Evaluation of models for multi-step forecasting of hand, foot and mouth disease using multi-input multi-output: A case study of Chengdu, China

Background: Hand, foot and mouth disease (HFMD) is a public health concern that threatens the health of children. Accurately forecasting of HFMD cases multiple days ahead and early detection of peaks in the number of cases followed by timely response are essential for HFMD prevention and control. However, many studies mainly predict future one-day incidence, which reduces the flexibility of prevention and control. Methods: We collected the daily number of HFMD cases among children aged 0–14 years in Chengdu from 2011 to 2017, as well as meteorological and air pollutant data for the same period. The LSTM, Seq2Seq, Seq2Seq-Luong and Seq2Seq-Shih models were used to perform multi-step prediction of HFMD through multi-input multi-output. We evaluated the models in terms of overall prediction performance, the time delay and intensity of detection peaks. Results: From 2011 to 2017, HFMD in Chengdu showed seasonal trends that were consistent with temperature, air pressure, rainfall, relative humidity, and PM10. The Seq2Seq-Shih model achieved the best performance, with RMSE, sMAPE and PCC values of 13.943~22.192, 17.880~27.937, and 0.887~0.705 for the 2-day to 15-day predictions, respectively. Meanwhile, the Seq2Seq-Shih model is able to detect peaks in the next 15 days with a smaller time delay. Conclusions: The deep learning Seq2Seq-Shih model achieves the best performance in overall and peak prediction, and is applicable to HFMD multi-step prediction based on environmental factors. Author summary: Hand, foot and mouth disease (HFMD) remains a serious public health concern in China. It is important to predict trends and understand peaks in the number of cases in advance for its prevention and control. The aim of this study was to consider the influence of meteorology and air pollution on the transmission of HFMD and establish multi-step prediction models for HFMD. In this study, we compared the performance of the Shih attention mechanism with the Luong attention mechanism, Seq2Seq model and LSTM model for future multi-day HFMD prediction based on multi-input multi-output. It was found that the Seq2Seq-Shih model performed best in predicting the trend for the next 2 days-15 days with RMSE, sMAPE and PCC values of 13.943~22.192, 17.880~27.937, and 0.887~0.705, respectively. Meanwhile, it was able to predict the peak within 15 days earlier by 17 days. This is the first study to use Seq2Seq models and perform daily multi-step prediction of HFMD. This study demonstrates the benefit of the Shih attention mechanism in multivariate time series multi-step prediction of infectious diseases.