How bursty infectiousness shapes epidemic dynamics

An epidemic's expected course is determined by the magnitude and timing of a typical person's infectiousness --- captured, in turn, by the basic reproduction number and the generation-time distribution. These fundamental, population-average quantities can mask individual-level variation that shapes how an epidemic actually unfolds: for example, individual variation in the magnitude of infectiousness (overdispersion) creates superspreading, a key feature of the SARS-CoV-1 and SARS-CoV-2 epidemics. However, the impact of individual variation in infectiousness timing is less well understood. Here, we demonstrate that individual infectiousness timing varies substantially and to different degrees across pathogens. For some common pathogens, including influenza, measles, and SARS-CoV-2, infectiousness is "bursty", or highly concentrated and variably-timed across individuals: for example, the window of appreciable infectiousness for SARS-CoV-2 may last for roughly a day, vs. the 9--12 days usually quoted. We show that bursty infectiousness creates superspreading without inherent superspreaders, makes epidemic timing more variable, amplifies the time-sensitivity of common interventions, and complicates inference of key epidemiological parameters. Together with the reproduction number, the generation-time distribution, and overdispersion, burstiness completes a family of basic parameters that govern how epidemics unfold.