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

Chowell, Gerardo

Example #4: Parameter non-identifiability arises from the limited amount of data available to quantify parameter uncertainty For this example, we first generate simulated data from the generalized-Richards model (GRM) using the parameter values: r ¼ 0:2; p ¼ 0:8; a ¼ 1; and K ¼ 1000. Next, we use the simulated data to attempt to estimate parameters r and p using the GGM from an increasing length of the early growth phase of the daily incidence curve simulated using the GRM. Fig. 10 shows the resulting empirical distributions of the parameters using an increasing length of the growth phase: 10, 20, …, 80 days. Importantly, Fig. 10 shows that 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, we conclude that it is not possible to discriminate between sub-exponential and exponential-growth dynamics based on data of only the first 10 days. In fact, the corresponding confidence interval of p include the values of 0.5 and 1.0, which indicate that both linear and exponential growth dynamics cannot be ruled out with the data at hand. 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 (Fig. 10) .