Identifiability, uncertainty, and parameter reduction in mathematical biology

The interactions between parameters, model structure, and outputs can determine what inferences, predictions, and control strategies are possible for a given system. Identifiability, estimability, and parameter space reduction methods are thus essential for many questions in mathematical modeling and uncertainty quantification. These approaches can help to determine what inferences and predictions are possible from a given model and data set, and help guide control strategies and new data collection. In this talk, I will discuss some of the ideas and methods from identifiability, how they link to ideas of model reduction and model selection, and present public health applications to recent epidemics of polio and cholera. We will illustrate how reparameterization and alternative data collection may help resolve various types of unidentifiability and allow for successful intervention predictions.