Who gets priority when Covid-19 shots are in short supply? Network theorists have a counterintuitive answer: Start with the social butterflies.
He was one of 750,000 people, give or take, who passed through Grand Central Terminal that day. He worked as an attorney in a high-rise on 42nd Street that had direct access to the station, where trains departed every few minutes to 122 towns in New York and Connecticut. He and his wife ran a small firm, specializing in estate law, on the 47th floor of the building; he spent his hours there helping people negotiate death. At the end of the workday on Friday, February 21, the man made his way to the platforms for the New Haven line, boarded a train, and rode 30 minutes north to a commuter town in Westchester County called New Rochelle. At that moment, there were 34 confirmed cases of Covid-19 in the United States, all of them linked to international travel.
The next day, the man went to his synagogue, Young Israel of New Rochelle, as he did every Saturday. He and his wife had four children, though only two lived with them at the time—a son who went to college in Manhattan and a daughter who was still in high school. Despite the demands of his job, he was a family man, someone who was as eager to play Connect 4 with his kids as write a brief for whatever big case he was working on. His house was close to Young Israel, within the boundaries of the eruv, a symbolic perimeter identified by telephone poles, power lines, and other landmarks. Inside the eruv, some rules of the sabbath are relaxed, as if the whole neighborhood were a communal home.
The man was back at the synagogue at 11 the next morning for a funeral. Hundreds of congregants turned out to honor a Holocaust survivor who had died the day before at age 93. That afternoon, some of them returned to Young Israel for a joint bar and bat mitzvah. As the children played, the man and the other adults chatted, ate hors d’oeuvres, and drank cocktails. During the two events, health officials later estimated, the man came into contact with between 800 and 1,000 people.
“I felt a cough, which wasn’t crazy, and I thought it was allergies,” the man later told the New York Law Journal. When the cough didn’t go away, he thought about making a doctor’s appointment. But it wasn’t until February 26, when he developed a fever, that he, as he put it, “started to put two and two together.” He was due to travel to Washington, DC, the following week for the annual conference of the American Israel Public Affairs Committee, where he would be in the same room with members of Congress and heads of state. The trip never happened. Instead, a friend drove him to the hospital, where a few days later he tested positive for SARS-CoV-2. He was one of the first people in the US known to have gotten the virus through community spread.
In the days that followed, the case count in New Rochelle began to climb. The man’s wife and two children tested positive. So did the friend who had driven him to the hospital, along with members of the friend’s family. Anyone who had been at Young Israel the weekend of February 22 was asked to quarantine, but dozens were already infected, including two of the caterers at the bar and bat mitzvah. The son’s college shut down, as did the daughter’s high school. On March 5, the rabbi of Young Israel announced that he, too, had contracted the virus.
By this point, Andrew Cuomo, the governor of New York, was holding daily press conferences about the outbreak. New Rochelle had “probably the largest cluster in the United States,” he said. “The numbers have been going up, the numbers continue to go up, the numbers are going up unabated.” The state authorities drew a circle around Young Israel, a 1-mile radius inside which all schools and places of worship had to close and large gatherings were banned. The rules were different within this perimeter, but not for long: The residents of New Rochelle were living in a future that would soon come to the rest of the United States.
The man’s condition worsened, and he was placed into a medically induced coma. His wife, who had a mild case, took to posting updates on Facebook. “We have wonderful friends who have cared for us despite the running fears all around us,” she wrote. The comments filled with wishes for a speedy recovery. “A whole community prays for your family every day,” one member of Young Israel wrote.
By March 11, more than 50 new cases had been linked back to the man. A week later, there were 50 cases tied to the daughter’s school alone. Cuomo called the outbreak “one of the more complicated situations that we’ve come across because of the number of interconnections that this family has presented.” By the end of the month, some 10,000 cases had been diagnosed in Westchester County.
