This course introduces the mathematical tools used to describe, analyze, and predict the behavior of biological systems, with an emphasis on population and infectious disease dynamics.
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: BIO301: Mathematical Biology
Semester: TBD
Credit Hours: 3
Meeting Time: TBD
Course Director: Michael E. DeWitt, MS
Email: medewitt@wakehealth.edu or dewime23@wfu.edu
Course description
This course provides an introduction to the mathematics of biological systems. Students will learn how to translate biological questions into mathematical models, analyze those models using both analytical and computational techniques, and interpret the results in their biological context. Topics include difference and differential equations, single- and multi-species population models, equilibria and stability analysis, and compartmental models of infectious disease. Throughout, we emphasize the connection between model structure and biological assumptions. No prior modeling experience is required, though familiarity with introductory calculus is expected.
Learning outcomes
Upon successful completion of this course, students will be able to:
- Translate a biological or epidemiological question into a mathematical model
- Analyze discrete and continuous dynamical systems and identify equilibria
- Perform local stability analysis using linearization and the Jacobian
- Build and interpret compartmental models of infectious disease (e.g., SIR)
- Use computational tools to simulate and explore model behavior
- Communicate modeling assumptions, results, and limitations clearly
Textbook and other resources
There is no single required textbook. Recommended references include:
- Mathematical Models in Biology by Leah Edelstein-Keshet
- Modeling Infectious Diseases in Humans and Animals by Keeling and Rohani
- An Introduction to Mathematical Epidemiology by Maia Martcheva
Supplementary notes are available in the Mathematics resources, including material on compartmental models and Jacobians.
Course structure and schedule
This course meets over 15 weeks. Each week combines lecture with computational lab work. The schedule below is a draft outline of topics.
| Week | Topic |
|---|---|
| 1 | Introduction to mathematical modeling in biology |
| 2 | Discrete-time models and difference equations |
| 3 | Continuous-time models and differential equations |
| 4 | Single-species population growth |
| 5 | Equilibria and stability |
| 6 | Linearization and the Jacobian |
| 7 | Multi-species interactions (competition, predation) |
| 8 | Introduction to compartmental disease models |
| 9 | The SIR model and its variations |
| 10 | The basic reproduction number () |
| 11 | Model fitting and parameter estimation |
| 12 | Stochastic models and demographic noise |
| 13 | Spatial and network models |
| 14 | Case studies in disease modeling |
| 15 | 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 |
|---|---|
| Problem sets | 40% |
| Computational labs | 25% |
| Midterm | 15% |
| Final project | 20% |
Final project: Students will develop, analyze, and present a mathematical model of a biological or epidemiological system of their choosing.
Course policies
Attendance: Regular attendance is expected. Each class builds on previous material. 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.