The Centers for Disease Control and Prevention recently shared a conclusion that shocked epidemiologists: The basic reproductive number for the delta variant is somewhere between 6 and 9.
The basic reproductive number R0, pronounced arr-naught, is a number you might have thought about in passing throughout the pandemic, but to review: It represents the average number of people directly infected by a single infectious person if no one in the population is immune to the disease. The R0 value of seasonal influenza varies between 1 and 2, while the R0 for measles lies between 12 and 18. The original nonvariant COVID-19 had an estimated R0 of about 3–larger than the flu, but nowhere near as high as measles. Now, the CDC has stated that the delta variant seems to be closer to measles on the contagion scale. Cue Kate Winslet in Contagion explaining how concerning things are.
The evidence to support this update was a new research article in the CDC’s Morbidity and Mortality Weekly Report detailing an outbreak of COVID-19 following July 4 celebrations on Cape Cod, Massachusetts. And in light of it, on July 27, the CDC issued updated guidance: All vaccinated and unvaccinated individuals should wear face masks when indoors or in crowds, to prevent COVID-19 spread.
We, as epidemiologists, would like to explain why the R0 number is so shocking—and what it means for managing the pandemic. We hope that walking through some of the math behind how contagious COVID-19 is, and particularly the delta variant, will help illustrate why the shift on masking makes sense as well as what else you can do to help (and, namely, a big thing to skip).
First, let’s define another key epidemiologic concept: the effective reproductive number, or Re (pronounced arr-ee). Re is basically the R0 as it plays out in real-world scenarios: It’s the average number of people directly infected by a single infectious person, taking into account people in the population who are immune or are taking precautions. If the R0 describes how the virus spreads in a population where no one is immune, the Re describes what happens when people are masking, physical distancing, and maybe even vaccinated. While the R0 value is typically constant for a given virus variant, the Re value will change over time and from place to place depending on how immunity and control measures vary.
Whether we’re talking about R0 or Re, the important threshold is 1. Anything over 1 will mean the outbreak that will grow, so a major goal of public health is to identify when a virus has an Re or R0 greater than 1—and intervene until the Re is less than 1. By examining the R0, and how it’s changed recently, we can figure out what strategies are worth focusing on in response to the new variant in order to bring down the Re.
The original nonvariant COVID-19 virus had an R0 of about 3, and we know from randomized controlled trials that the mRNA vaccines are about 95 percent effective at preventing severe death from the nonvariant virus. Now, a little math to get to the Re: We can estimate the Re in a given place and time by multiplying R0 by the proportion of the population that is currently susceptible to the disease (or 1 minus the proportion of the population that is fully immune to disease, say from vaccination). In mathematical notation, this is Re = R0(1-x*v). In this simplified equation, x*v represents the population that is immune: X is the percent of people who are fully vaccinated, and v is the vaccine’s effectiveness.
In a perfect world, we’d get the Re down by vaccinating everyone. If everyone in the U.S. had been vaccinated with an mRNA vaccine, we would expect that only 5 percent of people would remain susceptible to the virus. Putting those numbers together, if everybody received vaccines that are 95 percent effective, the Re for nonvariant COVID would be very much lower than 1. (If you do the math: 3*0.05 = 0.15.) That’s really good! Enough that the disease would, in this hypothetical, eventually disappear.
Now, vaccinating 100 percent of people is never realistic, and even if it were, we aren’t there yet. How do things look if we consider the actual number of people fully vaccinated in the U.S.? As of Aug. 2, about 58 percent of people in the U.S. had received at least one vaccine dose, and nearly 50 percent of the total population is fully vaccinated. For simplicity, let’s assume everyone got mRNA vaccines and that people who haven’t finished both doses aren’t yet protected—this isn’t true, but it makes the math easier and doesn’t change our conclusions (play with the math if you’re not convinced).