Finally, after more than two weeks in the intensive care unit, the man woke up. The first thing he did, his wife said, was to tell her over FaceTime that he loved her. Then he asked whether the rest of their extended family was OK. The press called him Patient Zero, the man who brought the disease from the dense city to New Rochelle, but that was assuming too much: The truth is, we don’t know how the novel coronavirus was introduced to his community. What’s clear, though, is that the virtues that made the man a good neighbor—there for friends and family in times of joy and pain alike—also made him highly efficient at spreading Covid-19. If he had come back from Grand Central and stayed at home that weekend, how many people would never have gotten the disease at all? Remove him from the chain of transmission, and the whole cluster might never have existed.
Eliminate the super-spreaders and you end the pandemic.
We’ve known about Covid-19 super-spreaders since the start of the pandemic. In January, a man transmitted the virus to 23 people during a bus ride on the Chinese coast south of Shanghai; in March, a member of a choir in Washington state passed it on to as many as 52 of her fellow singers; in August, the presence of an infected guest or guests at a wedding in Maine eventually led to more than 175 positive cases; and in September, President Trump hosted perhaps the most famous super-spreading event of all—a party to celebrate the nomination of Amy Coney Barrett to the Supreme Court that may have infected dozens of the most influential Republicans in Washington, along with members of the White House staff and press corps.
This is a pandemic defined by clusters. Some cause deadly outbreaks in nursing homes, prisons, and meatpacking plants. Others overwhelm families and friend groups. Although the numbers vary from study to study, SARS-CoV-2 seems to follow the 80/20 rule: 80 percent of cases stem from just 20 percent of infected individuals. Indeed, most people who test positive—one study in Hong Kong put the number at 69 percent—don’t spread the disease at all. They get infected, remain asymptomatic or fall sick, recover or die, all without passing along the virus to anyone. And then there are the patients like the lawyer from New Rochelle.
Super-spreading makes the virus especially confounding. It explains why some places had huge outbreaks while others were spared, at least for a while, and why the same risky behavior (an indoor wedding, say) can lead to dozens of cases—or none. But it’s also the virus’s weakness: Eliminate the super-spreaders and you end the pandemic.
Until now, our tools to stop outbreaks have been blunt. We’ve imposed nationwide lockdowns and universal social-distancing orders, lumping everyone together no matter how likely they are to transmit the disease. When the first vaccines for Covid-19 arrive, our instinct may be to pursue the same approach, to vaccinate everyone we can as quickly as we can, brute-forcing our way to herd immunity—the point at which there are no longer enough susceptible people in the population for the virus to hop easily between hosts. But supplies of the vaccine are likely to be limited through the middle of 2021, if not longer. A sharper, more tailored strategy will be required. So: Who are the members of this super-spreading 20 percent?
According to Alessandro Vespignani, a computational epidemiologist who has been consulting with the US government on the response to Covid-19, it would be a mistake to search for some physiological trait connecting them. “Super-spreading is a word that many people associate with the idea that, for some strange biological reason, you’re spreading the disease more,” he says. “This is not that. Generally it’s because you have more contacts and you go to places that favor spreading.” After all, if an infectious person is a recluse, it doesn’t matter how much virus he or she sheds.
To knock out the super-spreaders, the ideal target for a vaccine would be someone with many contacts in different settings—someone with a big, multigenerational family, a job that led to a lot of mixing with strangers, and a busy social life. But how do we find these highly connected individuals across 50 states and 330 million people? This is where most public health officials get stuck. To understand where the potential super-spreaders are in the general population, you would need a map of everyone’s friends, family, and casual contacts—the people they see every day and those they interact with for only a few minutes. But that map, of course, doesn’t exist, unless it’s hiding on Mark Zuckerberg’s laptop. In any case, it’s not available to the Centers for Disease Control and Prevention. At this point, we need to call in a different group of experts: the physicists.
