Temporal trends analysis of tuberculosis morbidity in mainland China from 1997 to 2025 using a new SARIMA-NARNNX hybrid model

Abstract

Objective: Tuberculosis (TB) remains a major deadly threat in mainland China. Early warning and advanced response systems play a central role in addressing such a wide-ranging threat. The purpose of this study is to establish a new hybrid model combining a seasonal autoregressive integrated moving average (SARIMA) model and a non-linear autoregressive neural network with exogenous input (NARNNX) model to understand the future epidemiological patterns of TB morbidity.

Methods: We develop a SARIMA-NARNNX hybrid model for forecasting future levels of TB incidence based on data containing 255 observations from January 1997 to March 2018 in mainland China, and the ultimate simulating and forecasting performances were compared with the basic SARIMA, non-linear autoregressive neural network (NARNN) and error-trend-seasonal (ETS) approaches, as well as the SARIMA-generalised regression neural network (GRNN) and SARIMA-NARNN hybrid techniques.

Results: In terms of the root mean square error, mean absolute error, mean error rate and mean absolute percentage error, the identified best-fitting SARIMA-NARNNX combined model with 17 hidden neurons and 4 feedback delays had smaller values in both in-sample simulating scheme and the out-of-sample forecasting scheme than the preferred single SARIMA(2,1,3)(0,1,1)₁₂ model, a NARNN with 19 hidden neurons and 6 feedback delays and ETS(M,A,A), and the best-performing SARIMA-GRNN and SARIMA-NARNN models with 32 hidden neurons and 6 feedback delays. Every year, there was an obvious high-risk season for the notified TB cases in March and April. Importantly, the epidemic levels of TB from 2006 to 2017 trended slightly downward. According to the projection results from 2018 to 2025, TB incidence will continue to drop by 3.002% annually but will remain high.

Conclusions: The new SARIMA-NARNNX combined model visibly outperforms the other methods. This hybrid model should be used for forecasting the long-term epidemic patterns of TB, and it may serve as a beneficial and effective tool for controlling this disease.

Keywords: forecasting; models; statistics; tuberculosis.

Figure 1

Decomposition of monthly TB time series in mainland China from 1997 to 2018 into trend and cyclical components using the Hodrick-Prescott filter. TB, tuberculosis.

Figure 2

Diagnostic checking for the residuals generated by the SARIMA(2,1,3)×(0,1,1)₁₂ method. (A) Standardised residual plot; (B) autocorrelation function (ACF) of the errors at various lags; (C) Partial ACF (PACF) of the errors at various lags. SARIMA, seasonal autoregressive integrated moving average.

Figure 3

The RMSE values corresponding to different smoothing factors for the SARIMA-GRNN combined technique. It can be seen that when smoothing factor is 0.006, the lowest RMSE value is 0.0024. GRNN, generalised regression neural network; SARIMA, seasonal autoregressive integrated moving average.

Figure 4

The resultant error autocorrelation function (ACF) plots for the three optimal hybrid models selected. (A) ACF plot of errors for the best-performing SARIMA-GRNN hybrid technique across varying lags; (B) ACF plot of errors for the best-performing SARIMA-NARNN hybrid technique across varying lags; (C) ACF plot of errors for the best-performing SARIMA-NARNNX hybrid technique across varying lags. GRNN, generalised regression neural network; NARNN, non-linear autoregressive neural network; NARNNX, non-linear autoregressive neural network with exogenous input; SARIMA, seasonal autoregressive integrated moving average; TB, tuberculosis.

Figure 5

The corresponding time series response plots of outputs and targets for the best-undertaking SARIMA-NARNN and SARIMA-NARNNX hybrid models at various time points. (A) Response plot of the outputs and targets for the best-undertaking SARIMA-NARNN hybrid model; (B) Response plot of the outputs and targets for the best-undertaking SARIMA-NARNNX hybrid model. NARNN, non-linear autoregressive neural network; NARNNX, non-linear autoregressive neural network with exogenous input; SARIMA, seasonal autoregressive integrated moving average; TB, tuberculosis.

Figure 6

The comparison graph of the fitting and forecasting results among various models. GRNN, generalised regression neural network; NARNN, non-linear autoregressive neural network; NARNNX, non-linear autoregressive neural network with exogenous input; SARIMA, seasonal autoregressive integrated moving average.

Figure 7

The comparison graph between the estimated epidemic trends of TB incidence from 2018 to 2025 and the milestones goals suggested by WHO. TB, tuberculosis.