Comparison of Filtering Methods for the Modeling and Retrospective Forecasting of Influenza Epidemics

A variety of filtering methods enable the recursive estimation of system state variables and inference of model parameters. These methods have found application in a range of disciplines and settings, including engineering design and forecasting, and, over the last two decades, have been applied to infectious disease epidemiology. For any system of interest, the ideal filter depends on the nonlinearity and complexity of the model to which it is applied, the quality and abundance of observations being entrained, and the ultimate application (e.g. forecast, parameter estimation, etc.). Here, we compare the performance of six state-of-the-art filter methods when used to model and forecast influenza activity. Three particle filters—a basic particle filter (PF) with resampling and regularization, maximum likelihood estimation via iterated filtering (MIF), and particle Markov chain Monte Carlo (pMCMC)—and three ensemble filters—the ensemble Kalman filter (EnKF), the ensemble adjustment Kalman filter (EAKF), and the rank histogram filter (RHF)—were used in conjunction with a humidity-forced susceptible-infectious-recovered-susceptible (SIRS) model and weekly estimates of influenza incidence. The modeling frameworks, first validated with synthetic influenza epidemic data, were then applied to fit and retrospectively forecast the historical incidence time series of seven influenza epidemics during 2003–2012, for 115 cities in the United States. Results suggest that when using the SIRS model the ensemble filters and the basic PF are more capable of faithfully recreating historical influenza incidence time series, while the MIF and pMCMC do not perform as well for multimodal outbreaks. For forecast of the week with the highest influenza activity, the accuracies of the six model-filter frameworks are comparable; the three particle filters perform slightly better predicting peaks 1–5 weeks in the future; the ensemble filters are more accurate predicting peaks in the past.Author Summary: Influenza, or the flu, is a significant public health burden in the U.S. that annually causes between 3,000 and 49,000 deaths. Predictions of influenza, if reliable, would provide public health officials valuable advanced warning that could aid efforts to reduce the burden of this disease. For instance, medical resources, including vaccines and antiviral drugs, can be distributed to areas in need well in advance of peak influenza incidence. Recent applications of statistical filtering methods to epidemiological models have shown that accurate and reliable influenza forecast is possible; however, many filtering methods exist, and the performance of any filter may be application dependent. Here we use a single epidemiological modeling framework to test the performance of six state-of-the-art filters for modeling and forecasting influenza. Three of the filters are particle filters, commonly used in scientific, engineering, and economic disciplines; the other three filters are ensemble filters, frequently used in geophysical disciplines, such as numerical weather prediction. We use each of the six filters to retrospectively model and forecast seasonal influenza activity during 2003–2012 for 115 cities in the U.S. We report the performance of the six filters and discuss potential strategies for improving real-time influenza prediction.