Fat Bottom Tails


This is an attempt at understanding R0 (reproductive number) as more than a numbing number. View these notes as less definitive. 

In his (2014) paper Risking It All: Why are public health authorities not concerned about Ebola in the US?, Yaneer Bar-Yam writes about why R0 isn't an even distribution.

One April report noted the coronavirus reproductive number was 5.7 but offered a range of 3.8-8.9. In January the estimate was 2.6. There's many reasons but one is that the reproductive number varies by the individual in the network.

Humans form the same (power-law graphed) networks over and over again. In research about Wikipedia edits the graphs of posts per user was nearly identical across languages. It holds across time too, we can imagine that church members knew their parson but not every other member. This network holds on TV shows too.


Image from Funkhauser.

These networks are so common, they may be part of our evolution, like ten fingers. Nicholas Christakis said, “Maybe natural selection had something to do with the topology of human networks.”

Christakis looks at networks to seed interventions like a farmer who avoids the arid or soaked parts of a his field. In lab research, Christakis found that when one person is nice to another person (via monetary rewards) then that person is nicer to the next. Courtesy is contagious.

In other studies, Christakis changed the visibility of charity (or selfishness) and the  contagion changed too. Visibility of inequality mattered a lot, unseen inequality mattered very little. That's kinda interesting.

Christakis has found three features which influence how things spread through networks.

  1. Connections, more lines between hubs

  2. Contagions, faster spread between hubs

  3. Positions, different originations hubs

If Larry David gets an idea for his television show and he wants Julia Louis-Dreyfus to guest star he can ask her (#1), but if it's someone he doesn't know he'll have 'his people call your people'. He could pitch Julia via text (#2) or write her a letter. If it's Jeff Garlin that has the idea and not Larry David, (#3) then the idea has to wind through Larry to get onto the show.

A real example of virality is the Zillow Zestimate. Co-founder Rich Barton wanted to advertise. That had worked for Barton at Expedia. But Bill Gurley said, "If you're buying ads to sells ads, then you're arbitraging traffic and that dog don't hunt very long." Barton wanted to focus on spreading the message (#3) far and wide. What worked better was creating something people would share (#2) among themselves.

Bar-Yam warns about an average R0 when he writes about Ebola:

"However, in a complex interdependent society it is possible for the actual number due to a single individual to dramatically differ from the average number, with severe consequences for the ability to contain an outbreak when it is just beginning."

Ebola needs to be a disease of more concern, he wrote in 2014, because the epidemiological models used the connections, contagions, and positions of Africa which is a different network structure. "One person is not likely to be in close contact with much more than about 10 or 20 family members." That is, the rural African figures for 1, 2, and 3 are quite different from the urban African figures. "In urban areas in Africa and in the US, the nature of the contact network is different."

Ebola is a hot virus and should be treated with extreme caution. Richard Preston's book, The Hot Zone is about the mid-90s almost crisis when the Ebola virus was spreading through the air in a monkey research facility just outside of Washington D.C.

(Here's Preston in 2019)

In the book Preston writes about the history of research. Recalling one trip in the mid-80s:

"Occasionally they (researchers) came to villages, and at each village they encountered a roadblock of fallen trees. Having had centuries of experience with the smallpox virus, the village elders had instituted their own methods for controlling the virus, according to their received wisdom, which was to cut their villages off from the world, to protect their people from a raging plague. It was reverse quarantine, an ancient practice in Africa, where a village bars itself from strangers during a time of disease, and drives away outsiders who appear."

Some strands of Ebola pass through he air (#2). Some do not. African villages follow the precautionary principle.

Thanks to Tim H and Tim B for the suggestions and trailheads for this post. For thinking about position (#3) check out the Friendship Paradox