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Propagation Dynamics on Complex Networks ModelsPDF|Epub|txt|kindle电子书版本网盘下载
- Methods and Stability Analysis 著
- 出版社： 北京：高等教育出版社
- ISBN：9787040307177
- 出版时间：2014
- 标注页数：314页
- 文件大小：47MB
- 文件页数：332页
- 主题词：计算机网络－传播学－研究－英文
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图书目录
1 Introduction1
1.1 Motivation and background1
1.2 A brief history of mathematical epidemiology2
1.2.1 Compartmental modeling3
1.2.2 Epidemic modeling on complex networks4
1.3 Organization of the book5
References6
2 Various epidemic models on complex networks10
2.1 Multiple stage models10
2.1.1 Multiple susceptible individuals11
2.1.2 Multiple infected individuals12
2.1.3 Multiple-staged infected individuals13
2.2 Staged progression models13
2.2.1 Simple-staged progression model14
2.2.2 Staged progression model on homogenous networks14
2.2.3 Staged progression model on heterogenous networks15
2.2.4 Staged progression model with birth and death16
2.2.5 Staged progression model with birth and death on homogenous networks16
2.2.6 Staged progression model with birth and death on heterogenous networks16
2.3 Stochastic SIS model17
2.3.1 A general concept:Epidemic spreading efficiency18
2.4 Models with population mobility19
2.4.1 Epidemic spreading without mobility of individuals20
2.4.2 Spreading of epidemic diseases among different cities20
2.4.3 Epidemic spreading within and between cities21
2.5 Models in meta-populations22
2.5.1 Model formulation22
2.6 Models with effective contacts24
2.6.1 Epidemics with effectively uniform contact25
2.6.2 Epidemics with effective contact in homogenous and heterogenous networks26
2.7 Models with two distinct routes26
2.8 Models with competing strains28
2.8.1 SIS model with competing strains28
2.8.2 Remarks and discussions30
2.9 Models with competing strains and saturated infectivity31
2.9.1 SIS model with mutation mechanism31
2.9.2 SIS model with super-infection mechanism33
2.10 Models with birth and death of nodes and links33
2.11 Models on weighted networks34
2.11.1 Model with birth and death and adaptive weights36
2.1 2 Models on directed networks38
2.1 3 Models on colored networks40
2.13.1 SIS epidemic models on colored networks41
2.13.2 Microscopic Markov-chain analysis42
2.14 Discrete epidemic models44
2.14.1 Discrete SIS model with nonlinear contagion scheme44
2.14.2 Discrete-time epidemic model in heterogenous networks45
2.14.3 A generalized model46
References47
3 Epidemic threshold analysis53
3.1 Threshold analysis by the direct method53
3.1.1 The epidemic rate is β/ni inside the same cities63
3.1.2 Epidemics on homogenous networks65
3.1.3 Epidemics on heterogenous networks66
3.2 Epidemic spreading efficiency threshold and epidemic threshold69
3.2.1 The case of λ1≠λ271
3.2.2 The case of λ1=λ274
3.2.3 Epidemic threshold in finite populations75
3.2.4 Epidemic threshold in infinite populations75
3.3 Epidemic thresholds and basic reproduction numbers76
3.3.1 Threshold from a self-consistencv equation77
3.3.2 Threshold unobtainable from a self-consistencv equation78
3.3.3 Threshold analysis for SIS model with mutation80
3.3.4 Threshold analysis for SIS model with super-infection83
3.3.5 Epidemic thresholds for models on directed networks86
3.3.6 Epidemic thresholds on technological and social networks87
3.3.7 Epidemic thresholds on directed networks with immunization89
3.3.8 Comparisons of epidemic thresholds for directed networks with immunization90
3.3.9 Thresholds for colored network models93
3.3.10 Thresholds for discrete epidemic models96
3.3.11 Basic reproduction number and existence of a positive equilibrium97
References98
4 Networked models for SARS and avian influenza101
4.1 Network models of real diseases101
4.2 Plausible models for propagation of the SARS virus102
4.3 Clustering model for SARS transmission:Application to epidemic control and risk assessment108
4.4 Small-world and scale-free models for SARS transmission114
4.5 Super-spreaders and the rate of transmission118
4.6 Scale-free distribution of avian influenza outbreaks124
4.7 Stratified model of ordinary influenza130
References136
5 Infectivity functions139
5.1 A model with nontrivialinfectivity function140
5.1.1 Epidemic threshold for SIS model with piecewise-linear infectivity141
5.1.2 Piecewise smooth and nonlinear infectivity142
5.2 Saturated infectivity143
5.3 Nonlinear infectivity for SIS model on scale-free networks143
5.3.1 The epidemic threshold for SIS model on scale-free networks with nonlinear infectivity144
5.3.2 Discussions and remarks148
References148
6 SIS models with an infective medium150
6.1 SIS model with an infective medium150
6.1.1 Homogenous complex networks151
