M., Derek J. Wilson Wilson, Derek J. 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 Munz, Phil 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 Ennentrout, Bard, Kyle Ermentrout Ermentrout, Kyle 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 Tippett, Ben 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 Woolley, Thomas E., Ruth E. Baker Baker, Ruth E., Eamorm A. Gaffney Gaffney, Eamorm A., Philip K. Maim Maim, Philip K. 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 Zelterman, Daniel 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 Calderhead, Ben, Mark Girolami Girolami, Mark, Desmond J. Higham Higham, Desmond J. 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 Hébert-Dufresne, Laurent, Vincent Marccau Marccau, Vincent, Pierre-André Noël Noël, Pierre-André, Antoine Allard Allard, Antoine, Louis J. Dubé Dubé, Louis J. 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 Couceiro, Micael S., Carlos M. Figueiredo Figueiredo, Carlos M., J. Miguel A. Luz Luz, J. Miguel A., Michael J. Delorme Delorme, Michael J. 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 Beeton, Nick, Alex Hoare Hoare, Alex, Brody Walker Walker, Brody 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 Badham, Jennifer, Judy-anne Osborn Osborn, Judy-anne 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 Ashlock, Daniel, Joseph Alexander Brown Brown, Joseph Alexander, Clinton limes limes, Clinton 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 Röst, Gergely 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 Sander, Evelyn, Chad M.

Topaz Topaz, Chad M. 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.

Notes:

Includes bibliographical references.

Other Format:

Mathematical modelling of zombies.

ISBN:

9780776622101

0776622102

OCLC:

881436991