A Simulation of a COVID-19 Epidemic Based on a Deterministic SEIR Model
A Simulation of a COVID-19 Epidemic Based on a Deterministic SEIR Model
复制标题
DOI：
10.3389/fpubh.2020.00230
复制
发表时间：
2020-05-28
影响因子：
5.2
通讯作者：
Ba, Jing
中科院分区：
文献类型：
--
作者：
Carcione, Jose M.;Santos, Juan E.;Ba, Jing
一种新型冠状病毒引起的流行病在意大利北部蔓延，传染性很强。我们实现了一个SEIR模型来计算这次流行病的感染人口和伤亡人数。这个例子可能理想地考虑到疫情于2月24日开始流行的意大利伦巴第地区的情况，但绝不会试图进行严格的案例研究，因为缺乏适当的数据，不同参数，即家庭隔离程度和社会距离作为时间函数的变化，接触者和感染者的初始数量，潜伏期和感染期，以及死亡率。首先，我们通过改变参数和初始条件对模型的结果进行分析(为了开始流行，应该至少有一个接触到病毒的人或一个有传染病的人)。然后，我们考虑了伦巴第案，用到目前为止(2020年5月5日)的死亡人数来校准模型，并根据文献中报告的值来约束参数。高峰大约出现在第37天(3月31日)，最初的繁殖率R(0)为3，第22天为1.36，第35天后为0.8，表明不同程度的封锁。预计死亡人数约为15600人，疫情结束时将有270万人感染。为死亡者提供更好适应的潜伏期为4.25天，感染期为4天，死亡率为0.00144/天[根据报告的(官方)伤亡人数计算]。感染死亡率(IFR)为0.57%，如果假设死亡人数是报告人数的两倍，则为2.37%。然而，这些比率取决于最初接触的人数。如果接触的人数大约增加九倍，那么在疫情结束时感染人数将增加三倍，IFR=0.47%。如果我们放松这些限制，并使用更大范围的潜伏期和感染期的上下限，我们观察到较长的潜伏期(13天对4.25天)会产生相同的IFR(0.6对0.57%)，但在第一个病例中暴露的个人要多9倍。这组参数的其他选择也提供了与数据很好的匹配，但某些结果可能不现实。因此，准确确定这一流行病的死亡率和特征取决于对参数的精确界限的了解。除了具体的例子，这项工作中提出的分析显示了隔离措施、社会距离和对传播条件的了解如何帮助我们理解流行病的动态。因此，重要的是量化这一过程，以验证封锁的有效性。
An epidemic disease caused by a new coronavirus has spread in Northern Italy with a strong contagion rate. We implement an SEIR model to compute the infected population and the number of casualties of this epidemic. The example may ideally regard the situation in the Italian Region of Lombardy, where the epidemic started on February 24, but by no means attempts to perform a rigorous case study in view of the lack of suitable data and the uncertainty of the different parameters, namely, the variation of the degree of home isolation and social distancing as a function of time, the initial number of exposed individuals and infected people, the incubation and infectious periods, and the fatality rate. First, we perform an analysis of the results of the model by varying the parameters and initial conditions (in order for the epidemic to start, there should be at least one exposed or one infectious human). Then, we consider the Lombardy case and calibrate the model with the number of dead individuals to date (May 5, 2020) and constrain the parameters on the basis of values reported in the literature. The peak occurs at day 37 (March 31) approximately, with a reproduction ratioR(0)of 3 initially, 1.36 at day 22, and 0.8 after day 35, indicating different degrees of lockdown. The predicted death toll is approximately 15,600 casualties, with 2.7 million infected individuals at the end of the epidemic. The incubation period providing a better fit to the dead individuals is 4.25 days, and the infectious period is 4 days, with a fatality rate of 0.00144/day [values based on the reported (official) number of casualties]. The infection fatality rate (IFR) is 0.57%, and it is 2.37% if twice the reported number of casualties is assumed. However, these rates depend on the initial number of exposed individuals. If approximately nine times more individuals are exposed, there are three times more infected people at the end of the epidemic and IFR = 0.47%. If we relax these constraints and use a wider range of lower and upper bounds for the incubation and infectious periods, we observe that a higher incubation period (13 vs. 4.25 days) gives the same IFR (0.6 vs. 0.57%), but nine times more exposed individuals in the first case. Other choices of the set of parameters also provide a good fit to the data, but some of the results may not be realistic. Therefore, an accurate determination of the fatality rate and characteristics of the epidemic is subject to knowledge of the precise bounds of the parameters. Besides the specific example, the analysis proposed in this work shows how isolation measures, social distancing, and knowledge of the diffusion conditions help us to understand the dynamics of the epidemic. Hence, it is important to quantify the process to verify the effectiveness of the lockdown.