One of the first things they teach wannabe epidemiologists is the shape of the exponential growth curve—how epidemics spread slowly at first, and then take off like a rocketship as the numbers of infected people double, double, and double. But unless you’re actually fighting an outbreak, or are in one, that can all feel academic. If the exponential liftoff is happening somewhere else, it’s not happening to you. Add to that peculiar form of emotional distancing a heavy dose of disinformation and partisanship, and depending on where you live and what your information diet is like, even the Covid-19 pandemic could start to seem almost unreal.
In a crisis, health communication experts agree, different kinds of people need to hear different kinds of narratives about what’s going on. Broadly, truthful information delivered clearly and without panic—but also without undue optimism—is the way to maintain credibility. But some people in the audience need a more emotional connection to fully engage. According to survey data from the Pew Research Center, nine out of 10 Americans say that Covid-19 has affected their lives in some way. But that means 10 percent of Americans say it hasn’t. Pew also finds that almost 80 percent of Fox News viewers think the media has exaggerated the threat of the virus (we haven’t) and 7 percent of people aren’t really following the news about it at all. Even President Trump seems to think that only people who “sadly lost a family member or friend” will even remember Covid-19 when it’s all over. These numbers are fast-changing, but still, watching the pandemic unfold as news from a distant city or as lines and numbers on charts might be very different than being in a hotspot, or knowing someone who dies from the disease.
That raises a grim question: What’ll it take before everyone personally knows someone who died from Covid-19? As of this writing, more than 11,800 people have died from it in the United States. (And that death toll may be an undercount.) If knowing one of those people would make the pandemic concrete for someone—real and actionable—how many have to die before every American knows one of the dead?
In a time of relentlessly cold equations, this one may be the coldest. It also turns out to be hard to solve.
The easiest answer, the back-of-the-envelope sketch, requires figuring out how many people anyone in the US is likely to know. Take one death from a group of that size, then multiply whatever percentage that is by the total US population. So, for example, one readily-accepted count of how many people any one person knows comes from a rigorous analysis of Facebook data from 2011. It’s about 200. Using this rough metric, if 1 in every 200 Americans dies from Covid-19—a fatality rate of 0.5 percent—everyone in the US will know someone who has perished. With a national population of 327.2 million, that’s 1.6 million US deaths.
But we get into the weeds right away. Is 200 … right? A 2006 paper using survey data and statistical models to calculate the number of people the average person knows arrived at 750. The Columbia University statistician Andrew Gelman, one of the authors of that paper, came back in 2013 with another estimate based on a different survey: 600.
“Our analysis from 2011 was about Facebook friends, where the average was 200ish,” says Johan Ugander, a Stanford professor of management science and co-author of the 200-count paper. He notes that the median number of Facebook friends was only 99, which means that half of all people had fewer than 99 friends. If you use that number, it would take an American death count of 3.3 million before everyone in the US lost someone they knew. Of course, all this depends on your definition of friend. “If you switch to looser notions of ‘know someone,’ you can quickly get numbers like 750,” Ugander says. “It’s reasonable to think of friendship tie strength as an onion with many layers,”
Princeton mathematician Chris Sims used one of those larger numbers—Gelman’s estimate of 600—and calculations of Covid-19’s prevalence and fatality rate that were operative in late March, for a related calculation. He wrote that if the disease kills slightly less than 1 percent of everyone who gets it, and about 60 percent of a population gets infected, a person who knows 600 people has a 95 percent chance of knowing someone who will die of the disease. Or to put it another way, if 1 in 600 people die, that means the US will have about 546,000 deaths—scarily, not much more than twice the best-case range estimated by the White House, though the president and his advisors haven’t been clear on exactly how they arrived at their numbers.
Now the weeds get even thicker—even if, for simplicity’s sake, we stick with 1-in-200 as our ratio. “Covid death is unlikely to be uniform or random,” Ugander says. “We can expect people with more friends to be more likely to be exposed, and then also die, and expect there to be clustering in the deaths on the network, for all sorts of reasons.”
This relates to a statistical concept known as the friendship paradox—in your network, your friends probably have more friends than you. That’s not an insult; some people are nodes, the extroverted superspreaders of bonhomie, so they’re shared across multiple networks. Don’t be too jealous of these social butterflies. Their “centrality,” their internodal connectedness, has a price. Because they come into physical contact with more people, they’re more likely to get infected during an epidemic.
