Finite mixture models of superspreading in epidemics

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.