Forecasting Acute Hemorrhagic Conjunctivitis Incidence in Henan, China: A Comparative Study of Seasonal Autoregressive Fractionally Integrated Moving Average and Seasonal Autoregressive Integrated Moving Average Models
Abstract
Background Acute hemorrhagic conjunctivitis (AHC) is a highly contagious viral disease causing significant public health burden. Accurate forecasting is essential for timely intervention. The seasonal autoregressive integrated moving average (SARIMA) model is widely used, but the seasonal autoregressive fractionally integrated moving average (SARFIMA) model, which captures long-range dependence, may perform better for complex incidence series. This study compared the forecasting performance of SARFIMA and SARIMA models for AHC in Henan. Methods Monthly AHC case data from January 2011 to June 2023 in Henan Province were analyzed. Data from January 2011 to June 2022 were used for model training, with the remaining 12 months reserved for testing. National-level data from mainland China were used for external validation. Model performance was assessed using mean absolute deviation (MAD), root mean square error (RMSE), mean absolute percentage error (MAPE), and mean error rate (MER). Results AHC incidence showed a significant upward trend (average annual percentage change: 6.973%, 95% CI: 3.963%–10.071%) and a pronounced seasonal peak from March to September. The optimal models were SARIMA(0,1,2)(0,1,1)12 and SARFIMA(0,0.410,2)(0,0.413,1)12. SARFIMA outperformed SARIMA on most metrics in both training (MAD: 23.392 vs 24.599; MAPE: 0.132 vs 0.134; RMSE: 31.218 vs 31.339; MER: 0.124 vs 0.131) and test sets (MAD: 39.375 vs 48.850; MAPE: 0.237 vs 0.280; RMSE: 50.390 vs 57.358; MER: 0.184 vs 0.229), with a substantially better fit (AIC: 987.59 vs 1231.50). National validation confirmed SARFIMA’s superiority for MAD, MAPE, and MER, although RMSE values were comparable between models. Conclusion The SARFIMA model offers improved forecasting accuracy over SARIMA for AHC incidence in most metrics, suggesting its potential utility for public health surveillance. However, its application requires sufficient data length, and prospective validation is needed before operational deployment.