Abstract
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.
Highlights
Influenza imposes a tremendous toll on global public health due to its recurrent worldwide spread and associated heavy morbidity and mortality burden [1]
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
Summary
Influenza imposes a tremendous toll on global public health due to its recurrent worldwide spread and associated heavy morbidity and mortality burden [1]. To better prepare for and mitigate future outbreaks, accurate forecasts of influenza transmission are needed. Forecast skill has advanced significantly, the predictability of nonlinear influenza transmission dynamics is limited by the errors in model forecast systems [12]. These errors derive from three major sources: errors in model initial conditions, stochasticity in model dynamics, and model misspecification. To further improve influenza forecast accuracy, a better understanding of these errors and their impact on forecast uncertainty is needed. We focus on the first two error sources (i.e., initial condition error and stochasticity) and do not investigate model misspecification
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