Center for Space and Habitability, University of Bern, Gesellschaftsstrasse 6, 3012, Bern, Switzerland.
Department of Physics, Astronomy & Astrophysics Group, University of Warwick, Coventry, CV4 7AL, United Kingdom.
Sci Rep. 2020 Nov 9;10(1):19365. doi: 10.1038/s41598-020-76563-8.
Compartmental transmission models have become an invaluable tool to study the dynamics of infectious diseases. The Susceptible-Infectious-Recovered (SIR) model is known to have an exact semi-analytical solution. In the current study, the approach of Harko et al. (Appl. Math. Comput. 236:184-194, 2014) is generalised to obtain an approximate semi-analytical solution of the Susceptible-Exposed-Infectious-Recovered (SEIR) model. The SEIR model curves have nearly the same shapes as the SIR ones, but with a stretch factor applied to them across time that is related to the ratio of the incubation to infectious periods. This finding implies an approximate characteristic timescale, scaled by this stretch factor, that is universal to all SEIR models, which only depends on the basic reproduction number and initial fraction of the population that is infectious.
房室传输模型已成为研究传染病动力学的宝贵工具。众所周知，易感-感染-恢复（SIR）模型具有精确的半解析解。在本研究中，Harko 等人的方法（Appl. Math. Comput. 236:184-194, 2014）被推广，以获得易感-暴露-感染-恢复（SEIR）模型的近似半解析解。SEIR 模型曲线的形状与 SIR 模型曲线几乎相同，但在时间上应用了一个拉伸因子，该因子与潜伏期和感染期的比值有关。这一发现意味着存在一个近似的特征时间尺度，该尺度由拉伸因子缩放，对所有 SEIR 模型都是通用的，仅取决于基本繁殖数和初始感染人群的比例。
