00826nam0-2200289 --450 991035975910332120200109155115.0978-88-339-3223-120200109d2019----kmuy0itay5050 baitaIT 001yy<<La >>nuova violenza illustrataNanni Balestrinia cura di Andrea CortellessaTorinoBollati Boringhieri2019280 p.21 cmVariantiViolenza858.91421itaBalestrini,Nanni<1935-2019>769819Cortellessa,AndreaITUNINAREICATUNIMARCBK9910359759103321IX E 3562460/2019FSPBCFSPBCNuova violenza illustrata1569903UNINA00842oam 2200193z- 450 99638927310331620200818223229.0(CKB)4940000000095797(EEBO)2273358633(EXLCZ)99494000000009579720191209c1632uuuu -u- -engCorydon aufuga. Vel potius iepoxenodoxia pastoritia. Excipiendo reverendo patri ac Domino, Iohanni episcopo roffensi, per binos scholae Hadleianae alumnos recitata April 90. 1632°..EnglandImpensis R. MilbovrnHawkins William1019134BOOK996389273103316Corydon aufuga. Vel potius iepoxenodoxia pastoritia. Excipiendo reverendo patri ac Domino, Iohanni episcopo roffensi, per binos scholae Hadleianae alumnos recitata April 90. 1632°.2421962UNISA09848nam 2200481 450 99646684110331620231110212947.09783030971786(electronic bk.)9783030971779(MiAaPQ)EBC6943652(Au-PeEL)EBL6943652(CKB)21448750900041(PPN)261518992(EXLCZ)992144875090004120221113d2022 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierCOVID-19 epidemiology and virus dynamics nonlinear physics and mathematical modeling /Till D. FrankCham, Switzerland :Springer,[2022]©20221 online resource (367 pages)Understanding Complex Systems Print version: Frank, Till D. COVID-19 Epidemiology and Virus Dynamics Cham : Springer International Publishing AG,c2022 97830309717799 Includes bibliographical references and index.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&gt -- 0 -- 4.2.7 Case λ2&lt -- 0 and the Impact of Nonlinear Terms -- 4.2.8 Fixed Points with Sst&lt -- 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&lt -- 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.Understanding Complex Systems Mathematical modelsMathematical models.614.592414Frank Till Daniel750689MiAaPQMiAaPQMiAaPQ996466841103316COVID-19 epidemiology and virus dynamics2973137UNISA