Mathematics of Public Health : Mathematical Modelling from the Next Generation

• Autore: David Jummy
• Pubblicazione: Cham : , : Springer International Publishing AG, , 2023; ©2023
• Edizione: 1st ed.
• Descrizione fisica: 1 online resource (325 pages)
• Disciplina: 614.4015118
• Altri autori: WuJianhong
• Nota di contenuto: Intro -- Preface -- Contents -- 1 Mathematical Models: Perspectives of Mathematical Modelers and Public Health Professionals -- 1.1 Natural History of Disease in Humans -- 1.2 Introduction to Mathematical Epidemiology -- 1.3 Model Formulation and Examples of Some Communicable Disease Models -- 1.3.1 Simple SIR Compartmental Models -- 1.3.2 Simple Endemic Models -- 1.3.3 Agent-Based Models -- 1.3.4 Network Models -- 1.3.5 Machine Learning Models -- 1.3.5.1 Estimating Parameters -- 1.3.5.2 Estimating Hidden States -- 1.4 Qualitative Analysis of Selected Models -- 1.4.1 Epidemic Model -- 1.4.2 Endemic Model -- 1.4.3 Network Model -- 1.5 Quantitative Analysis -- 1.6 Review of Mathematical Models of Selected Communicable Diseases and Their Impacts on Policy- and Decision-Making -- 1.6.1 SARS 2003 Pandemic Models -- 1.6.2 Pandemic Influenza Models -- 1.6.3 SARS-CoV-2 Pandemic Models -- 1.6.4 HIV Models -- 1.6.5 HCV Models -- 1.7 Model Algorithms for a Simple SIR Model -- 1.7.1 Python Code -- 1.7.2 Julia Code -- 1.7.3 R Code -- 1.7.4 MATLAB Code -- 1.8 Human Epidemiology Data, Model Fitting, and Parameter Estimation -- 1.9 Conclusion -- References -- 2 Discovering First Principle of Behavioural Change in Disease Transmission Dynamics by Deep Learning -- 2.1 Introduction -- 2.2 Expert-Based Behavioural Change Transmission Dynamics Models -- 2.2.1 Calculation of the Final Epidemic Size -- 2.2.2 Applications to the Ontario's First COVID-19 Pandemic Wave -- 2.3 Two-Step Recovering-Explaining Framework -- 2.3.1 Universal Differential Equations -- 2.3.2 Data-Driven Methods or Equation-Searching Methods -- 2.3.2.1 Symbolic Regression -- 2.3.2.2 Sparse Identification of Nonlinear Dynamics (SINDy) -- 2.3.3 Two-Step Recovering-Explaining Methods -- 2.4 Deep Learning-Based Behavioural Change Transmission Dynamics Models -- 2.4.1 The Behavioural Change Laws. ; 2.5 Discussions and Conclusions -- References -- 3 Understanding Epidemic Multi-wave Patterns via Machine Learning Clustering and the Epidemic Renormalization Group -- 3.1 Introduction -- 3.2 Renormalization Group Epidemiology: From eRG to CeRG -- 3.2.1 The Single-Wave eRG Approach -- 3.2.2 The Multi-wave CeRG Approach -- 3.3 A Machine Learning Approach to the Wave Pattern -- 3.3.1 The Status of Variants -- 3.3.2 Method -- 3.3.2.1 Cluster Algorithm -- 3.3.2.2 Emerging Variants as Persistent Time-Ordered Cluster Chains -- 3.3.3 Application to COVID-19 Data -- 3.4 An Epidemiological Theory of Variants: The MeRG Framework -- 3.4.1 The Model -- 3.4.2 Flow Among Variants: Fixed Points and (Ir)relevant Operators -- 3.4.3 Connecting Variant Dynamics to the CeRG -- 3.4.4 Fitting the Real Data -- 3.5 Conclusion -- References -- 4 Contact Matrices in Compartmental Disease Transmission Models -- 4.1 Introduction -- 4.2 Motivating Example -- 4.3 Defining Contact Matrices -- 4.3.1 What Is a Contact? -- 4.3.2 Sources of Contact Data -- 4.3.3 Assumptions and Parametric Forms -- 4.3.4 Example -- 4.4 Properties of Contact Matrices -- 4.4.1 Balancing Contact Matrices -- 4.4.2 Intrinsic Connectivity -- 4.4.3 Example -- 4.5 Restratifying Contact Matrices -- 4.5.1 Intuition and Equations for Restratification -- 4.5.2 Example -- 4.6 Mobility in Contact Matrices -- 4.6.1 Mobility Data and Mobility Matrices -- 4.6.2 Contact Matrices from Mobility Matrices -- 4.6.3 Integrating Age Mixing and Mobility Data in Contact Matrices -- 4.6.4 Example -- References -- 5 An Optimal Control Approach for Public Health Interventions on an Epidemic-Viral Model in Deterministic and Stochastic Environments -- 5.1 Introduction -- 5.1.1 A Fast Time Scale Viral Model -- 5.1.2 SIQR Epidemic Model with a Coupled Viral Model -- 5.1.3 Qualitative Analysis of the Coupled Model. ; 5.2 Optimal Control Analysis -- 5.2.1 Investigation of the Deterministic Optimal Control -- 5.2.2 Investigation of