How many Coloradans need to get vaccinated to reach coronavirus herd immunity? It’s complicated.

On Wednesday, Colorado officially crossed the 209,000 mark for the number of people who have received at least one dose of coronavirus vaccine — meaning that more than 3% of the state’s population is now on its way to immunity through inoculation.

But how much further do we still have to go?

The launch of the vaccination campaign reignites questions about what it means to reach “herd immunity” in the state — that glorious threshold shrouded in the mind’s eye in a magical fog, for beyond that point lies normalcy. More technically, once enough people in a community are immune from a virus to reach herd immunity, the virus can’t find enough susceptible people to jump into and the local epidemic begins to die out.

There’s a problem with this clean, perfect image of herd immunity, though. It is, alas, not quite as simple as it seems.

“There is not a magical number,” said Dr. Lisa Miller, an epidemiologist and a professor at the Colorado School of Public Health.

Miller, with more than 20 years working in public health, knows this problem well. She previously worked at the Colorado Department of Public Health and Environment as the head of the Communicable Disease Branch and as the state epidemiologist. 

“I think it’s easier to think of it as a range of numbers,” she said. “This really isn’t an exact number.”

And even that range of numbers is difficult to pin down with a virus as new and evolving as the SARS-CoV-2 coronavirus, the cause of the COVID-19 pandemic. There’s a bunch of different factors to consider.

The magic formula

Herd immunity is a complicated concept, but it’s also just a pretty simple formula. To calculate the percentage of people who need to be immune from a virus in order to reach herd immunity, all you have to know is the virus’ basic reproduction number — its R₀ (pronounced R-naught). The number represents the average number of people that each infected person will pass the virus to.

Once you know that, calculating herd immunity is something any schoolkid could do, using the formula. Here it is:

1 – (1 ÷ R₀)

Divide 1 by the R₀ value, then subtract the result from 1. If your R₀ is a terrifyingly high 18 (which it can be with measles), then the herd immunity threshold is 94%. If R₀ is 2 — something more akin to a slow-spreading common cold — the herd immunity threshold is 50%.

It’s also important to note that R₀ is separate from the severity of the virus. Some fearsome viruses, like ebola, have low R₀ values.

What is coronavirus’ R₀?

This is where we run into the first pothole on the way to herd immunity nirvana, though. R₀ isn’t a fixed number for any virus.

“There is no one exact number for R₀,” Miller said. “That can vary depending on the population, depending on the virus.”

And the R₀ for the SARS-CoV-2 coronavirus is especially uncertain. Some estimates come in as low as 2. Some are as high as almost 6.

Miller said most studies are pegging the R₀ for the coronavirus between 3 and 5. That means the herd immunity threshold is between 67% and 80%.

(Quick side note: We’re talking about the natural reproduction number here — how the virus would spread in a population with no immunity if we did nothing to stop it. Researchers in Colorado are also trying to estimate the effective reproduction number, which is how the virus is spreading now after taking into consideration everything we’re doing to slow it down, such as mask-wearing and social distancing. The latest estimates place the effective reproduction number in the state at 0.7, meaning the virus is in decline for now.)

Don’t forget that viruses can mutate

Even if we think we have a good handle on the R₀ for SARS-CoV-2, that doesn’t mean it will stay put.

The newly discovered variant of the virus first identified in the U.K. is a good example of this. Researchers estimate that the variant may be as much as 70% more transmissible. The researchers arrived at these estimates by looking at rates of spread during periods of high levels of social distancing in England, and warned that “extrapolation to other transmission contexts therefore requires caution.”

So it’s not clear what the new variant’s R₀ might be or, in turn, how much that would impact the herd immunity threshold. But a more transmissible coronavirus would require a community to have greater levels of immunity before it clears the bar.

Or forget that all populations are different

The concept of one, simple herd immunity number rests on a bit of a fallacy. It imagines that, in a large state like Colorado, everyone just mixes randomly like pingpong balls in a lotto drawing.

But Miller said that is obviously not the way society works.

“These are really theoretical measures,” she said.

So it is entirely possible that Colorado could reach an 80% overall vaccination rate against the coronavirus and still have large pockets of the population that are prone to outbreaks. This is the scenario that public health leaders have been warning about for years with diseases like measles.

Different communities within the state will also have different herd immunity thresholds. That is because R₀ for the virus will be different depending on how populations interact. Dense communities where people live closer together, giving the virus a better chance of spreading, will have a higher herd immunity thresholds. Less dense communities will have lower ones.

As a piece published in 2019 in the journal Emerging Infectious Diseases put it: “Because R₀ is a function of the effective contact rate, the value of R₀ is a function of human social behavior and organization, as well as the innate biological characteristics of particular pathogens.”

How good is the vaccine?

Now let’s talk about what it means to be immune. It’s not the same thing as being vaccinated.

Miller said no vaccine is perfect. Even the best don’t work for 100% of the people who receive them.

