Forecasting tuberculosis epidemics using an autoregressive fractionally integrated moving average model: a 17-year time series analysis

Tuberculosis (TB) remains a significant public health challenge in Henan, China, requiring accurate forecasting to guide prevention and control efforts. While traditional models like autoregressive integrated moving average (ARIMA) are commonly used, they may not fully capture long-term dependencies in the data. This study evaluates the autoregressive fractionally integrated moving average (ARFIMA) model, which incorporates fractional differencing, to improve TB forecasting by better modelling long-range dependencies and seasonal patterns.

Monthly TB incidence data from January 2007 to May 2023 in Henan were collected. The data set was split into a training set (January 2007-May 2022) and a test set (June 2022-May 2023). Both ARIMA and ARFIMA models were developed using the training set, and their predictive accuracy was assessed on the test set using metrics such as mean absolute deviation, mean absolute percentage error, mean square error, and mean error rate. A sensitivity analysis was conducted to evaluate the robustness of the forecasts.

There were 1 074 081 TB incident cases in Henan during the study period. The TB incidence was reducing at an annual rate of 5.83%, with the seasonal factor >1 between March-July and seasonal factor <1 in other months. The ARIMA (2,0,1)(0,1,1)₁₂ and ARFIMA (2,0,1)(0,0.38,1)₁₂ models were identified as suitable for the data. The ARFIMA model consistently outperformed ARIMA model in the forecasting phase, with lower errors across all metrics (e.g. mean absolute deviation: 467 vs. 569.54; mean absolute percentage error: 0.19 vs. 0.21; mean square error: 620.48 vs. 690.11; mean error rate: 0.14 vs. 0.17). This indicated that the ARFIMA model better captures long-term dependencies and seasonal patterns, leading to more accurate forecasts.

Tuberculosis incidence in Henan shows a clear downward trend with distinct seasonal variation. The ARFIMA model provides more accurate TB incidence forecasts than ARIMA, particularly in capturing long-term trends and seasonality. Effective management of TB at the population level requires proper monitoring and understanding of disease patterns. Forecasting serves as a critical tool for detecting deviations from expected trends, which may signal changes in disease dynamics. Continuous use of the ARFIMA model is essential for guiding public health interventions and ensuring timely responses to emerging challenges in TB control.