Tipping Points Modelling Social Problems and Health

This book focuses on the modelling of contemporary health and social problems, especially those considered a major burden to communities, governments and taxpayers, such as smoking, alcoholism, drug use, and heart disease. Based on a series of papers presented at a recent conference hosted by the Leverhulme-funded Tipping Points project at the University of Durham, this book illustrates a broad range of modelling approaches. Such a diverse collection demonstrates that an interdisciplinary approach is essential to modelling tipping points in health and social problems, and the assessment of associated risk and resilience.

J. J. Bissell, Department of Mathematical Sciences, University of Durham, UK.

C. C. S. Caiado, Department of Mathematical Sciences, University of Durham, UK.

S. E. Curtis, Institute of Hazard, Risk and Resilience, University of Durham, UK.

M. Goldstein, Department of Mathematical Sciences, University of Durham, UK.

Brian Straughan, Department of Mathematical Sciences, University of Durham, UK.

Acknowledgements xiii

Introduction xv

PART I THE SMOKING EPIDEMIC 1

1 Generalised Compartmental Modelling of Health Epidemics 3

1.1 Introduction 3

1.2 Basic compartmental model of smoking dynamics 5

1.3 Properties of the basic model 8

1.4 Generalised model inclusive of multiple peer recruitment 10

1.5 Bistability and 'tipping points' in the generalised model 15

1.6 Summary and conclusions 18

2 Stochastic Modelling for Compartmental Systems Applied to Social Problems 21

2.1 Introduction 21

2.2 Global sensitivity analysis of deterministic models 23

2.3 Sensitivity analysis of the generalised smoking model with peer influence 24

2.4 Adding randomness to a deterministic model 26

2.5 Sensitivity analysis of the stochastic analogue 28

2.6 Conclusion 30

3 Women and Smoking in the North East of England 32

3.1 Introduction 33

3.2 Background 33

3.3 Interrogating the figures 35

3.4 Materialist and cultural or behavioural explanations 39

3.5 The tobacco industry and the creation of social values 41

3.6 Local voices 43

3.7 Conclusions 44

PART II MATHEMATICAL MODELLING IN HEALTHCARE 49

4 Cardiac Surgery Performance Monitoring 51

4.1 Introduction 52

4.2 Statistical framework for monitoring 55

4.3 A non-stationary process 61

4.4 Dynamic modelling approaches 68

4.5 Case example 74

4.6 Discussion 75

4.7 Conclusion 77

5 Heart Online Uncertainty and Stability Estimation 82

5.1 Introduction 83

5.2 Monitoring live complex systems 83

5.3 The Bayes linear approach 85

5.4 The Fantasia and Sudden Cardiac Death databases 86

5.5 Exploring ECG datasets 87

5.6 Assessing discrepancy 91

5.7 Final remarks and conclusion 93

6 Stents, Blood Flow and Pregnancy 95

6.1 Introduction 96

6.2 Drug-eluting stents 97

6.3 Modelling blood flow 101

6.4 Modelling a capillary-fill medical diagnostic tool 103

6.5 Summary and closing remarks 110

PART III TIPPING POINTS IN SOCIAL DYNAMICS 113

7 From Five Key Questions to a System Sociology Theory 115

7.1 Introduction 116

7.2 Complexity features 117

7.3 Mathematical tools 119

7.4 Black Swans from the interplay of different dynamics 122

7.5 Validation of models 125

7.6 Conclusions: towards a mathematical theory of social systems 126

8 Complexity in Spatial Dynamics: The Emergence of Homogeneity /Heterogeneity in Culture in Cities 130

8.1 Introduction 131

8.2 Modelling approach 132

8.3 Description of the model 134

8.4 Sensitivity analysis and results 138

8.5 Discussion and conclusions 141

9 Cultural Evolution, Gene–Culture Coevolution, and Human Health 146

9.1 Introduction 147

9.2 Cultural evolution 149

9.3 Epidemiological modelling of cultural change 153

9.4 Gene–culture coevolution 157

9.5 Conclusion 163

10 Conformity Bias and Catastrophic Social Change 168

10.1 Introduction 168

10.2 Three-population compartmental model 171

10.3 Basic system excluding conformity bias 173

10.4 Including conformity bias 174

10.5 Comparative statics 176

10.6 Summary 178

10.7 Conclusions 179

Appendix 10.A: Stability in the conformity bias model 180

PART IV THE RESILIENCE OF TIPPING POINTS 183

11 Psychological Perspectives on Risk and Resilience 185

11.1 Introduction 185

11.2 Forensic psychological risk assessments in prisons 186

11.3 Suicide in prisons 187

11.4 Biases in human decision making – forensic psychologists making risky decisions 189

11.5 The Port of London Authority 192

11.6 Final thoughts and reflections 194

12 Tipping Points and Uncertainty in Health and Healthcare Systems 196

12.1 Introduction: 'tipping points' as 'critical events' in health systems 197

12.2 Prediction, prevention and preparedness strategies for risk resilience in complex systems 198

12.3 No such thing as a 'never event'? 200

12.4 Local versus large-scale responses to risk 202

12.5 Conclusions: the ongoing agenda for research on tipping points in complex systems 204

Endnotes and acknowledgements 205

References 205

Index 209

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