新型冠状病毒肺炎疫情的分时段分地区微分方程模型

The Differential Equation Model for the Novel Coronavirus Pneumonia by Time and Region

摘要: 利用2020年1月23日至2020年3月5日官方所给出的新冠肺炎疫情实时数据，考虑到感染者在潜伏期、发病期不切掉传播途径下均具有传染性，建立了新型冠状病毒肺炎传播动力学微分方程模型。湖北省较全国其他地区的疫情严重及2月12日确诊方案的改变对模型中各个参数的影响，为了减小误差，将预测的地区分为湖北省和湖北省外地区，并以2月12日为界，湖北省的模型内使用不同的参数，湖北省外则利用1月23日至3月5日的数据建模，运用数据拟合的方法给出该模型中各参数并龙格–库塔法求解微分方程，预测出全国的疫情在1月23日之后的第70天可基本结束，全国非输入确诊病例数约82,000多人，死亡人数约3300。

Abstract: Based on Novel coronavirus pneumonia’s real-time data from January 23rd to March 5th in 2020 provided by authority and considering the virus’s characteristic of infectivity, we establish a dif-ferential equation model of its transmission dynamics. Considering the great difference between Hubei and other parts of the country in epidemic situation, we divide the forecast areas into Hubei province and others in China. Since the influence to the parameters of the model caused by changes of diagnostic protocols on February 12th, we consider the different parameters in the model before and after February 12th for Hubei Province to minimize the error, while the parameters are not changed in other parts of China from January 23rd to March 5th. The numerical results of the differential equations are obtained by Runge-Kutta method. The numerical results tell that the na-tional epidemic can end basically at the seventieth day after January 23rd, and there will be more than 82,000 national no-imported cases, about 3300 the death toll.