Propagation Dynamics on Complex Networks ModelsPDF电子书下载

1 Introduction 1

1.1 Motivation and background 1

1.2 A brief history of mathematical epidemiology 2

1.2.1 Compartmental modeling 3

1.2.2 Epidemic modeling on complex networks 4

1.3 Organization of the book 5

References 6

2 Various epidemic models on complex networks 10

2.1 Multiple stage models 10

2.1.1 Multiple susceptible individuals 11

2.1.2 Multiple infected individuals 12

2.1.3 Multiple-staged infected individuals 13

2.2 Staged progression models 13

2.2.1 Simple-staged progression model 14

2.2.2 Staged progression model on homogenous networks 14

2.2.3 Staged progression model on heterogenous networks 15

2.2.4 Staged progression model with birth and death 16

2.2.5 Staged progression model with birth and death on homogenous networks 16

2.2.6 Staged progression model with birth and death on heterogenous networks 16

2.3 Stochastic SIS model 17

2.3.1 A general concept:Epidemic spreading efficiency 18

2.4 Models with population mobility 19

2.4.1 Epidemic spreading without mobility of individuals 20

2.4.2 Spreading of epidemic diseases among different cities 20

2.4.3 Epidemic spreading within and between cities 21

2.5 Models in meta-populations 22

2.5.1 Model formulation 22

2.6 Models with effective contacts 24

2.6.1 Epidemics with effectively uniform contact 25

2.6.2 Epidemics with effective contact in homogenous and heterogenous networks 26

2.7 Models with two distinct routes 26

2.8 Models with competing strains 28

2.8.1 SIS model with competing strains 28

2.8.2 Remarks and discussions 30

2.9 Models with competing strains and saturated infectivity 31

2.9.1 SIS model with mutation mechanism 31

2.9.2 SIS model with super-infection mechanism 33

2.10 Models with birth and death of nodes and links 33

2.11 Models on weighted networks 34

2.11.1 Model with birth and death and adaptive weights 36

2.1 2 Models on directed networks 38

2.1 3 Models on colored networks 40

2.13.1 SIS epidemic models on colored networks 41

2.13.2 Microscopic Markov-chain analysis 42

2.14 Discrete epidemic models 44

2.14.1 Discrete SIS model with nonlinear contagion scheme 44

2.14.2 Discrete-time epidemic model in heterogenous networks 45

2.14.3 A generalized model 46

References 47

3 Epidemic threshold analysis 53

3.1 Threshold analysis by the direct method 53

3.1.1 The epidemic rate is β/ni inside the same cities 63

3.1.2 Epidemics on homogenous networks 65

3.1.3 Epidemics on heterogenous networks 66

3.2 Epidemic spreading efficiency threshold and epidemic threshold 69

3.2.1 The case of λ1≠λ2 71

3.2.2 The case of λ1=λ2 74

3.2.3 Epidemic threshold in finite populations 75

3.2.4 Epidemic threshold in infinite populations 75

3.3 Epidemic thresholds and basic reproduction numbers 76

3.3.1 Threshold from a self-consistencv equation 77

3.3.2 Threshold unobtainable from a self-consistencv equation 78

3.3.3 Threshold analysis for SIS model with mutation 80

3.3.4 Threshold analysis for SIS model with super-infection 83

3.3.5 Epidemic thresholds for models on directed networks 86

3.3.6 Epidemic thresholds on technological and social networks 87

3.3.7 Epidemic thresholds on directed networks with immunization 89

3.3.8 Comparisons of epidemic thresholds for directed networks with immunization 90

3.3.9 Thresholds for colored network models 93

3.3.10 Thresholds for discrete epidemic models 96

3.3.11 Basic reproduction number and existence of a positive equilibrium 97

References 98

4 Networked models for SARS and avian influenza 101

4.1 Network models of real diseases 101

4.2 Plausible models for propagation of the SARS virus 102

4.3 Clustering model for SARS transmission:Application to epidemic control and risk assessment 108

4.4 Small-world and scale-free models for SARS transmission 114

4.5 Super-spreaders and the rate of transmission 118

4.6 Scale-free distribution of avian influenza outbreaks 124

4.7 Stratified model of ordinary influenza 130

References 136

5 Infectivity functions 139

5.1 A model with nontrivialinfectivity function 140

5.1.1 Epidemic threshold for SIS model with piecewise-linear infectivity 141

5.1.2 Piecewise smooth and nonlinear infectivity 142

5.2 Saturated infectivity 143

5.3 Nonlinear infectivity for SIS model on scale-free networks 143

5.3.1 The epidemic threshold for SIS model on scale-free networks with nonlinear infectivity 144

5.3.2 Discussions and remarks 148

References 148

6 SIS models with an infective medium 150

6.1 SIS model with an infective medium 150

6.1.1 Homogenous complex networks 151

6.1.2 Scale-free networks:The Barabási-Albert model 152

6.1.3 Uniform immunization strategy 156

6.1.4 Optimized immunization strategies 157

6.2 A modified SIS model with an infective medium 159

