Abstract: Uncertainty quantification (UQ) is mature in fields such as climate science and engineering, yet rigorous UQ remains understudied and underutilized in mathematical epidemiology. Structural identifiability analysis—which examines whether model parameters can, in principle, be uniquely determined from ideal observations (which could be thought of as noise-free, continuous data for all time)—represents a natural first step toward UQ. However, most studies focus exclusively on parameter identifiability. I will present theoretical identifiability results for the basic reproduction number, demonstrating that structurally unidentifiable models can still yield identifiable quantities of epidemiological interest. This reframes the central question from “Is the model-observation pairing structurally identifiable?” to “Are the quantities that matter for the decision at hand structurally identifiable?” I will also present a rigorous methodology showing how adding even a single data point from complementary data streams can resolve identifiability issues.
Of course, real data are discrete, noisy, and model-data mismatch always persists. I will discuss how working with synthetic noisy data can serve as a bridge between structural identifiability and real data. Finally, through two examples, I will demonstrate the consequences of model-data mismatch: the impact of ignoring undetected cases and the impact of neglecting human behavioral responses during epidemics.