Ebola, and Mongol Modernity

Attentionconservation notice:An old courseslide deck, turned in to prose on the occasion of a vaguely-related newsstory from 2014. Not posted at the time because it felt over-dramatic. Ihave, of course, no authority to opine about either world history orepidemiology, 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 JanetAbu-Lughod's BeforeEuropean Hegemony: The World System A.D. 1250--1350. It gave me thesense, as few other things have, of historical contingency, or more exactly ofmodernity as a belated phenomenon,and changed myteaching. She depicts an integrated (part-of-the-) world economy, an"archipelago of towns" linked by trade-routes stretching from Flanders toHangzhou and centered in the Indian Ocean. This archipelago is wheremodernity should have begun. Beyond the market-oriented,urban-centered economy, China has the beginnings of an industrial revolution (apoint explored by Mark Elvin in hisPattern of the Chinese Past, and his sources in Japanese scholarsof Chinese economic history, and emphasized by William McNeill inhis Pursuit of Power); the beginnings of a truly globalperspective. All of this was politically supported by the unification of themost economically and technologically advanced regions (namely China and theIslamic world) under the Mongol Empire, admittedly at the cost of theoccasional "shock and awe" campaign, destruction of Baghdad, etc.

Exhibit B

So what, according to Abu-Lughod, happened? What happened was Yersiniapestis, the bubonic plague, a bacterium transmitted by fleas that live onrodents. It long has been, and is, endemic to the rodents ofCentral Asia, such as the giant gerbil {\em Rhombomys opimus}, which seems to be perpetually perchedat the edge of the epidemic threshold. The Mongol Empire didn't just unifythe most advanced parts of Eurasiafrica; it brought them into intimate contactwith Central Asia. And then, asusual, the plague followed the routes of trade and imperial travel:

It's impossible to know just how deadly it was, but estimates put it ataround 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 andre-purposed by western European pirates/traders poking into the post-pandemiclandscape.

One aspect to this is how slowly, and how progressively, the plaguespread. 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 putsit, this is strong evidence that "thesmall-world effect is a modern phenomenon". The small-world effect, afterall, is that the maximum distance between any two people in the social networkof size $n$ grows like $O(\log{n})$. This implies that the number of peoplereachable in $d$ steps grows exponentially with $d$, which is hardlycompatible with the steady geographic progress of the disease.

The argument here is sopretty that I can't resist sketching it. Suppose that every infectedperson passes it on to any one of their contacts with probability $t$, at leaston average. We start the infection at a random person, say Irene, who selectsa random one of their acquaintances, say Joey, for passing it on. Theprobability that Irene, or any other random person, has $k$ contacts is, byconvention, $p(k)$. But Joey isn't a random person; Joey is someone reachableby 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 degre