Note: Intro -- Preface -- Acknowledgements -- Contents -- 1 Cell-Based, Continuum and Hybrid Models of Tissue Dynamics -- 1.1 Introduction -- 1.1.1 Dictyostelium Discoideum as a Model System -- 1.2 Actin Dynamics -- 1.2.1 The Basic Biochemistry -- 1.2.2 Regulation of Polymerization, Filament Severing and Branching -- 1.3 A Mathematical Model for In Vitro Filament Dynamics -- 1.3.1 The Initial Evolution of the Distribution -- 1.3.2 The Long-Time Evolution of the Distribution -- 1.4 Stochastic Analysis of Actin Dynamics -- 1.4.1 The Mathematical Description of Reaction Networks -- 1.4.2 The Stochastic Simulation Algorithm -- 1.4.3 Actin Wave Dynamics in Dictyostelium Discoideum -- 1.5 Signal Transduction, Direction Sensing and Relay -- 1.5.1 The Model for Signal Transduction and Relay -- 1.5.2 The Dynamics Under Imposed and Self-Generated Stimuli -- 1.5.3 The Reaction-Diffusion Equations for Early Aggregation -- 1.6 Multicellular Problems -- 1.6.1 The Mechanics of a Single Cell -- 1.6.2 The Multicell Problem -- 1.6.3 Who Does the Work in the Slug? -- 1.7 Conclusion -- Appendix: Singular Perturbation Reduction -- 1.8 Glossary -- References -- 2 The Diffusion Limit of Transport Equations in Biology -- 2.1 Introduction to Movement Models -- 2.1.1 Measurements -- 2.1.2 Random Walk on a Grid -- 2.1.3 A Continuous Random Walk -- 2.1.4 Outline of This Manuscript -- 2.2 Correlated Random Walk in One Dimension -- 2.2.1 The Goldstein-Kac Model in 1-D -- 2.2.2 Boundary Conditions -- 2.2.3 Abstract Formulation -- 2.2.4 Explicit Solution Using Bessel Functions -- 2.2.5 Correlated Random Walk Models for Chemotaxis -- 2.2.6 Reaction Random Walk Systems -- 2.2.7 Correlated Random Walk Models for Swarming -- 2.3 Transport Equations -- 2.3.1 The Mathematical Set-Up -- 2.3.2 The Turning Operator -- 2.3.3 Normal Operators -- 2.3.4 Important Examples. , 2.3.4.1 Example 1: Pearson Walk -- 2.3.4.2 Example 2: Movement on Fibre Networks -- 2.3.4.3 Example 3 (Homework) Symmetric Kernels -- 2.3.5 Main Spectral Result -- 2.3.6 Existence and Uniqueness -- 2.4 The Formal Diffusion Limit -- 2.4.1 Scalings -- 2.4.2 The Formal Diffusion Limit -- 2.4.2.1 Example: Pearson Walk -- 2.4.3 Ellipticity of the Diffusion Tensor -- 2.4.4 Graphical Representations of the Diffusion Tensor -- 2.4.4.1 An Anisotropic Random Walk -- 2.4.5 Anisotropic vs. Isotropic Diffusion -- 2.4.5.1 Examples -- 2.4.6 Chemotaxis -- 2.4.6.1 Other Cases -- 2.4.7 Persistence -- 2.4.7.1 Example -- 2.4.8 Summary and Conclusions -- 2.5 Further Reading for Transport Equations in Oriented Habitats -- References -- 3 Mathematical Models of the Interaction of Cells and Cell Aggregates with the Extracellular Matrix -- 3.1 Biological Relevance of Cell-ECM Interaction -- 3.2 A Model of Cell-ECM Adhesion -- 3.2.1 Evolution of the Distribution of Adhesion Bonds -- 3.2.2 The Quasi-Stationary Limit -- 3.2.3 Examples of Interaction Forces -- 3.3 Modelling the Influence of the Nucleus -- 3.3.1 Modelling the Deformation of the Elastic Nucleus -- 3.3.2 Modelling the Cell Traction Force -- 3.3.3 A Penetration Criterium from an Energy Balance -- 3.4 Cell Migration by Cellular Potts Models -- 3.4.1 Compartmentalized Cellular Potts Models -- 3.4.2 Cell Migration in a 3D Microchannel Device -- 3.4.3 Cell Migration in Two-Dimensional Matrix Microtracks -- 3.4.3.1 MMP-Independent Cell Migration -- 3.4.3.2 MMP-Dependent Cell Migration -- 3.4.4 Cell Migration in a Three-Dimensional Fibrous Scaffold -- 3.5 Multicomponent and Multiphase Modelling -- 3.5.1 Mass Balance Equations -- 3.5.2 Force Balance Equations -- 3.5.3 Model Reduction for the Saturated Case -- 3.6 Linking Multiphase Models to the Result of Microscopic Models -- 3.6.1 Cell Motility. , 3.6.2 Compartmentalization and Invasion -- 3.6.3 A Two-Population Case -- 3.6.4 MMP-Induced Invasion -- 3.7 Chemotaxis as an Active Stress -- 3.8 Perspectives on Mechanosensing and Mechanotransduction -- References -- 4 Mathematical Modeling of Morphogenesis in Living Materials -- 4.1 Introduction -- 4.2 An Historical Overview of Morphogenetic Theories -- 4.2.1 Epigenesis Versus Pre-formationism: From Ancient Times to the Advent of Microscopy -- 4.2.2 The Birth of Modern Embryology: Evolutionary Theories and Mechanical Causation -- 4.2.3 The Contemporary Approaches to Morphogenesis -- 4.2.3.1 The First Mathematical Approach on Growth and Form -- 4.2.3.2 The Chemical Bases of Morphogenesis -- 4.2.3.3 The New Course of Genetics and the Return of an Ancient Dichotomy -- 4.2.4 The Open Quest for the Chemo-Mechanical Cues of Morphogenesis -- 4.3 A Continuous Chemo-Mechanical Theory of Morphogenesis -- 4.3.1 Basic Kinematic Notions -- 4.3.1.1 Balance of Mass -- 4.3.2 Balance of Linear and Angular Momentum -- 4.3.3 Balance of Internal Energy and Entropy Inequality -- 4.3.4 Balance Laws for Interfacial Morphogenetic Processes -- 4.4 Free-Boundary Morphogenesis for Fluid-Like Living Matter -- 4.4.1 Definition of the Chemotactic Model in a Hele Shaw Cell -- 4.4.2 Dimensionless Form of the Governing Equations -- 4.4.3 Traveling Wave Solution -- 4.4.4 Linear Stability Analysis -- 4.4.5 Pattern Formation in the Nonlinear Regime -- 4.5 Growth, Remodelling and Morphogenesis for Soft Elastic Matter -- 4.5.1 An Interpretation of Morphogenesis in Solids Using the Theory of Configurational Forces -- 4.5.2 Mathematical Theory of Volumetric Growth in Soft Solids -- 4.5.3 Constitutive Assumptions and Evolution Laws for Growth and Remodelling -- 4.5.4 Morpho-Elasticity of Growing Living Matter -- 4.5.4.1 Basic Solution of the Quasi-Static Elastic Problem. , 4.5.4.2 Method of Incremental Deformations Superposed on Finite Deformations -- 4.5.4.3 Summary of the Incremental Boundary Value Problem -- 4.6 Pattern Formation in a Growing Bilayer Under Lateral Constraint -- 4.6.1 Definition of the Model and Basic Morpho-Elastic Solution -- 4.6.2 Linear Stability Analysis -- 4.6.2.1 Solution Using an Elastic Stream Functions -- 4.6.2.2 Solution Using the Stroh Formalism -- 4.6.2.3 Theoretical Results: Critical Growth Threshold and Pattern Selection -- 4.6.2.4 Numerical Results: Post-buckling Behavior -- 4.7 Concluding Remarks -- References -- 5 Multiscale Computational Modelling and Analysis of Cancer Invasion -- 5.1 Introduction -- 5.2 A Basic Tissue-Scale Cancer Invasion Model -- 5.2.1 Model Formulation -- 5.2.2 Specific Choices for Simulations in Two Spatial Dimensions -- 5.2.3 The Non-local Model for a Single Cancer Cell Population -- 5.2.3.1 Constant Cell-Cell Adhesion Coefficient -- 5.2.3.2 Time-Dependent Cell-Cell Adhesion Coefficient -- 5.2.4 The Non-local Model with Two Cancer Cell Sub-Populations -- 5.2.4.1 The Effect of ECM Remodelling and the Influence of the Cross-Adhesion Coefficient -- 5.3 Macroscopic Spatio-Temporal-Structural Modelling Approach with Application to the uPA System -- 5.3.1 General Spatio-Temporal-Structured Cell Population Modelling Framework -- 5.3.2 Cell Population Dynamics -- 5.3.2.1 Source -- 5.3.2.2 Spatial Flux -- 5.3.2.3 Structural Flux -- 5.3.3 Extracellular Matrix -- 5.3.4 Molecular Species -- 5.3.5 Summary of the General Spatio-Temporal-Structural Model for Cell Migration -- 5.3.6 Application of the Structured-Population Approach to a Model of Cancer Invasion Based on the uPA System -- 5.4 Multiscale Moving Boundary Modelling Framework for Tumour Invasion -- 5.4.1 Modelling Framework Set-Up: The Macroscopic Dynamics and Top-Down Link. , 5.4.2 Exploring the MDEs Micro-Dynamics -- 5.4.2.1 The uPA Micro-Dynamics on Each Micro-Domain in Hε -- 5.4.3 The Macroscale Boundary Movement Induced by the Invasive Edge MDE Micro-Dynamics -- 5.4.4 Multiscale Computational Simulation Results -- 5.5 Concluding Remarks -- References.