Again, the vaccine isn’t perfect—accounting for this, about 47 percent of the U.S. is currently protected, and 53 percent is susceptible to infection. If we plug that into our equation, along with the R0 of 3 for the nonvariant virus, we get a current overall Re of about 1.6—even if we take no other precautions. This is still higher than 1, which indicates why going back to “normal” earlier this summer may not have been the right thing to do. It’s also why unvaccinated people have been advised to take precautions against infection. But it is pretty close to 1, and that’s why vaccinated people were previously told they could stop wearing masks—the hope was that unvaccinated people alone wearing masks would be enough. If we didn’t have any variants, that strategy might have worked pretty well.
Unfortunately, we’ve got the delta variant. The CDC estimates the R0 of the delta variant as between 6 and 9, so let’s see what happens to the calculation above if we use an R0 value of 8. We also need to consider how the delta variant affects the effectiveness of the vaccines. We don’t know for sure how effective our vaccines are against delta, but the best estimates we have range at about 85 to 88 percent. Using a value of 85 percent (with 53 percent of the population susceptible), we find that the current Re for the delta variant in the U.S. might be as high as 5.
You read that right—even after vaccinating half the population, we still expect that people infected with the delta variant will, on average, infect more people than they would have with original virus. That’s a big deal, and it’s likely why the CDC has updated its guidance on masks. The delta variant is a game-changer and the current level of vaccination in the U.S. is not enough to stop it spreading.
So, what do we do? We need to use all our tools from 2020, like masking, capacity limits, widespread testing, and quarantine and isolation of infected or exposed individuals. But, since we have vaccines that are still very effective against delta, we also can figure out how to use them to decrease the number of susceptible people. There are two main options for that: giving vaccinated people booster doses, and vaccinating more people. These aren’t mutually exclusive, necessarily, but it’s useful to have a sense of where to put energy and resources. So, which strategy is better? Our equation can help!
Let’s imagine a booster dose would make the vaccine work just as well against the delta variant as it did in the original trials (95 percent effectiveness). Then let’s imagine we can find and give all 164 million fully vaccinated people in the U.S. a booster dose. This hypothetical scenario gives us an Re of about 4—still higher than the nonvariant virus’s R0 of 3. This tells us that boosters are not a great solution. Sure, they could bring the Re down a little, but even if every vaccinated person went and got a booster, we’d still be facing a big problem. We can do better.
Next, let’s imagine that, instead of a booster, we persuade more people to get vaccinated. If 75 percent of our population were vaccinated (another 80 million people), the Re would drop to just below 3. At that level, we know that our other public health measures (masking, business closures, etc.) should be enough to control the virus because the measures we took before the vaccines were available did reduce the spread of COVID whenever they were implemented.
Maybe you think convincing 80 million more people in the U.S. to get vaccinated is a big stretch? Let’s aim lower then. If we could make sure that the roughly 30 million people who have already received one dose of an mRNA vaccine get their second dose, then we would be up to 60 percent fully vaccinated. That would put our Re number for the delta variant down to 4—the same level of benefit as getting boosters to 180 million people!
One last question many people ask us: Does this math apply to individual decisions about boosters, too? The answer is yes and no. In general, boosters won’t do much to help individuals, either: Most vaccinated people have fairly high immunity already, so they can’t be boosted much further. On the other hand, some very specific groups of individuals, such as immunocompromised individuals or the oldest of the elderly, might have responded less well to the initial vaccine. Those people might be able to give their immunity a boost with another dose and could potentially consider a booster in discussion with their medical doctor. But if you aren’t in one of those specific groups, your time is better spent convincing friends, family, and neighbors to go get their shots.
If you play with this equation, you’ll find that getting vaccines to unvaccinated people is pretty much always a better move than giving boosters to the already vaccinated, at least until we’ve gotten almost everyone vaccinated. So, let’s not get distracted by boosters and instead focus on encouraging and supporting vaccination efforts (the World Health Organization recently announced that’s where it’s putting its resources). We may be masking for a while longer in an effort to get the Re of the delta variant closer to 1, or even below. But hopefully, if we all work together toward this goal, we can get to a point where masks are no longer needed to control the spread of COVID.