In recent months, Albert-László Barabási has tried to walk around Budapest while taking calls, “to get some steps.” At 53, he is still youthful and fit, though the pandemic has kept him unusually busy. His standard route around town takes him by the peach-colored facade of the Alfréd Rényi Institute, named for a Hungarian mathematician who, with his collaborator Paul Erdős, helped lay the cornerstone of network science in the 1950s and ’60s. Today the discipline informs all sorts of pursuits, from generating algorithmic recommendations on Facebook to mapping terrorist networks to, yes, forecasting the spread of lethal diseases. But when Rényi got started, he wanted the answer to a simple question: What would a network organized completely at random look like? How would it behave?
Although Erdős and Rényi were theoreticians, they thought their work might eventually have some practical application—say, in understanding the evolution of railways or the power grid. But a few decades later, Barabási and Réka Albert, his colleague in the physics department at Notre Dame, determined that the Erdős-Rényi model was actually too random to accurately describe most naturally occurring networks.
“Our first key discovery,” Barabási says, “was that there’s really no random network out there.” They found that in most settings, from Hollywood to academia to the World Wide Web, networks tended to be “extremely heterogeneous, in the sense that their connectivity is dominated by a few very, very highly connected hubs.” Barabási and Albert called these networks “scale-free”: Most nodes could contact just a handful of others, but a small fraction were off the scale in terms of connectivity. Your website might link to four pages. Google links to 800 million.
It was Alessandro Vespignani, then at the International Centre for Theoretical Physics in Trieste, Italy, who tied this work directly into the study of epidemics, beginning with the digital kind. Why, Vespignani wondered, were computer networks still susceptible to viruses even though millions of individual users had antivirus software? The answer, he discovered, was that if you didn’t inoculate the nodes, malicious code could still zip around the internet with relative ease.
Not long after that, a colleague asked whether all this work on the structure of networks had ever been applied to the spread of real biological epidemics. “I thought, probably they have already done that,” Vespignani says. They hadn’t, and in 2002 he and a colleague wrote a paper on a “targeted immunization scheme in which we progressively make immune the most highly connected nodes, i.e., the ones more likely to spread the disease.” They ran a computer simulation of the effect of such a strategy on a scale-free network, which was meant to mimic “the web of human sexual contacts.” The results, they wrote, were “arresting”: You could protect the whole system by immunizing as little as 16 percent of the population, as long as you started with the most highly connected people.
Barabási remembers reading Vespignani’s paper and trying to apply its logic to the AIDS epidemic in sub-Saharan Africa, where the US government had just announced an ambitious program to combat the disease. An epidemiologist schooled in network theory would give HIV drugs to the members of society with the highest number of sexual contacts, Barabási says—but that wasn’t the government’s approach. “The Bush administration was giving the treatment to mothers with children because that sounds really good, and it’s soft and cozy,” he says. (It also protects against mother-to-child transmission.) “But what our measurement has shown is, no, no, no, you should actually give the HIV drugs to prostitutes, because those are the ones who are the biggest hubs when it comes to the spread of HIV.”
For sexually transmitted diseases, the barriers to targeting the super-spreaders may have been political. But for respiratory infections like influenza, SARS, and Covid-19, the limit is computational. There is no practical way to track down the most highly connected nodes in a network that is as big as the whole world, and where the definition of a link includes almost every type of human interaction. The physicists weren’t done yet, however. They set themselves to that very problem: Can you find the nodes without a complete map?
In 2003, during the first SARS epidemic, Shlomo Havlin, a physicist at Bar-Ilan University near Tel Aviv, proposed one of the most ingenious solutions to this problem. In a paper called “Efficient Immunization Strategies for Computer Networks and Populations,” Havlin and two colleagues argued that you could achieve global effects on a complex network using only local knowledge. All you had to do was follow a simple script: Take a random sample of a population, ask each individual to name a single acquaintance, and vaccinate the acquaintance. “In this way,” Havlin says, “you can reach the hubs, the super-spreaders, very easily.”
