The coronavirus pandemic is terrifying, but the solution is almost shockingly simple: We have to stop spreading the virus. In fact, if every single one of us took extreme social distancing measures and all of the sick were isolated, the curve we’ve been attempting to flatten would start plummeting toward zero.
While a gradual increase of COVID-19 cases that don't overwhelm healthcare followed by a decline is the goal of most public health agencies, basic math suggests we can actually turn exponential growth into exponential decline quite rapidly.
That’s the perspective that Yaneer Bar-Yam, a complex systems scientist who uses his specialized branch of mathematics study systems with many interactive components, like the stock market or social movements, is attempting to share with the world. His field’s basic premise is that all of the interdependencies within complex systems result in various "tipping points" and non-linear responses that are difficult to describe using simpler mathematical models. Over the last few months, Bar-Yam’s research organization, the New England Complex Systems Institute, has produced a series of coronavirus-focused white papers and guides that use the fundamental dynamics of a global pandemic to explain how to stop it.
In a short explanatory paper published online last month, Bar-Yam shows how pandemic spread is a simple problem of matrix multiplication. If you haven’t brushed up on your high school algebra in a while, a matrix is just a set of numbers arranged in rows and columns. In this case, the matrix is a “contagion network,” with columns and rows representing different individuals in a population. If two individuals interact enough to spread the disease, the value where their row and column meet is one. Otherwise, it’s zero.
In an ideal scenario where we know exactly who’s sick and who’s not, this contagion network could be multiplied by the list of people who are sick—a column of ones (sick) and zeros (healthy)—to produce a new list showing who’s likely to be sick during the next infectious period. Repeat the process over and over, and the illness either spreads or declines over time.
Critically, which of those two paths a virus follows, growth or decay, depends on the connectedness of the contagion network. Epidemiologists use a variable called R0, or the number of people each sick person infects, to describe this connectivity. If R0 is greater than 1, the number of sick will rise over time; if it’s less than one, the sick cases will shrink.
For now, estimates for COVID-19’s R value (called the “effective R” when it’s measured in populations) vary from around 2 to nearly 5. Either end of this range indicates a disease capable of spreading exponentially, which is exactly what we’re seeing in the US. But Bar-Yam’s math also demonstrates that if everyone on Earth were to self isolate for a couple of weeks — either alone, or with family members who also aren’t sick — COVID-19 would run out of new hosts to infect, and the pandemic would be brought under control. In a best-case scenario, effective R would fall to zero, and the illness could be eliminated in a single infectious period—in this case, about two weeks. In essence, instead of flattening the infection curve we’d be arresting it.
“The point is, it’s a multiplicative process and that creates an exponential growth or an exponential decline,” Bar-Yam told Motherboard. “The trick is if you have an exponentially growing disease, [switch it] to make it exponentially declining.”
Everyone eliminating all contact outside the home is impossible, of course, meaning we can’t realistically expect to vanquish the pandemic in just a couple of weeks. Health care workers risk infection simply by treating the sick; workers at elderly care facilities can’t easily abandon all physical interaction with their charges. We still need people working closely together in emergency services, running power plants and sanitation systems, and much more. Society can’t just cease to function.
But altering the contagion network in order to drive the effective R value down and change COVID-19’s trajectory from one of exponential growth to exponential decay is far from impossible. In fact, several countries have been able to do just that, most notably China, which was able to exponentially bend its infection curve toward zero through rapid testing and contact tracing, isolating the sick, and placing over fifty million citizens on lockdown. While China was seeing thousands of new cases of COVID-19 a day at the height of its outbreak in late January, on Monday it only saw one new local infection, at least according to official numbers from the National Health Commission.
“China’s taken criticism for coming in late,” said Shannon Bennett, a microbiologist at the California Academy of Sciences. “But when they did decide to do the social distancing they came in hard. Now they’re still getting new cases per day but fewer and fewer.”
However, if math tells us that countries with exponentially-rising caseloads can flatten and reverse their infection curves through collective action, other aspects of complex systems behavior lead to more sobering conclusions. For one, there’s the issue of time delay: It might take days to weeks for our responses to COVID-19 to start having a demonstrable impact. All the while, the number of cases is likely to keep rising fast.
Bar-Yam noted that even though China began taking aggressive control measures when there were fewer than 1,000 officially-reported cases in the country, by the time the outbreak was under control, the number of cases had topped 80,000.
As of Wednesday morning, The New York Times’ database indicated nearly 6,000 coronavirus cases in the United States, but Bennet and other experts have said that number is likely a severe underestimate due to inadequate testing. Unfortunately, this suggests that if the U.S. took immediate and radical nationwide action—as we saw the Bay Area do yesterday, when officials ordered nearly 7 million people to go into a near-lockdown—the scale of our outbreak would still likely be considerably worse than China’s.
“I would definitely say we are on the exponential part of the curve,” Bennett told Motherboard. “The power function of that exponential increase I would say is still uncertain, and certainly hampered in its estimation by the fact that we have a mess going on with under-testing.”
Complex systems also have tipping points that cause them to go through “phase changes,” as Danny Buerkli, the co-founder of Swiss government innovation lab Staatslabor, noted in a recent blog post on how this branch of math is relevant to coronavirus. In this case, a tipping point might be when hospitals run out of beds or critical equipment, forcing the entire healthcare system to go into triage mode.
“We’ve seen the [health care system] overload happening in China, Italy, possibly elsewhere,” Buerkli told Motherboard. “It’s misleading to think that just because everything is OK now it will be in the future."
In the U.S., we (hopefully) still have time to prevent COVID-19 from crossing a dangerous tipping point where the healthcare system is overwhelmed. But the clock is ticking. Bennett noted the importance of rolling out more widespread testing immediately; Bar-Yam, meanwhile, emphasizes the role of personal behavior and individual responsibility through aggressive social distancing, practicing good hygiene, and self-isolating at the first sign of symptoms. Businesses also have a key role to play by telling their employees work from home or providing paid time off (a challenge many companies aren’t exactly living up to).
All of these measures, Bar-Yam says, will help to weaken the contagion network and steer us onto a new, far less terrifying trajectory.
“In our current context, the network is connected everywhere and gets transited very rapidly,” he said. “But it’s possible by changing how people behave to radically prune that network."
Update: This article was updated with details on China's response to the coronavirus.