Time-dependent heterogeneity leads to transient suppression of COVID-19 epidemic, not herd immunity

Epidemics generally spread through a succession of waves that reflect factors on multiple time-scales. On short time-scales, superspreading events lead to burstiness and overdispersion, while long-term persistent heterogeneity in susceptibility is expected to lead to a reduction in the infection peak and the herd immunity threshold (HIT). Here, we develop a general approach to encompass both time-scales, including time variations in individual social activity, and demonstrate how to incorporate them phenomenologically into a wide class of epidemiological models through parameterization. We derive a non-linear dependence of the effective reproduction number Re on the susceptible population fraction S. We show that a state of transient collective immunity (TCI) emerges well below the HIT during early, high-paced stages of the epidemic. However, this is a fragile state that wanes over time due to changing levels of social activity, and so the infection peak is not an indication of herd immunity: subsequent waves can and will emerge due to behavioral changes in the population, driven (e.g.) by seasonal factors. Transient and long-term levels of heterogeneity are estimated by using empirical data from the COVID-19 epidemic as well as from real-life face-to-face contact networks. These results suggest that the hardest-hit areas, such as NYC, have achieved TCI following the first wave of the epidemic, but likely remain below the long-term HIT. Thus, in contrast to some previous claims, these reqions can still experience subsequent waves. O_TEXTBOXSignificance Statement Epidemics generally spread through a succession of waves that reflect factors on multiple time-scales. Here, we develop a general approach to encompass super-spreading and population heterogeneity, and demonstrate that a fragile state of transient collective immunity (TCI) emerges well below the HIT during early, high-paced stages of the epidemic. However, this is not an indication of herd immunity: subsequent waves can and will emerge due to behavioral changes in the population, driven (e.g.) by seasonal factors. Analysis of empirical data suggests that even in locations with strong first waves of COVID-19, subsequent waves will still emerge. C_TEXTBOX