[Evaluation of performance of influenza trend prediction based on three time series models in Beijing]

Objective: To explore the trend of influenza positive rate in Beijing by using classic autoregressive integrated moving average (ARIMA) model, autoregressive integrated moving average model with exogenous variables (ARIMAX) and vector autoregression model (VAR) to compare the performance of three models in influenza prediction and select the most suitable one for Beijing. Methods: The weekly positive rate of influenza virus nucleic acid test and meteorological data in Beijing from week 1 of 2013 to week 40 of 2024 were collected. The data were divided into four groups with expanding training sets and corresponding testing sets. The training set of the first group was from week 1 of 2013 to week 40 of 2016, and the testing set was from week 41 of 2016 to week 40 of 2017. Subsequent groups extended the training set by one year each time. Data from 2020 to 2023 were excluded due to COVID-19 pandemic. The fourth group used data from the week 1 of 2013 to week 40 of 2023 for training and from the week 41 of 2023 to week 40 of 2024 for testing. Results: The incidence of influenza had seasonality in Beijing with higher incidence in winter and spring. The positive rate of influenza virus was positively correlated with the weekly average atmospheric pressure (r=0.482, P<0.001) and weekly average wind speed (r=0.003, P=0.034), and negatively correlated with the weekly average temperature (r=-0.541, P<0.001). The ARIMAX model incorporating meteorological factors had the best prediction performance, with test set's root mean square error (RMSE) of 0.115 3 and mean absolute error (MAE) of 0.076 7 (the RMSE and MAE values for ARIMA and VAR models were 0.117 1 and 0.163 8, and 0.078 6 and 0.122 3, respectively). The prediction results of the optimal model showed that the positive rate of influenza virus would continue to rise in Beijing after October 2024 and reach peak in the second week of 2025, but the peak positive rate would be lower than that of previous influenza season. Conclusions: Compared with the ARIMA model and the VAR model,the ARIMAX model which used meteorological parameters is more suitable for prediction of long-term influenza trend in Beijing. The influenza trend peak was predicted to occur in the second week of 2025, but lower than that in previous influenza season.