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.
Author(s): Ottar N. Bjørnstad
Series: Use R!
Edition: 2
Publisher: Springer
Year: 2022
Language: English
Pages: 385
City: Cham
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
