How to Waste Vaccine
The CDC estimates that, as of the end of September, there had been 53 million Covid infections in the U.S., 7.7 times the number of reported cases. The current figure is 16.2 million cases, so if the ratio holds, total number of infections is about 125 million. That is probably too high, since the ratio of infections to cases goes down as the amount of testing goes up, so I will guess a current figure of 100 million.
The U.S. has contracted for enough vaccine from the two sources that have been or almost certainly will be approved to vaccinate another 100 million over the next few months. Combine those numbers and we should have 200 million people who either have had the disease and so are very nearly immune or have been vaccinated and so are very nearly immune, getting us at least close to the level required for herd immunity. Add in the number who will have gotten the infection by then and we should probably be over that level, which means the number of infections should start falling.
There is one problem with this optimistic story. As best I can tell from online discussions, the current plan for allocating the vaccine does not include any attempt to avoid giving it to people who have already had the disease, not even to those who have been diagnosed with it. If so, about a third of the first hundred million doses will be wasted on people who don't need them.
One possible argument for doing it that way is that having Covid does not create perfect immunity, there having been a few cases reported of someone who got the disease, recovered, and was later reinfected. But the vaccine does not create perfect immunity either — reported effectiveness for the first two is about 95%. If as many as five percent of those who had had the disease and recovered were still vulnerable to it, we should have had a lot more than a few cases of reinfections.
To make that argument more precise, consider that, as of the end of September, there had been about seven million reported cases. If infection gave only 95% immunity, about 350,000 of them should have still been vulnerable, a little more than one thousandth of the population. Since the end of September there have been another nine million cases, so more than nine thousand of them should have been known reinfections, individuals who were diagnosed with the disease, recovered, and were then diagnosed again. That did not happen. It follows that, while infection may not give complete immunity, it gives considerably better immunity than the vaccines.
Another possible argument is that tests for whether someone has already had the disease have a significant false positive rate. Checking online, it looks as though the false positive rate for most such tests is below ten percent (specificity>.9). At ten percent, that means that if you skip the people who test positive you are vaccinating an additional ten people for every false positive you are not vaccinating, which sounds like a substantial positive. If we had enough vaccine for everybody it might be better for everyone to get vaccinated, but we don't.
If my analysis is correct, current policy is lethally stupid.
People who know more about this than I do are invited to correct either my interpretation of what is currently being done or my argument for what ought to be.