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

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.

Forecasting influenza outbreak dynamics in Melbourne from Internet search query surveillance data

“…With regard to seasonal influenza, existing forecasting studies have focused on cities across the USA, but as Yang et al . state, ‘the performance of any filter may be application dependent’ 11. The results presented here are the first application of such forecasting methods to Australian data and demonstrate that we are able to obtain similar forecasting accuracy in the Australian context.…”

“…A recent comparison of filtering methods for influenza epidemic forecasting (applied to 115 cities in USA) found that the peak timing forecasts were comparably accurate for the six surveyed methods 11. It was also observed that the particle filters performed ‘slightly better predicting peaks 1–5 weeks in the future’, while ‘ensemble [Kalman] filters were better at indicating that the seasonal peak had already occurred’.…”

Transmission network of the 2014–2015 Ebola epidemic in Sierra Leone

“…S, E, I, for each district) and model parameters, including the transmission rate b for each district, the incubation period, the infectious period and the three exponents (t 1 , t 2 and r) for the gravity model. The EAKF [15,23,[25][26][27]] is a data assimilation method that uses an ensemble of system replicas to represent the distribution of possible model state and parameter values. It approximates a Bayesian update to the model states and parameters using the observational data and an estimate of the errors in the data.…”

Inference for dynamic and latent variable models via iterated, perturbed Bayes maps

“…One could, for example, modify IF2 to use an ensemble Kalman filter (20,34) or an unscented Kalman filter (35). Or, one could take advantage of variations of sequential Monte Carlo that may improve the numerical performance (36).…”