Department of Mathematics, University of California, Berkeley, USA.
Department of Epidemiology and Biostatistics, University of California, Berkeley School of Public Health, Berkeley, USA.
J Math Biol. 2022 Jun 30;85(1):2. doi: 10.1007/s00285-022-01771-x.
We study a susceptible-exposed-infected-recovered (SEIR) model considered by Aguas et al. (In: Herd immunity thresholds for SARS-CoV-2 estimated from unfolding epidemics, 2021), Gomes et al. (In: J Theor Biol. 540:111063, 2022) where individuals are assumed to differ in their susceptibility or exposure to infection. Under this heterogeneity assumption, epidemic growth is effectively suppressed when the percentage of the population having acquired immunity surpasses a critical level - the herd immunity threshold - that is lower than in homogeneous populations. We derive explicit formulas to calculate herd immunity thresholds and stable configurations, especially when susceptibility or exposure are gamma distributed, and explore extensions of the model.
我们研究了 Aguas 等人考虑的易感性-暴露-感染-恢复（SEIR）模型。（在：从爆发性流行中估计的 SARS-CoV-2 群体免疫阈值，2021 年），Gomes 等人。（在：J 理论生物学。540:111063，2022 年），其中假设个体在易感性或感染暴露方面存在差异。在这种异质性假设下，当具有免疫力的人群百分比超过临界水平-群体免疫阈值-时，流行病的增长将得到有效抑制，而这一水平低于同质人群。我们推导出了计算群体免疫阈值和稳定配置的显式公式，特别是在易感性或暴露呈伽马分布时，并探讨了模型的扩展。
