COVID-19: Why The Vaccinated Can’t Throw Caution To The Wind

by Raywat Deonandan, PhD
Epidemiologist & Associate Professor
University of Ottawa
(I add my credentials to these COVID-19 blog posts in case they get shared. I want readers to know that my opinion is supposedly an educated and informed one)

Today’s post was motivated by four things.  First, news that the CDC is recommending that vaccinated people be free to interact without masks with other vaccinated people. Second, is news that vaccinated people are now rushing to the airports to engage in world travel. Third, the common refrain from some political corners that “experts want us to wear masks after we’re vaccinated. We’re never going to be rid of masks!” And fourth, this heartbreaking tweet from Dr Brian Levine:

I think it’s important to explain why we simply can’t interact with others willy-nilly, unless we really have to, even if we’ve been vaccinated against COVID-19.

Efficacy is Not 100%

First, let’s acknowledge once more the miracle of the COVID vaccines, in particular how efficacious they are. There is a misunderstanding, though, of what vaccine “efficacy” or “effectiveness” means.

Consider this contingency table, which I have created from the real clinical trial data for Pfizer’s COVID vaccine, called BNT162b2:

We compute a “relative risk” or “risk ratio” by dividing the disease incidence rate of the vaccinated group by the placebo group:

RR = (8/21720) / (162/21728)

…which gives us a relative risk of 4.9%.  This means that vaccinated people were only 4.9% as likely as the unvaccinated to get symptomatic COVID-19.

The vaccine efficacy is given by:

VE = 1 – RR = 1 – 0.049 = 95.1%

So the Pfizer vaccine is remarkably efficacious at ~95%. And while that number is very very high, it’s not 100%. It’s not perfect. Some people who get vaccinated and who become exposed to the SARS-CoV2 virus are still going to get the disease.


Transmission is Not 0%

The next question we need to ask is, how much does vaccination reduce actual disease transmission? Sure, the vaccines are great at preventing symptomatic disease, but do they prevent someone from getting asymptomatic disease? This is important because we know that asymptomatic people can still pass it on. By some estimates, more than half of cases are the result of transmission from those without symptoms. (Of course, we must distinguish between the truly asymptomatic and the merely pre-symptomatic; but that’s another story. Suffice it to say that some transmission is due to people who do not have symptoms and who never will develop symptoms. We can argue over how big of a number “some” is.)

One of the big questions surrounding the vaccines early was how well they would prevent asymptomatic infection.

The clinical trial of the AstraZeneca vaccine had sufficient testing capacity to answer that question for that particular formulation, and found that that vaccine could prevent 67% of asymptomatic cases, which is pretty good.

And a recent study of the mRNA vaccines found that people who had had two doses of one of those vaccines were 80% less likely to develop asymptomatic COVID-19 than people who had not been vaccinated. That’s an even better number.

But 80%, while good, is not 100%. Prevention of transmission is imperfect.


So What Does That Mean?

Consider two scenarios. In one scenario, two vaccinated people get together. In another scenario, one vaccinated person meets an unvaccinated person.

Scenario One:

Two vaccinated people (Mohammed and Rahul) meeting up without masks or distancing. What is the probability of one of them giving COVID to the other? At its most basic, that probability can be estimated by:

P = Pe X Pi X Pt1 X Pt2


Pe = probability that the first vaccinated person (Mohammed) was exposed to someone with COVID-19

Pi = probability that Mohammed actually contracted COVID from that exposure

Pt1 = probability that Mohammed’s vaccination could fail to prevent onward transmission

Pt2 = probability that Rahul’s vaccination could fail to prevent receiving that infection


I suggest that:

Pe = the incidence of COVID-19 in the community

Pi = the vaccine ineffectiveness rate, or ~5%. (Some will argue that this should be the incidence rate in in the vaccinated group, or 0.04%. But this is a handwaving argument, so bear with me.)

Pt1 = the transmission failure rate, or 20%

Pt2 = the vaccine ineffectiveness rate again, or 5%


All of this works out to:

P = Pe X 0.05 X 0.20 X 0.05  = 0.05% of Pe

That’s vanishingly small, even if Pe is large. This is why the CDC said it’s probably okay for two vaccinated people to lick peanut butter off of each other’s mucous membranes.


Scenario Two.

Now consider if Rahul was not vaccinated. The probability of him becoming infected by Mohammed is:

P = Pe X Pi X Pt = Pe X 0.05 X 0.20 = 1% of Pe

Okay, 1% doesn’t sound very high, and it isn’t… but it’s much higher than 0.05%.

The takeaway message, though, is that whether P is low or high in scenario #2 depends entirely on how high Pe is. If Pe is large, then the risk to Rahul is noticeably higher.


What Is Pe?

Pe is the probability of exposure. It’s the community incidence rate. It’s how much COVID is zipping around the population.

In other words, while the community has a high burden of COVID, even the vaccinated have a real chance of passing it on to someone else, as Dr Levine’s mother and grandmother discovered. And frankly, even the vaccinated have a non-zero chance of becoming infected.


So What Does This All Mean?

Vaccination is not a panacea. It’s a mitigation tool, like mask-wearing and social distancing. It’s just our best mitigation tool. Think of it as a really really good mask. It’s great protection, but it’s not perfect.

Even when community levels are high, the risk posed by two vaccinated people interacting is low. (Assuming, of course, that my efficacy and transmission numbers are in the right ballpark).

When community levels are high, the risk posed by a vaccinated person to an unvaccinated one depends on how fragile the unvaccinated person is. If you’re a vaccinated senior and you want to socialize with your young, healthy, unvaccinated loved ones, then I think that that’s a risk worth taking, if your mental health needs demand it.

But if community levels are high, it is unwise for a vaccinated person to socialize with a fragile unvaccinated person without substantial mitigation tools in place (i.e., mask wearing.)


No no no. Only until community levels drop. Only until Pe is low enough that 1% of Pe is vanishingly small.

Remember: the goal of vaccination is not to make individuals untouchable by the disease. The goal of vaccination is to reduce the amount of COVID circulating in the community so the the probability of anyone being exposed, and anyone transmitting, becomes so low that it’s not worth talking about. And we will get there sometime this year. I promise you.


Please don’t cite these numbers as if they are peer-reviewed gospel. I have done these back-of-the-napkin calculations as a demonstration of how to think about cascading probabilities of disease transmission and to point out that the probability of exposure (Pe) remains the thing that we have to drive down. These are not “take it to the bank” numbers.

There are other ways to arrange these equations, different numbers you might want to multiply, and different data one could cite. I don’t want to argue about that. I just want to stress that vaccination is not a license to socialize… not until the overall levels of infection in the population fall considerably.