Department of Mathematics and Statistics, Chonnam National University, Gwangju, South Korea.
Department of Mathematics and Physics, Luoyang Institute of Science and Technology, Henan, China.
Sci Rep. 2024 May 27;14(1):12147. doi: 10.1038/s41598-024-62719-3.
The E/S (exposed/susceptible) ratio is analyzed in the SEIR model. The ratio plays a key role in understanding epidemic dynamics during the 2014-2016 Ebola outbreak in Sierra Leone and Guinea. The maximum value of the ratio occurs immediately before or after the time-dependent reproduction number (R) equals 1, depending on the initial susceptible population (S(0)). It is demonstrated that transmission rate curves corresponding to various incubation periods intersect at a single point referred to as the Cross Point (CP). At this point, the E/S ratio reaches an extremum, signifying a critical shift in transmission dynamics and aligning with the time when R approaches 1. By plotting transmission rate curves, β(t), for any two arbitrary incubation periods and tracking their intersections, we can trace CP over time. CP serves as an indicator of epidemic status, especially when R is close to 1. It provides a practical means of monitoring epidemics without prior knowledge of the incubation period. Through a case study, we estimate the transmission rate and reproduction number, identifying CP and R = 1 while examining the E/S ratio across various values of S(0).
在 SEIR 模型中分析了 E/S（暴露/易感）比值。该比值在理解 2014-2016 年塞拉利昂和几内亚埃博拉疫情期间的疫情动态方面发挥着关键作用。比值的最大值出现在时变繁殖数（R）等于 1 之前或之后，具体取决于初始易感人群（S(0)）。研究表明，对应不同潜伏期的传播率曲线在一个称为交叉点（CP）的单点相交。在这一点上，E/S 比值达到极值，标志着传播动力学的关键转变，与 R 接近 1 的时间一致。通过绘制任意两个潜伏期的传播率曲线β(t)，并跟踪它们的交点，我们可以随着时间推移追踪 CP。CP 是疫情状况的一个指标，特别是在 R 接近 1 时。它提供了一种实用的监测疫情的方法，无需事先了解潜伏期。通过案例研究，我们估计了传播率和繁殖数，确定了 CP 和 R=1，同时检查了各种 S(0)值下的 E/S 比值。
