As someone who’s watched Rt pretty closely, I find this Atlantic article about K from Zeynep Tufekci pretty interesting:
The now-famed R0 (pronounced as “r-naught”) is an average measure of a pathogen’s contagiousness, or the mean number of susceptible people expected to become infected after being exposed to a person with the disease. If one ill person infects three others on average, the R0 is three. This parameter has been widely touted as a key factor in understanding how the pandemic operates. News media have produced multiple explainers and visualizations for it. Movies praised for their scientific accuracy on pandemics are lauded for having characters explain the “all-important” R0. Dashboards track its real-time evolution, often referred to as R or Rt, in response to our interventions. (If people are masking and isolating or immunity is rising, a disease can’t spread the same way anymore, hence the difference between R0 and R.)
Unfortunately, averages aren’t always useful for understanding the distribution of a phenomenon, especially if it has widely varying behavior. If Amazon’s CEO, Jeff Bezos, walks into a bar with 100 regular people in it, the average wealth in that bar suddenly exceeds $1 billion dollars. If I also walk into that bar, not much will change. Clearly, the average is not that useful a number to understand the distribution of wealth in that bar, or how to change it. Sometimes, the mean is not the message. Meanwhile, if the bar has a person infected with COVID-19, and if it is also poorly ventilated and loud, causing people to speak loudly at close range, almost everyone in the room could potentially be infected—a pattern that’s been observed many times since the pandemic begin, and that is similarly not captured by R. That’s where the dispersion comes in.