A primer on stable parameter estimation and forecasting in epidemiology by a problem-oriented regularized least squares algorithm

Smirnova, Alexandra; Chowell, Gerardo

The selection of the initial vector, q 0 , and the reference vector,q, in the penalty term is rather difficult. In the beginning of an emerging outbreak, it is not straightforward to make a sophisticated guess about when the disease is going to peak. Hence, in our experiment, we take t 0 in q 0 to be slightly greater than t m , the last week for which the data is available, and we take t in Fig. 4 . Guinea: Estimation of r, t, p, a, and K, and Forecasting. r ¼ 1.3 (95% CI: 0.03, 2.7), t ¼ 41 (95% CI: 33, 49), p ¼ 0.87 (95% CI: 0.7, 0.9), a ¼ 0.96 (95% CI: 0.95, 1), K ¼ 1.1 ,10 4 (95% CI: 1 ,10 3 , 5.9 ,10 4 ). q to be equal to 60, i.e., we assume the incidence curve will turn before 60 weeks of the epidemic have passed. The values of p in q 0 andq are taken to be 0.7 and 0.1, respectively, to enforce the sub-exponential growth rate. The values of two remaining parameters, b (used to compute r) and a are taken to be 1 in both vectors for the lack of better information. Fig. 3 illustrates parameter estimation and the epidemic forecasts based on the generalized Richards model with 20 weeks of incident case data for the Ebola epidemic in Sierra Leone. After the five unknown parameters have been recovered from early epidemic data, 100 additional data bootstrap curves are generated by adding a Poisson error structure to the weekly series of reported cases (see (Chowell, Ammon, Hengartner, & Hyman, 2006) ) in order to quantify uncertainty in the recovered parameters. An alternative is to employ analytic results from asymptotic theory to estimate parameter uncertainty (Banks, Davidian, Samuels, & Sutton, 2009) . The histograms in the upper row show the recovered values of the parameters, while the collection of curves at the bottom of the figure demonstrates the accuracy of the forecasting.