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

Chowell, Gerardo

We can observe that the uncertainty of the forecasts narrows down as more data of the early growth phase is employed to estimate parameters of the GGM. Importantly, using less than 10 days of data, it is not possible to reliably estimate discriminate between sub-exponential and exponential-growth dynamics. The corresponding performance of the GGM during the calibration and forecasting periods is shown in Fig. 16 Matlab code for 1) fitting the GGM, 2) derive parameter uncertainty, and 3) generate short-term forecasts using incidence data of the Zika outbreak is provided in the supplement. Fig. 13 . 30-day ahead forecasts derived using the GGM by estimating parametersr and p with quantified uncertainty when the model is fitted to an increasing length of the growth phase (10, 20, …, 80 days) of a synthetic daily incidence curve simulated using the GRM with parameters r ¼ 0:2; p ¼ 0:8; a ¼ 1; and K ¼ 1000. We can observe that the uncertainty of the forecasts narrows down as more data of the early growth phase is employed to estimate parameters of the GGM. That is, the uncertainty in parameter estimates is not only reduced, but the parameter estimates are also increasingly constrained around their true values (Fig. 8) . Importantly, using only 10 days of data, it is not possible to reliably estimate discriminate between sub-exponential and exponential-growth dynamics. The cyan curves correspond to the uncertainty during the model calibration period while the gray curves correspond to the uncertainty in the forecast. The mean (solid red line) and 95% CIs (dashed red lines) of the model fit are also shown. The vertical line separates the calibration and forecasting periods.