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

Chowell, Gerardo

The RMSE, MAE, and MAPE of the fits provided by the GGM and EXPM models to the first 15 weeks of the Ebola epidemic in Sierra Leone (See also Figs. 2e3) are as follows: Fig. 9 . Fitting the GGM to the first 15 weeks of the 2014-15 Ebola epidemic in Sierra Leone. Parameter estimates with quantified uncertainty generated using the bootstrap approach with a negative binomial error structure with variance 5 times higher than the mean as described in the text (Section 7). The histograms display the empirical distributions of the parameter estimates using 200 bootstrap realizations. The bottom panel shows the fit of the GGM to the 15 weeks of the 2014-15 Ebola epidemic in Sierra Leone. The blue circles are the weekly data while the solid red line corresponds to the best fit of the GGM to the data. The dashed red lines correspond to the 95% confidence bands around the best fit of the model to the data. The confidence intervals of the parameter estimates are wider than those obtained using a Poisson error structure in the data (Fig. 8 . 10 . Empirical distributions of r and p of the GGM model derived from our bootstrap uncertainty method after fitting the GGM to an increasing length of the growth phase (10, 20, …, 80 days) of the daily incidence curve derived from the GRM model with parameters r ¼ 0:2; p ¼ 0:8; a ¼ 1; and K ¼ 1000. Importantly, using only 10 days of data, it is not possible to reliably estimate the deceleration of growth parameter, p, because its confidence interval ranges widely from 0.5 to 1.0. Indeed, it is not possible to discriminate between sub-exponential and exponential-growth dynamics based on data of only the first 10 days. However, as more data of the early growth phase is employed to estimate parameters of the GGM, the uncertainty in parameter estimates is not only reduced, but the parameter estimates are better constrained around their true values.