title: The development of a combined mathematical model to forecast the incidence of hepatitis E in Shanghai, China.
abstract: BACKGROUND
  Sporadic hepatitis E has become an important public health concern in China. Accurate forecasting of the incidence of hepatitis E is needed to better plan future medical needs. Few mathematical models can be used because hepatitis E morbidity data has both linear and nonlinear patterns. We developed a combined mathematical model using an autoregressive integrated moving average model (ARIMA) and a back propagation neural network (BPNN) to forecast the incidence of hepatitis E.
  
  
  METHODS
  The morbidity data of hepatitis E in Shanghai from 2000 to 2012 were retrieved from the China Information System for Disease Control and Prevention. The ARIMA-BPNN combined model was trained with 144 months of morbidity data from January 2000 to December 2011, validated with 12 months of data January 2012 to December 2012, and then employed to forecast hepatitis E incidence January 2013 to December 2013 in Shanghai. Residual analysis, Root Mean Square Error (RMSE), normalized Bayesian Information Criterion (BIC), and stationary R square methods were used to compare the goodness-of-fit among ARIMA models. The Bayesian regularization back-propagation algorithm was used to train the network. The mean error rate (MER) was used to assess the validity of the combined model.
  
  
  RESULTS
  A total of 7,489 hepatitis E cases was reported in Shanghai from 2000 to 2012. Goodness-of-fit (stationary R2=0.531, BIC= -4.768, Ljung-Box Q statistics=15.59, P=0.482) and parameter estimates were used to determine the best-fitting model as ARIMA (0,1,1)×(0,1,1)12. Predicted morbidity values in 2012 from best-fitting ARIMA model and actual morbidity data from 2000 to 2011 were used to further construct the combined model. The MER of the ARIMA model and the ARIMA-BPNN combined model were 0.250 and 0.176, respectively. The forecasted incidence of hepatitis E in 2013 was 0.095 to 0.372 per 100,000 population. There was a seasonal variation with a peak during January-March and a nadir during August-October.
  
  
  CONCLUSIONS
  Time series analysis suggested a seasonal pattern of hepatitis E morbidity in Shanghai, China. An ARIMA-BPNN combined model was used to fit the linear and nonlinear patterns of time series data, and accurately forecast hepatitis E infections.
authors.affiliation: The Key Laboratory of Public Health Safety of Minister of Education - Department of Epidemiology, Fudan University School of Public Health, Building 8 Room 441, 138 Yi Xue Yuan Road, Shanghai 200032, China. yuyan08@yahoo.com.
authors.forename: Hong
authors.initials: H
authors.lastname: Ren
authors.forename: Jian
authors.initials: J
authors.lastname: Li
authors.forename: Zheng-An
authors.initials: ZA
authors.lastname: Yuan
authors.forename: Jia-Yu
authors.initials: JY
authors.lastname: Hu
authors.forename: Yan
authors.initials: Y
authors.lastname: Yu
authors.forename: Yi-Han
authors.initials: YH
authors.lastname: Lu
mesh_terms: D002681:China / Q000453:epidemiology; D005544:Forecasting; D016751:Hepatitis E / Q000453:epidemiology*; D006801:Humans; D015994:Incidence; D008962:Models, Theoretical