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Epidemics generally spread through a succession of waves that reflect factorson multiple timescales. On short timescales, super-spreading events lead toburstiness and overdispersion, while long-term persistent heterogeneity insusceptibility is expected to lead to a reduction in the infection peak and theherd immunity threshold (HIT). Here, we develop a general approach to encompassboth timescales, including time variations in individual social activity, anddemonstrate how to incorporate them phenomenologically into a wide class ofepidemiological models through parameterization. We derive a non-lineardependence of the effective reproduction number Re on the susceptiblepopulation fraction S. We show that a state of transient collective immunity(TCI) emerges well below the HIT during early, high-paced stages of theepidemic. However, this is a fragile state that wanes over time due to changinglevels of social activity, and so the infection peak is not an indication ofherd immunity: subsequent waves can and will emerge due to behavioral changesin the population, driven (e.g.) by seasonal factors. Transient and long-termlevels of heterogeneity are estimated by using empirical data from the COVID-19epidemic as well as from real-life face-to-face contact networks. These resultssuggest that the hardest-hit areas, such as NYC, have achieved TCI followingthe first wave of the epidemic, but likely remain below the long-term HIT.Thus, in contrast to some previous claims, these regions can still experiencesubsequent waves.

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