Comparison of the predictive performance of SARIMA, Prophet, and BSTS models in forecasting the incidence of hand, foot, and mouth disease
LU Wenhai1, KONG Xiaojie2, SONG Lixia3, LU Chunru1, YU Bikun1, XIE Yan2
1. Pingdi Street Public Health Service Center, Longgang District, Shenzhen, Guangdong 518117, China; 2. The Third People's Hospital of Futian District, Shenzhen, Guangdong 518029, China; 3. Shenzhen Center for Disease Control and Prevention, Shenzhen, Guangdong 518054, China
Abstract：Objective To compare the predictive performance of the seasonal autoregressive integrated moving average (SARIMA) model, the Prophet model, and the Bayesian structural time series (BSTS) model in forecasting the incidence of hand, foot, and mouth disease (HFMD) , so as to provide a basis for optimizing the early warning system of this disease. Methods Weekly incidence data of HFMD in Longgang District, Shenzhen City from 2014 to 2024 were collected. The HFMD incidence data from 2014-2019 and 2023 were used as the training set to construct SARIMA, Prophet, and BSTS models, while the data from 2024 were used as the test set to compare and evaluate the predictive performance of the three models. The technique for order preference by similarity to ideal solution (TOPSIS) method was employed to calculate the C-value. This approach integrates multiple evaluation metrics, such as the mean absolute error (MAE), mean squared error (MSE), root mean squared error (RMSE), and symmetric mean absolute percentage error (SMAPE), to comprehensively assess model performance. Results A total of 150 111 cases of HFMD were reported in Longgang District from 2014 to 2024, with an average annual incidence of 400.72/105. The weekly incidence fluctuated between 0 and 63.78/105, exhibiting a bimodal seasonal pattern characterized by a primary peak from May to July and a secondary peak from September to October. In the training set, all three models demonstrated a good fit to the bimodal epidemic trend of HFMD, with the BSTS model achieving the best fit. The BSTS model yielded performance metrics as follows: MAE=0.124, MSE=0.050, RMSE=0.223, SMAPE=0.021, and a C-value of 1.000. In the test set, all three models, including SARIMA, Prophet, and BSTS, performed well for short-term predictions (≤16 weeks), with the Prophet model showing relatively superior predictive performance. However, the prediction accuracy of all models declined as the forecast horizon extended. During the primary peak period (May-July), the Prophet model exhibited better predictive performance, whereas the BSTS model performed relatively better during the secondary peak period (September-October). Conclusions For the short-term forecasting of weekly HFMD incidence, the Prophet model outperformed both the SARIMA and BSTS models. During the primary peak period, the Prophet model demonstrated superior predictive performance, whereas the BSTS model exhibited better accuracy in forecasting the secondary peak period.
卢文海, 孔校杰, 宋丽霞, 卢春如, 于碧鲲, 谢延. SARIMA、Prophet与BSTS模型预测手足口病发病率的效果比较[J]. 预防医学, 2026, 38(1): 79-84.
LU Wenhai, KONG Xiaojie, SONG Lixia, LU Chunru, YU Bikun, XIE Yan. Comparison of the predictive performance of SARIMA, Prophet, and BSTS models in forecasting the incidence of hand, foot, and mouth disease. Preventive Medicine, 2026, 38(1): 79-84.
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