This seems to have actually happened during the 2009 pandemic of H1N1 influenza—people with more connections were also more likely to get the virus. “The friendship paradox, plus the fact that connected people are more likely to get sick, makes one expect that less than 0.5 percent of the population needs to die for everyone to expect to have seen one person die,” Ugander says.
Other mathematical forces push the numbers back up, though. The major one is a phenomenon called overdispersion. People are likely to connect with clusters of people like themselves, and not every cluster has the same risk of getting Covid-19, or dying from it. Health care workers are likely to be in networks with other health care workers, and they’re at higher risk of dying because of their jobs. “Age homophily” means older people are likely to know more older people—the group at highest risk of dying from Covid-19. Likewise, “geographic homophily” is a factor—for now, New Yorkers are, tragically, much more likely to know someone who died than San Franciscans, and both are more likely to know someone than people from a place with fewer connections to either city.
“It’s reasonable to say that the grief will be unevenly distributed in terms of age, geography, profession, wealth, and other relevant factors,” Ugander says. People outside these networks will be much less likely to know someone who dies than people within them, no matter the overall death toll.
It’s possible that these quantitative weeds are so choking as to be fundamentally unwhackable. “The problem is deceptively hard,” says Babak Fotouhi, a computational social scientist at the University of Maryland. “It can be articulated in one sentence, easily, and everyone understands. It’s hard to believe that it's such a mathematically hard problem to solve even approximately.”
Mathematically, says Fotouhi, this kind of question is called a “Minimum Dominating Set” problem: “For a given graph, what is the minimum set of nodes such that every node in the graph has at least one neighbor in that set?” Finding the Minimum Dominating Set is a one of a class of problems that mathematicians call “NP-complete.” They can tell it’s solvable, but they know it’s wicked hard.
It’s even more wicked here, because the network is all of us, with all the complicated and unmapped interrelationships that Ugander talked about. You’d need a Big Brotherish surveillance project to tease out the connections we have to each other. In math language: Nobody knows how this particular graph is structured. And the “set” here is dominated by the epidemiology of the disease and how it spreads, a “diffusion process” that isn’t characterized yet. That makes it even harder still.
“We have an unknown diffusion process, on an unknown network structure, and we have a problem whose simplified version would be NP-complete. We have both theoretical-algorithmic obstacles and serious lack of data,” Fotouhi says. “I don't think any estimate would be reasonable—even crude approximations.”
Ugander turns out to be slightly more willing to take a stab at it. “If I had to guess, the assortativity patterns probably dominate the friendship paradox thing,” he says. “The percentage could get quite high while significant portions of the population still don’t know anyone directly.” Which is to say, it might take more than 1.6 million people dying—a lot more—before everybody knows just one of them.
The now-infamous March 16 report from the modelers at Imperial College warned that 2.2 million people would die in the US alone, absent any mitigation measures. Now it’s possible to imagine that even that apocalyptic outcome would leave some individuals essentially untouched by the virus—though they’d still suffer through its knock-on effects on the economy and society. And on the other side of that tilted see-saw would be highly-affected clusters, connected to many deaths—health care workers, first responders, transit workers, older people, New Yorkers, New Orleanians, and uncounted others clustered around epicenters yet to come.
If the Covid-19 pandemic leaves some people blessedly untouched, that could actually magnify the tragedy. Around the world, more than 81,000 people have died from Covid-19, and those deaths connect every person in grief. But part of why that communal grief is especially painful is that it is diffuse. Knowing one of the dead might not change the mind of the most rugged individualist who can’t see past the catastrophic economic effects of social distancing and shelter-in-place orders—or, worse, who believes Covid-19 is a plot by liberals to destroy freedom. And the disinformation squads that spout conspiratorial nonsense about Covid-19 deaths being due to pre-existing conditions or the flu or Chinese spies—if they’re happening at all!—probably won’t alter course.
But what if enough reasonable people dance between the acid raindrops? If they don’t think they have to care? That’s bad for the rest of the population, too. Those untouched people become the ones least likely to adhere to life-saving social distancing rules as the pandemic rolls from hotspot to hotspot. Different kinds of stories have different effects on different kinds of people, which makes this a hard disease to fight. Without a drug or a vaccine, the only weapon is collective action, and sometimes that requires a leap of faith.
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