Epidemics: Models and Data Using R

Description

This book is designed to be a practical study in infectious disease dynamics. It offers an easy-to-follow implementation and analysis of mathematical epidemiology. It focuses on recent case studies in order to explore various conceptual, mathematical, and statistical issues. The dynamics of infectious diseases shows a wide diversity of pattern. Some have locally persistent chains-of-transmission, others persist spatially in consumer-resource metapopulations. Some infections are prevalent among the young, some among the old and some are age-invariant. Temporally, some diseases have little variation in prevalence, some have predictable seasonal shifts and others exhibit violent epidemics that may be regular or irregular in their timing. Models and ‘models-with-data’ have proved invaluable for understanding and predicting this diversity, and thence help improve intervention and control. Using mathematical models to understand infectious disease, dynamics has a very rich history in epidemiology. The field has seen broad expansions of theories as well as a surge in real-life application of mathematics to dynamics and control of infectious disease. The chapters of Epidemics: Models and Data Using R have been organized as follows: chapters 1-10 is a mix and match of models, data and statistics pertaining to local disease dynamics; chapters 11-13 pertains to spatial and spatiotemporal dynamics; chapter 14 highlights similarities between the dynamics of infectious disease and parasitoid-host dynamics; Finally, chapters 15 and 16 overview additional statistical methodology useful in studies of infectious disease dynamics. This book can be used as a guide for working with data, models and ‘models-and-data’ to understand epidemics and infectious disease dynamics in space and time. All the code and data sets are distributed in the epimdr2 R package to facilitate the hands-on philosophy of the text. Preface Contents 1 Introduction 1.1 Preamble 1.2 In-Host Persistence 1.3 Patterns of Endemicity 1.4 R 1.5 Resources Part I Time 2 SIR 2.1 Introduction 2.2 The SIR Model 2.3 Numerical Integration of the SIR Model 2.4 Final Epidemic Size 2.5 The Open Epidemic 2.6 Phase Analysis 2.7 Stability and Periodicity 2.8 Heterogeneities 2.9 Advanced: More Realistic Infectious Periods 2.10 An SIR shinyApp 3 R0 3.1 Primacy of R0 3.2 Rates and Probabilities 3.3 Estimating R0 from a Simple Epidemic 3.4 The Chain-Binomial Model 3.5 Stochastic Simulation 3.6 Further Examples 3.7 R0 from S(E)IR Flows 3.8 Other Rules of Thumb 3.9 Advanced: The Next-Generation Matrix 3.10 SEIHFR 3.11 A Next-Generation R0 Function 3.12 A Two-Strain shinyApp 4 FoI and Age-Dependence 4.1 Force of Infection 4.2 Burden of Disease 4.3 WAIFW 4.4 A RAS Model 4.5 Virgin Epidemics 4.6 Vaccination by Age-Dependent Risk 4.7 Projecting Host Age-Structure 5 The Catalytic Model 5.1 Immune Memory 5.2 The Catalytic Model 5.3 More Flexible φ-Functions 5.4 A Log-Spline Model 5.5 Rubella 6 Seasonality 6.1 Environmental Drivers 6.2 The Seasonally Forced SEIR Model 6.3 Seasonality in β 6.4 Bifurcation Analysis 6.5 Stroboscopic Section 6.6 Susceptible Recruitment 6.7 A Forced SEIR shinyApp 6.8 A Jacobian Function 