| Description |
1 online resource (330 pages) |
| Contents |
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 |
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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 |
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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 |
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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 |
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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 |
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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 |
| Summary |
"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 students explores models evolving over complex networks and presents results concerning dynamics of Network-based models on a macroscopic scale. The text presents the fundamental knowledge needed to demonstrate how epidemic dynamical networks can be modeled, analyzed, and controlled along the state-of-the-art and recent progress in the field and related issues arising from various epidemic systems"-- Provided by publisher |
| Analysis |
Australian |
| Bibliography |
Includes bibliographical references and index |
| Notes |
English |
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Online resource; title from PDF title page (ebrary, viewed January 15, 2013) |
| Subject |
Epidemiology -- Mathematical models
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Epidemiology -- Methodology
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Biomathematics.
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Mathematical models.
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Epidemiologic Methods
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Models, Theoretical
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mathematical models.
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MEDICAL -- Forensic Medicine.
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MEDICAL -- Preventive Medicine.
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MEDICAL -- Public Health.
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Mathematical models
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Biomathematics
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Epidemiology -- Mathematical models
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Epidemiology -- Methodology
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| Genre/Form |
Electronic books
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| Form |
Electronic book
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| Author |
Small, Michael (Professor)
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Chen, G. (Guanrong)
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| ISBN |
9781118762806 |
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1118762800 |
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9781118762783 |
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1118762789 |
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1118534506 |
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9781118534502 |
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130625468X |
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9781306254687 |
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1118762819 |
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9781118762813 |
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