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Accurate incidence forecasting of infectious disease is critical for early prevention and for better government strategic planning. In this paper, we present a comprehensive study of different forecasting methods based on the monthly incidence of typhoid fever. The seasonal autoregressive integrated moving average (SARIMA) model and three different models inspired by neural networks, namely, back propagation neural networks (BPNN), radial basis function neural networks (RBFNN), and Elman recurrent neural networks (ERNN) were compared. The differences as well as the advantages and disadvantages, among the SARIMA model and the neural networks were summarized and discussed. The data obtained for 2005 to 2009 and for 2010 from the Chinese Center for Disease Control and Prevention were used as modeling and forecasting samples, respectively. The performances were evaluated based on three metrics: mean absolute error (MAE), mean absolute percentage error (MAPE), and mean square error (MSE). The results showed that RBFNN obtained the smallest MAE, MAPE and MSE in both the modeling and forecasting processes. The performances of the four models ranked in descending order were: RBFNN, ERNN, BPNN and the SARIMA model. [ABSTRACT FROM AUTHOR]