This acquaintance immunization strategy wasn’t as efficient as one that targeted the most highly connected nodes based on complete knowledge of a network. But it was close. “If you do this,” Havlin says, “you reduce the number of units that you need to immunize by a factor of three or four.” Diseases that would normally keep spreading until 60 or 80 percent of the population was infected—the herd immunity threshold—could be stopped by vaccinating just 10 or 20 percent. Havlin likens the effect to a phase transition: A solid network of ice crystals melts suddenly into water.
Acquaintance immunization works because of a phenomenon known as the friendship paradox, which holds that, on average, your friends have more friends than you do. The very act of asking someone to choose a friend, any friend, played out over hundreds or thousands of iterations, leads inevitably to the most connected people. Consider, for example, a very simple network of three people from Casablanca, Morocco: Rick, Ilsa, and Louis. Ilsa and Louis both know Rick, but they don’t know each other. If you ask each of them to name a friend, two out three times you wind up with the most-connected person: Rick.
Once a Covid-19 vaccine is available, if we asked every Louis and Ilsa and Rick in all the towns in all the world to choose a friend to receive it, occasionally we would end up vaccinating the “wrong” person—someone with fewer connections than the randomly chosen person. More often than not, however, we’d be eliminating a hub from the network of infection. Do it enough times and the disease eventually has nowhere to go.
Havlin’s strategy worked when he modeled it on real computer networks, and there’s also experimental evidence for its effectiveness with biological epidemics: In 2009, when H1N1 flu was circulating, the network scientists Nicholas Christakis and James Fowler followed two groups of Harvard undergraduates. The first group was randomly chosen; the second consisted of the first group’s friends. On average, the members of the friend group got the flu two weeks before the random group, whose infection rates matched the undergraduate population as a whole. If the friend group had been vaccinated at the beginning, the campus might have been spared an outbreak entirely.
Vespignani says that whenever there’s an outbreak, network epidemiologists usually bring up acquaintance immunization as a possible solution. Its great appeal lies in its simplicity—no small matter when considering a plan that has to be implemented and effectively communicated by the government. When it comes to a vaccination campaign as big as the one planned for Covid-19, however, simplicity might not be an option.
Since the pandemic began, the Advisory Committee on Immunization Practices at the CDC has been studying the question of who should get the first doses of a vaccine for SARS-CoV-2. In August the committee held a public meeting on Zoom. The members gave presentations on the makeup of the groups at highest risk of severe disease and heard an update on the clinical trials at Pfizer and Moderna, the two US producers that were farthest along in the vaccine approval process. Doctors and public health experts from around the country were allowed to ask questions. Nancy Messonnier, the CDC’s director for immunization and respiratory diseases, weighed in occasionally as the voice of institutional wisdom—she had been planning for a scenario like this her entire career. Then, about five hours into the meeting, the floor was opened to public comment.
One of the first people to address the committee was Santa Claus. Or, more precisely, it was Ric Erwin, chairman of the board of the Fraternal Order of Real Bearded Santas. The committee members didn’t quite take him seriously (one confessed that he had never stopped believing in Santa), but Erwin had come in earnest. “This year, Christmas will be more important to the American psyche than ever before,” he said. It was vital that the country have a cadre of vaccinated Santas ready to safely hear the wish lists of children everywhere. “We’re asking that professional Santas and other frontline seasonal workers be granted early access to the Covid-19 vaccine as soon as practical after tier-one release.”
Erwin had done his homework: The vaccine will be released in tiers, or phases. The earliest doses, perhaps as many as 20 million, will go to the groups deemed most essential by the CDC committee, according to a prioritization scheme that has not yet been finalized. After that, larger and larger groups of Americans will be granted permission to be vaccinated, until everyone is covered. Erwin wanted the Santas as close to the top of the list as possible, though his December deadline would be hard to meet.
In considering whom to prioritize for the vaccine, the committee highlighted some of the difficulties in getting it out to the public once it is approved. First, both the Pfizer and Moderna vaccines will require at least one booster shot, so the number of people who can be inoculated is half of the number of total doses available. The Pfizer vaccine will also need to be kept at -94 degrees Fahrenheit during transport and storage—quite a lot colder than most of the other shots in doctors’ freezers.
