## March 10, 2020

### Ebola, and Mongol Modernity

Attention conservation notice: An old course slide deck, turned in to prose on the occasion of a vaguely-related news story from 2014. Not posted at the time because it felt over-dramatic. I have, of course, no authority to opine about either world history or epidemiology, and for that matter no formal training in networks.

#### Exhibit A

One of the books which most re-arranged my vision of the past was Janet Abu-Lughod's Before European Hegemony: The World System A.D. 1250--1350. It gave me the sense, as few other things have, of historical contingency, or more exactly of modernity as a belated phenomenon, and changed my teaching. She depicts an integrated (part-of-the-) world economy, an "archipelago of towns" linked by trade-routes stretching from Flanders to Hangzhou and centered in the Indian Ocean. This archipelago is where modernity should have begun. Beyond the market-oriented, urban-centered economy, China has the beginnings of an industrial revolution (a point explored by Mark Elvin in his Pattern of the Chinese Past, and his sources in Japanese scholars of Chinese economic history, and emphasized by William McNeill in his Pursuit of Power); the beginnings of a truly global perspective. All of this was politically supported by the unification of the most economically and technologically advanced regions (namely China and the Islamic world) under the Mongol Empire, admittedly at the cost of the occasional "shock and awe" campaign, destruction of Baghdad, etc.

#### Exhibit B

So what, according to Abu-Lughod, happened? What happened was Yersinia pestis, the bubonic plague, a bacterium transmitted by fleas that live on rodents. It long has been, and is, endemic to the rodents of Central Asia, such as the giant gerbil Rhombomys opimus, which seems to be perpetually perched at the edge of the epidemic threshold. The Mongol Empire didn't just unify the most advanced parts of Eurasiafrica; it brought them into intimate contact with Central Asia. And then, as usual, the plague followed the routes of trade and imperial travel:

It's impossible to know just how deadly it was, but estimates put it at around 25% of global population; up to 90% in some regions. It destroyed (according to Abu-Lughod) the world economy, that "archipelago of towns", leaving isolated and barely-functional fragments which could be dominated and re-purposed by western European pirates/traders poking into the post-pandemic landscape.

One aspect to this is how slowly, and how progressively, the plague spread. It took decades to spread from Central Asia to the peripheral region of western Europe, where it chewed steadily across the landscape:

As my old friend and sometime co-author Mark Newman and collaborators puts it, this is strong evidence that "the small-world effect is a modern phenomenon". The small-world effect, after all, is that the maximum distance between any two people in the social network of size $n$ grows like $O(\log{n})$. This implies that the number of people reachable in $d$ steps grows exponentially with $d$, which is hardly compatible with the steady geographic progress of the disease.

The argument here is so pretty that I can't resist sketching it. Suppose that every infected person passes it on to any one of their contacts with probability $t$, at least on average. We start the infection at a random person, say Irene, who selects a random one of their acquaintances, say Joey, for passing it on. The probability that Irene, or any other random person, has $k$ contacts is, by convention, $p(k)$. But Joey isn't a random person; Joey is someone reachable by following an edge in the social network. Joey's degree distribution is $\propto k p(k)$, since people with more contacts are more reachable. Specifically, Joey's degree distribution is $k p(k) / \langle K \rangle$, where $\langle K \rangle \equiv \sum_{k=0}^{\infty}{k p(k)}$, the average degree. If Joey gets infected, the number of additional infections he could create is up to $k-1$. So our initial random infection of Irene creates, on average, $t \sum_{k=1}^{\infty}{k(k-1)p(k)}/\langle K \rangle = t \langle K^2 - K\rangle / \langle K \rangle$ at one step away. At $d$ steps, we've reached $\left(t \langle K^2 - K\rangle / \langle K \rangle \right)^d$ nodes. So long as $t > \langle K \rangle / \langle K^2 - K\rangle$, this is exponential growth:

If $t$ is above this critical level, the only way to avoid exponential growth is to have lots and lots of overlapping routes to the same nodes. [Some people might've had 1024 ancestors ten generations back, but most of us didn't.] Geographic clustering will do this, but the small-world effect makes it very hard to avoid. And the small-world effect is very much a part of modernity; whether the diameter of the social network is six or twelve or twenty is secondary to the fact that it's not a thousand.

#### Exhibit C

Zeynep Tufekci, "The Real Reason Everyone Should Panic: Our Global Institutions are Broken" (23 October 2014):
The conventional (smart) wisdom is that we should not panic about Ebola in the United States (or Europe). That is certainly true because, even with its huge warts, US and European health-care systems are well-equipped to handle the few cases of Ebola that might pop up.
However, we should panic. We should panic at the lack of care and concern we are showing about the epidemic where it is truly ravaging; we should panic at the lack of global foresight in not containing this epidemic, now, the only time it can be fully contained; and we should panic about what this reveals about how ineffective our global decision-making infrastructure has become. Containing Ebola is a no-brainer, and not that expensive. If we fail at this, when we know exactly what to do, how are we going to tackle the really complex problems we face?
Climate Change? Resource depletion? Other pandemics?
So, I have been panicking. ...
Globalization, in essence, means we really are one big family, in sickness and in health.
The more connected we are, the easier it is for a virus to spread wide and deep, before we get a chance to contain it.
And that is partially why Ebola is now ravaging through three countries in West Africa: it broke through in cities and large-enough settlements, and due to an accumulation of reasons, including recent civil wars, at a time when they were least equipped to handle it.
Containing an outbreak requires circumscribing the outbreak (isolating and treating the ill, tracing their contacts, isolating and treating them as well) so that it can no longer find new hosts, and healing those who are ill, or mourning those who die. Circumscribing an outbreak is easier when the cases are a few, or a few dozen, or a few hundred.
In fact, we know from previous Ebola outbreaks which parameter brings down the dreaded transmission rate: "the rapid institution of control measures." It’s that simple.
After thousands of cases, this gets harder and harder.
After millions, it is practically impossible.

Of course, Ebola got under control (in 2014). It took far too much misery and fear and time, but it happened. But it left no sign that the powers that be had learned any lessons, about (to quote Tufekci again) either "basic math [or] basic humanity".

The Mongols, at least, had the excuse that they had no idea what they were doing. (It's not as though Nasir al-din al-Tusi had, between doing theology and pioneering Fourier analysis, worked out how network connectivity related to the likelihood of epidemic outbreaks.) Compared to them, our predecessors in globalization, we are as gods; we're just not very good at it.

Posted at March 10, 2020 23:46 | permanent link