Department of Medicine, Department of Neuroscience, Rockefeller Neuroscience Institute, West Virginia University Health Science Center, Morgantown, West Virginia, United States of America.
PLoS One. 2023 Jun 14;18(6):e0287196. doi: 10.1371/journal.pone.0287196. eCollection 2023.
The Susceptible-Exposed-Infectious-Recovered (SEIR) epidemic model has been commonly used to analyze the spread of infectious diseases. This 4-compartment (S, E, I and R) model uses an approximation of temporal homogeneity of individuals in these compartments to calculate the transfer rates of the individuals from compartment E to I to R. Although this SEIR model has been generally adopted, the calculation errors caused by temporal homogeneity approximation have not been quantitatively examined. In this study, a 4-compartment l-i SEIR model considering temporal heterogeneity was developed from a previous epidemic model (Liu X., Results Phys. 2021; 20:103712), and a closed-form solution of the l-i SEIR model was derived. Here, l represents the latent period and i represents the infectious period. Comparing l-i SEIR model with the conventional SEIR model, we are able to examine how individuals move through each corresponding compartment in the two SEIR models to find what information may be missed by the conventional SEIR model and what calculation errors may be introduced by using the temporal homogeneity approximation. Simulations showed that l-i SEIR model could generate propagated curves of infectious cases under the condition of l>i. Similar propagated epidemic curves were reported in literature, but the conventional SEIR model could not generate propagated curves under the same conditions. The theoretical analysis showed that the conventional SEIR model overestimates or underestimates the rate at which individuals move from compartment E to I to R in the rising or falling phase of the number of infectious individuals, respectively. Increasing the rate of change in the number of infectious individuals leads to larger calculation errors in the conventional SEIR model. Simulations from the two SEIR models with assumed parameters or with reported daily COVID-19 cases in the United States and in New York further confirmed the conclusions of the theoretical analysis.
易感-暴露-感染-恢复（SEIR）传染病模型已广泛用于分析传染病的传播。这个四 compartment（S、E、I 和 R）模型使用个体在这些 compartment 中的时间均匀性的近似值来计算个体从 compartment E 到 I 再到 R 的转移率。尽管这个 SEIR 模型已经被广泛采用，但时间均匀性近似所导致的计算误差尚未得到定量检验。在这项研究中，我们从之前的一个传染病模型（Liu X., Results Phys. 2021; 20:103712）中开发了一个考虑时间异质性的四 compartment l-i SEIR 模型，并推导出了 l-i SEIR 模型的封闭解。这里，l 代表潜伏期，i 代表传染期。通过比较 l-i SEIR 模型和传统的 SEIR 模型，我们可以检查个体如何在两个 SEIR 模型中通过每个相应的 compartment，以找到传统 SEIR 模型可能错过的信息，以及使用时间均匀性近似可能引入的计算误差。模拟结果表明，在 l>i 的条件下，l-i SEIR 模型可以产生传染病病例的传播曲线。文献中报道了类似的传播流行病曲线，但在相同条件下，传统 SEIR 模型无法产生传播曲线。理论分析表明，在传染病病例数量上升或下降阶段，传统 SEIR 模型高估或低估了个体从 compartment E 到 I 再到 R 的转移率。传染病病例数量变化率的增加会导致传统 SEIR 模型的计算误差更大。基于假设参数的两个 SEIR 模型的模拟结果或来自美国和纽约的每日 COVID-19 病例的模拟结果进一步证实了理论分析的结论。
