A Blog by Jonathan Low


Feb 10, 2021

Math Explains Why the US May Never Reach Herd Immunity

Vaccine efficacy of less than 100%, the number of people swearing they will never be vaccinated, reinfection and new variants all combine to make it likely that the US will never achieve the threshold required to achieve the scientific definition of herd immunity. 

The good news is that vaccines and new monoclonal antibody drugs may make herd immunity unnecessary by decreasing the instance of severe infection and mortality from the virus. JL

Sarah Zhang reports in The Atlantic:

For COVID-19, herd-immunity is 60 and 90% of people who have immunity from vaccination or prior infection. (But) COVID-19 will continue to circulate, evolve, and reinfect. 15% of Americans say they will never get vaccinated. We expect immunity to be less effective against transmission than against disease, to wane over time, and to be eroded by new variants. If vaccine efficacy against transmission falls below the herd-immunity threshold, we need to vaccinate more than 100% of the population to achieve herd immunity. In other words, it becomes impossible.Let’s begin by defining our terms. Herd immunity is the hazy, long-promised end of the pandemic, but its requirements are quite specific. Jennie Lavine, a biologist at Emory University, likens it to wet logs in a campfire. If there’s enough water in the logs—if there’s enough immunity in a population—“you can’t get the fire to start, period,” she says. To be more technical about it, a population reaches herd immunity when the average number of people infected by a single sick person falls below one. Patient zero might infect another person, but that second person can’t infect a third. This is what happens with measles, polio, and several other diseases for which vaccines have achieved herd immunity in the United States. A case might land here, but the spark never finds much dry fuel. The outbreak never sustains itself.

For COVID-19, the herd-immunity threshold is estimated to be between 60 and 90 percent. That’s the proportion of people who need to have immunity either from vaccination or from prior infection. In the U.S., the countdown to when enough people are vaccinated to reach herd immunity has already begun.

But what if we still can’t get the logs wet enough? What if they are drying out faster than we can douse them? A number of signs now point to a future in which the transmission of this virus cannot be contained through herd immunity. COVID-19 will likely continue to circulate, to evolve, and to reinfect. In that case, the goal of vaccination needs to be different.

While COVID-19 vaccines are very good—even unexpectedly good—at preventing disease, they are still unlikely to be good enough against transmission of the virus, which is key to herd immunity. On the whole, we should expect immunity to be less effective against transmission than against disease, to wane over time, and to be eroded by the new variants now emerging around the world. If vaccine efficacy against transmission falls below the herd-immunity threshold, then we would need to vaccinate more than 100 percent of the population to achieve herd immunity. In other words, it becomes downright impossible.

Even if herd immunity remains theoretically within reach, 15 percent of Americans say they will never get a COVID-19 vaccine, making that threshold all the harder to hit.

The role of COVID-19 vaccines may ultimately be more akin to that of the flu shot: reducing hospitalizations and deaths by mitigating the disease’s severity. The COVID-19 vaccines as a whole are excellent at preventing severe disease, and this level of protection so far seems to hold even against a new coronavirus variant found in South Africa that is causing reinfections. This, rather than herd immunity, is a more achievable goal for the vaccines. “My picture of the endgame is we will, as fast as we can, start taking people out of harm’s way” through vaccination, says Marc Lipsitch, an epidemiologist at Harvard. The virus still circulates, but fewer people die.

At the same time, we don’t need to hit the herd-immunity threshold before transmission begins to slow. With less transmission, fewer people will get exposed, and if those who do are vaccinated, even fewer will become seriously sick or die. The pandemic will slowly fade as hospitalizations and deaths inch down.

We likely won’t cross the threshold of herd immunity. We won’t have zero COVID-19 in the U.S. And global eradication is basically a pipe dream. But life with the coronavirus will look a lot more normal.

The variants are the newest and potentially most pressing challenge to herd immunity. As the virus evolves, our vaccines and our immunity will continually have to catch up. “The trillion-dollar question for where we go from here is this relationship we have with the variants,” says Michael Osterholm, the director of the Center for Infectious Disease Research and Policy at the University of Minnesota.

For about a year, the coronavirus seemed to gain mutations at a steady and unspectacular rate. But recently, new variants have accumulated an unusually large number of mutations, and worrisome new data are now coming out every week.

The South Africa and Brazil variants, which are the most concerning for immunity, share several mutations, including a key one called E484K. These mutations change the shape of the virus’s spike protein, making it less recognizable to the immune system. In South Africa, the variant is reinfecting some people who had COVID-19 before. On Sunday, the country even paused its rollout of the AstraZeneca vaccine after data came to light suggesting that it does not protect against mild or moderate disease from the new variant. And the Johnson & Johnson and Novavax vaccines, which were trialed in parallel in multiple countries, also seem less effective in South Africa—falling from 72 to 57 percent efficacy and 89 to 49 percent efficacy, respectively. In Brazil, the region around Manaus is experiencing a huge second wave of COVID-19 despite high levels of previous immunity from a first wave last year. The new variant in Brazil may be responsible.

All of these data are pointing in the same direction: Immunity, whether from vaccines or from prior infection, is weaker against these variants. However, the U.K. variant, which is significantly more transmissible than earlier iterations of the virus, has not been linked to significant  reductions in vaccine efficacy. But scientists are beginning to find E484K in some samples of the U.K. variant too. In multiple infection hot spots around the world, the coronavirus is independently converging on some of the same key mutations.

