[Application of multiple seasonal autoregressive integrated moving average model in predicting the mumps incidence]

To establish multiple seasonal autoregressive integrated moving average model(ARIMA) according to mumps disease incidence in Hunan province, and to predict the mumps incidence from May 2015 to April 2016 in Hunan province by the model.

The data were downloaded from "Disease Surveillance Information Reporting Management System" in China Information System for Disease Control and Prevention. The monthly incidence of mumps in Hunan province was collected from January 2004 to April 2015 according to the onset date, including clinical diagnosis and laboratory confirmed cases. The predictive analysis method was the ARIMA model in SPSS 18.0 software, the ARIMA model was established on the monthly incidence of mumps from January 2004 to April 2014, and the date from May 2014 to April 2015 was used as the testing sample, Box-Ljung Q test was used to test the residual of the selected model. Finally, the monthly incidence of mumps from May 2015 to April 2016 was predicted by the model.

The peak months of the mumps incidence were May to July every year, and the secondary peak months were November to January of the following year, during January 2004 to April 2014 in Hunan province. After the data sequence was handled by smooth sequence, model identification, establishment and diagnosis, the ARIMA(2,1,1) × (0,1,1)(12) was established, Box-Ljung Q test found, Q=8.40, P=0.868, the residual sequence was white noise, the established model to the data information extraction was complete, the model was reasonable. The R(2) value of the model fitting degree was 0.871, and the value of BIC was -1.646, while the average absolute error of the predicted value and the actual value was 0.025/100 000, the average relative error was 13.004%. The relative error of the model for the prediction of the mumps incidence in Hunan province was small, and the predicting results were reliable. Using the ARIMA(2,1,1) ×(0,1,1)(12) model to predict the mumps incidence from April 2016 to May 2015 in Hunan province, the peak months of the mumps incidence were May to July, and the secondary peak months were November to January of the following year, the incidence of the peak month was close to the same period.

The ARIMA(2,1,1)×(0,1,1)(12) model is well fitted the trend of the mumps disease incidence in Hunan province, it has some practical value for the prevention and control of the disease.