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Accurate prediction is a fundamental and leading work of the emergency medicine reserve management. Given that the emergency medicine reserve demand is affected by various factors during the public health events and thus the observed data are composed of different but hard-to-distinguish components, the traditional demand forecasting method is not competent for this case. To bridge this gap, this paper proposes the EMD-ELMAN-ARIMA (ELA) model which first utilizes Empirical Mode Decomposition (EMD) to decompose the original series into various components. The Elman neural network and ARIMA models are employed to forecast the identified components and the final forecast values are generated by integrating the individual component predictions. For the purpose of validation, an empirical study is carried out based on the influenza data of Beijing from 2014 to 2018. The results clearly show the superiority of the proposed ELA algorithm over its two rivals including the ARIMA and ELMAN models.