Kooperativer Bibliotheksverbund

UID:

Umfang: XIV, 355 p. 91 illus. , online resource.

Ausgabe: 1st ed. 2022.

ISBN: 9783030971786

Serie: Understanding Complex Systems,

Inhalt: This book addresses the COVID-19 pandemic from a quantitative perspective based on mathematical models and methods largely used in nonlinear physics. It aims to study COVID-19 epidemics in countries and SARS-CoV-2 infections in individuals from the nonlinear physics perspective and to model explicitly COVID-19 data observed in countries and virus load data observed in COVID-19 patients. The first part of this book provides a short technical introduction into amplitude spaces given by eigenvalues, eigenvectors, and amplitudes.In the second part of the book, mathematical models of epidemiology are introduced such as the SIR and SEIR models and applied to describe COVID-19 epidemics in various countries around the world. In the third part of the book, virus dynamics models are considered and applied to infections in COVID-19 patients. This book is written for researchers, modellers, and graduate students in physics and medicine, epidemiology and virology, biology, applied mathematics, and computer sciences. This book identifies the relevant mechanisms behind past COVID-19 outbreaks and in doing so can help efforts to stop future COVID-19 outbreaks and other epidemic outbreaks. Likewise, this book points out the physics underlying SARS-CoV-2 infections in patients and in doing so supports a physics perspective to address human immune reactions to SARS-CoV-2 infections and similar virus infections.

Anmerkung: Chapter 1. Introduction -- Chapter 2. Nonlinear physics and synergetics -- Chapter 3. Epidemiological models and COVID-19 epidemics -- Chapter 4. Nonlinear physics of epidemics: part A -- Chapter 5. Nonlinear physics of epidemics: part B -- Chapter 6. Nonlinear physics of epidemics: part C -- Chapter 7. Model-based reproduction numbers -- Chapter 8. Modeling interventions -- Chapter 9. Models of virus dynamics -- Chapter 10. Virus dynamics in humans: unstable directions and order parameters.

In: Springer Nature eBook

Weitere Ausg.: Printed edition: ISBN 9783030971779

Weitere Ausg.: Printed edition: ISBN 9783030971793

Weitere Ausg.: Printed edition: ISBN 9783030971809

Sprache: Englisch

DOI: 10.1007/978-3-030-97178-6

URL: https://doi.org/10.1007/978-3-030-97178-6

URL: Volltext  (URL des Erstveröffentlichers)

UID:

Umfang: 1 Online-Ressource(XIV, 355 Seiten)

ISBN: 9783030971786

Serie: Understanding complex systems

Inhalt: This book addresses the COVID-19 pandemic from a quantitative perspective based on mathematical models and methods largely used in nonlinear physics. It aims to study COVID-19 epidemics in countries and SARS-CoV-2 infections in individuals from the nonlinear physics perspective and to model explicitly COVID-19 data observed in countries and virus load data observed in COVID-19 patients. The first part of this book provides a short technical introduction into amplitude spaces given by eigenvalues, eigenvectors, and amplitudes.In the second part of the book, mathematical models of epidemiology are introduced such as the SIR and SEIR models and applied to describe COVID-19 epidemics in various countries around the world. In the third part of the book, virus dynamics models are considered and applied to infections in COVID-19 patients. This book is written for researchers, modellers, and graduate students in physics and medicine, epidemiology and virology, biology, applied mathematics, and computer sciences. This book identifies the relevant mechanisms behind past COVID-19 outbreaks and in doing so can help efforts to stop future COVID-19 outbreaks and other epidemic outbreaks. Likewise, this book points out the physics underlying SARS-CoV-2 infections in patients and in doing so supports a physics perspective to address human immune reactions to SARS-CoV-2 infections and similar virus infections.

Anmerkung: Chapter 1. Introduction -- Chapter 2. Nonlinear physics and synergetics -- Chapter 3. Epidemiological models and COVID-19 epidemics -- Chapter 4. Nonlinear physics of epidemics: part A -- Chapter 5. Nonlinear physics of epidemics: part B -- Chapter 6. Nonlinear physics of epidemics: part C -- Chapter 7. Model-based reproduction numbers -- Chapter 8. Modeling interventions -- Chapter 9. Models of virus dynamics -- Chapter 10. Virus dynamics in humans: unstable directions and order parameters.

