Objective  To explore the feasibility of autoregressive fractionally integrated moving average (ARFIMA) model in predicting the incidence of hand foot and mouth disease(HFMD).

  Methods  Based on the Python language, the ARFIMA model and autoregressive integrated moving average (ARIMA) model were established by using the incidence data of HFMD in Shanxi province from January 2008 to August 2021 as the training set, and the data from September 2021 to August 2022 were used as the test set to evaluate the effects of these two models constructed. The optimal model was selected to predict the incidence of HFMD in Shanxi from September 2022 to August 2023.

  Results  ARFIMA (4,0.05,5) model and ARIMA (5,1,2) model were constructed, and the residual white noise test indicated that p-values were greater than 0.05. Using the constructed ARFIMA model and ARIMA model for prediction of the test set, the mean absolute errors were 0.92 and 1.58, the mean absolute percentage errors were 1.28 and 1.67, the mean square errors were 1.18 and 3.56, and the root mean square errors were 1.09 and 1.89, respectively. The optimal ARFIMA (4,0.05,5) model was used to predict the monthly incidence of HFMD in Shanxi from September 2022 to August 2023, indicating that the incidence of HFMD would range from 0.13/100 000 to 3.51/100 000.

  Conclusion  Compared with the ARIMA model, the ARFIMA model, which takes the long memory of the series into account, can predict the incidence trend of HFMD more accurately in Shanxi and is more feasible in the prevention and control of HFMD.