Should businesses and universities require vaccinations for employees and students to return? It’s a topic of intense and sometimes heated debate, especially with recent updates to mask-wearing recommendations by the Centers for Disease Control and Prevention. As a mathematician who has studied coronavirus risk at large-scale sporting events and in other places, I believe the answer is a resounding yes.
The reason is simple. Universal vaccination provides a double benefit. On the one hand, with everyone vaccinated, the likelihood drops of unvaccinated people being infectious. On the other hand, even if they do happen to be infectious, your vaccination gives you a second layer of protection.
Straightforward enough. But let’s dig in a little deeper. The numbers show why requiring vaccinations is in workers’ and students’ best interest.
The CDC currently estimates that vaccines reduce the chance of infection from a given exposure by 66% for the Johnson & Johnson vaccine and 94% for the Pfizer and Moderna vaccines. Let us conservatively average this to 80%. (Protection is actually higher, since many more people have received the Pfizer and Moderna vaccines than the Johnson & Johnson vaccine.)
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Moreover, a recent study from Israel suggests that if a vaccinated person does become infected with the virus, the person’s viral load — and hence chance of infecting somebody else — is quartered.
Suppose an office or college requires vaccinations for everyone, and everyone returns. What are the chances of getting the coronavirus from a co-worker or another student? Let’s say that person is Alice. To be any risk to others, she must have encountered an infected person, whom we’ll call Bob, probably outside of work.
First, because Alice is vaccinated, the chance that she gets infected from Bob is reduced to 20%. But even if she is infected, her reduced viral load means that her chance of infecting you — even if you were not vaccinated — would be only a quarter of this, or 5%. However, since you are also vaccinated, that risk in turn is cut by 80%. So the chance that Bob’s infection gets transmitted to you via Alice is reduced to 1% of what it would have been without vaccinations — a massive reduction.
Now, let’s suppose that vaccination is popular but not universal. How much risk reduction does this achieve?
If only 75% of people in the workplace are vaccinated, the chance of transmission (like from Bob to Alice to you) rises more than tenfold, from 1% to 11.5% of what it would have been with no vaccinations. This is still better than if nobody were vaccinated, but not nearly as good as universal vaccination.
Here is the key point: You are protected more by Alice’s vaccination than you are by your own. Just like mask-wearing, vaccination’s greatest societal benefit is preventing outgoing infections, not incoming ones.
Universal vaccination at a workplace has an additional benefit. It increases the vaccination rate in the whole city. This means the number of coronavirus cases will drop (and so Alice’s friend Bob is less likely to be infected in the first place). The way epidemiologists measure this is by estimating the average number of new infections caused by each infected person.
They call this number R0. If R0 is bigger than 1, the number of cases will grow exponentially. To achieve so-called herd immunity, enough of the population must be immune to an infection (either through vaccination or recovery from the disease) to get R0 below 1.
Missouri still has a long way to go to reach herd immunity. According to the Missouri Department of Health and Senior Services, currently only 33% of the population is fully vaccinated.
Last year, Dr. Anthony Fauci, now chief medical adviser to the president, estimated herd immunity would be achieved at 60% to 70% immunity, but as new, more infectious, variants have emerged, he has increased his estimate to 75% to 85%.
As long as the state’s cases persist, you will continue to encounter infections outside the workplace. But at a vaccinated workplace, you will be protected by a double shield — your own vaccination and your co-workers’ shot. Employees who really don’t want to get vaccinated could get biweekly tests instead — that would also be a second shield for their coworkers. Occasional breakthrough coronavirus cases will occur at work, but outbreaks will fizzle out quickly. By requiring vaccinations, businesses and universities can fully, safely and responsibly reopen.
John E. McCarthy is the Spencer T. Olin professor of mathematics and statistics at Washington University. The views expressed are solely the opinion of the writer.