Study Of The Grey Swing Model GM(1,1,sinω) In Forecasting Incidence Of Hemorrhagic Fever With Renal Syndrome

IntroductionHemorrhagic fever with renal syndrome(HFRS) is a human diseases with natural foci caused by hantavirus(HV),its prevalence is extensive and serious,which has become a global public health problem,China is the most severe endemic area of HFRS in the world,which account for >90%of total reported numbers worldwide. HFRS is one of important infectious diseases to prevent and control in China.On the basis of disease surveillance,the prediction of HFRS has an important guiding significance in prevention and control of HFRS,which combined with targeted anti-rodent and vaccination measures.Over the years,lots of scientists have attempted to build many forecast models on HFRS,such as time series model,regression model,grey forecast model and Markov model and so on.However,grey forecast model and time series model are common used at present.Using mathematical models to explore practical problem aims to find the better model which consistence with objective laws.Because each model has its own application conditions,we should set up model basing on characters of data in order to predict for incidence of HFRS more accurately.Grey swing model is more applicable for data with volatility and lager swing.The incidence of HFRS has larger fluctuations and cyclical from long-term trend,therefore HFRS is in line with the application conditions of the grey swing model.However,there was no relevant report of comparative study about this method,The model was compared with GM(1,1) model and ARIMA model to explore the application of GM(1,1,sinω) in predicting incidence of HFRS. Materials and MethodsThe data of incidence was from Liaoning Center for Disease Control and prevention,selecting the annual incidence of HFRS(1/100000) in Shenyang,Liaoning Province from 1984 to 2006.The data was accurate and reliable through a sample survey,checking the report of infectious diseases,correcting cases of mistaken reported and supplementing omitted cases.These models were setted up with statistical software excel2003,SPSS13.0 and Matlab7.0.It was divided into three steps to build models of the GM(1,1) and GM(1,1,sinω):First,according to the formula cumulate each step with excel2003;Second,using Matlab7.0 to determine the grey parameters and then setting up prediction equation;Finally,applying excel to predict.Using ARIMA module in SPSS 13.0 to set up ARIMA model,it was carried out in three steps:(1) model identification:using auto-correlation and partial auto-correlation analysis to analyze the model's smooth,and then determinning alternative model;(2) Model parameter estimation and diagnosis:comparing alternative models in the previous phase and selecting the most appropriate model;(3) prediction.Finally, comparing effect of prediction among three types of models with the indicators of mean error rate(MER) and the coefficient of determination(R²).ResultsARIMA model was ARIMA(1,0,0).grey parameter of GM(1,1)a=-0.0008, b=4.5812,its model:(?)(t+1)=5736.45 e^0.008t-5726.50,GM(1,1,sinω) model grey parameters were a=0.0652,b=7.222,c=-1.184,d=3.7619,grey frequencyω=2Ï€/23,its model was(?)_ω(t+1)=-135.87 e^-0.0652t+134.08+9.70 sin 2kÏ€/23+11.73 cos2kÏ€/23. MERs of ARIMA model,GM(1,1) model and GM(1,1,sinω) model were 24.80%,46.94%and 18.77%,respectively.R² were 0.6770,0.1381 and 0.8497, respectively.Effect of prediction for GM(1,1,sinω) was better than GM(1,1) model and ARIMA model.ConclusionsThe predictive effect of GM(1,1,sinω) was better than GM(1,1) model and ARIMA model,which reflect its having more advantage in volatility and cyclical data. Therefore,GM(1,1,sinω) was valuable in prediction of incidence of HFRS and was worth promoting widely.