Cover -- Title Page -- Copyright -- Contents -- Preface -- Summary -- Chapter 1 Introduction -- 1.1 Motivation and background -- 1.2 A brief history of mathematical epidemiology -- 1.2.1 Compartmental modeling -- 1.2.2 Epidemic modeling on complex networks -- 1.3 Organization of the book -- References -- Chapter 2 Various epidemic models on complex networks -- 2.1 Multiple stage models -- 2.1.1 Multiple susceptible individuals -- 2.1.2 Multiple infected individuals -- 2.1.3 Multiple-staged infected individuals -- 2.2 Staged progression models -- 2.2.1 Simple-staged progression model -- 2.2.2 Staged progression model on homogenous networks -- 2.2.3 Staged progression model on heterogenous networks -- 2.2.4 Staged progression model with birth and death -- 2.2.5 Staged progression model with birth and death on homogenous networks -- 2.2.6 Staged progression model with birth and death on heterogenous networks -- 2.3 Stochastic SIS model -- 2.3.1 A general concept: Epidemic spreading efficiency -- 2.4 Models with population mobility -- 2.4.1 Epidemic spreading without mobility of individuals -- 2.4.2 Spreading of epidemic diseases among different cities -- 2.4.3 Epidemic spreading within and between cities -- 2.5 Models in meta-populations -- 2.5.1 Model formulation -- 2.6 Models with effective contacts -- 2.6.1 Epidemics with effectively uniform contact -- 2.6.2 Epidemics with effective contact in homogenous and heterogenous networks -- 2.7 Models with two distinct routes -- 2.8 Models with competing strains -- 2.8.1 SIS model with competing strains -- 2.8.2 Remarks and discussions -- 2.9 Models with competing strains and saturated infectivity -- 2.9.1 SIS model with mutation mechanism -- 2.9.2 SIS model with super-infection mechanism -- 2.10 Models with birth and death of nodes and links.

2.11 Models on weighted networks -- 2.11.1 Model with birth and death and adaptive weights -- 2.12 Models on directed networks -- 2.13 Models on colored networks -- 2.13.1 SIS epidemic models on colored networks -- 2.13.2 Microscopic Markov-chain analysis -- 2.14 Discrete epidemic models -- 2.14.1 Discrete SIS model with nonlinear contagion scheme -- 2.14.2 Discrete-time epidemic model in heterogenous networks -- 2.14.3 A generalized model -- References -- Chapter 3 Epidemic threshold analysis -- 3.1 Threshold analysis by the direct method -- 3.1.1 The epidemic rate is B/ni inside the same cities -- 3.1.2 Epidemics on homogenous networks -- 3.1.3 Epidemics on heterogenous networks -- 3.2 Epidemic spreading efficiency threshold and epidemic threshold -- 3.2.1 The case of 1 ≠ 2 -- 3.2.2 The case of 1 = 2 -- 3.2.3 Epidemic threshold in finite populations -- 3.2.4 Epidemic threshold in infinite populations -- 3.3 Epidemic thresholds and basic reproduction numbers -- 3.3.1 Threshold from a self-consistency equation -- 3.3.2 Threshold unobtainable from a self-consistency equation -- 3.3.3 Threshold analysis for SIS model with mutation -- 3.3.4 Threshold analysis for SIS model with super-infection -- 3.3.5 Epidemic thresholds for models on directed networks -- 3.3.6 Epidemic thresholds on technological and social networks -- 3.3.7 Epidemic thresholds on directed networks with immunization -- 3.3.8 Comparisons of epidemic thresholds for directed networks with immunization -- 3.3.9 Thresholds for colored network models -- 3.3.10 Thresholds for discrete epidemic models -- 3.3.11 Basic reproduction number and existence of a positive equilibrium -- References -- Chapter 4 Networked models for SARS and avian influenza -- 4.1 Network models of real diseases.

