新型冠状病毒肺炎传播与控制数学建模研究

Mathematical Modeling for Spread and Control of COVID-19

为了能准确模拟新型冠状病毒肺炎(COVID-19)的传播动态,给疫情防控政策制定提供一定的参考,提出了一个新的COVID-19传播非线性动力学模型。该模型考虑实际防控措施,将总人口分为易感、潜伏、隔离观察、无症状感染、有症状感染、住院隔离治疗和康复等7类人群;求出并分析了基本再生数;将模型的出院率和病死率拟合为时变函数,利用现有确诊病例数对模型其余参数和部分状态初值进行最小二乘拟合。分别利用湖北省武汉市和湖北省除武汉市外其他地区20天(2020年2月14日~3月4日)内感染COVID-19的实际数据对模型进行仿真验证,仿真结果表明,模型参数拟合的平均相对误差为0.629%;与累计确诊病例数、累计治愈出院数和累计死亡病例数的实际数据相比,所提出模型的武汉市疫情预测平均相对误差分别为0.772%、3.517%和2.025%,湖北省除武汉市外的地区的平均相对误差分别为0.808%、2.241%和2.39%,表明该模型能较准确模拟COVID-19的传播动态,而且具有广泛的适用性。对模型参数进行灵敏性分析,讨论了各种防控措施对COVID-19传播的影响,结果表明,最有效的防控措施依次为减少人与人之间的接触、加强密切接触者的追踪隔离、加大检测和治疗能力使感染者尽快隔离治疗等。

In order to accurately simulate the spread of the coronavirus disease 2019(COVID-19)and provide certain reference for formulation of epidemic prevention and control policies,a new nonlinear dynamics model is presented.Considering real prevention and control measures,the total population is divided into seven groups in the model,including susceptible,latent,quarantined,asymptomatic,symptomatic,hospitalized and recovered groups.The basic reproduction number is calculated and analyzed.The cure rate and mortality rate are fitted as time-varying functions,and the remaining parameters and initial values of some states are fitted by least squares with the number of currently confirmed cases.The real data of COVID-19 in Wuhan and other regions of Hubei Province within 20 days(February 14 to March 4,2020)are used to simulate and verify the model.Simulation results show that the mean relative error of fitting is 0.629%.Compared with the real data of cumulatively confirmed cases,cured cases and deaths,the mean relative errors of the epidemic prediction by the model in Wuhan are 0.772%,3.517%,and 2.025%,respectively,and in other regions of Hubei Province are 0.808%,2.241%and 2.39%,respectively.It indicates that the model can accurately simulate the spread of COVID-19 and has a wide range of applicability.Moreover,sensitivity analysis is made and simulated on the model parameters.The impacts of various prevention and control measures on the spread of COVID-19 are discussed.The analysis results show that the most effective prevention and control measures include reducing contact among people,strengthening tracking and quarantine of close contacts,and increasing detection and treatment capabilities so that the infected people can be isolated and treated as soon as possible.