Then there is the risk that large portions of the country will refuse to be vaccinated. During the Salk vaccine trials of 1954, when hundreds of thousands of schoolchildren were inoculated against polio, the parental consent form was edited to change “I give my permission” to “I hereby request”; the implied scarcity was intended as an extra nudge to anxious parents. For Covid, there will be plenty of scarcity to go around (so to speak), but persuading the public to commit to being vaccinated is far from assured, and it gets less likely with every blusterous statement from the White House. (As Senator Kamala Harris said at the vice presidential debate in October, “If the doctors tell us that we should take it, then I’ll be the first in line to take it—absolutely. But if Donald Trump tells us that we should take it, I’m not taking it.”)
Each of these obstacles was a stubborn reminder of the way that the real world might not match a network scientist’s computer model. Acquaintance immunization is simple in theory, but what happens if the acquaintance is an antivaxxer? Or if her town doesn’t have the ability to keep the vaccine’s cold chain intact? Or if she’s so busy being the life of the party that she forgets to show up for her booster shot?
Even if a targeted strategy works as designed, it can lead to outcomes that feel morally questionable. Let’s say you’ve got one course of the vaccine and two people to choose between: Candidate 1 is a college student who doesn’t social distance, wears his mask slung beneath his chin, and plays beer pong all weekend at underground frat parties. Candidate 2 is his 87-year-old widowed grandmother, who lives on her own and has barely been out of the house since March. If your goal is to protect the more vulnerable person, you should vaccinate grandma. If your goal is to reduce transmission, you should vaccinate the frat bro. From society’s perspective, he’s a jerk; from the network’s, he’s a hub.
The prioritization committee seemed to be making a similar sort of utilitarian calculus. Rachel Slayton, a CDC epidemiologist who heads the committee’s data, analytics, and modeling task force, talked about the benefits of vaccinating the staff of a nursing home rather than its residents. “Because older adults have lower numbers of contacts,” she said, “the impact on the broader community of vaccinating the residents I would expect would be relatively small.” The best approach for the community would be to target the nodes. That should keep the virus out of the nursing homes, but it would also require a counterintuitive decision: Don’t vaccinate the people most likely to die of Covid-19.
Marc Lipsitch, an epidemiologist at Harvard’s School of Public Health, says the CDC committee is grappling with a fundamental question. “Essentially there are two approaches to using a vaccine,” he says. “One is to protect individuals by vaccinating them, and the other is to reduce transmission and therefore protect the population.” Although the committee would not make any formal recommendations until Pfizer and Moderna released their results, it seemed to be settling, cautiously, on an approach that would attempt to disrupt transmission. Under a plan presented in September, the very first doses would be reserved for health care workers, a population the committee estimates at 17 to 20 million. (The World Heath Organization has made a similar recommendation for its member countries.)
Some of the reasons for favoring this group above others are practical: The cold chain is easier to control if the population you’re trying to vaccinate is already working in a hospital. Hesitancy also is less of a concern—indeed, having doctors and nurses get the vaccine first might increase confidence in the treatment among the general public. And, of course, we need hospital staffs to be healthy to continue to fight the pandemic.
But controlling transmission was also a prominent consideration. In one study at a hospital in London, 15 percent of all SARS-CoV-2 infections were nosocomial—that is, acquired inside the hospital. And as Slayton’s report made clear, active health care workers are more likely to spread the disease to their families, friends, and communities than are the elderly. The plan’s second phase would include essential workers, as many as 80 million of them, who are both highly connected nodes and necessary to keep society functioning. The elderly might have to wait for phase three.