Weitere Ausg.: ISBN 9783030971779

Weitere Ausg.: Erscheint auch als Druck-Ausgabe Frank, Till D. COVID-19 epidemiology and virus dynamics Cham, Switzerland : Springer, 2022 ISBN 9783030971779

Sprache: Englisch

Schlagwort(e): COVID-19 ; Pandemie ; Epidemiologie ; Nichtlineare Dynamik ; Mathematisches Modell

DOI: 10.1007/978-3-030-97178-6

URL: lizenzpflichtig

UID:

Umfang: 1 online resource (367 pages)

ISBN: 9783030971786

Serie: Understanding Complex Systems

Anmerkung: Intro -- Preface -- Contents -- 1 Introduction -- 1.1 COVID-19 Outbreaks and SARS-CoV-2 Infections and the Physics Behind Them -- 1.2 Epidemic Viral Infections -- 1.3 Virus Dynamics -- 1.4 Instabilities -- 1.5 Phase Transitions, Bifurcations, Unstable Eigenvectors, and Order Parameters -- 1.6 Religion and Physics -- References -- 2 Nonlinear Physics and Synergetics -- 2.1 State and Time -- 2.2 Structure -- 2.3 Fixed Points and Stability -- 2.4 Attractors and Repellors -- 2.5 Phase Transitions and Bifurcations -- 2.6 The Linear Domain: Basic Concepts -- 2.6.1 Linearization -- 2.6.2 Eigenvalues and Eigenvectors -- 2.6.3 Amplitudes, Amplitude Description, and Amplitude Space -- 2.7 Linear Domain Dynamics and Characterization of Fixed Points -- 2.8 Stable and Unstable Amplitudes and Eigenvectors, Order Parameters Amplitudes, and Order Parameters -- 2.9 The Linear and Nonlinear Domain: Amplitude Equations -- 2.9.1 Where We are and Where We Go Next -- 2.9.2 Method 1: Scalar Calculations -- 2.9.3 Method 2: Vector Calculations -- 2.9.4 Method 3: Matrix Calculations -- 2.10 Reduced Amplitude Spaces -- References -- 3 Epidemiological Models and COVID-19 Epidemics -- 3.1 Type of Models and Some Definitions -- 3.2 Effective Contact Rate, Rate Constant k0, and ``Force of Infection'' -- 3.3 Continuity Equations -- 3.4 Linear Terms and Their Coefficients -- 3.5 SIR Model -- 3.5.1 Without Demographic Terms -- 3.5.2 With Demographic Terms -- 3.6 SIR Models Describing COVID-19 Epidemics -- 3.6.1 SIR Model-Based COVID-19 Studies -- 3.6.2 COVID-19 Outbreaks in China and Italy 2020 -- 3.7 SEIR Model -- References -- 4 Nonlinear Physics of Epidemics: Part A -- 4.1 SIR-Type Models and 2D Autonomous Amplitude Descriptions -- 4.1.1 n-Dimensional Approach -- 4.1.2 Two-Dimensional Approach -- 4.2 SIR Model Without Demographic Terms -- 4.2.1 Eigenvalues and Eigenvectors. , 4.2.2 State Space and Amplitude Space -- 4.2.3 Stability Analysis -- 4.2.4 Special Case λ2=0 -- 4.2.5 Nonlinear Parts Gk: Scalar Calculation Method -- 4.2.6 SIR Model State Space and Amplitude Equations: Equivalence, SI Order Parameter, and Case λ2> -- 0 -- 4.2.7 Case λ2< -- 0 and the Impact of Nonlinear Terms -- 4.2.8 Fixed Points with Sst< -- N and Nonlinear Parts Gk -- 4.3 SIR Model with Demographic Terms -- 4.4 SIR-Type Models Revisited: 2D Autonomous Amplitude Descriptions -- 4.5 COVID-19 Outbreak in Italy 2020 and Its SI Order Parameter -- 4.5.1 Active Cases Within the SIR Model Interpretation by Fanelli and Piazza (2020) -- 