Description
Short course taught by Sarah Cobey and Trevor Bedford for SISMID 2023.
This module provides an introduction to modeling antigenically diverse pathogen populations. The first part of the course will introduce multistrain compartmental models and potential mechanisms of competition. These simple models will be contrasted with models with more complex assumptions (e.g., multiple forms of immunity and spatial structure). We will review how to statistically fit multistrain models to longitudinal data from individuals and time series data from populations. The second part of the course will show how, using the coalescent as a neutral expectation, evolutionary pressures can be quantified using sequence data. We will detail bioinformatic methods to build phylogenies, quantify selective pressures and estimate pathogen population structure. Methods to measure pathogen phenotypic similarity and antigenic evolution, such as antigenic cartography, will be introduced. Assumes material from Module 2 (Mathematical Models of Infectious Diseases). Material from Module 4 (Evolutionary Dynamics and Molecular Epidemiology of Viruses) would complement course material, but is not required.
Outline
Day 1, Wed July 19
Pathogen diversity
1:30pm to 3:00pm
- Antigenically (and otherwise) variable pathogens
- Exercise: Assigning study groups and picking pathogens
Immunity and immune-mediated competition
3:30pm to 5:00pm
- The biological basis of antigenic diversity: innate, cellular, and humoral responses
Day 2, Thur July 20
Serology
8:30am to 10:00am
- Serological binding and neutralization data
- Antigenic cartography
- Exercise: Antigenic map
- Original antigenic sin
Multistrain models
10:30am to 12:00pm
- Statistical, compartmental, and agent-based models
- The many forms of competition
- Analytic solutions
- Numerical integration
- Exercise: Dynamics of a multistrain SIR system
Timeseries analysis
1:30pm to 3:00pm
- Maximum likelihood
- When to trust a model
- Tips & tricks: insights from natural experiments
- State-space reconstruction
The coalescent and phylogenetics
3:30pm to 5:00pm
- Introduction to Kingman’s coalescent
- Effective population size and demographic inference
- Exercise: Skyline plots
- Effects of selection on tree topology
- Introduction to phylogenetic inference
- Exercise: Parsimony reconstruction
- Maximum likelihood and Bayesian methods
- Phylogeography and recombination
Day 3, Fri July 21
Selection and Wright-Fisher Dynamics
8:30am to 10:00am
- Introduction to Wright-Fisher model
- Wright-Fisher with mutation and genetic drift
- Exercise: Effects of mutation and population size on population dynamics
- Wright-Fisher with mutation, genetic drift and selection
- Exercise: Effects of positive and negative selection on population dynamics
- Tests of selection
Forecasting
10:30am to 12:00pm
- Mechanistic models
- Nonlinear forecasting
- Fitness model projections
Synthesis
1:30pm to 3:00pm
- Exercise: Group presentations on specific pathogens
B cell selection and evolution
3:30pm to 5:00pm
- VDJ recombination and somatic hypermutation
- Clonal dynamics and repertoire diversity
- Unsolved problems and vaccine design
Resources
Run exercise iPython notebooks online with MyBinder: 
All contents including slides, course materials and code are copyright 2015-2023 Sarah Cobey and Trevor Bedford. All slides / course materials (files ending in .html and .md) are licensed under Creative Commons Attribution 4.0 and all code (files ending in .py and .ipynb) is licensed under an MIT License.