Real-Time Forecasting of Hand-Foot-and-Mouth Disease Outbreaks using the Integrating Compartment Model and Assimilation Filtering

Figure 1. The weekly rate of HFMD infections in Beijing from 2008–11.

Figure 2. The relationships among the observed data, prior forecast outcomes, and posterior analysis outcomes in 2008 (a), 2009 (b), 2010 (c), and 2011 (d). Light green dots are the observed data for the weekly infection rate. Blue dots represent the prior forecast from the SEIR model. Red dots represent the posterior infection rate predicted using EnKF.

Figure 3. The forecast accuracy of the HFMD peak magnitudes from 2008–2011. Negative numbers on the horizontal axis represent numbers of weeks before the arrival of a peak week. The vertical axis measures the proximity of a forecasted peak infection rate is to the observed peak infection rate. A magnitude of 1 indicates a perfect forecast of the peak infection rate. The offset of the peak magnitude is defined as 1 − (Mpre − Mobs)/Mobs, where Mobs is the observed peak magnitude and Mpre is the predicted peak magnitude.

Figure 4. The forecast accuracy of the peak week arrival times for 2009, 2010, and 2011. The forecast result for 2008 is not included because of the lack of available training data before the peak week.

Figure 5. RMSE calculated for the forecast data and the observed data for 2008–2011.

Figure 6. Estimation of the HFMD transmission and recovery rates during the indicated weeks in each of the four years using the SEIR-EnKF model. The thick horizontal line is the median, the edges of the boxes are the 25th and 75th percentiles, and the whiskers span the full range.

Figure 7. The cumulative error of (a) the infection forecasting, (b) the peak magnitude forecasting, and (c) the peak time (week) forecasting. These errors are defined as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sum _{i=1}^{n}\sum _{j=1}^{m}{e}_{ij}$$\end{document}∑i=1n∑j=1meij, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sum _{i=1}^{n}\sum _{j=1}^{m}|FP{T}_{ij}-TP{T}_{i}|$$\end{document}∑i=1n∑j=1m|FPTij−TPTi| and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sum _{i=1}^{n}\sum _{j=1}^{m}|FP{M}_{ij}-TP{M}_{i}|$$\end{document}∑i=1n∑j=1m|FPMij−TPMi| respectively. In these equations, n is the number of years and m is the number of steps in…