Abstract
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.
Highlights
Influenza exacts an enormous toll on human health and economic well-being
The SIRS model is comprised of state variables, which document the evolution of conditions within the simulated population, and parameters, which represent biological properties inherent to a given influenza strain and host population and which can vary from region to region and season to season
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
Summary
Influenza exacts an enormous toll on human health and economic well-being It leads to an average of 610,000 life-years lost, 3.1 million hospitalization days, 31.4 million outpatient visits, and a total economic cost of $87.1 billion in the United States [1]. Recent work has shown that influenza outbreaks can be accurately predicted with mathematical models of influenza transmission dynamics that have been recursively optimized using real-time observations of influenza incidence and data assimilation methods [2,3,4,5] These findings indicate that infectious disease forecasting is achievable; much work remains to be done testing, validating and improving these prediction systems. It is important for prediction that model parameters and initial conditions be well specified
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