Propagation dynamics on complex networks : models, methods and stability analysis /

"Providing an introduction of general epidemic models, Propagation Dynamics on Complex Networks explores emerging topics of epidemic dynamics on complex networks, including theories, methods, and real-world applications with elementary and wide-coverage. This valuable text for researchers and s...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Fu, Xinchu
Otros Autores: Small, Michael (Professor), Chen, G. (Guanrong)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Chichester, West Sussex : Wiley, 2014.
Temas:
Epidemiology > Mathematical models.
Epidemiology > Methodology.
Biomathematics.
Mathematical models.
Epidemiologic Methods
Models, Theoretical
Épidémiologie > Modèles mathématiques.
Épidémiologie > Méthodologie.
Biomathématiques.
Modèles mathématiques.
mathematical models.
MEDICAL > Forensic Medicine.
MEDICAL > Preventive Medicine.
MEDICAL > Public Health.
Mathematical models
Biomathematics
Epidemiology > Mathematical models
Epidemiology > Methodology
Australian
Electronic books.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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 networks2.2.3 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 cities2.5 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 links2.11 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 cities3.1.2 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.
  • Machine generated contents note: 1. Introduction
  • 1.1. Motivation and background
  • 1.2. 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 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. 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. generalized model
  • References
  • 3. Epidemic threshold analysis
  • 3.1. Threshold analysis by the direct method
  • 3.1.1. epidemic rate is ?/ni inside the same cities
  • 3.1.2. Epidemics on homogenous networks
  • 3.1.3. Epidemics on heterogenous network's
  • 3.2. Epidemic spreading efficiency threshold and epidemic threshold
  • 3.2.1. case of ?1 [≠] lambda;2
  • 3.2.2. case of ?1 = ?2
  • 3.2.3. Epidemic threshold in finite populations
  • 3.2.4. Epidemic thresholdin in finite 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
  • 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
  • 5. Infectivity functions
  • 5.1. 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. epidemic threshold for SIS model on scale-free networks with nonlinear infectivity
  • 5.3.2. Discussions and remarks
  • References
  • 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 Barabasi-Albert model
  • 6.1.3. Uniform immunization strategy
  • 6.1.4. Optimized immunization strategies
  • 6.2. modified SIS model with an infective medium
  • 6.2.1. 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
  • 7. Epidemic control and awareness
  • 7.1. SIS model with awareness
  • 7.1.1. Background
  • 7.1.2. 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
  • 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 synchrohization 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. 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
  • 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
  • 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

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