Author Fu, Xinchu
Title Propagation Dynamics on Complex Networks : Models, Methods and Stability Analysis
Imprint New York : John Wiley & Sons, Incorporated, 2014
©2013
book jacket
Edition 1st ed
Descript 1 online resource (330 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
Note 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 -- A.2 Proof of Lemma 6.1 -- A.3 Proof of Theorem 10.4 -- A.4 Proof of Theorem 10.3 -- A.5 Proof of Theorem 10.42 -- Appendix B Further proofs of results -- B.1 Eigenvalues of the matrix F in (6.27) -- B.2 The matrix T in (6.32) -- B.3 Proof of (7.6) in Chapter 7
B.4 The positiveness of ð': proof of ð' > 0 in Sec 9.1.2
Explores the emerging subject of epidemic dynamics on complex networks, including theories, methods, and real-world applications Throughout history epidemic diseases have presented a serious threat to human life, and in recent years the spread of infectious diseases such as dengue, malaria, HIV, and SARS has captured global attention; and in the modern technological age, the proliferation of virus attacks on the Internet highlights the emergent need for knowledge about modeling, analysis, and control in epidemic dynamics on complex networks.  For advancement of techniques, it has become clear that more fundamental knowledge will be needed in mathematical and numerical context about how epidemic dynamical networks can be modelled, analyzed, and controlled. This book explores recent progress in these topics and looks at issues relating to various epidemic systems. Propagation Dynamics on Complex Networks covers most key topics in the field, and will provide a valuable resource for graduate students and researchers interested in network science and dynamical systems, and related interdisciplinary fields. Key Features: Includes a brief history of mathematical epidemiology and epidemic modeling on complex networks. Explores how information, opinion, and rumor spread via the Internet and social networks. Presents plausible models for propagation of SARS and avian influenza outbreaks, providing a reality check for otherwise abstract mathematical modeling. Considers various infectivity functions, including constant, piecewise-linear, saturated, and nonlinear cases. Examines information transmission on complex networks, and investigates the difference between information and epidemic spreading
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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries
Link Print version: Fu, Xinchu Propagation Dynamics on Complex Networks : Models, Methods and Stability Analysis New York : John Wiley & Sons, Incorporated,c2014 9781118534502
Subject Epidemiology -- Mathematical models.;Epidemiology -- Methodology.;Biomathematics
Electronic books
Alt Author Small, Michael
Chen, Guanrong