Mathematics Seminar - 09/02/26

Abstract: Differential equation-based models are routinely fit to data to gain insight into epidemiological and other biological phenomena. Before fitting, it is essential to understand a model's theoretical limitations under perfect observation (noise-free, continuous, and model-generated), a property known as structural identifiability. A model is structurally identifiable if the model-observation pairing yields unique parameters; when it does not, downstream uncertainty quantification is compromised from the outset.

In this talk, I will first show that structurally unidentifiable models can still yield key quantities, such as the reproduction number, that are themselves structurally identifiable, reframing the central question from "Is the model identifiable?" to "Are the decision-relevant quantities identifiable?" Second, examining several epidemiological models, I will show that an unidentifiable model-observation pairing can become globally identifiable by incorporating as little as a single discrete data point from a complementary data stream. Finally, since structural identifiability assumes perfect, error-free observation, I will discuss scenarios of model-data mismatch, where meaningful insight can still be gained despite the underlying model being misspecified.