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

Alexei V. Tkachenko, Sergei Maslov, Ahmed Elbanna, George N. Wong, Zachary J. Weiner, Nigel Goldenfeld

Research output: Contribution to journalArticlepeer-review


Epidemics generally spread through a succession of waves that reflect factors on multiple timescales. On short timescales, superspreading events lead to burstiness and overdispersion, whereas long-term persistent heterogeneity in susceptibility is expected to lead to a reduction in both the infection peak and the herd immunity threshold (HIT). Here, we develop a general approach to encompass both timescales, including time variations in individual social activity, and demonstrate how to incorporate them phenomenologically into a wide class of epidemiological models through reparameterization. We derive a nonlinear 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, highpaced 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 long-lasting herd immunity: Subsequent waves may emerge due to behavioral changes in the population, driven by, for example, seasonal factors. Transient and long-term levels of heterogeneity are estimated using empirical data from the COVID-19 epidemic and from real-life faceto-face contact networks. These results suggest that the hardest hit areas, such as New York City, 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 regions can still experience subsequent waves.

Original languageEnglish (US)
Article numbere2015972118
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number17
StatePublished - Apr 27 2021


  • COVID-19
  • epidemic theory
  • overdispersion
  • heterogeneity
  • Heterogeneity
  • Covid-19
  • Overdispersion
  • Epidemic theory

ASJC Scopus subject areas

  • General


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