4.5.2 Confirmed Cases and SIQR Modeling -- References -- 5 Nonlinear Physics of Epidemics: Part B -- 5.1 Grouping Compartment Variables into Two Classes -- 5.2 SEIR-Type Models -- 5.2.1 Latent Versus Incubation Period and SEIR-Type Models -- 5.2.2 SEIR-Type Models and 3D Autonomous Amplitude Descriptions -- 5.2.3 SEIR-Type Models as Staged-Progression or Age-Structured Models -- 5.3 Beyond SEIR-Type Models -- 5.3.1 r< -- n-Dimensional Approaches: Epidemic Models with r-Dimensional Autonomous Amplitude Descriptions -- 5.3.2 Examples -- 5.4 Eigenvalues and Eigenvectors Revisited: Explicit Approaches -- 5.4.1 Road Map: Asking and Solving Nonlinear Physics Questions -- 5.4.2 Case n -- 5.4.3 Case n=2 -- 5.5 Application: Stability Analysis of SEIR Models -- 5.5.1 Eigenvalues and Stability of Disease-Free States -- 5.5.2 EI Order Parameters of SEIR Models in E-I Subspaces -- 5.6 Biorthogonal Vectors of Amplitude Spaces: 2D, 3D, and Beyond -- 5.7 Applications and SEI Order Parameters -- 5.7.1 1β SEIR Model and Its 3D Autonomous Amplitude Description -- 5.7.2 2β SEIR Model and Its 3D Autonomous Amplitude Description -- 5.7.3 SEIR-Type Models: 3D Autonomous Amplitude Descriptions. , 5.8 COVID-19 Outbreak in Wuhan city 2020 and its SEI Order Parameter -- References -- 6 Nonlinear Physics of Epidemics: Part C -- 6.1 Higher-Dimensional Models and Non-autonomous Amplitude Equation Descriptions -- 6.1.1 Model Formulation and Decomposition of States -- 6.1.2 Non-autonomous Amplitude Equation Descriptions -- 6.1.3 Epidemic Outbreaks and Subsiding Epidemics -- 6.2 SIR and SEIR Models: Non-autonomous Amplitude Equation Descriptions -- 6.2.1 SIR Model: Trivial Case m=1 -- 6.2.2 1β and 2β SEIR Models and m=2 -- 6.2.3 SEIR-Type Models and Their Non-autonomous m=2 Amplitude Equation Descriptions -- 6.3 COVID-19 Outbreak in Wuhan City 2020 and Its EI Order Parameter -- 6.4 COVID-19 Outbreak in West Africa 2020 and Its EIA Order Parameter -- References -- 7 Model-Based Reproduction Numbers -- 7.1 Basic and Effective Reproduction Numbers -- 7.2 Case of a Single Infected Compartment -- 7.2.1 Heuristic Approach -- 7.2.2 SIR Model: Heuristic Approach -- 7.2.3 SIR Model: Towards a Next Generation Approach -- 7.2.4 Next Generation Time Grid -- 7.3 Two Infected Compartments -- 7.4 m Infected Compartments -- 7.4.1 Next Generation Approach -- 7.4.2 Theorems Involving Reproduction Numbers -- 7.5 Applications -- 7.5.1 SIR Model and 1β SEIR Model -- 7.5.2 2β SEIR Model and COVID-19 Outbreak in Wuhan City 2020 -- 7.5.3 SIR- and SEIR-Type Models and Beyond -- 7.5.4 Determining Critical Effective Contact Rates -- 7.5.5 COVID-19 Epidemic in Pakistan 2020 -- References -- 8 Modeling Interventions -- 8.1 Motivation -- 8.2 Types of Intervention Models -- 8.2.1 Overview -- 8.2.2 SIR-Type Models Used in Studies Examining the Impact of Interventions -- 8.2.3 Modeling COVID-19 Interventions Beyond SIR Models -- 8.3 Models with Analytical Solutions -- 8.3.1 SIR-Type Models -- 8.3.2 