Propagation Dynamics on Complex Networks

Xinchu Fu, Department of Mathematics, Shanghai  University, ChinaMichael Small, School of Mathematics and Statistics, The University of Western Australia, AustraliaGuanrong Chen, Department of Electronic Engineering, City University of Hong Kong, China

• Preface xiSummary xiii1 Introduction 11.1 Motivation and background 11.2 A brief history of mathematical epidemiology 21.3 Organization of the book 5References 62 Various epidemic models on complex networks 102.1 Multiple stage models 102.2 Staged progression models 132.3 Stochastic SIS model 172.4 Models with population mobility 192.5 Models in meta-populations 222.6 Models with effective contacts 242.7 Models with two distinct routes 262.8 Models with competing strains 282.9 Models with competing strains and saturated infectivity 312.10 Models with birth and death of nodes and links 332.11 Models on weighted networks 342.12 Models on directed networks 382.13 Models on colored networks 402.14 Discrete epidemic models 44References 473 Epidemic threshold analysis 533.1 Threshold analysis by the direct method 533.2 Epidemic spreading efficiency threshold and epidemic threshold 693.3 Epidemic thresholds and basic reproduction numbers 76References 984 Networked models for SARS and avian influenza 1014.1 Network models of real diseases 1014.2 Plausible models for propagation of the SARS virus 1024.3 Clustering model for SARS transmission: Application to epidemic control and risk assessment 1084.4 Small-world and scale-free models for SARS transmission 1144.5 Super-spreaders and the rate of transmission 1184.6 Scale-free distribution of avian influenza outbreaks 1244.7 Stratified model of ordinary influenza 130References 1365 Infectivity functions 1395.1 A model with nontrivial infectivity function 1405.2 Saturated infectivity 1435.3 Nonlinear infectivity for SIS model on scale-free networks 143References 1486 SIS models with an infective medium 1506.1 SIS model with an infective medium 1506.2 A modified SIS model with an infective medium 1596.3 Epidemic models with vectors between two separated networks 1626.4 Epidemic transmission on interdependent networks 1676.4.1 Theoretical modeling 1686.5 Discussions and remarks 179References 1817 Epidemic control and awareness 1847.1 SIS model with awareness 1847.2 Discrete-time SIS model with awareness 1927.3 Spreading dynamics of a disease-awareness SIS model on complex networks 1987.4 Remarks and discussions 201References 2038 Adaptive mechanism between dynamics and epidemics 2078.1 Adaptive mechanism between dynamical synchronization and epidemic behavior on complex networks 2078.2 Interplay between collective behavior and spreading dynamics 216References 2289 Epidemic control and immunization 2319.1 SIS model with immunization 2319.2 Edge targeted strategy for controlling epidemic spreading on scale-free networks 2359.3 Remarks and discussions 237References 23910 Global stability analysis 24010.1 Global stability analysis of the modified model with an infective medium 24010.2 Global dynamics of the model with vectors between two separated networks 24110.3 Global behavior of disease transmission on interdependent networks 24710.4 Global behavior of epidemic transmissions 25010.5 Global attractivity of a network-based epidemic SIS model 26010.6 Global stability of an epidemic model with birth and death and adaptive weights 26410.7 Global dynamics of a generalized epidemic model 268References 27411 Information diffusion and pathogen propagation 27711.1 Information diffusion and propagation on complex networks 27711.2 Interplay between information of disease spreading and epidemic dynamics 28111.3 Discussions and remarks 284References 286Appendix A Proofs of theorems 289A.1 Transition from discrete-time linear system to continuous-time linear system 289A.2 Proof of Lemma 6.1 291A.3 Proof of Theorem 10.4 291A.4 Proof of Theorem 10.3 292A.5 Proof of Theorem 10.42 296Appendix B Further proofs of results 302B.1 Eigenvalues of the matrix Þ F in (6.27) 302B.2 The matrix 𝛤 in (6.32) 304B.3 Proof of (7.6) in Chapter 7 305B.4 The positiveness of 𝜎′: proof of 𝜎′ > 0 in Section 9.1.2 306B.5 The relation between 𝛬 and 𝜅 in Section 9.1.3 308Index 311