6.1.2 Scale-free networks:The Barabási-Albert model152
6.1.3 Uniform immunization strategy156
6.1.4 Optimized immunization strategies157
6.2 A modified SIS model with an infective medium159
6.2.1 The modified model159
6.2.2 Epidemic threshold for the modified model with an infective medium160
6.3 Epidemic models with vectors between two separated networks162
6.3.1 Model formulation162
6.3.2 Basic reproduction number164
6.3.3 Sensitivity analysis166
6.4 Epidemic transmission on interdependent networks167
6.4.1 Theoretical modeling168
6.4.2 Mathematical analysis of epidemic dynamics172
6.4.3 Numerical analysis:Effect of model parameters on the basic reproduction number174
6.4.4 Numerical analysis:Effect of model parameters on infected node densities177
6.5 Discussions and remarks179
References181
7 Epidemic control and awareness184
7.1 SIS model with awareness184
7.1.1 Background185
7.1.2 The model186
7.1.3 Epidemic threshold190
7.1.4 Conclusions and discussions191
7.2 Discrete-time SIS model with awareness192
7.2.1 SIS model with awareness interactions193
7.2.2 Theoretical analysis:Basic reproduction number195
7.2.3 Remarks and discussions197
7.3 Spreading dynamics of a disease-awareness SIS model on complex networks198
7.3.1 Model formulation198
7.3.2 Derivation of limiting systems200
7.3.3 Basic reproduction number and local stability201
7.4 Remarks and discussions201
References203
8 Adaptive mechanism between dynamics and epidemics207
8.1 Adaptive mechanism between dynamical synchronization and epidemic behavior on complex networks207
8.1.1 Models of complex dynamicalnetwork and epidemic network209
8.1.2 Models of epidemic synchronization and its analysis210
8.1.3 Local stability of epidemic svnchronization212
8.1.4 Global stability of epidemic svnchronization214
8.2 Interplay between collective behavior and spreading dynamics216
8.2.1 A general bidirectional model217
8.2.2 Global synchronization and spreading dynamics218
8.2.3 Stability of global synchronization and spreading dynamics220
8.2.4 Phase synchronization and spreading dynamics226
8.2.5 Control of spreading networks227
8.2.6 Discussions and remarks227
References228
9 Epidemic control and immunization231
9.1 SIS model with immunization231
9.1.1 Proportionalimmunization231
9.1.2 Targeted immunization232
9.1.3 Acquaintance immunization233
9.1.4 Active immunization234
9.2 Edge targeted strategy for controlling epidemic spreading on scale-free networks235
9.3 Remarks and discussions237
References239
10 Global stability analysis240
10.1 Global stability analysis of the modified model with an infective medium240
10.2 Global dynamics of the model with vectors between two separated networks241
10.2.1 Global stability of the disease-free equilibrium and existence of the endemic equilibrium243
10.2.2 Uniqueness and global attractivity of the endemic equilibrium245
10.3 Global behavior of disease transmission on interdependent networks247
10.3.1 Existence and global stability of the endemic equilibrium for a disease-awareness SIS model248
10.4 Global behavior of epidemic transmissions250
10.4.1 Stability of the model equilibria250
10.4.2 Stability analysis for discrete epidemic models252
10.4.3 Global stability of the disease-free equilibrium256
10.4.4 Global attractiveness of epidemic disease257
10.5 Global attractivity of a network-based epidemic SIS model260
10.5.1 Positiveness.boundedness and equilibria260
10.5.2 Global attractivity of the model262
10.5.3 Remarks and discussions263
10.6 Global stability of an epidemic model with birth and death and adaptive weights264
10.6.1 Global dynamics of the model264
10.6.2 Discussions and remarks266
10.7 Global dynamics of a generalized epidemic model268
10.7.1 Model formulation268
10.7.2 Global dynamics of the model270
10.7.3 Discussions and remarks273
References274
11 Information diffusion and pathogen propagation277
11.1 Information diffusion and propagation on complex networks277
11.1.1 Information diffusion on complex networks278
11.1.2 Some essential differences between information propagation and epidemic spreading280
11.2 Interplay between information of disease spreading and epidemic dynamics281
11.2.1 Preliminaries281
11.2.2 Theoretical analysis of the model282
11.3 Discussions and remarks284
References286
Appendix A Proofs of theorems289
A.1 Transition from discrete-time linear system to continuous-time linear system289
A.2 Proof of Lemma 6.1291
A.3 Proof of Theorem 10.4291
A.4 Proof of Theorem 10.3292
A.5 Proof of Theorem 10.42296
Appendix B Further proofs of results302
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 7305
B.4 The positiveness of σ′:proof ofσ′＞0 in Section 9.1.2306
B.5 The relation between ∧ and k in Section 9.1.3308
Index311