R0 tells you how many others each person infects on average. So R0 is in one sense the measure of contagiousness--it just tells you how contagious people with the disease are on average.
Consider two different diseases with the same R0, let's say R0 = 2. So each person on average infects 2 others. For the first disease, almost all patients infect exactly two others, but for the second, plenty infect two, many infect one, and a much smaller number infect 10 or even more others. So the average is the same, but the distribution is very different.
Given some oth
...Someone on Reddit linked to this preprint paper arguing that the other moments of the secondary infection curve (variance, skewness, kurtosis) can overwhelm the mean (i.e., the R0) in predicting the number of people ultimately infected. With a high variance, right-skewed, high kurtosis curve (loosely, with relatively few "super-infectors" bringing up the average), there are more chances for the outbreak to stochastically die out before those super-infectors get their chance to keep things going. The authors conclude that "higher moments of the distribution
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Specifically, this is known as a hubness effect (when the distribution of the number of times an item is one of the k nearest neighbors of other items becomes increasingly right skewed as the number of dimensions increases) and (with certain assumptions) should be related to the phenomenon of these being closer to the centroid.