Time Series Analysis and Forecasting of the Hand-Foot-Mouth Disease Morbidity in China Using An Advanced Exponential Smoothing State Space TBATS Model

Abstract

Objective

The high morbidity, complex seasonality, and recurring risk of hand-foot-and-mouth disease (HFMD) exert a major burden in China. Forecasting its epidemic trends is greatly instrumental in informing vaccine and targeted interventions. This study sets out to investigate the usefulness of an advanced exponential smoothing state space framework by combining Box-Cox transformations, Fourier representations with time-varying coefficients and autoregressive moving average (ARMA) error correction (TBATS) method to assess the temporal trends of HFMD in China.

Methods

Data from January 2009 to December 2019 were drawn, and then they were split into two segments comprising the in-sample training data and out-of-sample testing data to develop and validate the TBATS model, and its fitting and forecasting abilities were compared with the most frequently used seasonal autoregressive integrated moving average (SARIMA) method.

Results

Following the modelling procedures of the SARIMA and TBATS methods, the SARIMA (1,0,1)(0,1,1)₁₂ and TBATS (0.024, {1,1}, 0.855, {<12,4>}) specifications were recognized as being the optimal models, respectively, for the 12-step ahead forecasting, along with the SARIMA (1,0,1)(0,1,1)₁₂ and TBATS (0.062, {1,3}, 0.86, {<12,4>}) models as being the optimal models, respectively, for the 24-step ahead forecasting. Among them, the optimal TBATS models produced lower error rates in both 12-step and 24-step ahead forecasting aspects compared to the preferred SARIMA models. Descriptive analysis of the data showed a significantly high level and a marked dual seasonal pattern in the HFMD morbidity.

Conclusion

The TBATS model has the capacity to outperform the most frequently used SARIMA model in forecasting the HFMD incidence in China, and it can be recommended as a flexible and useful tool in the decision-making process of HFMD prevention and control in China.

Keywords:

• HFMD
• morbidity
• TBATS
• SARIMA
• models
• time series analysis

Acknowledgments

We thanked all the people who took part in the gathering of HFMD cases. This study was supported by the Innovation and Entrepreneurship Training Project for University Students of Henan Province and Xinxiang Medical University (S202010472007 and XYXSKYZ201932), the Key Scientific Research Project of Universities in Henan (21A330004), and the National Natural Fund Youth Project (31802024)

Data Sharing Statement

All data for this work are presented in the results and conclusions or please contact the corresponding author on the reproducibility of this work.

Author Contributions

All authors contributed to the conceptualization, data curation, investigation, methodology, project administration, software, validation, visualization, and review of the manuscript, and agreeing to publish this work.

Disclosure

The authors report no conflicts of interest in this work.