How much safer would an event be, from the point of view of COVID-19 infection, if all participants were required to be vaccinated? Here is a preliminary analysis, based on the best information I can find as of 17/April/2021.
I am using information from https://www.cdc.gov/coronavirus/2019-ncov/science/science-briefs/fully-vaccinated-people.html The two pieces of information I need for this analysis are:
(i) How much less likely you are to become infected if you have been vaccinated.
(ii) How much less likely a vaccinated person is to be a transmitter of infection.
Neither of these numbers are known, and they vary by the sort of vaccine, what strains of COVID are circulating locally, and perhaps other factors. The CDC currently estimates that in the United States, the effectiveness of vaccines in preventing infection ranges from 74% to 89%. Let us assume for the purpose of this article that it is 80% on average; the numbers will change if this assumption is changed, but not the qualitative conclusion.
Moreover, preliminary data from Israel suggests that if a vaccinated person does become infected, they carry 1/4 the viral load of an uninfected person.
Let us think through what this means if you attend an event, like an in-person class, or a sporting event. Compare hypothetically attending this event when nobody is vaccinated to the following scenarios.
Scenario 1: You are vaccinated, nobody else is. Your risk is reduced to 20%.
Scenario 2: You are not vaccinated, everybody else is. Your probability of getting infected goes down for two reasons: the expected number of interactions with an infected person is only 20% of what it would otherwise have been, and during any such interaction with someone who is infected, you are exposed to only 1/4 of the viral load. So your probability of becoming infected will decrease to roughly 1/4 of 20%, which is 5%.
Scenario 3: Everybody is vaccinated. Then your probability of becoming infected is 20% of 5%, which is 1%.
Scenario 4: Most people are vaccinated, but not all. Suppose 
is the percentage of people vaccinated. How would the expected number of infections at the event change? First, the release of virions decreases by 
. Second, once somebody is exposed, their probability of becoming infected is decreased by a factor of 
. So the total reduction in risk is the product 
. The quadratic nature of this reduction means that if 
, the reduction is to 31.5%. At 
, it reduces the risk to 11.5%.
Notice the following conclusions.
- Like mask-wearing, being vaccinated protects against both getting and transmitting infections, but the reduction in transmission risk is much greater.
- There is a big difference between most people being vaccinated and everybody being vaccinated. Universal vaccination is more than ten times better than 75% vaccination.
- The benefit of everybody being vaccinated is even higher than the reduction to 1% risk outlined above. That is because the analysis assumed that the chance of a random member of the community being infectious was constant. But if transmission probabilities get greatly reduced, the number of infected individuals will go down, so the overall risk from any event will be further reduced.
So for any country, like the United States, that is fortunate enough to have sufficient vaccines to vaccinate the whole population, I strongly favor requiring vaccinations for somebody to participate in any activity that is moderate to high risk, such as going to University, attending a sporting event or concert, going to a restaurant or bar, or working indoors with other people. (Obviously exceptions should be made for those who cannot get vaccinated for medical reasons.) A further benefit of this policy is that reducing the overall number of people catching the disease reduces the chance of a new mutation arising that is worse in some respect than the current ones (more infectious, less affected by vaccines, more deadly, etc).