Time series modeling of pertussis incidence in China from 2004 to 2018 with a novel wavelet based SARIMA-NAR hybrid model

BACKGROUND: It is a daunting task to discontinue pertussis completely in China owing to its growing increase in the incidence. While basic to any formulation of prevention and control measures is early response for future epidemic trends. Discrete wavelet transform(DWT) has been emerged as a powerful tool in decomposing time series into different constituents, which facilitates better improvement in prediction accuracy. Thus we aim to integrate modeling approaches as a decision-making supportive tool for formulating health resources. METHODS: We constructed a novel hybrid method based on the pertussis morbidity cases from January 2004 to May 2018 in China, where the approximations and details decomposed by DWT were forecasted by a seasonal autoregressive integrated moving average (SARIMA) and nonlinear autoregressive network (NAR), respectively. Then, the obtained values were aggregated as the final results predicted by the combined model. Finally, the performance was compared with the SARIMA, NAR and traditional SARIMA-NAR techniques. RESULTS: The hybrid technique at level 2 of db2 wavelet including a SARIMA(0,1,3)(1,0,0)(12)modelfor the approximation-forecasting and NAR model with 12 hidden units and 4 delays for the detail d1-forecasting, along with another NAR model with 11 hidden units and 5 delays for the detail d2-forecasting notably outperformed other wavelets, SARIMA, NAR and traditional SARIMA-NAR techniques in terms of the mean square error, root mean square error, mean absolute error and mean absolute percentage error. Descriptive statistics exhibited that a substantial rise was observed in the notifications from 2013 to 2018, and there was an apparent seasonality with summer peak. Moreover, the trend was projected to continue upwards in the near future. CONCLUSIONS: This hybrid approach has an outstanding ability to improve the prediction accuracy relative to the others, which can be of great help in the prevention of pertussis. Besides, under current trend of pertussis morbidity, it is required to urgently address strategically within the proper policy adopted.