Above is a plot of estimated viral load for a sample of people infected with COVID-19. It is a probability (density) distribution, so the x axis is how much virus is in the saliva of the person, and the height of the points (y axis) tells you how many people have that load. Note that there are two studies, one by Viloria Winnett and coworkers and one by Takatsuki and coworkers, and that both found an enormous range of amounts of virus. Many orders of magnitude in both cases. The units are estimated numbers of copies of the viral RNA gene, per millilitre (ml). The points are the data while the lines are my power law fits, in both cases the exponents are close to minus one. The probability of having a viral load v scales approximately as one over v.
But what has this to do with Elon Musk? Elon Musk is very very rich. Below is an analogous plot to the one above but below the x axis is not the amount of virus, but wealth in billions of dollars. The data is from a Forbes magazine list of the few thousand dollar billionaires on Earth. Note that both plots are log-log plots, although as the Forbes list only looks at the richest few thousand people, in the plot below there is only a dynamic range of around 100, from mere billionaires at the bottom up to the richest men on Earth, Musk, Bezos etc, who are worth of order 100 billion. As with the virus data, the data is reasonably well fit by a power law, this time with an exponent around minus two.
So the distributions of SARS-CoV-2 virus in infected people’s throats and in people’s wealth are similar, both are very broad, approximately power-law distributions. We know that those in far right of the wealth distribution, like Musk, Bezos and Gates, have disproportionate amounts of influence over our lives. What about those in the far right of the virus distribution? Do they too have a disproportionate influence, but in this case on the spread of COVID-19?
Maybe. There is evidence for superspreaders: people infected with COVID-19 who infect ten or even tens of people, sometimes within an hour or two, at a superspreading event. It seems very likely that superspreaders are at the very high end of the viral load distribution, but I don’t think we have direct evidence of this. Typically superspreading events are only identified after the event, when it is too late to obtain viral loads.
Chance & Necessity 