A Time-Dependent SIR Model for COVID-19 With Undetectable Infected Persons
A Time-Dependent SIR Model for COVID-19 With Undetectable Infected Persons
复制标题
DOI：
10.1109/tnse.2020.3024723
复制
发表时间：
2020-10-01
影响因子：
6.6
通讯作者：
Liu, Tzu-Hsuan
中科院分区：
文献类型：
--
作者：
Chen, Yi-Cheng;Lu, Ping-En;Liu, Tzu-Hsuan
在本文中，我们对新冠肺炎进行了数学和数值分析。为了预测新冠肺炎的趋势，我们提出了一个时间相关的SIR模型，该模型跟踪了时间t的传输和恢复率。使用中国权威机构提供的数据，我们的单日预测误差几乎小于3%。利用该模型对中国疫情的转折点和确诊病例总数进行了预测。为了分析未检测到的感染对疾病传播的影响，我们扩展了我们的模型，考虑了两种类型的感染者：可检测到的感染者和不可检测的感染者。是否有暴发用2×2矩阵的谱半径来表征。如果R-0和GT；1，则该矩阵的谱半径大于1，并且存在爆发。我们绘制了疫情爆发的阶段转变图，显示2020年3月2日有几个国家处于爆发新冠肺炎的边缘。为了说明社会距离的有效性，我们分析了配置随机网络中疾病传播的独立级联模型。我们展示了两种社会距离的方法，这两种方法可以导致有效繁殖数R-e的减少。
In this paper, we conduct mathematical and numerical analyses for COVID-19. To predict the trend of COVID-19, we propose a time-dependent SIR model that tracks the transmission and recovering rate at time t. Using the data provided by China authority, we show our one-day prediction errors are almost less than 3%. The turning point and the total number of confirmed cases in China are predicted under our model. To analyze the impact of the undetectable infections on the spread of disease, we extend our model by considering two types of infected persons: detectable and undetectable infected persons. Whether there is an outbreak is characterized by the spectral radius of a 2 x 2 matrix. If R-0 > 1, then the spectral radius of that matrix is greater than 1, and there is an outbreak. We plot the phase transition diagram of an outbreak and show that there are several countries on the verge of COVID-19 outbreaks on Mar. 2, 2020. To illustrate the effectiveness of social distancing, we analyze the independent cascade model for disease propagation in a configuration random network. We show two approaches of social distancing that can lead to a reduction of the effective reproduction number R-e.