The arguments that we should require or even encourage vaccination for COVID of people who do not want to get vaccinated, or that one has a moral duty to be vaccinated, make no sense. The premise behind these is that vaccinated people are less likely to carry COVID and infect others. That premise is false. The reverse is probably true: the vaccinated are MORE likely to infect others than the unvaccinated.
Vaccination gives 90% or better protection against death from the alpha, beta, and delta strains of COVID, but probably no better than 50% protection against be infected and developing any symptoms at all. Here I calculated from British data that the vaccines reduced the likelihood of testing positive for COVID by 66%. But that is probably an overstatement because they reduce severity of disease and the sicker people are more likely to go in for testing. So the vaccines may reduce the likelihood that you are sick enough to go to a hospital for testing by 66%, but undoubtedly less than that that you develop any symptoms at all.
So at best the vaccines reduce the likelihood of developing symptomatic disease by about 50%, which would mean at best they reduce the likelihood you infect others by about 50%. But because the vaccines result in milder illness, the vaccinated are less likely to realize or be sure they have COVID once they are infected, and more likely to continue to go out in public than unvaccinated persons who are infected. They are therefore probably MORE likely to infect others than the unvaccinated.
The data supports this. Here is a chart of COVID cases in the U.S. up to about December 2021.
The trend in cases in August 2021 compared to November 2020 had about the same slope and reached almost as high a plateau. In November 2020 no one had been vaccinated, whereas in August 2021 about two-thirds of the U.S. adult population had been. If the vaccines prevented or even reduced the rate of spread, it is unlikely the slopes of those two peaks and their height would be so similar. It was mostly the delta strain at both times, so it is not that the strain in August 2021 was more contagious or different.
A simple model for COVID spread, or spread of any upper respiratory tract epidemic would be:
new infections = current infections x factor for likelihood of infecting others x number of non-immune people (not previously infected).
Here is a model for November 2020, where I get new cases by multiplying the population (that is infected) x the susceptible population x a transmission factor.
And here is the same model in November 2021 assuming vaccinated people do not transmit at all, as is implicitly suggested by the argument that it is urgent that everyone be vaccinated for the good of others and that you have a moral duty to be vaccinated for the good of others because by being vaccinated you will not transmit COVID to others. By August 2021, 2/3 of the population was vaccinated, so the previous 3 people who were all unvaccinated are now 1 unvaccinated person and 2 vaccinated people. By November 2020 approximately 1/3 of the population had been infected and by August 2021 approximately 2/3 had by my estimates. So the susceptible population was half as large, represented by 1 susceptible in August 2021 compared to 2 previously.
Aug. 2021 model: Vaccinated Do Not Transmit
The result is you would expect relative new infections of 1 compared to 6 in Nov. 2020. That is not what we saw. We saw roughly the same number of new infections.
Next, let’s assume the transmission factor is 0.5 for vaccinated people—that they are half as likely to transmit as the unvaccinated.
Aug. 2021 model: Vaccinated Half as Likely to Transmit
Now the ratio of new cases is 2 compared to 6 in the prior peak. Still too low.
Next try assuming a transmission factor for the vaccinated of 1, meaning they are equally likely to infect others as the unvaccinated.
Aug. 2021 model: Vaccinated Equally Likely to Transmit
Now we have 3 new infections compared to 6 prior to vaccinating anyone, or half as many new cases. That is still lower than the observed ratio of about the same number of new cases and same rate of growth in both the Nov. 2020 and August 2021 peaks.
So let’s try assuming the vaccinated are twice as likely to infect others as the unvaccinated.
Aug. 2021 model: Vaccinated Twice as Likely to Transmit
Now we expect 5 new cases compared to 6 in the Nov. 2020 peak. That is about right. Almost as many new cases and as fast growth of cases as previously. That is about what we observed.
None of this proves anything. There is a lot of randomness in the time of peaks and it is possible that you would get the same size peak in August 2021 as you had had in Nov. 2020 even if the vaccinated are half as likely to infect others as the unvaccinated are. But the better fit is if you assume they are about twice as likely to infect others.
Logic and experience suggest that vaccinated people are MORE likely to infect others than the unvaccinated. Logically they would be more likely to infect others because they are nearly as likely to be infected and carry the virus, since the vaccines prevent serious disease but they do not prevent infection or at best reduce infections by 50%, and then, once infected, the vaccinated have milder disease, so they are less likely to know they are infected, less likely to be sure it is COVID, and more likely to continue to go out and not stay at home bedridden. And the numbers fit that model. The best fit to the fact that our peak in August 2021 was about the same size and grew at about the same rate as the peak in November 2020 comes when you model with an assumption that vaccinated people are twice as likely to infect others as unvaccinated people.
Also, the demand that previously infected people be vaccinated makes no sense. Prior infection gives far greater protection against both death and infection than vaccination does.