It has become increasingly clear that the COVID-19 epidemic is characterized by overdispersion whereby the majority of the transmission is driven by a minority of infected individuals. Such a strong departure from the homogeneity assumptions of the traditional well-mixed compartment model is usually hypothesized to be the result of short-term super-spreader events , such as an individual's extreme rate of virus shedding at the peak of infectivity while attending a large gathering without appropriate mitigation. However, we demonstrate that the spread of epidemics is primarily sensitive to long-term, or persistent heterogeneity of individual susceptibility or infectivity. We demonstrate how to incorporate this 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. Persistent heterogeneity has three important consequences compared to the effects of short-term overdispersion: (1) It results in a major modification of the early epidemic dynamics; (2) It significantly suppresses the herd immunity threshold; (3) It also significantly reduces the final size of the epidemic. We estimate social and biological contributions to persistent heterogeneity using data on real-life face-to-face contact networks and age variation of the incidence rate during the COVID-19 epidemic. In addition, empirical data from the COVID-19 epidemic in New York City (NYC) and Chicago, as well as 50 US states provide a consistent characterization of the level of heterogeneity. 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 .
Epidemics generally spread through a succession of waves that reflect factors on multiple timescales. On short timescales, super-spreading 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 timescales, 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 regions can still experience subsequent waves .
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It has become increasingly clear that the COVID-19 epidemic is characterized by overdispersion whereby the majority of the transmission is driven by a minority of infected individuals. Such a strong departure from the homogeneity assumptions of the traditional well-mixed compartment model is usually hypothesized to be the result of short-term super-spreader events , such as an individual's extreme rate of virus shedding at the peak of infectivity while attending a large gathering without appropriate mitigation. However, we demonstrate that the spread of epidemics is primarily sensitive to long-term, or persistent heterogeneity of individual susceptibility or infectivity. We
Epidemics generally spread through a succession of waves that reflect factors on multiple timescales. On short timescales, super-spreading 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 timescales, including time variations in individual social activity, and
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this heterogeneity
them phenomenologically
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through parameterization. We
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Persistent heterogeneity has three important consequences compared to the effects of short-term overdispersion: (1) It results in a major modification of the early epidemic dynamics; (2) It significantly suppresses the herd immunity threshold; (3) It also significantly reduces the final size
We show that a state of transient collective immunity (TCI) emerges well below the HIT during early, high-paced stages
R
We estimate social and biological contributions to persistent heterogeneity using data on real-life face-to-face contact networks and age variation of the incidence rate during the COVID-19 epidemic. In addition,
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
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in New York City (NYC) and Chicago,
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50 US states provide a consistent characterization of the level of heterogeneity. Our estimates
from real-life face-to-face contact networks. These results
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are close to the heterogeneity-modified herd immunity threshold
have achieved TCI
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. However, this type of immunity is fragile as it wanes over time if the pattern of social interactions changes substantially
, but likely remain below the long-term HIT. Thus, in contrast to some previous claims, these regions can still experience subsequent waves