Table_2_Mathematical modeling of SARS-CoV-2 variant substitutions in European countries: transmission dynamics and epidemiological insights.XLSX

BackgroundCountries across Europe have faced similar evolutions of SARS-CoV-2 variants of concern, including the Alpha, Delta, and Omicron variants.Materials and methodsWe used data from GISAID and applied a robust, automated mathematical substitution model to study the dynamics of COVID-19 variants in Europe over a period of more than 2 years, from late 2020 to early 2023. This model identifies variant substitution patterns and distinguishes between residual and dominant behavior. We used weekly sequencing data from 19 European countries to estimate the increase in transmissibility (Δβ)  between consecutive SARS-CoV-2 variants. In addition, we focused on large countries with separate regional outbreaks and complex scenarios of multiple competing variants.ResultsOur model accurately reproduced the observed substitution patterns between the Alpha, Delta, and Omicron major variants. We estimated the daily variant prevalence and calculated Δβ between variants, revealing that: (i) Δβ increased progressively from the Alpha to the Omicron variant; (ii) Δβ showed a high degree of variability within Omicron variants; (iii) a higher Δβ was associated with a later emergence of the variant within a country; (iv) a higher degree of immunization of the population against previous variants was associated with a higher Δβ for the Delta variant; (v) larger countries exhibited smaller Δβ, suggesting regionally diverse outbreaks within the same country; and finally (vi) the model reliably captures the dynamics of competing variants, even in complex scenarios.ConclusionThe use of mathematical models allows for precise and reliable estimation of daily cases of each variant. By quantifying Δβ, we have tracked the spread of the different variants across Europe, highlighting a robust increase in transmissibility trend from Alpha to Omicron. Additionally, we have shown that the geographical characteristics of a country, as well as the timing of new variant entrances, can explain some of the observed differences in variant substitution dynamics across countries.

欧洲各国在 SARS-CoV-2 变异株的演变过程中呈现出相似的态势，包括 Alpha、Delta 和 Omicron 变异株。本研究采用 GISAID 的数据，并运用了一种稳健的、自动化的数学替代模型，对 2020 年末至 2023 年初超过 2 年的时间里欧洲 COVID-19 变异株的动态进行了研究。该模型能够识别变异株的替代模式，并区分残余和主导行为。我们利用来自 19 个欧洲国家的每周测序数据，估计了连续 SARS-CoV-2 变异株之间的传播能力增加（Δβ）。此外，我们还专注于那些经历独立区域性暴发和复杂多变异株竞争场景的大国。研究结果揭示，我们的模型准确再现了 Alpha、Delta 和 Omicron 主要变异株之间的替代模式。我们估计了每日变异株的流行率，并计算了不同变异株之间的 Δβ，发现：（i）从 Alpha 变异株到 Omicron 变异株，Δβ 逐步增加；（ii）Omicron 变异株内部的 Δβ 存在高度可变性；（iii）较高的 Δβ 与变异株在某一国家内的较晚出现相关；（iv）针对先前变异株的较高疫苗接种率与 Delta 变异株的较高 Δβ 相关；（v）较大国家表现出较小的 Δβ，暗示同一国家内部的区域性暴发存在多样性；（vi）模型能够可靠地捕捉竞争变异株的动态，即使在复杂场景下。结论：数学模型的应用使得对每日每个变异株的病例数进行精确可靠的估计成为可能。通过量化 Δβ，我们追踪了不同变异株在欧洲的传播，凸显了从 Alpha 到 Omicron 变异株的传播能力呈现稳健增长的趋势。此外，我们还展示了国家的地理特征以及新变异株的出现时机可以解释各国在变异株替代动态中观察到的某些差异。