4.2 Plausible models for propagation of the SARS virus -- 4.3 Clustering model for SARS transmission: Application to epidemic control and risk assessment -- 4.4 Small-world and scale-free models for SARS transmission -- 4.5 Super-spreaders and the rate of transmission -- 4.6 Scale-free distribution of avian influenza outbreaks -- 4.7 Stratified model of ordinary influenza -- References -- Chapter 5 Infectivity functions -- 5.1 A model with nontrivial infectivity function -- 5.1.1 Epidemic threshold for SIS model with piecewise-linear infectivity -- 5.1.2 Piecewise smooth and nonlinear infectivity -- 5.2 Saturated infectivity -- 5.3 Nonlinear infectivity for SIS model on scale-free networks -- 5.3.1 The epidemic threshold for SIS model on scale-free networks with nonlinear infectivity -- 5.3.2 Discussions and remarks -- References -- Chapter 6 SIS models with an infective medium -- 6.1 SIS model with an infective medium -- 6.1.1 Homogenous complex networks -- 6.1.2 Scale-free networks: The Barabási-Albert model -- 6.1.3 Uniform immunization strategy -- 6.1.4 Optimized immunization strategies -- 6.2 A modified SIS model with an infective medium -- 6.2.1 The modified model -- 6.2.2 Epidemic threshold for the modified model with an infective medium -- 6.3 Epidemic models with vectors between two separated networks -- 6.3.1 Model formulation -- 6.3.2 Basic reproduction number -- 6.3.3 Sensitivity analysis -- 6.4 Epidemic transmission on interdependent networks -- 6.4.1 Theoretical modeling -- 6.4.2 Mathematical analysis of epidemic dynamics -- 6.4.3 Numerical analysis: Effect of model parameters on the basic reproduction number -- 6.4.4 Numerical analysis: Effect of model parameters on infected node densities -- 6.5 Discussions and remarks -- References -- Chapter 7 Epidemic control and awareness.

7.1 SIS model with awareness -- 7.1.1 Background -- 7.1.2 The model -- 7.1.3 Epidemic threshold -- 7.1.4 Conclusions and discussions -- 7.2 Discrete-time SIS model with awareness -- 7.2.1 SIS model with awareness interactions -- 7.2.2 Theoretical analysis: Basic reproduction number -- 7.2.3 Remarks and discussions -- 7.3 Spreading dynamics of a disease-awareness SIS model on complex networks -- 7.3.1 Model formulation -- 7.3.2 Derivation of limiting systems -- 7.3.3 Basic reproduction number and local stability -- 7.4 Remarks and discussions -- References -- Chapter 8 Adaptive mechanism between dynamics and epidemics -- 8.1 Adaptive mechanism between dynamical synchronization and epidemic behavior on complex networks -- 8.1.1 Models of complex dynamical network and epidemic network -- 8.1.2 Models of epidemic synchronization and its analysis -- 8.1.3 Local stability of epidemic synchronization -- 8.1.4 Global stability of epidemic synchronization -- 8.2 Interplay between collective behavior and spreading dynamics -- 8.2.1 A general bidirectional model -- 8.2.2 Global synchronization and spreading dynamics -- 8.2.3 Stability of global synchronization and spreading dynamics -- 8.2.4 Phase synchronization and spreading dynamics -- 8.2.5 Control of spreading networks -- 8.2.6 Discussions and remarks -- References -- Chapter 9 Epidemic control and immunization -- 9.1 SIS model with immunization -- 9.1.1 Proportional immunization -- 9.1.2 Targeted immunization -- 9.1.3 Acquaintance immunization -- 9.1.4 Active immunization -- 9.2 Edge targeted strategy for controlling epidemic spreading on scale-free networks -- 9.3 Remarks and discussions -- References -- Chapter 10 Global stability analysis -- 10.1 Global stability analysis of the modified model with an infective medium.

10.2 Global dynamics of the model with vectors between two separated networks -- 10.2.1 Global stability of the disease-free equilibrium and existence of the endemic equilibrium -- 10.2.2 Uniqueness and global attractivity of the endemic equilibrium -- 10.3 Global behavior of disease transmission on interdependent networks -- 10.3.1 Existence and global stability of the endemic equilibrium for a disease-awareness SIS model -- 10.4 Global behavior of epidemic transmissions -- 10.4.1 Stability of the model equilibria -- 10.4.2 Stability analysis for discrete epidemic models -- 10.4.3 Global stability of the disease-free equilibrium -- 10.4.4 Global attractiveness of epidemic disease -- 10.5 Global attractivity of a network-based epidemic SIS model -- 10.5.1 Positiveness, boundedness and equilibria -- 10.5.2 Global attractivity of the model -- 10.5.3 Remarks and discussions -- 10.6 Global stability of an epidemic model with birth and death and adaptive weights -- 10.6.1 Global dynamics of the model -- 10.6.2 Discussions and remarks -- 10.7 Global dynamics of a generalized epidemic model -- 10.7.1 Model formulation -- 10.7.2 Global dynamics of the model -- 10.7.3 Discussions and remarks -- References -- Chapter 11 Information diffusion and pathogen propagation -- 11.1 Information diffusion and propagation on complex networks -- 11.1.1 Information diffusion on complex networks -- 11.1.2 Some essential differences between information propagation and epidemic spreading -- 11.2 Interplay between information of disease spreading and epidemic dynamics -- 11.2.1 Preliminaries -- 11.2.2 Theoretical analysis of the model -- 11.3 Discussions and remarks -- References -- Appendix A Proofs of theorems.

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