The Geographic Spread of Infectious Diseases: Models and Applications

Preface ix

Chapter 1. Introduction 1
1.1 Mathematical Models and the Geographic Spread of Epidemics 5
1.2 Structure of this Book 11

Chapter 2. The Art of Epidemic Modeling: Concepts and Basic Structures 12
2.1 Essential Biological and Epidemiological Concepts 12
2.2 The Cornerstone of Many Epidemic Models | the SIR Model 16
2.3 Demography and Epidemic Models 23
2.4 More Complex Models 25
2.5 The Basic Reproductive Number Revisited 53

Chapter 3. Modeling the Geographic Spread of Inuenza Epidemics 58
3.1 A Brief Overview of the Biology of Inuenza 58
3.2 Population-based Inuenza Models 61
3.3 Individual-based Inuenza Models 77
3.4 So What Kind of Model Should One Use to Study Inuenza Transmission? 84

Chapter 4. Modeling Geographic Spread I: Population-based Approaches 86
4.1 Spatial Structure and Disease Transmission: Basic Themes 86
4.2 Spatial Modeling Frameworks 89
4.3 Metapopulation Models 90
4.4 Spatially Continuous Models 102

Chapter 5. Spatial Heterogeneity and Endemicity: The Case of Measles 117
5.1 The Persistence and Long-term Cycling of Measles 122
5.2 Spatial Heterogeneity, Synchrony, and the Spatial Spread of Measles 125

Chapter 6. Modeling Geographic Spread II: Individual-based Approaches 134
6.1 Historical Underpinnings of the Use of Networks in Epidemiology 137
6.2 The Nature of Networks 140
6.3 The Language of Network Analysis 142
6.4 Major Classes of Networks 150
6.5 The Inuence of Networks on the Dynamics of Epidemic Spread 159
6.6 Theoretical Analysis of Network Models 162
6.7 The Basic Reproductive Number in Network Models 168
6.8 Infection Control on Networks 171
6.9 Why Aren't There More Applications of Network Models for Spatial Spread? 173

Chapter 7. Spatial Models and the Control of Foot-and-Mouth Disease 176
7.1 Modeling the Geographic Spread of FMD 180
7.2 The Official Response to the Epidemic and Its Aftermath 185

Chapter 8. Maps, Projections, and GIS: Geographers' Approaches 191
8.1 Mapping Methods 191
8.2 Identifying Patterns of Disease Di_usion 195
8.3 Epidemic Projections 204
8.4 Detection of Disease Clustering 208
8.5 New and Potential Directions 211

Chapter 9. Revisiting SARS and Looking to the Future 215
9.1 Did Mathematical Modeling Help to Stop the 2003 SARS Epidemic? 215
9.2 Modeling the Geographic Spread of Past, Present, and Future Infectious Disease Epidemics: Lessons and Advice 223

Bibliography 237
Index 279