Forecast model analysis for the morbidity of tuberculosis in Xinjiang, China

Abstract

Tuberculosis is a major global public health problem, which also affects economic and social development. China has the second largest burden of tuberculosis in the world. The tuberculosis morbidity in Xinjiang is much higher than the national situation; therefore, there is an urgent need for monitoring and predicting tuberculosis morbidity so as to make the control of tuberculosis more effective. Recently, the Box-Jenkins approach, specifically the autoregressive integrated moving average (ARIMA) model, is typically applied to predict the morbidity of infectious diseases; it can take into account changing trends, periodic changes, and random disturbances in time series. Autoregressive conditional heteroscedasticity (ARCH) models are the prevalent tools used to deal with time series heteroscedasticity. In this study, based on the data of the tuberculosis morbidity from January 2004 to June 2014 in Xinjiang, we establish the single ARIMA (1, 1, 2) (1, 1, 1)12 model and the combined ARIMA (1, 1, 2) (1, 1, 1)12-ARCH (1) model, which can be used to predict the tuberculosis morbidity successfully in Xinjiang. Comparative analyses show that the combined model is more effective. To the best of our knowledge, this is the first study to establish the ARIMA model and ARIMA-ARCH model for prediction and monitoring the monthly morbidity of tuberculosis in Xinjiang. Based on the results of this study, the ARIMA (1, 1, 2) (1, 1, 1)12-ARCH (1) model is suggested to give tuberculosis surveillance by providing estimates on tuberculosis morbidity trends in Xinjiang, China.

Fig 1. The annual morbidity of tuberculosis from 2008 to 2012 in Xinjiang and in China.

Xinjiang is one of the autonomous regions of China; its morbidity of tuberculosis (TB) is much higher than the national situation.

Fig 2. Tuberculosis morbidity from January 2004 to June 2014 in Xinjiang.

The Data was obtained from the website of Bureau of Health, Xinjiang Uyghur Autonomous Region, China. The tuberculosis morbidity has roughly seasonal fluctuations and slightly rising trend.

Fig 3. The ACF and PACF graphs of stabilized tuberculosis morbidity series.

ACF = autocorrelation function, PACF = partial autocorrelation function. Based on the ACF, we determine the possible values of q (q = 1, 2 or 3) and Q(Q = 1) of ARIMA (p, d, q) (P, D, Q) ₁₂, and based on PACF, we determine the possible values of p (p = 1, 2 or 3) and P (P = 1) of ARIMA (p, d, q) (P, D, Q)₁₂.

Fig 4. Histogram-Normality test of residual series of the ARIMA (1, 1, 2) (1, 1, 1)₁₂ model.

Skewness is not 0, Kurtosis is more than 3, Probability is 0.000000, all that suggest the residual series do not obey normal distribution and obey heavier-tailed distribution.

Fig 5. Fitted values of ARIMA (1, 1, 2) (1, 1, 1)₁₂ model and ARIMA (1, 1, 2) (1, 1, 1)₁₂-ARCH (1) model versus the actual monthly morbidity of tuberculosis before December 2013.

We can see fitting performance of the two models by this Figure.

Fig 6. Forecast values of ARIMA (1, 1, 2) (1, 1, 1)₁₂ model and ARIMA (1, 1, 2) (1, 1, 1)₁₂-ARCH (1) model versus the actual monthly morbidity of tuberculosis from January 2014 to June 2014.

We can see predication performance of the two models by this Figure.