In the last few days, there have been quite a few reports of studies suggesting that the number of people who have been exposed to Covid-19 is far larger than previously thought. These studies have been based on testing for antibodies against coronavirus (it is unclear whether they are specific to Covid-19, or might reflect exposure to other coronaviruses).
I’m finding it difficult to square these estimates with inferences from direct testing, which (as I understand it) tests whether people currently have the disease. This is a point on which I would really like to see a clear explanation from an epidemiologist, but I haven’t seen one, so I am going to set out my own thoughts.
Alert: Unlike my discussion of the exponential growth rate R, where I was confident in the analysis and rapidly proved correct, this is an amateur effort and I could easily be missing something crucial
- the virus has been around for some number of days D
- infected people will give a positive response to a direct test for d days
- the proportion of positive test results in a random sample of the population is p
Then, as a first approximation, the proportion of people ever exposed is (D/d)p. To estimate D, I’ll assume that very few* people outside China were infected before 1 February, which gives D = 84 as of April 25. I’m less clear about d, but 14 days appears to be the standard estimate for asymptomatic cases. That gives D/d = 6.
The big problem is p. Most places are only testing people who are at high risk because of symptoms or known contacts. Iceland gave 1800 tests to randomly selected volunteers in March, and got a positive rate of 1 per cent, suggesting that the proportion ever exposed would be 6 per cent. That’s a lot of people, but nowhere near enough to make herd immunity a relevant possibility.
- Some were, it’s clear, but if the numbers had been large, we would have seen many more deaths.