ARIMA and ARIMA-ERNN models for prediction of pertussis incidence in mainland China from 2004 to 2021

Objective To compare an autoregressive integrated moving average (ARIMA) model with a model that combines ARIMA with the Elman recurrent neural network (ARIMA-ERNN) in predicting the incidence of pertussis in mainland China. Background The incidence of pertussis has increased rapidly in mainland China since 2016, making the disease an increasing public health threat. There is a pressing need for models capable of accurately predicting the incidence of pertussis in order to guide prevention and control measures. We developed and compared two models for predicting pertussis incidence in mainland China. Methods Data on the incidence of pertussis in mainland China from 2004 to 2019 were obtained from the official website of the Chinese Center for Disease Control and Prevention. An ARIMA model was established using SAS (ver. 9.4) software and an ARIMA-ERNN model was established using MATLAB (ver. R2019a) software. The performances of these models were compared. Results From 2004 to 2019, there were 104,837 reported cases of pertussis in mainland China, with an increasing incidence over time. The incidence of pertussis showed obvious seasonal characteristics, with the peak lasting from March to September every year. Compared with the mean squared error (MSE), mean absolute error (MAE), and mean absolute percentage error (MAPE) of the ARIMA model, those of the ARIMA-ERNN model were 81.43%, 95.97% and 80.86% lower, respectively, in fitting performance. In terms of prediction performance, the MAE, MSE and MAPE were 37.75%, 56.88% and 43.75% lower, respectively. Conclusion The fitting and prediction performances of the ARIMA-ERNN model were better than those of the ARIMA model. This provides theoretical support for the prediction of infectious diseases and should be beneficial to public health decision making.