In the previous post I suggested that data from the NHS’s COVID app was consistent with a power law distribution of the rates at which an infected person infects a susceptible person. If this is true, then can we understand why there should be a power law distribution of rates of COVID transmission? Transmission of infectious diseases is very complex, it is between two human beings – and we are very complex – in a complex variable environment – small and large rooms with good and bad ventilation and with the two people close or far apart. So there are many possible candidates for source of the power law in transmission rates. One is plotted above.
This is a plot of the (probability density) distribution of a measure of how much virus is in the mucus of someone infected with COVID-19. The measure is a bit technical, roughly speaking it estimates the concentration of a fragment of the virus’s RNA genome, using a technique called reverse-transcription quantitative polymerase chain reaction (RT-qPCR). The data is from a study by Viloria Winnett and coworkers. Note that this is not the same as the amount of infectious virus present. But semi-quantitatively measuring the concentration of copies of part of a virus’ genome is much easier than quantifying how much infectious virus is present, so RT-qPCR is what is usually done.
As you can see from the log x scale there is a very broad distribution of the concentration of viral gene fragments. Some infected people may have a billion times as much virus as others. Viloria Winnett and coworkers’ data spans about nine decades, i.e., a factor of a billion between lowest and highest viral loads. And the data is well fit by a power law with an exponent -1.1. Data with broad distributions are often well fit by power laws so this is not very surprising but it really does look near perfect here, which did surprise me a bit.
I am not aware of any data directly on the relationship between how much virus is in an infected person, and how infectious they are. But clearly given a choice, you’d want to share a room with someone on the left side of this distribution, not with someone on the right side, with possibly a billion times more virus in their system.
It also seems likely that superspreading events, where one infected person infects many others, are often (always?) caused by those with unusually high viral loads? It also may be true that when say two people spend a lot of time together, for example if they are couple, but the infected one does not infect the other, the viral load of the infected person may be on low side. In any case, the huge range of amount of virus very naturally suggests a huge range in transmission rates.
Chance & Necessity 