COVID-19 epidemic is characterized by the short-term overdispersion manifested in the phenomenon of super-spreading, whereby the majority of the transmission is driven by a minority of infected individuals. On the other hand, as demonstrated in this work, the eventual outcome of the epidemic is determined by the persistent heterogeneity of the population. While this long-term heterogeneity leads, e.g., to a reduction of the Herd Immunity Threshold (HIT), the overall progression of the epidemic is shaped by both persistent and short-term variations in individual susceptibilities and infectivities. We demonstrate how to incorporate persistent heterogeneity into a wide class of epidemiological models, and derive a non-linear dependence of the effective reproduction number Re on the susceptible population fraction S. This approach is further generalized to account for time variations in individual social activity. It is shown that the suppression of the early waves of the COVID-19 epidemic has been facilitated in some locations by Transient Collective Immunity (TCI). This is a fragile state that could be achieved below HIT, but would wane over time due to changing levels of individual social activity. 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.Significance StatementBoth short-term overdispersion, associated, in particular, with superspreading events, and long-term persistent heterogeneity are shown to shape the spread of the COVID-19 pandemic. While the latter is expected to reduce the Herd Immunity Thresh-old (HIT), a suppression of the first wave of the epidemic could be facilitated by a combination of both long- and short-term variations of social activity across the population. By developing the epidemic theory which accounts for heterogeneity and temporal effects, we demonstrate that the 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 would wane over time due to changing levels of social activity. Analysis of the empirical data suggests that by the end of the first wave of the COVID-19 epidemic, hardest-hit areas, such as NYC, have been close TCI, but likely below the long-term HIT.