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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.
We model and calculate the fraction of infected population necessary to reach herd immunity, taking into account the heterogeneity in infectiousness and susceptibility, as well as the correlation between those two parameters. We show that these cause
It is well recognized that population heterogeneity plays an important role in the spread of epidemics. While individual variations in social activity are often assumed to be persistent, i.e. constant in time, here we discuss the consequences of dyna
SARS-CoV-2 has disrupted the life of billions of people around the world since the first outbreak was officially declared in China at the beginning of 2020. Yet, important questions such as how deadly it is or its degree of spread within different co
We estimate the growth in demand for ICU beds in Chicago during the emerging COVID-19 epidemic, using state-of-the-art computer simulations calibrated for the SARS-CoV-2 virus. The questions we address are these: (1) Will the ICU capacity in Chicag
We present modeling of the COVID-19 epidemic in Illinois, USA, capturing the implementation of a Stay-at-Home order and scenarios for its eventual release. We use a non-Markovian age-of-infection model that is capable of handling long and variable ti