  We describe the population-based SEIR (susceptible, exposed, infected,
removed) model developed by the Irish Epidemiological Modelling Advisory Group
(IEMAG), which advises the Irish government on COVID-19 responses. The model
assumes a time-varying effective contact rate (equivalently, a time-varying
reproduction number) to model the effect of non-pharmaceutical interventions. A
crucial technical challenge in applying such models is their accurate
calibration to observed data, e.g., to the daily number of confirmed new cases,
as the past history of the disease strongly affects predictions of future
scenarios. We demonstrate an approach based on inversion of the SEIR equations
in conjunction with statistical modelling and spline-fitting of the data, to
produce a robust methodology for calibration of a wide class of models of this
type.