Note: Intro -- Preface -- Contents -- Modelling, Simulations, and Social Impact of Evolutionary Virus Pandemics -- 1 Aims and Plan of the Chapter -- 2 On the Contents of the Edited Book -- 3 Reasonings on Research Perspectives -- References -- Understanding COVID-19 Epidemics: A Multi-Scale ModelingApproach -- 1 Introduction -- 2 Mathematical Modeling Applied to Infectious Diseases: COVID-19 as a Case Study -- 2.1 The SIR and SHAR Models -- 2.2 The SHARUCD Modeling Framework -- 2.3 Modeling the Implementation of Control Measures -- 2.4 The Refined SHARUCD Model -- 2.4.1 Further Refinements: Detection Rate and Import -- 3 KTAP Modeling Framework -- 3.1 Modeling Contagion, Progression, and Recovery -- 3.2 Application of the KTAP Model to Selected Case Studies -- 3.2.1 Effect of Lockdown Measures and Restrictions Lifting -- 3.2.2 Effect of Heterogeneity -- 4 Discussion -- References -- Kinetic Modelling of Epidemic Dynamics: Social Contacts, Control with Uncertain Data, and Multiscale Spatial Dynamics -- 1 Introduction -- 2 Kinetic Modelling of Social Heterogeneity in Epidemic Dynamics -- 2.1 Modelling Contact Heterogeneity -- 2.1.1 Kinetic Model for Contact Formation -- 2.1.2 Quasi-Invariant Scaling and Steady States -- 2.1.3 The Macroscopic Social-SIR Dynamics -- 2.1.4 A Social-SIR Model with Saturated Incidence Rate -- 2.1.5 Extrapolation of the Shape of the Incidence Rate from Data -- 2.2 The Interplay Between Economy and the Pandemic -- 2.2.1 Wealth Exchanges in Epidemic Modelling -- 2.2.2 Fokker-Planck Scaling and Steady States -- 2.2.3 The Formation of Bimodal Wealth Distributions -- 2.2.4 The Increase of Wealth Inequalities -- 3 Social Control and Data Uncertainty -- 3.1 Control of Socially Structured Models -- 3.1.1 Optimal Control Formulation -- 3.1.2 Feedback Controlled Compartmental Models. , 3.1.3 Containment in Homogeneous Social Mixing Dynamics -- 3.2 Dealing with Data Uncertainty -- 3.2.1 Feedback Controlled and Socially Structured Models with Uncertain Inputs -- 3.2.2 Application to the COVID-19 Outbreak -- 4 Multiscale Transport Models -- 4.1 Spatial Dynamics on Networks -- 4.1.1 1D Hyperbolic Compartmental Model -- 4.1.2 Macroscopic Formulation and Diffusion Limit -- 4.1.3 Extension to Multi-Compartmental Modelling -- 4.1.4 Network Modelling -- 4.1.5 Effect of Spatially Heterogeneous Environments in Hyperbolic and Parabolic Configuration -- 4.1.6 Application to the Emergence of COVID-19 in Italy -- 4.2 Realistic Geographical Settings -- 4.2.1 2D Kinetic Transport Model -- 4.2.2 Macroscopic Formulation and Diffusion Limit -- 4.2.3 Extension to Multi-Compartmental Modelling -- 4.2.4 Application to the Spatial Spread of COVID-19 in Italy in Emilia-Romagna and Lombardy Region -- 5 Concluding Remarks and Research Perspectives -- 5.1 Data sources -- References -- The COVID-19 Pandemic Evolution in Hawai`i and New Jersey: A Lesson on Infection Transmissibility and the Role of HumanBehavior -- 1 Introduction -- 2 Mathematical Models -- 2.1 Agent-Based Models -- 2.1.1 COVID-19 Agent-Based Simulator (Covasim) -- 2.2 Compartmental SEIR Models and Variants -- 2.3 Comparison of Agent-Based and Compartmental Models -- 3 Archipelagos and Islands -- 3.1 March 2020-June 2021 -- 3.1.1 CM Model Fit from March 06, 2020 to January 15, 2021 -- 3.1.2 Comparing CM and ABM Models -- 3.2 July 2021-September 2021 -- 3.3 Discussion -- 4 The Pandemic Waves in New Jersey -- 4.1 Comparing New Jersey to the US -- 4.2 Spatial and Temporal Patterns in COVID-19 Cases in New Jersey -- 4.3 Sociodemographic Variables -- 4.4 Discussion -- 5 The Use of Compartmental Models in New Jersey -- 5.1 Time-Evolution of the Basic Reproduction Number. , 5.2 Infected Confirmed