Seminar by Jonas Juul

Descendant distributions for simple contagions on networks
- How widespread will the next Spanish flu get?
Jonas Juul (NBI)

The concept of contagion originated in epidemiology, but it has now been generalized to diverse phenomena in which some infectious agent propagates from node to node on a network. Examples include the spread of innovations, bank failures, and electrical  blackouts. Sometimes, as in the Spanish flu epidemic of 1918, a contagion also mutates from a milder form to a deadlier form as it spreads. Here, using a simple mathematical model, we quantify the downstream impact of a contagion that mutates exactly once as it travels. We present exact results for this impact in terms of the distribution of the number of "descendants", d, of the origin of the mutation on several infinite-dimensional networks. In all cases, we find that the tail of all the distribution follows an inverse-square law d^(-2). This prediction is consistent with the observed statistics of memes propagating and mutating on Facebook, as reported by Adamic and colleagues in 2016, and is predicted to hold for other effectively infinite-dimensional networks such as the global human contact network. 
The work is joint with Steven Strogatz, Cornell University.