These same mutations keep popping up probably because they are the lowest-hanging fruit. They are relatively simple genetic changes. Other mutations that confer certain advantages to the virus may exist but require more dramatic genetic changes, says Benhur Lee, a virologist at the Icahn School of Medicine. Given enough time and enough opportunities to replicate, the virus may sometimes be lucky enough to reach higher up the tree. But “if you don’t give it a chance, it takes even longer,” Lee told me. Slowing down the coronavirus’s evolution requires preventing infections whenever and however we can.

This needs to happen globally. Right now, wealthy countries have largely bought out the vaccine supply. Even if they are able to vaccinate large segments of their population by the end of 2021, the virus will keep circulating elsewhere and keep gaining mutations, eventually evolving so much that the original vaccines may become even less effective. Rampant spread in unvaccinated countries may very well seed new variants that come back to cause new outbreaks in vaccinated countries. As my colleague James Hamblin has written, “The countries that hoard the vaccine without a plan to help others do so at their own peril.” Taking away the virus’s chance to acquire other advantageous mutations means reducing its spread everywhere. Vaccines can be updated against any new variants, but it will be a constant race to catch up.

It’s not just the variants that make reaching herd immunity a challenge.

Think of immunity from vaccines not as an on-off switch but as a dampener on the virus’s ability to replicate inside you. There are four important thresholds, from easiest to hardest to achieve: protection against severe symptoms, protection against any symptoms, protection against transmission, and protection against infection. Most of the topline efficacy numbers for vaccines are against symptoms; to prevent transmission, though, which is key for herd immunity, the vaccine needs to tamp down viral replication even further. That’s why vaccine efficacy against transmission is expected to be lower than efficacy against symptoms—exactly how much lower is still unclear.

Efficacy against transmission will probably be the first to erode too. In the long term, immunity in general tends to wane, with protection against severe disease being the most durable. New variants may further knock vaccine efficacy down a rung or two. A vaccine that might have protected a recipient from getting infected with the original virus might now protect only against symptomatic infection. That’s still good for the vaccine recipient but not so good for herd immunity: The recipient could now carry enough virus to asymptomatically transmit it to others.

This pattern has biological explanations. First, the location of immunity matters. Respiratory viruses such as the coronavirus infect through the nose and throat, but current COVID-19 vaccines are all given as shots into arm muscle. These vaccines elicit a strong immune response and high levels of antibodies, also known as titers, inside the body—but not necessarily in the mucous membranes of the nose and throat, which are the first line of defense against the coronavirus. “It’s possible that over time, as titers fall away, you start to get infections in the upper respiratory tract,” says Jason McLellan, a biochemist at the University of Texas at Austin. “Hopefully you’re still protected in the lower respiratory tract, preventing pneumonia, the severe disease, and the hospitalization.”

Second, the type of immunity also matters. After an initial vaccination or infection, antibodies spike in the blood. Antibodies are the fast-twitch part of immune memory that neutralizes invading viruses and prevents infection from taking hold. But as antibody levels fall over time, as is already being documented in COVID-19 survivors, they might lose effectiveness. Another piece of the immune system, T cells, are more stalwart soldiers, important in long-term immunity. They take longer to spring into action, though, so they prevent severe disease but not necessarily infection or transmission.

What does that mean for the future of COVID-19? One possible scenario is that the disease could follow the path of the four coronaviruses that cause common colds, which frequently reinfect people but rarely seriously. In one study that tried to infect and then reinfect volunteers with one of these common-cold coronaviruses one year apart, some of the volunteers indeed got reinfected but without symptoms. They also had detectable amounts of the virus in their nose for a shorter period of time. For COVID-19, “the optimistic future is that there are still infections but they are less frequent than now,” Jesse Bloom, a virologist at the Fred Hutchinson Cancer Research Center, wrote in an email, “and most infected people have something more resembling a cold than a life-threatening infection.” (There is speculation, in fact, that the coronavirus OC43 emerged during an 1889 pandemic before fading into the background as a common cold.)

Lavine, at Emory, has co-authored a paper modeling how COVID-19 could eventually end up like these cold coronaviruses. The four that already exist are so common that most of us were probably infected with them in childhood. This early encounter lays down initial immunity against these coronaviruses so that reinfections later in life are milder. Frequent reinfection, when immunity fades and the cold coronavirus evolves, may also update that immunity.

COVID-19 is clearly and dramatically more deadly for older patients. We might think of the vaccines, then, as a replacement for the immunity that adults never got to build against COVID-19 as children. But because this is a new coronavirus, Lavine cautions about uncertainties that remain, especially in how new variants may continue to evolve and whether immunity first elicited in adulthood is equivalent to immunity first elicited in childhood.

Kids will likely end up getting COVID-19 vaccines too, at least in wealthy countries where they are available. Lipsitch, at Harvard, notes that severe illness and death from COVID-19 and its associated syndrome MIS-C in kids is still high enough—on the order of the flu—to justify vaccinating children rather than letting natural infections take their course. And even if vaccine protection against transmission is imperfect, including kids in the vaccinated pool will help dampen transmission in the larger community.

It’s helpful to think of the collective immunity in a community as a dampener rather than an on-off switch, too.  Even if the herd-immunity threshold is not reached, every additional person vaccinated is a person who would generally be spreading less virus than if they were not vaccinated. A person exposed to less virus is also a person less likely to get sick, to go to the hospital, or to die.

In the analogy of the campfire, our current pandemic is a big, raging one. We might not have enough water to douse it completely, and we might not prevent future sparks from catching, but the water we do have will still help. The fire will burn slower and cooler. Every drop of water matters.


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