Introduction to Epidemiological Modeling

Mathematical models are an essential tool in epidemiology. Models are used in a number of ways, including: to predict the course of an epidemic; to estimate key epidemiological parameters; to determine an optimal vaccination strategy; or to gain a general, qualitative understanding of the salient features of the dynamics of a disease. This course will focus on differential equations, a class of mathematical models used across the sciences to model quantities that change continuously in time. The course will begin with a short introduction to differential equations. We will then step through the full “pipeline” of mathematical modeling using epidemiology as a case study. We will begin with a first-principles derivation of several models and will consider how the natural history of an infectious disease influences modeling choices. We will then see how to solve and analyze differential equations computationally. We will then cover how to calibrate a model to epidemiological data and estimate key model parameters in a principled way. Finally, we will see how to create model projections for different intervention scenarios and will explore the strengths and limitations of a mathematical model in relation to given research and policy questions. Through this process, students will gain skills and experiences that will apply to mathematical modeling in a range of settings across the natural and social sciences.

In addition to learning the mathematics of differential equations applied to epidemiology, a central goal of this course is to gain skills necessary for research in the mathematical, natural, and social sciences. This includes conceptualizing and framing a research question, formulating a model to explore that question, engaging with peer-reviewed research publications, and giving a research presentation and preparing a short technical report.

Evaluation will be based on class participation, problem sets and programming exercises, and a term-long project culminating in a research presentation and short technical report.

Course Number
ES3097
Area of Study
Mathematics and Physical Sciences
Course Level
Intermediate
Instructors
David Feldman, Laurie Baker