7 Time Series Analysis 7.1 Taxonomy of Methods 7.2 Time Domain: ACF and ARMA 7.3 ARMA 7.4 Frequency Domain 7.5 Time/Frequency Hybrids: Wavelets 7.6 Measles in London 7.7 Project Tycho 7.8 Lomb Periodogram: Whooping Cough 7.9 Triennial Cycles: Philadelphia Measles 7.10 Wavelet Reconstruction and Wavelet Filter: Diphtheria 7.11 Advanced: FFT and Reconstruction 8 TSIR 8.1 Estimating Parameters in Dynamic Models 8.2 Stochastic Variability 8.3 Estimation Using the TSIR 8.4 Inference (Hypothetical) 8.5 Susceptible Reconstruction 8.6 Simulating the TSIR Model 8.7 Emergent Simplicity 8.8 Project Tycho 8.9 In-Host Malaria Dynamics 8.10 A TSIR shinyApp 8.11 Malapropos: A Ross–Macdonald Malaria Model 9 Stochastics 9.1 Preamble: Prevalence versus Incidence 9.2 Event-Based Stochastic Simulation 9.3 Trajectory Matching 9.4 Likelihood Theory 101 9.5 SEIR with Error 9.6 Boarding School Flu Data 9.7 Measles 9.8 Outbreak Response Vaccination 9.9 An ORV shinyApp 10 Stability and Resonant Periodicity 10.1 Preamble: Rabies 10.2 Linear Stability Analysis 10.3 Finding Equilibria 10.4 Evaluating the Jacobian 10.5 Influenza 10.6 Raccoon Rabies 10.7 Critical Host Density 10.8 Advanced: Transfer Functions 10.9 (Even More) Advanced: Transfer Functions and DelayCoordinates 10.10 SEIRS and TSIR shinyApps 11 Exotica 11.1 Too Nonlinear 11.2 Chaos 11.3 Local Lyapunov Exponents 11.4 Coexisting Attractors 11.5 Repellors/Almost Attractors 11.6 Invasion Orbits 11.7 Stochastic Resonance 11.8 Predictability: Empirical Dynamic Modeling 11.9 Appendix: Making a Pomp Simulator Part II Space 12 Spatial Dynamics 12.1 Introduction 12.2 Dispersal Kernels 12.3 Filipendula Rust Data 12.4 Simulation 12.5 Gypsy Moth 12.6 A Coupled Map Lattice SI Model 12.7 Making Movies 12.8 Covariance Functions for Spatiotemporal Data 12.9 Gravity Models 12.10 Appendix: A Spatial Gypsy Moth Model 13 Spatial and Spatiotemporal Patterns 13.1 Spatiotemporal Patterns 13.2 A Plant-Pathogen Case Study 13.3 Spatial Autocorrelation 13.4 Testing and Confidence Intervals 13.5 Mantel test 13.6 Correlograms 13.7 Nonparametric Spatial Correlation Functions 13.8 LISA 13.9 Cross-Correlations 13.10 Gypsy Moth 14 Transmission on Networks 14.1 Social Heterogeneities 14.2 S Preamble: Objects, Classes, and Functions 14.3 Networks 14.4 Models of Networks 14.5 Epidemics on Networks 14.6 Epidemic Size Distribution 14.7 Empirical Networks 14.8 Vaccinating Networks 15 Invasion and Eradication 15.1 Invasion 15.2 Stage III Branching Processes 15.3 Phocine Distemper Virus 15.4 Rabies 15.5 Initial Control 15.6 Synchrony 15.7 Coupling 15.8 A Synthesis Part III Miscellany 16 Parasitoids 16.1 Introduction 16.2 Parasitoid-Host Dynamics 16.3 Stability and Resonant Periodicity 16.4 Biological Control 16.5 Larch Bud Moth 16.6 Host-Parasitoid Metapopulation Dynamics 16.7 Parasitoid-Host shinyApps 17 Quantifying In-Host Patterns 17.1 Motivation 17.2 Two Experiments 17.3 Data 17.4 PCA of the FIV Data 17.5 LDA of the FIV Data 17.6 MANOVA of the FIV Data 17.7 PCA of the Mouse Malaria Data 17.8 FDA of the Mouse Malaria Data 18 Non-Independent Data 18.1 Non-Independence 18.2 Spatial Dependence 18.3 Spatial Regression 18.4 Repeated Measures 18.5 Sibling Correlation 18.6 The End References Index