Study on the prediction effect of a combined model of SARIMA and LSTM based on SSA for influenza in Shanxi Province, China

Influenza is an acute respiratory infectious disease that is highly infectious and seriously damages human health. Reasonable prediction is of great significance to control the epidemic of influenza.

Our Influenza data were extracted from Shanxi Provincial Center for Disease Control and Prevention. Seasonal-trend decomposition using Loess (STL) was adopted to analyze the season characteristics of the influenza in Shanxi Province, China, from the 1st week in 2010 to the 52nd week in 2019. To handle the insufficient prediction performance of the seasonal autoregressive integrated moving average (SARIMA) model in predicting the nonlinear parts and the poor accuracy of directly predicting the original sequence, this study established the SARIMA model, the combination model of SARIMA and Long-Short Term Memory neural network (SARIMA-LSTM) and the combination model of SARIMA-LSTM based on Singular spectrum analysis (SSA-SARIMA-LSTM) to make predictions and identify the best model. Additionally, the Mean Squared Error (MSE), Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE) were used to evaluate the performance of the models.

The influenza time series in Shanxi Province from the 1st week in 2010 to the 52nd week in 2019 showed a year-by-year decrease with obvious seasonal characteristics. The peak period of the disease mainly concentrated from the end of the year to the beginning of the next year. The best fitting and prediction performance was the SSA-SARIMA-LSTM model. Compared with the SARIMA model, the MSE, MAE and RMSE of the SSA-SARIMA-LSTM model decreased by 38.12, 17.39 and 21.34%, respectively, in fitting performance; the MSE, MAE and RMSE decreased by 42.41, 18.69 and 24.11%, respectively, in prediction performances. Furthermore, compared with the SARIMA-LSTM model, the MSE, MAE and RMSE of the SSA-SARIMA-LSTM model decreased by 28.26, 14.61 and 15.30%, respectively, in fitting performance; the MSE, MAE and RMSE decreased by 36.99, 7.22 and 20.62%, respectively, in prediction performances.

The fitting and prediction performances of the SSA-SARIMA-LSTM model were better than those of the SARIMA and the SARIMA-LSTM models. Generally speaking, we can apply the SSA-SARIMA-LSTM model to the prediction of influenza, and offer a leg-up for public policy.