Forecasting the final disease size: comparing calibrations of Bertalanffy-Pütter models

Using monthly data from the Ebola-outbreak 2013-2016 in West Africa, we compared two calibrations for data fitting, least-squares (SSE) and weighted least-squares (SWSE) with weights reciprocal to the number of new infections. To compare (in hindsight) forecasts for the final disease size (the actual value was observed at month 28 of the outbreak) we fitted Bertalanffy-Pütter growth models to truncated initial data (first 11, 12, …, 28 months). The growth curves identified the epidemic peak at month 10 and the relative errors of the forecasts (asymptotic limits) were below 10%, if 16 or more month were used; for SWSE the relative errors were smaller than for SSE. However, the calibrations differed insofar as for SWSE there were good fitting models that forecasted reasonable upper and lower bounds, while SSE was biased, as the forecasts of good fitting models systematically underestimated the final disease size. Furthermore, for SSE the normal distribution hypothesis of the fit residuals was refuted, while the similar hypothesis for SWSE was not refuted. We therefore recommend considering SWSE for epidemic forecasts.