6.2.1 The modified model 159

6.2.2 Epidemic threshold for the modified model with an infective medium 160

6.3 Epidemic models with vectors between two separated networks 162

6.3.1 Model formulation 162

6.3.2 Basic reproduction number 164

6.3.3 Sensitivity analysis 166

6.4 Epidemic transmission on interdependent networks 167

6.4.1 Theoretical modeling 168

6.4.2 Mathematical analysis of epidemic dynamics 172

6.4.3 Numerical analysis:Effect of model parameters on the basic reproduction number 174

6.4.4 Numerical analysis:Effect of model parameters on infected node densities 177

6.5 Discussions and remarks 179

References 181

7 Epidemic control and awareness 184

7.1 SIS model with awareness 184

7.1.1 Background 185

7.1.2 The model 186

7.1.3 Epidemic threshold 190

7.1.4 Conclusions and discussions 191

7.2 Discrete-time SIS model with awareness 192

7.2.1 SIS model with awareness interactions 193

7.2.2 Theoretical analysis:Basic reproduction number 195

7.2.3 Remarks and discussions 197

7.3 Spreading dynamics of a disease-awareness SIS model on complex networks 198

7.3.1 Model formulation 198

7.3.2 Derivation of limiting systems 200

7.3.3 Basic reproduction number and local stability 201

7.4 Remarks and discussions 201

References 203

8 Adaptive mechanism between dynamics and epidemics 207

8.1 Adaptive mechanism between dynamical synchronization and epidemic behavior on complex networks 207

8.1.1 Models of complex dynamicalnetwork and epidemic network 209

8.1.2 Models of epidemic synchronization and its analysis 210

8.1.3 Local stability of epidemic svnchronization 212

8.1.4 Global stability of epidemic svnchronization 214

8.2 Interplay between collective behavior and spreading dynamics 216

8.2.1 A general bidirectional model 217

8.2.2 Global synchronization and spreading dynamics 218

8.2.3 Stability of global synchronization and spreading dynamics 220

8.2.4 Phase synchronization and spreading dynamics 226

8.2.5 Control of spreading networks 227

8.2.6 Discussions and remarks 227

References 228

9 Epidemic control and immunization 231

9.1 SIS model with immunization 231

9.1.1 Proportionalimmunization 231

9.1.2 Targeted immunization 232

9.1.3 Acquaintance immunization 233

9.1.4 Active immunization 234

9.2 Edge targeted strategy for controlling epidemic spreading on scale-free networks 235

9.3 Remarks and discussions 237

References 239

10 Global stability analysis 240

10.1 Global stability analysis of the modified model with an infective medium 240

10.2 Global dynamics of the model with vectors between two separated networks 241

10.2.1 Global stability of the disease-free equilibrium and existence of the endemic equilibrium 243

10.2.2 Uniqueness and global attractivity of the endemic equilibrium 245

10.3 Global behavior of disease transmission on interdependent networks 247

10.3.1 Existence and global stability of the endemic equilibrium for a disease-awareness SIS model 248

10.4 Global behavior of epidemic transmissions 250

10.4.1 Stability of the model equilibria 250

10.4.2 Stability analysis for discrete epidemic models 252

10.4.3 Global stability of the disease-free equilibrium 256

10.4.4 Global attractiveness of epidemic disease 257

10.5 Global attractivity of a network-based epidemic SIS model 260

10.5.1 Positiveness.boundedness and equilibria 260

10.5.2 Global attractivity of the model 262

10.5.3 Remarks and discussions 263

10.6 Global stability of an epidemic model with birth and death and adaptive weights 264

10.6.1 Global dynamics of the model 264

10.6.2 Discussions and remarks 266

10.7 Global dynamics of a generalized epidemic model 268

10.7.1 Model formulation 268

10.7.2 Global dynamics of the model 270

10.7.3 Discussions and remarks 273

References 274

11 Information diffusion and pathogen propagation 277

11.1 Information diffusion and propagation on complex networks 277

11.1.1 Information diffusion on complex networks 278

11.1.2 Some essential differences between information propagation and epidemic spreading 280

11.2 Interplay between information of disease spreading and epidemic dynamics 281

11.2.1 Preliminaries 281

11.2.2 Theoretical analysis of the model 282

11.3 Discussions and remarks 284

References 286

Appendix A Proofs of theorems 289

A.1 Transition from discrete-time linear system to continuous-time linear system 289

A.2 Proof of Lemma 6.1 291

A.3 Proof of Theorem 10.4 291

A.4 Proof of Theorem 10.3 292

A.5 Proof of Theorem 10.42 296

Appendix B Further proofs of results 302

B.1 Eigenvalues of the matrix F in(6.27) 302

B.2 The matrix Γ in (6.32) 304

B.3 Proof of(7.6)in Chapter 7 305

B.4 The positiveness of σ′:proof ofσ′＞0 in Section 9.1.2 306

B.5 The relation between ∧ and k in Section 9.1.3 308

Index 311