O'Regan Suzanne M, Drake John M
Odum School of Ecology, University of Georgia, Athens, GA 30602, USA.
Center for the Ecology of Infectious Diseases, University of Georgia, Athens, GA 30602, USA.
Math Biosci Eng. 2025 Mar 28;22(5):1081-1108. doi: 10.3934/mbe.2025039.
Superspreading transmission is usually modeled using the negative binomial distribution, simply because its variance is larger than the mean and it can be long-tailed. However, populations are often partitioned into groups by social, behavioral, or environmental risk factors, particularly in closed settings such as workplaces or care homes. While heterogeneities in infectious histories and contact structure have been considered separately, models for superspreading events that include the joint effects of social and biological risk factors are lacking. To address this need, we developed a mechanistic finite mixture model for the number of secondary infections that unites population partitioning with individual-level heterogeneity in infectious period duration. We showed that the variance in the number of secondary infections is composed of both sources of heterogeneity: risk group structuring and infectiousness. We used the model to construct the outbreak size distribution and to derive critical thresholds for elimination resulting from control activities that differentially target the high-contact subpopulation vs. the population at large. We compared our model with the standard negative binomial distribution and showed that the tail behavior of the outbreak size distribution under a finite mixture model differs substantially. Our results indicate that even if the infectious period follows a bell-shaped distribution, heterogeneity in outbreak sizes may arise due to the influence of population risk structure.
超级传播通常使用负二项分布进行建模，仅仅是因为其方差大于均值且可能具有长尾特性。然而，人群通常会根据社会、行为或环境风险因素被划分为不同的组，特别是在工作场所或养老院等封闭环境中。虽然感染史和接触结构的异质性已被分别考虑，但缺乏包含社会和生物风险因素联合效应的超级传播事件模型。为满足这一需求，我们针对二代感染数量开发了一种机制性有限混合模型，该模型将人群划分与感染期持续时间的个体层面异质性结合起来。我们表明，二代感染数量的方差由两种异质性来源构成：风险组结构和传染性。我们使用该模型构建疫情规模分布，并推导针对高接触亚人群与整个人群的不同控制活动所导致的消除临界阈值。我们将我们的模型与标准负二项分布进行了比较，结果表明有限混合模型下疫情规模分布的尾部行为有很大差异。我们的结果表明，即使感染期遵循钟形分布，由于人群风险结构的影响，疫情规模仍可能出现异质性。
