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
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 models2.1 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
3 Epidemic threshold analysis
3.1 Threshold analysis by the direct method
3.1.1 The epidemic rate is βln inside the same cities
3.1.1 Epidemics on homogenous networks
3.1.1 Epidemics on heterogenous networks
3.2 Epidemic spreading efficiency threshold and epidemic threshold
3.2.1 The case of λ1 ≠λ2
3.2.2 The case of λ1≠λ2
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 immunizationdel
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4 Networked models for SARS and avian influenza
5 Infectivity functions
6 SIS models with an infective medium
7 Epidemic control and awareness
8 Adaptive mechanism between dynamics and epidemics
9 Epidemic control and immunization
10 Global stability analysis
11 Information diffusion and pathogen propagation
Appendix A Proofs of theorems
Appendix B Further proofs of results
Index