the Stochastic Optimal Control -- 5.3 Numerical Simulations -- 5.4 Conclusion -- References -- 6 Modeling Airborne Disease Dynamics: Progress and Questions -- 6.1 Introduction -- 6.2 Viral Matter in an Infectious Individual -- 6.3 Aerosol Size Distribution in Human Exhalations -- 6.4 Airborne Transmission of Aerosols -- 6.5 Transmission Through Fomites -- 6.6 Infection Probability of a Susceptible -- 6.7 Probability Distribution for Number of Secondary Infections Z -- 6.8 Conclusion -- References -- 7 Modeling Mutation-Driven Emergence of Drug-Resistance: A Case Study of SARS-CoV-2 -- 7.1 Introduction -- 7.2 Methods -- 7.2.1 Model Structure -- 7.2.2 Model Equations -- 7.2.3 Reproduction Number -- 7.3 Results -- 7.3.1 Baseline Scenario -- 7.3.2 Waning Immunity and Reinfection -- 7.4 Discussion -- References -- 8 A Categorical Framework for Modeling with Stock and Flow Diagrams -- 8.1 Introduction -- 8.2 The Syntax of Stock-Flow Diagrams -- 8.3 The Semantics of Stock-Flow Diagrams -- 8.3.1 ODEs (Ordinary Differential Equations) -- 8.3.2 Causal Loop Diagrams -- 8.3.3 System Structure Diagrams -- 8.4 Composing Open Stock-Flow Diagrams -- 8.5 Stratifying Typed System Structure Diagrams -- 8.6 ModelCollab: A Graphical Real-Time Collaborative Compositional Modeling Tool -- 8.7 Conclusion -- References -- 9 Agent-Based Modeling and Its Trade-Offs: An Introduction and Examples -- 9.1 Introduction -- 9.2 Characteristics of Agent-Based Models -- 9.2.1 Parameters -- 9.2.2 State, Actions, and Rules -- 9.2.3 Environment -- 9.2.4 Outputs and Emergent Behavior -- 9.2.5 Stochastics -- 9.2.6 Interventions -- 9.3 Example: Chickenpox -- 9.3.1 Chickenpox and Shingles -- 9.3.2 Model Scope -- 9.3.3 Statecharts -- 9.3.4 Model Fit -- 9.3.5 Costs and QALYs. ; 9.3.6 Suitability of ABM -- 9.3.7 Choice of AnyLogic as a Tool -- 9.4 Example: Pertussis -- 9.4.1 Pertussis -- 9.4.2 Model Scope -- 9.4.3 Model Structure -- 9.4.4 Model Fit -- 9.4.5 Scenarios -- 9.4.6 Suitability of ABM -- 9.5 Trade-Offs Between ABMs and Aggregate Models -- 9.6 Summary -- References -- 10 Mathematical Assessment of the Role of Interventions Against SARS-CoV-2 -- 10.1 Introduction -- 10.2 Formulation of Vaccination Model for COVID-19 -- 10.2.1 Data Fitting and Parameter Estimation -- 10.2.2 Basic Qualitative Properties -- 10.3 Existence and Asymptotic Stability of Equilibria -- 10.3.1 Disease-Free Equilibrium -- 10.3.1.1 Local Asymptotic Stability of DFE -- 10.3.1.2 Existence of Backward Bifurcation -- 10.3.1.3 Global Asymptotic Stability of DFE: Special Cases -- 10.3.2 Existence and Stability of Endemic Equilibria: Special Case -- 10.3.2.1 Existence -- 10.3.2.2 Local Asymptotic Stability -- 10.3.3 Vaccine-Induced Herd Immunity Threshold -- 10.3.4 Global Parameter Sensitivity Analysis -- 10.4 Numerical Simulations -- 10.4.1 Effect of Masking as a Singular Control and Mitigation Intervention -- 10.4.2 Assessing the Combined Impact of Vaccination and Masks on Herd Immunity Threshold -- 10.4.3 Assessing the Combined Impact of Vaccination and Masks on Daily New Cases -- 10.5 Discussion and Conclusions -- Appendix 1: Proof of Theorem 3 -- Computation of Left and Right Eigenvectors of Jβp* -- Computation of Backward Bifurcation Coefficients, a and b -- Appendix 2: Proof of Theorem 4 -- Appendix 3: Proof of Theorem 5 -- Proof of Positive Invariance and Attractivity of Ω** -- Next-Generation Matrices for the Second Special Case of the Model -- Proof of Theorem 5 -- Appendix 4: Proof of Theorem 7 -- Case 1: θ= 0 -- Case 2: θ≠0 -- References -- 11 Long-Term Dynamics of COVID-19 in a Multi-strain Model -- 11.1 Introduction -- 11.2 Methodology. ; 11.2.1 Model Description -- 11.2.2 Parameter Estimation -- 11.2.3 Data Sources -- 11.3 COVID-19 Long-Term Scenarios Modelling -- 11.4 Results -- 11.5 Discussion -- 11.6 Conclusion -- 11.7 Supplementary Information -- References -- Correction to: Contact Matrices in Compartmental Disease Transmission Models.
• Titolo autorizzato: Mathematics of Public Health
• ISBN: 3-031-40805-5
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910799203303321
• Lo trovi qui: Univ. Federico II
• Serie: Fields Institute Communications Series