Use of a Seasonal Autoregressive Fractionally Integrated Moving Average Model for the Time Series Analysis of Human Brucellosis.

Introduction: Human brucellosis (HB) has re-emerged as a critical public health threat in China, necessitating robust forecasting tools for early intervention. This study evaluates the seasonal autoregressive fractionally integrated moving average (SARFIMA) model's performance in predicting HB epidemics, comparing it with the widely used seasonal autoregressive integrated moving average (SARIMA).

Methods: Monthly HB morbidity data from January 2012 to May 2023 in Henan were collected retrospectively and divided into training (January 2012 to December 2021) and testing (January 2022 to May 2023) segments to evaluate the predictive ability of SARFIMA, comparing it with the seasonal autoregressive integrated moving average (SARIMA). Sensitivity and secondary analyses were also conducted using HB incidence data in different periods in Henan and mainland China to confirm the predictive robustness.

Results: HB incidence exhibited marked seasonality (peaks: May-June; troughs: December-January) and surged post-2018 (annual increase: 34.9%). The analysis identified distinct SARIMA and SARFIMA configurations for different prediction horizons in Henan. 17-step forecasts required autoregressive components with seasonal differencing, while 5-step predictions benefited from moving average terms. The SARFIMA models consistently exhibited fractional differencing parameters (0.329-0.487), indicating persistent temporal dependencies in the data structure. Although the SARFIMA produced smaller forecast errors than the best SARIMA in both horizons, the forecast errors were still large, and the prediction intervals of the SARFIMA were wider than those of the SARIMA. Further cross-validation and secondary analysis also showed that SARFIMA outperformed SARIMA in assessing HB epidemics.

Conclusions: SARFIMA marginally improves HB forecasting accuracy over SARIMA by addressing long-range dependence, but prediction reliability remains limited. Hybrid models integrating environmental/livestock data are recommended. Escalating HB incidence underscores urgent needs for livestock vaccination, public education on unpasteurized dairy risks, and real-time surveillance to mitigate zoonotic transmission in high-risk regions.