SEIR-Type Models -- 8.4 Three-Stage Models and the Bifurcation Scenario …. , 8.4.1 Bifurcation Scenario of Epidemic Waves -- 8.4.2 Bigger Picture: Dynamical Diseases and D1-Systems -- 8.4.3 Three-Stage Epidemic Waves -- 8.4.4 COVID-19 First-Waves of 2020 in Europe: Stabilization Bifurcations and the Sign Switching Phenomenon -- 8.4.5 First-Wave COVID-19 Epidemic in Thailand, 2020: EI Order Parameter and Its Remnant -- 8.5 Three-Stage Models and the Bifurcation Scenario in Higher Dimensions -- 8.6 Sequences of Stages in Amplitude Space -- 8.6.1 Semi-analytical Approach -- 8.6.2 Numerical Stage Analysis -- 8.7 Examples of Three-Stage COVID-19 Waves and 5D Order Parameters -- 8.7.1 First COVID-19 Wave of 2020 in the State of New York -- 8.7.2 First COVID-19 Wave of 2020 in Pakistan -- References -- 9 Models of Virus Dynamics -- 9.1 Coronaviruses -- 9.1.1 Classification -- 9.1.2 Possible SARS-CoV-2 Target Cells -- 9.1.3 Target Cells in SARS-CoV-2 Infections of the Human Lung -- 9.2 Models Overview -- 9.3 TIV Model -- 9.3.1 Model Formulation -- 9.3.2 Target Cell-Limited Models -- 9.3.3 Equivalence of TIV and SEIR Models -- 9.4 Viral Load Patterns, Infection Order Parameters … -- 9.5 TV Model -- 9.5.1 Model Derivation -- 9.5.2 Equivalence of TV and SIR Models -- 9.6 TIIV Model -- 9.7 Beyond Acute Virus Infections -- 9.8 Modeling Studies of SARS-CoV-2 Dynamics in COVID-19 Patients -- References -- 10 Virus Dynamics in Humans: Unstable Directions and Order Parameters -- 10.1 Analysis of the TIV Model -- 10.1.1 3D Approach: Original Model -- 10.1.2 3D Approach: Scaled Model -- 10.1.3 2D Approach -- 10.1.4 2D Versus 3D Approach -- 10.2 TIV Model and Viral Load in a Sample of COVID-19 Patients -- 10.2.1 3D Approach: TIV Order Parameters of COVID-19 Patients -- 10.2.2 Illustrations of λmax Increase of Viral Load and k2 Disease Decline in COVID-19 Patients -- 10.2.3 2D Approach: Initiation of Disease Decline by Self-induced Bifurcations. , 10.3 Initial-Stage Disease and Disease Decline: Nonlinear Physics Perspective -- 10.4 Analysis of the TIIV Model -- 10.4.1 Stability Analysis -- 10.4.2 TIIV Model Amplitude Equations -- 10.4.3 The TIIV Unstable Eigenvector and Order Parameter -- 10.4.4 Dominant Role of the TIIV Order Parameter During Initial Infection and Disease Decline -- 10.5 TIIV Model and Viral Load in a Sample of COVID-19 Patients -- 10.5.1 Main Results Illustrated for Four Patients -- 10.5.2 Eigenvalues, Doubling Times, and Peak Viral Loads -- 10.5.3 λmax Increase of Viral Load -- 10.5.4 Peak Viral Load Vmax Determined by Order Parameter Amplitude A4,max -- 10.5.5 Latent Stage Determined by Order Parameter -- 10.6 Other Models -- 10.6.1 TIIVV Model -- 10.6.2 TV Model -- 10.7 Complex-Valued Eigenvalues λ of the TIIV Model and Analytical Expressions for λ -- References -- Index.

Weitere Ausg.: Print version: Frank, Till D. COVID-19 Epidemiology and Virus Dynamics Cham : Springer International Publishing AG,c2022 ISBN 97830309717799

Sprache: Englisch