Predictability in process-based ensemble forecast of influenza

Process-based models have been used to simulate and forecast a number of nonlinear dynamical systems, including influenza and other infectious diseases. In this work, we evaluate the effects of model initial condition error and stochastic fluctuation on forecast accuracy in a compartmental model of influenza transmission. These two types of errors are found to have qualitatively similar growth patterns during model integration, indicating that dynamic error growth, regardless of source, is a dominant component of forecast inaccuracy. We therefore examine the nonlinear growth of model initial error and compute the fastest growing directions using singular vector analysis. Using this information, we generate perturbations in an ensemble forecast system of influenza to obtain more optimal ensemble spread. In retrospective forecasts of historical outbreaks for 95 US cities from 2003 to 2014, this approach improves short-term forecast of incidence over the next one to four weeks.Author summary: Mathematical models are now used to forecast infectious disease incidence at the population scale. By better understanding how errors in prediction systems are introduced, grow and impact the predictability of infectious disease, forecast accuracy could be improved. Here we explore the growth pattern of errors introduced from two major sources–model initial conditions and stochastic fluctuation–in a simple, compartmental model describing influenza transmission. We find that model initial error typically undergoes faster growth due to nonlinear amplification during model evolution. Adopting techniques used in numerical weather prediction, we leverage this growth of uncertainty and modify an ensemble forecast system to generate optimal perturbations along the fastest growing direction of initial error. This perturbation procedure increases ensemble spread, which better captures observations with large uncertainties. In retrospective forecasts for 95 US cities during the 2003 through 2014 flu seasons, this procedure leads to a substantial improvement of short-term forecast quality.