Research on the predictive effect of a combined model of ARIMA and neural networks on human brucellosis in Shanxi Province, China: a time series predictive analysis

Abstract

Background: Brucellosis is a major public health problem that seriously affects developing countries and could cause significant economic losses to the livestock industry and great harm to human health. Reasonable prediction of the incidence is of great significance in controlling brucellosis and taking preventive measures.

Methods: Our human brucellosis incidence data were extracted from Shanxi Provincial Center for Disease Control and Prevention. We used seasonal-trend decomposition using Loess (STL) and monthplot to analyse the seasonal characteristics of human brucellosis in Shanxi Province from 2007 to 2017. The autoregressive integrated moving average (ARIMA) model, a combined model of ARIMA and the back propagation neural network (ARIMA-BPNN), and a combined model of ARIMA and the Elman recurrent neural network (ARIMA-ERNN) were established separately to make predictions and identify the best model. Additionally, the mean squared error (MAE), mean absolute error (MSE) and mean absolute percentage error (MAPE) were used to evaluate the performance of the model.

Results: We observed that the time series of human brucellosis in Shanxi Province increased from 2007 to 2014 but decreased from 2015 to 2017. It had obvious seasonal characteristics, with the peak lasting from March to July every year. The best fitting and prediction effect was the ARIMA-ERNN model. Compared with those of the ARIMA model, the MAE, MSE and MAPE of the ARIMA-ERNN model decreased by 18.65, 31.48 and 64.35%, respectively, in fitting performance; in terms of prediction performance, the MAE, MSE and MAPE decreased by 60.19, 75.30 and 64.35%, respectively. Second, compared with those of ARIMA-BPNN, the MAE, MSE and MAPE of ARIMA-ERNN decreased by 9.60, 15.73 and 11.58%, respectively, in fitting performance; in terms of prediction performance, the MAE, MSE and MAPE decreased by 31.63, 45.79 and 29.59%, respectively.

Conclusions: The time series of human brucellosis in Shanxi Province from 2007 to 2017 showed obvious seasonal characteristics. The fitting and prediction performances of the ARIMA-ERNN model were better than those of the ARIMA-BPNN and ARIMA models. This will provide some theoretical support for the prediction of infectious diseases and will be beneficial to public health decision making.

Keywords: ARIMA-BPNN model; ARIMA-ERNN model; Human brucellosis; Predictive effect.

Fig. 1

Seasonal decomposition based on STL of human brucellosis in Shanxi Province from 2007 to 2017

Fig. 2

Monthplot of the cases of human brucellosis in Shanxi Province from 2007 to 2017

Fig. 3

Time series plot for the incidence of human brucellosis in Shanxi Province from January 2007 to December 2016

Fig. 4

Plot of human brucellosis incidence after a first-order difference and a seasonal difference

Fig. 5

Autocorrelation and partial autocorrelation plots for the adjusted time series

Fig. 6

Predictive values obtained by using the ARIMA, ARIMA-BPNN and ARIMA-ERNN models and the incidence of human brucellosis in Shanxi Province. The figure is divided into two parts by a dashed line. The left side of the figure is the fitting part, and the right side is the prediction part