Centre for Mathematical Sciences, Lund University, Lund, Sweden.
Department of Engineering, University of Borås, Borås, Sweden.
PLoS One. 2023 Feb 15;18(2):e0279454. doi: 10.1371/journal.pone.0279454. eCollection 2023.
The unfolding of the COVID-19 pandemic has been very difficult to predict using mathematical models for infectious diseases. While it has been demonstrated that variations in susceptibility have a damping effect on key quantities such as the incidence peak, the herd-immunity threshold and the final size of the pandemic, this complex phenomenon is almost impossible to measure or quantify, and it remains unclear how to incorporate it for modeling and prediction. In this work we show that, from a modeling perspective, variability in susceptibility on an individual level is equivalent with a fraction θ of the population having an "artificial" sterilizing immunity. We also derive novel formulas for the herd-immunity threshold and the final size of the pandemic, and show that these values are substantially lower than predicted by the classical formulas, in the presence of variable susceptibility. In the particular case of SARS-CoV-2, there is by now undoubtedly variable susceptibility due to waning immunity from both vaccines and previous infections, and our findings may be used to greatly simplify models. If such variations were also present prior to the first wave, as indicated by a number of studies, these findings can help explain why the magnitude of the initial waves of SARS-CoV-2 was relatively low, compared to what one may have expected based on standard models.
新冠疫情的发展非常难以用传染病的数学模型进行预测。虽然已经证明易感性的变化对发病率峰值、群体免疫阈值和疫情最终规模等关键数量具有阻尼效应，但这种复杂现象几乎无法测量或量化，而且目前尚不清楚如何将其纳入建模和预测中。在这项工作中，我们表明，从建模的角度来看，个体水平上的易感性变化等同于人群中有θ部分人具有“人工”绝育免疫力。我们还推导出了群体免疫阈值和疫情最终规模的新公式，并表明在存在易感性变化的情况下，这些值远低于经典公式的预测值。就 SARS-CoV-2 而言，由于疫苗和先前感染导致的免疫力下降，现在无疑存在易感性变化，如果在第一波疫情之前也存在这种变化，正如许多研究表明的那样，这些发现可以帮助解释为什么 SARS-CoV-2 的初始波幅相对较低，与基于标准模型可能预期的幅度相比。
