This course teaches the statistical machinery behind infectious disease modeling: likelihood, the Bayesian workflow, hierarchical structure, and fitting mechanistic transmission models to data. Graduate students doing IDEEE research in Biology or Molecular Medicine will learn to write a transmission model as a statistical model and fit it in Stan. The course formalizes the workflow that many of the site’s reference pages already assume.
The course syllabus is shown below.
Draft syllabus. This is a scaffold for the concentration. Dates, meeting times, and specific assignments will be finalized before the semester begins.
Course title and instructors
Title: Statistical Modeling of Infectious Disease Dynamics
Course Number: BIO 6xx (proposed; with an undergraduate cross-list where
noted)
Semester: TBD
Credit Hours: 3
Meeting Time: TBD
Prerequisites: Mathematical Biology, Biostatistics
(BIO 380), and programming experience
Course Director: Michael E. DeWitt, MS
Email: medewitt@wakehealth.edu or dewime23@wfu.edu
Course description
Fitting a transmission model to data is a statistical problem. This course treats mechanistic models of infectious disease as statistical models built from an observation process and a latent transmission process. Students learn likelihood and maximum likelihood estimation, Bayesian inference and Markov chain Monte Carlo, and hierarchical (partial-pooling) models for multi-site or multi-strain data. We work through the full Bayesian workflow end to end: prior predictive checks, fitting in Stan, convergence diagnostics, and posterior predictive checks. We also cover model calibration, identifiability, sensitivity analysis, and scoring for model comparison. Students estimate key quantities such as the basic reproduction number and the generation interval using the next-generation approach and propagate the resulting uncertainty.
Learning outcomes
Upon successful completion of this course, students will be able to:
- Write down and fit a mechanistic transmission model as a statistical model with an observation component and a process component
- Carry out a full Bayesian workflow: prior predictive checks, fitting in Stan, convergence diagnostics, and posterior predictive checks
- Build hierarchical and partial-pooling models for multi-site or multi-strain data
- Estimate key quantities such as the basic reproduction number and the generation interval using the next-generation approach and propagate uncertainty
- Assess identifiability and calibrate models against observed data
- Compare models using proper scoring rules and sensitivity analysis
Textbook and other resources
There is no single required textbook. Recommended references and readings include:
- Gelman A, et al. Bayesian Data Analysis, 3rd ed. CRC Press, 2013.
- McElreath R. Statistical Rethinking, 2nd ed. CRC Press, 2020.
- Stan Development Team. Stan User’s Guide. https://mc-stan.org/docs/
- Bjørnstad ON. Epidemics: Models and Data in R. Springer, 2018.
Additional primary literature will be assigned throughout the semester.
Site resources
This course draws on the following IDEEE reference pages:
- Maximum likelihood
- Bayesian inference
- Markov chains
- MCMC
- Hierarchical models
- Model calibration
- Sensitivity analysis
- Proper scoring rules
- The next-generation matrix
- The reproduction number and Rt
- SEIR models
- Epidemiological intervals
- Delay distributions and censoring
Planned reference pages on prior predictive checks, posterior predictive checks, and identifiability will be added and assigned as they come online.
Course structure and schedule
This course meets over 15 weeks and combines lecture with hands-on model fitting in Stan. The schedule below is a draft outline of topics.
| Week | Topic |
|---|---|
| 1 | Transmission models as statistical models |
| 2 | Likelihood and maximum likelihood estimation |
| 3 | The observation process and count data |
| 4 | Bayesian inference and prior specification |
| 5 | Markov chains and MCMC |
| 6 | Fitting models in Stan and convergence diagnostics |
| 7 | Prior predictive checks |
| 8 | Posterior predictive checks and model criticism |
| 9 | Hierarchical and partial-pooling models |
| 10 | Multi-site and multi-strain data |
| 11 | Model calibration and identifiability |
| 12 | Estimating R0 and the generation interval |
| 13 | Sensitivity analysis and uncertainty propagation |
| 14 | Model comparison and proper scoring rules |
| 15 | Student project presentations and wrap-up |
Note: Specific dates will be provided at the beginning of the semester. Topics may be adjusted based on class progress and student interests.
Grades and assignments
| Activity | Weight |
|---|---|
| Participation and discussion | 15% |
| Problem sets (Stan-based) | 35% |
| Midterm modeling exercise | 20% |
| Final project | 30% |
Final project: Students will fit a mechanistic transmission model to a real data set, carrying out the full Bayesian workflow and reporting estimates with uncertainty in a written report and presentation.
Course policies
Attendance: Regular attendance is expected, particularly for discussion sessions. Please alert the instructor if you are unable to attend for any reason.
Late/Makeup work: Assignments are due on the dates provided. We recognize that extenuating circumstances arise, and assignments may be submitted up to 2 days late without penalty. If you need an extension, contact the instructor as soon as possible and before the due date.
Artificial intelligence: Artificial intelligence tools and large language models such as ChatGPT, Claude, and Gemini are now part of the academic and professional landscape and we encourage you to find ways to use them to enhance your learning. However, if you use these tools, you must cite your sources and provide a detailed description of the tools you used to complete the assignment. In no way can these tools take the place of your own work and understanding of the material. They should be used to supplement your learning, not replace it. You are ultimately responsible for your work including content and the use of valid citations and references. Using these tools without proper attribution is plagiarism and will be treated as such.
Department/School/University policies
Academic Integrity: Wake Forest University is committed to a culture of academic integrity. As a part of this community, you share the responsibility for creating a place of honesty, intellectual curiosity, and individual accountability. As you committed to with your honor pledge signature, you agree “not to deceive any member of the community; not to steal, cheat, or plagiarize on academic work; and not to engage in any other form of academic misconduct.” If you have questions about documenting your work, working with external sources, or working with peers on assigned work, consult with me as soon as possible. Instances of academic dishonesty will be referred to the Honor and Ethics Council.
Accessibility: Wake Forest University provides reasonable accommodations to students with disabilities. If you are in need of an accommodation, please contact me privately as early in the term as possible. Retroactive accommodations will not be provided. Students requiring accommodations must also consult the Center for Learning, Access, and Student Success (118 Reynolda Hall, 336-758-5929, class.wfu.edu).
Accommodations for Religious or Spiritual Practices: Wake Forest University benefits from the multitude of faiths and spiritual identities held by members of our learning community. Should you need accommodations this semester, email me as soon as possible to ensure we have time to develop equitable alternatives.
Class recordings: In case any class recordings are provided, they are reserved only for students in this class for educational purposes and are protected under FERPA. The recordings should not be shared outside the class in any form.
Syllabus change notice
This syllabus and the dates herein are subject to change.