How to think about controlling the delta variant like an epidemiologist.

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The Centers for Disease Control and Prevention recently shared a finding that shocked epidemiologists: The baseline reproductive number for the delta variant is somewhere between 6 and 9.

The basic reproductive number R0, pronounced arr-naught, is a number that you may have thought of 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 for seasonal influenza ranges between 1 and 2, while the R0 for measles is between 12 and 18. The original non-variant COVID-19 had an estimated R0 of approximately 3 greater than the influenza, but nowhere near as high as measles. Now the CDC has said the delta variant appears to be closer to measles on the contagion scale. Signal Kate Winslet in Contagion explain how worrying things are.

The evidence supporting this update was a new research article in the CDC’s weekly morbidity and mortality report detailing a COVID-19 outbreak after the July 4 celebrations in Cape Cod, Massachusetts. And in light of this, on July 27, the CDC released updated guidelines: All vaccinated and unvaccinated people should wear face masks indoors or in crowds, to prevent the spread of COVID-19.

We, as epidemiologists, would like to explain why the R0 number is so shocking and what it means for the management of the pandemic. We hope that going through some of the math behind the contagiousness of COVID-19, and in particular the delta variant, will help illustrate why the change in 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 epidemiological concept: the effective reproduction number, or Re (pronounced stop). Re is basically the R0 as it plays out in real-world scenarios: it is the average number of people directly infected by a single infectious person, taking into account those in the population who are immune or take precautions . If the R0 describes how the virus spreads in a population where no one is immune, the Re describes what happens when people mask themselves, move away physically, and maybe even get vaccinated. While the R0 value is usually constant for a given viral variant, the Re value will change over time and from location to location depending on how immunity and control measures vary.

Whether we are talking about R0 or Re, the important threshold is 1. Anything above 1 will mean the epidemic will grow, so a major public health goal is to identify when a virus has a Re or R0 greater than 1. and intervene until the Re is less than 1. By looking at the R0 and how it has changed recently, we can determine which strategies are worth focusing on in response to the new variant in order to bring down the Re .

The original non-variant COVID-19 virus had an R0 of about 3, and we know from randomized controlled trials that mRNA vaccines are about 95% effective in preventing serious deaths from the non-variant virus. Now, a little calculation to arrive at 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 vaccination). In mathematical notation, it is Re = R0 (1-x * v). In this simplified equation, x * v represents the immunized population: X is the percentage of people fully vaccinated and v is the efficacy of the vaccine.

In a perfect world, we would drop the Re by vaccinating everyone. If everyone in the United States had been vaccinated with an mRNA vaccine, we would expect only 5% of people to remain susceptible to the virus. Putting these numbers together, if everyone received vaccines that were 95% effective, the Re for non-variant COVID would be much less than 1. (If you do the math: 3 * 0.05 = 0.15.) C is really good! Enough for the disease, in this hypothesis, to eventually go away.

Now, vaccinating 100 percent of people is never realistic, and even if it was, we’re not there yet. What do things look like when you consider the actual number of people fully vaccinated in the United States? As of August 2, about 58% of people in the United States have received at least one dose of the vaccine, and nearly 50% of the total population is fully vaccinated. For simplicity’s sake, suppose everyone has received mRNA vaccines and people who have not completed both doses are not yet protected – this is not true, but it makes the math easier and does not change our conclusions (play with the math if you are not convinced).

Again, the vaccine is not perfect. Taking this into account, about 47 percent of the United States is currently protected and 53 percent is susceptible to infection. If we integrate this into our equation, with the R0 of 3 for the non-variant virus, we get a current overall Re of around 1.6, although we do not take any other precautions. That number is still above 1, indicating why returning to “normal” earlier this summer may not have been the right thing to do. This is also why unvaccinated people have been advised to take precautions against infection. But it’s pretty close to 1, and that’s why vaccinated people were previously told they could stop wearing masks – the hope was that unvaccinated people wearing masks would suffice. If we didn’t have variations, this strategy might have worked pretty well.

Unfortunately we have the delta variant. The CDC estimates the R0 of the delta variant to be between 6 and 9, so let’s see what happens to the above calculation if we use an R0 value of 8. We also need to consider how the delta variant affects vaccine effectiveness. We don’t know for sure how effective our vaccines are against delta, but the best estimates we have are between 85 and 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 United States could reach 5.

You read that right, even after vaccinating half the population, we still expect people infected with the delta variant to infect on average Following people than they would with the original virus. That’s a big deal, and that’s probably why the CDC updated its mask guidelines. The delta variant is a game-changer and the current level of vaccination in the United States is not sufficient to stop its spread.

So what do we do? We need to use all of our tools from 2020, like masking, capacity limits, widespread testing, quarantine, and isolation of those infected or exposed. But, since we have vaccines that are still very effective against delta, we can also figure out how to use them to decrease the number of susceptible people. There are two main options for this: give booster doses to people who have been vaccinated and vaccinate more people. These are not necessarily mutually exclusive, but knowing where to put energy and resources is helpful. So which strategy is the best? Our equation can help you!

Suppose that a booster dose would make the vaccine work as well against the delta variant as in the original trials (95 percent effectiveness). Then imagine that we can find and give a booster dose to the 164 million fully vaccinated people in the United States. This hypothetical scenario gives us a Re of around 4, still higher than the R0 of the non-variant virus of 3. This tells us that boosters are not a good solution. Of course they could bring down the Re a little, but even if all person vaccinated went for a booster, we would still face a big problem. We can do better.

Next, imagine that instead of a booster, more people are persuaded to get the vaccine. If 75 percent of our population were vaccinated (an additional 80 million people), the Re would drop to just below 3. At this level, we know our other public health measures (masking, business closures, etc.) should be enough to control the virus because the steps we took before vaccines became available reduced the spread of COVID every time they were implemented.

Maybe you think convincing an additional 80 million people in the United States to get vaccinated is a big push? 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 receive their second dose, then we would be up to 60 percent fully vaccinated. This would reduce our Re number for the delta variant to 4 — the same level of advantage than getting boosters for 180 million people!

One last question many people ask us: Does this calculation also apply to individual decisions about boosters? The answer is yes and no. In general, boosters won’t do much to help individuals either: most people vaccinated already have fairly high immunity, so they can’t be boosted much further. In contrast, some very specific groups of individuals, such as immunocompromised individuals or the oldest of the elderly, may have responded less well to the initial vaccine. These people may be able to boost their immunity with another dose and may possibly consider a booster by talking to their doctor. But if you’re not in one of these specific groups, it’s best to spend your time convincing your friends, family, and neighbors to go for the shot.

If you play with this equation, you will find that getting vaccinated people who have not been vaccinated is almost always a better decision than giving boosters to people who have already been vaccinated, at least until almost everyone has been vaccinated. So, let’s not get distracted by the reminders and instead focus on encouraging and supporting immunization efforts (the World Health Organization recently announced that this is where it is putting its resources). We can mask a little longer in order to bring the Re of the delta variant closer to 1, or even lower. But I hope that if we all work together to achieve this goal, we can get to a point where masks are no longer needed to control the spread of COVID.


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