GM(1,1)模型在我国梅毒发病率预测中的应用

目的 探讨GM(1,1)模型及其新陈代谢模型在我国梅毒发病率预测中的效果,为我国梅毒病情控制提供理论参考。 方法 收集2008－2017年全国梅毒年发病率数据,用R3.4.3软件建立GM(1,1)模型及其新陈代谢模型并预测,比较两类模型的拟合及预测效果。 结果 拟建立的两个GM(1,1)模型及两个新陈代谢模型分别为x⁽¹⁾(k+1)=511.37e^(0.048k)-491.88,x⁽¹⁾(k+1)=1 830.61e^(0.016k) -1 803.75,x⁽¹⁾(k+1)=753.35e^(0.036k)-730.28,x⁽¹⁾(k+1)=922.35e^(0.016k)-895.48。其拟合相对误差为4.38%、0.79%、2.55%、1.96%,预测相对误差为5.46%、5.51%、6.85%、1.48%,模型精度高。 结论 新陈代谢GM(1,1)模型的效果优于普通模型,用监测数据建立GM(1,1)模型优于用预测数据建立模型。

Application of GM (1,1) model to forecasting the incidence rate of syphilis in China

Objective To explore the performance of basic GM(1,1) model and metabolic GM(1,1) model in forecasting the incidence rate of syphilis in China so as to provide theoretical references for syphilis control. Methods The data about yearly incidence rates in China from 2008 to 2017 were collected, and R 3.4.3 software was used to develop models. The fitting and forecasting performance of the models was compared. Results The expression of two basic GM(1,1) models and metabolic GM(1,1) models wasx⁽¹⁾(k+1)=511.37e^(0.048k)-491.88,x⁽¹⁾(k+1)=1 830.61e^(0.016k) -1 803.75,x⁽¹⁾(k+1)=753.35e^(0.036k)-730.28, and x⁽¹⁾(k+1)=922.35e^(0.016k)-895.48,respectively. The relative errors of fitting of these four models were 4.38%, 0.79%, 2.55% and 1.96%, respectively. The relative error of forecastingwas 5.46%, 5.51%, 6.85% and 1.48%, respectively. The accuracy of the four models was high. Conclusions The performance of metabolic GM(1,1) model is better than that of basic GM(1,1) model, and the performance of GM(1,1) model built with actual data is superior to that of model built with forecasted data.