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目的应用改进的GM(1,1)模型对衡水市乙肝的发病率进行趋势分析和预测,并比较其与原GM(1,1)模型的预测效果。方法收集2005年-2015年衡水市乙肝发病率资料,并组成时间序列,对前10年的数据进行建模,2015年的发病率作为检验数据,对四种模型的预测效能进行验证与评价。结果改进的GM(1,1)模型的拟合及预测的平均相对误差分别为0.93%、0.12%,原GM(1.1)模型的拟合及预测的平均相对误差分别为1.41%、0.52%,精度分别提高了34.0%和76.9%。结论改进的GM(1,1)模型拟合和预测效果均优于原GM(1,1)模型。提高背景值精度、优化初值可以提高GM(1,1)模型的拟合和预测效果,对发病率的趋势预测具有较好的应用价值。
Objective To analyze and predict the incidence of hepatitis B in Hengshui City by using the improved GM (1,1) model and compare its predictive value with the original GM (1,1) model. Methods The data of incidence of hepatitis B in Hengshui City from 2005 to 2015 were collected and the time series was compiled. The data of the first 10 years were modeled and the incidence in 2015 was used as the test data to verify and evaluate the predictive efficacy of the four models. Results The average relative error of the improved GM (1,1) model was 0.93% and 0.12%, respectively. The average relative error of the original GM (1.1) model was 1.41% and 0.52%, respectively. Accuracy increased by 34.0% and 76.9% respectively. Conclusion The improved GM (1,1) model fits and predicts better than the original GM (1,1) model. Increasing the precision of the background value and optimizing the initial value can improve the fitting and forecasting effect of the GM (1,1) model, which has a good application value in predicting the trend of the incidence.