Cases, Hospitalizations, and Deaths -- 5.3 Discussion -- 6 Conclusion -- References -- A Novel Point Process Model for COVID-19: Multivariate Recursive Hawkes Process -- 1 Introduction -- 1.1 Hawkes Point Process Modeling of Infectious Diseases -- 1.2 Multivariate Hawkes Processes -- 1.3 Recursive Hawkes Processes -- 1.4 Outline -- 2 Theoretical Properties of Temporal Multivariate Recursive Hawkes Models -- 2.1 Existence -- 2.2 Mean -- 2.3 Variance -- 3 Parameter Fitting and Simulation Algorithms -- 3.1 Parameter Fitting Algorithms -- 3.1.1 Parametric (or Semi-parametric) Estimation -- 3.1.2 Temporal Version of Parameter Fitting Algorithms -- 3.2 Simulation Algorithm -- 4 Reconstruct Multivariate Point Process from Data with Imprecise Time -- 4.1 Time Reconstruction -- 4.2 Category Index Reconstruction -- 5 Numerical Experiments and Results -- 5.1 Synthetic Data Sets -- 5.1.1 Comparison Between Parametric Fitting and Non-parametric Fitting -- 5.1.2 Verification of the Parameter Fitting Algorithm -- 5.1.3 Experiments About Data Sets with Imprecise Time -- 5.2 Experiments on Real COVID-19 Data -- 5.2.1 Model Validation -- 5.2.2 Prediction Based on MRHP and Historical Information -- 6 Conclusion -- References -- Multiscale Aspects of Virus Dynamics -- 1 Introduction -- 1.1 On the Biology of the Virus -- 1.2 Modeling the Complexity of COVID-19 -- 2 Epistemic and Empirical Uncertainties in Compartmental and Individual-Based Models -- 2.1 SIR Model -- 2.2 Individual-Based Interpretation of λ -- 2.3 An Example of Modified SIR Model -- 2.4 Individuals Behind the Modified SIR Model -- 2.5 Time-Discretization -- 3 The Individual-Based Model of FlaLaFauciRiva -- 3.1 A Formula for the Parameter λ of Compartmental Models -- 3.2 Analysis of the Fluctuations -- 3.3 Simulations -- 3.4 Presence of Immunized Population and Virus Variants. , Appendix -- References -- Productivity in Times of Covid-19: An Agent-Based Model Approach -- 1 Introduction -- 2 Model -- 3 Mean Field Approximation -- 4 Setting the Model Functions -- 5 Simulations -- 6 Conclusion -- References -- Transmission Dynamics and Quarantine Control of COVID-19 in Cluster Community -- 1 Introduction -- 2 Mathematical Modeling -- 2.1 Stage 1: SEIR-Type Model Without Quarantine -- 2.2 Stage 2: Transmission-Quarantine (TQ) Model -- 3 Analytic Results and Case Study for Emerging Stage -- 3.1 Analytic Results -- 3.2 A Real World Case Study for Stage 1 -- 4 Case Study and Sensitivity Analysis for Quarantine Stage -- 4.1 A Real World Study for Stage 2 -- 4.2 Sensitivity Analysis -- 5 Discussion -- Appendix: Proofs of Theorems -- References -- A 2D Kinetic Model for Crowd Dynamics with Disease Contagion -- 1 Introduction -- 2 A Simplified Two-Dimensional Kinetic Model -- 3 Discretization in Space and Time -- 4 Numerical Results -- 4.1 Tests with v = 0 -- 4.2 Tests with Prescribed Walking Velocity -- 5 A More Complex 2D Kinetic Model -- 6 Conclusions -- References -- Multiscale Derivation of a Time-Dependent SEIRD Reaction-Diffusion System for COVID-19 -- 1 Introduction -- 2 Phenomenological Modeling of Diffusion Population Dynamics -- 3 From Kinetic Theory Model to SEIRD Reaction-Diffusion System -- 3.1 Kinetic Theory Model -- 3.2 Micro-Macro Formulation -- 4 Numerical Method -- 4.1 Semi-Implicit Time Discretization -- 4.2 Fully Discrete Asymptotic Preserving Numerical Scheme in 1D -- 4.3 Boundary Conditions -- 5 Numerical Results -- 5.1 Test 1: Asymptotic Preserving Numerical Scheme Property -- 5.2 Test 2: Diffusion Effect -- 5.3 Test 3: Role of the Transmission Function -- 6 Conclusion and Perspectives -- References.

Note: Intro -- Copyright -- Table of Contents -- Preface -- Introduction -- Index.