logistic模型在新型冠状病毒肺炎疫情中的应用

Application of logistic model to the COVID-19 epidemic

目的拟合新型冠状病毒肺炎疫情发展趋势,为logistic模型在新发传染病流行中的应用提供依据。方法使用logistic模型,基于官方公布的2020年1月10日—3月12日新冠肺炎疫情报告数据,采用非线性最小二乘法进行拟合。结果logistic模型拟合效果较好,4个模型的决定系数R;均高于0.99。拟合曲线与真实疫情的变化趋势吻合。始盛期前模型平均相对误差较大(74.1%~427.0%),始盛期之后降至1.0%~4.1%。模型拟合结果显示全国(湖北省除外)、湖北省(武汉市除外)和上海市于2020年2月2—5日达到疫情峰值,2月6—11日进入缓增期。武汉市则于2月11日达到高峰期,2月16日进入缓增期。模型显示首例病例报告到疫情高峰期的时间间隔以及启动一级响应到疫情盛末期的时间间隔均约为一个最长潜伏期。结论logistic模型对新型冠状病毒肺炎疫情的拟合效果较好,能够对疫情发展态势进行分期,为疫情防控决策和防控措施效果评价提供科学依据。

Objective To fit the epidemic trend of COVID-19 so as to provide evidence for application of logistic model to the epidemic of emerging infectious diseases.Methods Based on logistic model,the officially-reported data about the COVID-19 epidemic from January 10 to March 12,2020 were used to fit the model.The parameters were estimated with non-linear least square estimation method.Results Logistic model fitted well,with the determination coefficients R~2 of 4 models being all higher than 0.99.The fitting curves were consistent with the changing trend of the real epidemic.The average relative errors of the model were large(74.1%-427.0%)before the gradually growing point and decreased to 1.0%-4.1%after the increasingly growing point.The fitting results revealed that the epidemic reached its peak in the whole country(except Hubei Province),Hubei Province(except Wuhan City)and Shanghai on February 2-5,2020,and entered the slow-growing stage on February 6-11,2020.The epidemic reached its peak in Wuhan on February 11,2020,and entered the slow-growing stage on February 16,2020.The model showed that the interval between the first case report and the peak of the epidemic as well as the interval between initiationg the first level emergency response and the decreasingly growing point were both the longest incubation period.Conclusion Logistic model fitted well for the COVID-19 epidemic.It can divide the epidemic trend into stages,and provide a scientific basis for decision making in epidemic prevention and control and effect evaluation of prevention and control measures.