The current coronavirus vaccines, made by Pfizer and Moderna, put up mind-blowingly-good efficacy numbers in clinical trials — both around 95%. When one of the key researchers who helped develop the vaccines heard those results, he reportedly sat down at his desk in his home office and wept.

A really good vaccine makes herd immunity a lot easier. It means that more of those who have been vaccinated are also immune, allowing them to count toward reaching the threshold, something Gov. Jared Polis nodded to in a news conference in December.

“The pandemic aspect of it is over once a sufficient number of people have been vaccinated,” Polis said. “I’ll leave that to the scientists to say whether that is 50% or 70% or 80%, but it’s a lot lower percentage of people before the pandemic is over at 94% efficacy than it would be if the vaccine were only 60 or 70% effective.”

Remember that efficacy is not effectiveness

Miller cautioned that efficacy and effectiveness are two different concepts in the public health world. Efficacy is what happens in a study, when everything is done as by-the-book as possible. Effectiveness is what happens in the grime and grind of the real world.

We don’t yet know what the effectiveness of the coronavirus vaccines is.

Miller said this probably isn’t a huge deal with the current vaccines. As long as they keep their real-world effectiveness near their clinical trial numbers, the population of vaccinated-but-not-immune people won’t be large enough to make much of a difference.

But this analysis changes if vaccines that come online in the future aren’t as successful. Preliminary data for the vaccine made by AstraZeneca — one of the next up in the pipeline — showed it to have 70% efficacy, on average. That’s low enough that it could impact herd immunity calculations.

“In that case,” Miller said, “it might be useful to understand if it changes this range we’re talking about.”

Include people who have been infected

There’s another way people could potentially be added to a herd immunity calculation, and it’s a crude one: by gaining immunity the old-fashioned way through infection.

In the race between virus and vaccine in Colorado right now, the virus is way out in front. The latest modeling estimates project that more than 1.3 million Coloradans have been infected with the coronavirus. That’s nearly a quarter of the state.

But there’s no consensus on whether those people should count when thinking about the state’s herd immunity threshold. Many people who have been infected develop at least short-term immunity — and maybe longer-term, as well. 

Dr. Eric France, CDPHE’s chief medical officer, said in an interview last month that so-called natural immunity gained through infection will be “an important contribution” to reaching herd immunity in Colorado.

“Add to that the 70 to 90% of people who will say they want to be vaccinated and we’ll be fine with regards to herd immunity,” France said.

Or maybe don’t

But some medical experts note that natural immunity appears to vary from person to person. And some people have reported two separate coronavirus infections over the course of the pandemic.

At a news conference last month, the current state epidemiologist, Dr. Rachel Herlihy, said there had been about 300 people in Colorado who had tested positive once and then, some time later, tested positive again. It is unclear, though, how many of those are true reinfections.

“I think there’s, unfortunately, lots of things we still don’t know about reinfection with this virus,” Herlihy said then.

This uncertainty causes Miller to urge caution. Stick with what you’re sure of, she said.

“What we’re really focused on and what we can control is that vaccine herd immunity,” she said. “The goal and what public health is focused on is looking at the percentage of the population that is vaccinated.”

Do kids count?

Colorado’s vaccination campaign currently envisions inoculating only people 18 and older. That may change if clinical trials show the vaccines are also safe and effective for kids. But, right now, kids are off the table.

So does that mean they count against the herd immunity calculation?

If they do, it would be incredibly difficult for Colorado to reach herd immunity statewide. There are nearly 1.3 million kids ages 17 and younger in Colorado, according to State Demography Office estimates. They make up nearly 22% of the state’s population.

If none of them are vaccinated and natural immunity is not counted, it means Colorado would have to vaccinate over 85% of the adult population just to reach the lowest level in the estimated herd immunity range.

But what if kids don’t spread the virus as easily as adults? Some studies have suggested that younger kids are less likely to be virus-spreaders. Others have found evidence of the opposite.

Miller said the unknowns are reason to continue testing the vaccines in order to one day make them available to children.

“They are part of the population, so I think that’s an important issue,” she said.

It’s probably not one-and-done

The good news about COVID-19 is that, as vaccines go into arms, herd immunity can now be reached without accepting the massive death toll that would go along with trying to achieve it through infection.

The bad news about COVID-19 is that it is likely here to stay, even after we reach herd immunity. And it is uncertain how often we’re going to need to keep getting vaccinated in the future in order to stave it off.

“There’s still lots we still have to learn about how to maintain immunity with the vaccine,” Miller said. ”This is all assuming vaccine protection is maintained, so we have to figure out how to do that.”

To public health professionals like Miller, this means the message on herd immunity has to be one about endurance and vigilance. Thus, Miller thinks the focus on a single, magical number for herd immunity is counterproductive.

It’s not a finish line we can cross and then immediately declare victory. This is a race we’re just going to have to keep running for a while.

“The debates about the number,” she said, “are missing the point.”