A novel time-series modeling framework for predicting tuberculosis incidence in Sichuan, China

Tuberculosis (TB) remains a major infectious disease and public health issue in Sichuan Province, China. This study aimed to explore and validate a novel adaptive hybrid model integrating Ensemble Empirical Mode Decomposition (EEMD), Seasonal Autoregressive Integrated Moving Average (SARIMA), and Exponential Smoothing (ES), and apply it to forecasting TB incidence in Sichuan Province, China, for the first time.

We collected monthly TB incidence data from 2006 to 2020 in Sichuan Province, China, and divided the time series into training and test sets. The dataset comprised 180 monthly data points, which were split in an 8:2 ratio, with the training set covering 2006-2017 (144 months) and test set covering 2018-2020 (36 months). Subsequently, SARIMA, ES, and EEMD-SARIMA-ES hybrid models were developed based on the training set. The predictive performance was evaluated using a set of metrics, including the Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and Mean Absolute Percentage Error (MAPE).

The TB incidence from 2006 to 2020 exhibited distinct seasonal and cyclical patterns. The optimal ES model was the Holt-Winters additive (BIC=-0.845; residuals: Ljung Box Q = 22.721, p > 0.05). The optimal SARIMA model was SARIMA(1,0,0)(0,1,1)₁₂ (AIC = 282.18, BIC = 293.71; residuals: Ljung Box Q = 0.079, p > 0.05). The constructed EEMD-SARIMA-ES hybrid model demonstrated superior predictive performance, achieving the lowest error metrics on both the training set (MSE = 3.5050, MAPE = 6.69%, RMSE = 4.9568) and test set (MSE = 0.6897, MAPE = 3.92%, RMSE = 0.9754), thereby outperforming either the ES or SARIMA model alone.

The EEMD-SARIMA-ES hybrid model effectively captured the TB incidence trend in Sichuan Province, China. This model serves as an effective tool for TB surveillance and early warning in Sichuan Province.