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

Chowell, Gerardo

A key question in model parameterization is whether the model parameters are identifiable from the available data. As a general rule, a parameter is identifiable when its confidence interval lies in a finite range of values (Cobelli & Romanin-Jacur, 1976; Jacquez, 1996; Raue et al., 2009) . Conversely, lack of parameter identifiability can be recognized when large perturbations in the model parameters generate small changes in the model output (Capaldi et al., 2012; Chowell et al., 2006b; Pillonetto, Sparacino, & Cobelli, 2003) . Multiple factors can give rise to lack of parameter identifiability. For instance, structural parameter non-identifiability (Cobelli & Romanin-Jacur, 1976 ) results from the particular structure of the model independently of the characteristics of the observed time series data used to estimate parameters. However, even when structural identifiability is not an issue, a parameter may still be non-identifiable in practice due to other factors including: 1) the amount and quality of the data available and/or 2) the number of parameters that are jointly estimated from the available data. This type of parameter non-identifiability is commonly referred to as practical non-identifiability (Raue et al., 2009) .