Before revision:  Our estimates suggest that the hardest-hit areas, such as NYC, are close to the heterogeneity-modified herd immunity threshold following the first wave of the epidemic . However, this type of immunity is fragile as it wanes over time if the pattern of social interactions changes substantially .
After revision:  Our estimates suggest that the hardest-hit areas, such as NYC, are close to the heterogeneity-modified herd immunity threshold following the first wave of the epidemic , but likely remain below the long-term HIT. Thus, in contrast to some previous claims, these regions can still experience subsequent waves .