Fitting dynamic models to epidemic outbreaks with quantified uncertainty: A primer for parameter uncertainty, identifiability, and forecasts

Mathematical models provide a quantitative framework with which scientists can assess hypotheses on the potential underlying mechanisms that explain patterns in observed data at different spatial and temporal scales, generate estimates of key kinetic parameters, assess the impact of interventions, optimize the impact of control strategies, and generate forecasts. We review and illustrate a simple data assimilation framework for calibrating mathematical models based on ordinary differential equation models using time series data describing the temporal progression of case counts relating, for instance, to population growth or infectious disease transmission dynamics. In contrast to Bayesian estimation approaches that always raise the question of how to set priors for the parameters, this frequentist approach relies on modeling the error structure in the data. We discuss issues related to parameter identifiability, uncertainty quantification and propagation as well as model performance and forecasts along examples based on phenomenological and mechanistic models parameterized using simulated and real datasets.