Statistics and Disease: an Introduction to Mathematical Epidemiology
The onset of the COVID-19 pandemic placed a spotlight on the statistical models mathematical epidemiologists were devising to measure the extent of the disease and predict its spread, globally and locally. Often serving as the basis for determining policy, the accuracy of the models took on the stakes of life and death. Esoterica quickly became common currency: R0, exponential growth, herd immunity, SIR models, vectors, etc. Meanwhile, the competing models produced by various research centers became grist for heated debate: How can we evaluate one model against another? Why do they differ? Which methodology is more reliable—and how can we tell?
This course is an introduction to topics and methods in mathematical epidemiology? We will consider whether—and if so, how—mathematical models can help us understand and analyze infectious diseases and epidemics: How severe will an epidemic be? How quickly is it spreading? How might various public health interventions affect the spread of the disease? What is the threshold for herd immunity? Specific topics will include: exponential (and logistic) models of population growth, as relatively simple introductions to mathematical modeling; “SIR” models, which divide the population into “susceptible,” “infected” and “recovered” subpopulations, and attempt to model the interacting dynamics of those subpopulations; discrete probabilistic models which can incorporate social network structures and/or heterogeneity in infectiousness (e.g., “superspreaders”); and techniques for estimating R0, the basic reproduction number.
Readings will consist of selections from textbooks (such as Maia Martcheva’s Introduction to Mathematical Epidemiology and Mathematical Models in Population Biology and Epidemiology by Fred Brauer and Carlos Castillo-Chavez); survey papers such as Brauer’s “Mathematical Epidemiology: Past, Present, and Future”; more general treatments of these topics, such as Kucharski’s Rules of Contagion: Why Things Spread; and articles (both scientific and in the press) outlining recent mathematical models for the coronavirus.
Course ScheduleThursday, 6:30-9:30pm ET
March 04 — March 25, 2021