An improved state filter algorithm for SIR epidemic forecasting

In epidemic modeling, state filtering is an excellent tool for enhancing the performance of traditional epidemic models. We introduce a novel state filter algorithm to further improve the performance of state-of-the-art approaches based on Susceptible-Infected-Recovered (SIR) models. The proposed algorithm merges two techniques, which are typically used separately: linear correction, as seen in the Ensemble Kalman Filter (EnKF), and resampling, as used in the Particle Filter (PF). We compare the inferential accuracy of our approach against the EnKF and the Ensemble Adjustment Kalman Filter (EAKF), using algorithms employing both an uncentered covariance matrix (UCM) and the standard column-centered covariance matrix (CCM). Our algorithm requires O(DN) more time than EnKF does, where D is the ensemble dimension and N denotes the ensemble size. We demonstrate empirically that our algorithm with UCM achieves the lowest root-mean-square-error (RMSE) and the highest correlation coefficient (CORR) amongst the selected methods, in 11 out of 14 major real-world scenarios. We show that the EnKF with UCM outperforms the EnKF with CCM, while the EAKF gains better accuracy with CCM in most scenarios.