Does an infectious dose of a virus exist?

Maybe not. The basic model for the transmission of infectious diseases like COVID assumes that there is such a thing as an infectious dose of a virus, and that these doses act independently. By independently I mean that if you are exposed to one infectious dose, then the probability that you do not become infected is some probability, call it p, while if you are exposed to two infectious doses, then the probability that neither of them infects you is p² — independent probabilities multiply. As 2 here is an exponent, the probability you avoid infection decreases exponentially with the number of these doses. This predicts a sharp – exponential – increase in the probability of becoming infected, with increasing amounts of virus.

We do not have data on infections in people, but we do have data on infections for cells growing in culture (ie growing in a petri dish or similar). And this exponential variation is not what is observed. See the figure above*. The data are the blue discs and are from the work of Jaafar et al.. The fit of an exponential function is shown as the green dotted curve. The fit is terrible.

The data of Jaafar are not for infection of humans, but Jaafar’s virus samples are saliva samples taken from humans, that are then tested to see if they infect cells growing in culture. The x axis is the concentration of virus in the saliva sample, as assessed via qPCR (=quantitative Polymerase Chain Reaction – a fancy technique that semi-quantitatively counts how many copies of the one the RNA-encoded genes of the virus is present). A big question is whether the probability of infection of one of us, also varies in this way. We just don’t know the answer to this.

The data for the probability of infection of Jaafar and coworkers clearly varies much more slowly than the model predicts. The infection probability only increases very slowly (not x axis is a log scale!) with the concentration of viral RNA (which is what qPCR measures). We can rule out each copy of the viral RNA being a virus that acts independently and has the same probability of leading to an infection, independent of virus concentration.

So, what is going on? The concentration of the viral RNA is given in terms of copies per microlitre (μl), and a swab probably has a volume which is also roughly a microlitre. So, when the concentration is around 10 to 20/μl, the sample used to try and infect the cells in cell culture, should also contain 10 to 20 copies of the viral RNA. From the plot above, the probability of infection is then around 10%. If indeed these samples have around 10 to 20 viruses, it looks like around 10 viruses have a 10% chance of establishing an infection.

I would say that it is not surprising that you may need 10 or a few 10s of viruses to get a 10% infection probability. In principle one virus can establish an infection but the virus could be damaged (while the viral RNA still shows in qPCR), and cells resist invasion by viruses: they have defences that can destroy viruses. So infection of a cell by a virus is not guaranteed.

What is surprising is that although apparently 10 viruses give a roughly 10% chance of infection, a million viruses give only around an 80% chance of infection. Increasing the number of viruses by 999,990, or by a factor of 100,000, whichever way you look, only increases the chances of infection by a factor of 8. The cells still have a 20% chance of avoiding infection.

Other than ruling out the idea that individual viruses act independently, I am not sure we know much about what is going on here. It is true that PCR does not actually measure the amount of virus present. But it may well be that there is something collective going on. Virologists may have studied this, but it may be a buried in the virology literature.

The fact that we don’t know what is going on is a problem. Ultimately, we are not interested in infecting cells in culture medium, we are interested in infections in humans. Without any model of what is happening in cells in culture, we are guessing a bit when we extrapolate from data on cells in culture (where we have lots of quantitative data) to humans (where we have little quantitative data).

* The orange curve is a fit of a stretched exponential function, which is not a great fit but does capture the slowly varying probability of infection.