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Black Swans, Networks, and Covid-19

Not all vectors are created equal.
March 10, 2020
Black Swans, Networks, and Covid-19

Scientists studying infectious diseases such as Covid-19 focus on how contagious it is. The measure they use is the base infection rate, known as R0 (R-naught), which captures how many other people a given subject is likely to infect. For measles, which used to spread like wildfire prior to the arrival of a highly effective vaccine (effective if you actually use it), the R0 is over 10. For the seasonal flu, the R0 is just slightly over 1.0 (see this useful summary by Julia Belluz in Vox).

But for many infectious diseases—including Middle East Respiratory Syndrome (MERS) and Severe Acute Respiratory Syndrome (SARS), both of which are caused by other types of coronaviruses—not all infected subjects are created equal.

Some subjects are much more likely to transmit the virus than others. They are referred to as “superspreaders.” For example, a 2003 outbreak of SARS in Singapore was subsequently attributed to five “superspreaders” who each infected more than ten people, even though the R0 for SARS was estimated to be in the range between 2 and 4.

As Niall Ferguson recently described in the Wall Street Journal, superspreaders represent why traditional epidemiological models may not be well-suited to the study of the coronavirus epidemic and why researchers need a deeper understanding of network behavior. (Ferguson, author of The Square And The Tower, has long been captivated by the historical impact of social networks.)

While Ferguson assumes transmissibility is simply a function of the number of contacts (viewing superspreaders as those who get around the most, like Gaetan Dugas, the promiscuous flight attendant who was reportedly “Patient Zero” of the AIDS epidemic), this isn’t necessarily the case. As Penn State infectious disease expert Elizabeth McGraw explains,

Some infected individuals might shed more virus into the environment than others because of how their immune system works. Highly tolerant people do not feel sick and so may continue about their daily routines, inadvertently infecting more people. Alternatively, people with weaker immune systems that allow very high amounts of virus replication may be very good at transmitting even if they reduce their contacts with others. Individuals who have more symptoms—for example, coughing or sneezing more—can also be better at spreading the virus to new human hosts.

Whatever the biology, the existence of superspreaders reinforces a concern about the vulnerability of networks that Nassim Taleb articulated in The Black Swan over a decade ago. “Networks have a natural tendency to organize themselves around an extremely concentrated architecture,” he wrote. “A few nodes are extremely connected; others barely so.” This pattern, says Taleb, is seen in the internet, social networks, communication networks, and electricity grids.

And also biology. Taleb’s “extremely connected nodes” are analogous, in the context of epidemics, to viral superspreaders.

The implication for Taleb’s thesis in the world he was examining was that “random insults to most parts of the network will not be consequential since they are likely to hit a poorly connected spot. But it also makes networks more vulnerable to Black Swans.” Which is to say, that the effects aren’t really felt until the insult hits a highly-connected node; at which point it looks not like part of a pattern, but a Black Swan event.

Seen through this framework, what drives contagion of many epidemics may not be the typical person who gets the disease, but rather the unfortunate infection of a person who has just the right combination of physiological, geographical, and behavioral features to lead to the disease’s exuberant spread.

As is often the case in the early stages of an outbreak, the explosive spread of Covid-19 has outstripped traditional methods of contact tracing, making it impossible to pick out disease superspreaders in real time. But in the future, a combination of improved diagnostics, better data gathering, and more sophisticated analytics (now with AI…) might make it possible to identify—or even anticipate—superspreaders and intervene specifically, and perhaps preemptively, to staunch a contagion before it takes down a large human network.

Because whatever else it may be, Covid-19 is also a test-case for the next pandemic, and an important opportunity for us to learn how to effectively marshal digital technologies to combat it.

David Shaywitz

David Shaywitz is a physician-scientist at a biopharmaceutical company, an adjunct scholar at the American Enterprise Institute, and a lecturer in the Department of Biomedical Informatics at Harvard Medical School.