Lipsitch, for one, thinks that any approach that doesn’t start with the elderly is a mistake. It’s true, he says, that to reduce the total size of the pandemic, it’s a better strategy to target those who have the most connections—but lockdowns have scrambled traditional contact networks. (Or they did until large portions of the public decided it was time to return to business as usual.) In the meantime, we know one thing about Covid-19 without a doubt: Death rates skew heavily toward the old. That’s the group that should be first in line for the vaccine, Lipsitch believes. “Even if you put a small dent in those people’s risk,” he says, “it’s so much larger than the risk of the general population. A small dent in a large risk is bigger than a large dent in a small risk.” The only exception, he adds, would be if the vaccine simply wasn’t effective in the elderly.
Lipsitch’s objection might be specific to Covid-19, but it reflects a drawback inherent in all network-based immunization strategies. By their very nature, they require the cascading effects of interventions reaching across an entire population. But as soon as you have a disease that’s afflicting millions—or billions—of people, the stakes are too high to start experimenting. With lives on the line, who would choose an immunization plan that has never been tested outside of computer models and college campuses? “There are some clever things you could try,” Lipsitch says, “but I think for a lot of reasons it makes sense to try to be not too clever.”
“The old people, it will save their life, but it will not stop the spreading.”
If acquaintance immunization is ever adopted as a framework, it might be in a country in which Covid-19 was never allowed to become an epidemic in the first place. New Zealand and Taiwan, for example, are already protecting their vulnerable by maintaining low case numbers. Vaccinating probable super-spreaders first could ensure that the virus doesn’t get a chance to take hold while those countries wait for a stockpile large enough to cover everyone. If that happens, the end of the crisis may resemble its beginning: The most effective governments will be able to think about the pandemic in terms of protecting the whole population. The rest will leave individuals to fend for themselves.
During the CDC prioritization hearings, Nancy Messonnier urged flexibility and humility in the face of all the unknowns presented by this virus. Some countries that had SARS-CoV-2 under control early on faced debilitating outbreaks later. The most celebrated models of the disease’s spread have struggled to keep up with reality. Since the start of the pandemic, making predictions about Covid-19 has proved a dangerous endeavor for armchair and distinguished-chair epidemiologists alike.
The arrival of dozens of new vaccines will only continue this period of uncertainty. Each will each have its own limitations and advantages, and a strategy that works with one may fail with another. That’s why New Zealand’s Ministry of Health, like the CDC, is waiting on the results of the various vaccine trials before committing to any prioritization scheme—although a spokeswoman listed “those at risk of spreading Covid-19” first among the groups being considered for early vaccination.
A surprising outcome of the prioritization debate is that, while the CDC and the WHO have so far embraced network epidemiology to argue against vaccinating the vulnerable first, Barabási and Vespignani, like Lipsitch, dissent from that approach. The highest-risk populations are clearly defined, Vespignani argues, and it would be foolish not to protect them directly. “I don’t think that it’s possible to have a discussion on this point,” he says. But he does leave open one door to using the insights of network science: “Once we have protected the high-risk strata, but we don’t have the resources to immediately blanket the rest of the population with vaccine—at that point, differential strategies might be beneficial.”
One person who disagrees strongly with his colleagues is Havlin, who at 78 is decades older than the others. “They say to give it to old people,” he says. “I’m old, I’m happy to get it, but I’m not going out from home, you see? So I cannot help the global system. Of course, the old people, it will save their life, but it will not stop the spreading.”
Since Covid-19 reached Israel, Havlin has been staying at home near Tel Aviv. He adheres to a rigid daily schedule: He works from 8 am to 10 pm and takes two breaks—one for lunch and a siesta, one for a walk with Hava, his wife of more than 50 years. Not long ago, he came out with a paper suggesting another strategy for combating Covid-19; it would involve randomly surveying the population 10 people at a time and vaccinating the person who reports having the most connections. It provides a way, in theory, of finding a network’s hubs even faster than acquaintance immunization.
Havlin’s world these days is small, extending not much farther than a 1-mile radius around his apartment. He has been able to see some of his 23 grandchildren, but only from his balcony or on Zoom. Still, he’s happy to wait. The vaccine will get to him eventually, and by then, he thinks, the pandemic ought to be over.
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