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Background  The early warning model of infectious diseases plays a key role in prevention and control. This study aims to using seasonal autoregressive fractionally integrated moving average (SARFIMA) model to predict the incidence of hemorrhagic fever with renal syndrome (HFRS) and comparing with seasonal autoregressive integrated moving average (SARIMA) model to evaluate its prediction effect.    Methods  Data on notified HFRS cases in Weifang city, Shandong Province were collected from the official website and Shandong Center for Disease Control and Prevention between January 1, 2005 and December 31, 2018. The SARFIMA model considering both the short memory and long memory was performed to fit and predict the HFRS series. Besides, we compared accuracy of fit and prediction between SARFIMA and SARIMA which was used widely in infectious diseases.    Results  Model assessments indicated that the SARFIMA model has better goodness of fit (SARFIMA (1, 0.11, 2)(1, 0, 1) 12 : Akaike information criterion (AIC):-631.31; SARIMA (1, 0, 2)(1, 1, 1) 12 : AIC: − 227.32) and better predictive ability than the SARIMA model (SARFIMA: root mean square error (RMSE):0.058; SARIMA: RMSE: 0.090).    Conclusions  The SARFIMA model produces superior forecast performance than the SARIMA model for HFRS. Hence, the SARFIMA model may help to improve the forecast of monthly HFRS incidence based on a long-range dataset.

SARFIMA model prediction for infectious diseases: application to hemorrhagic fever with renal syndrome and comparing with SARIMA