The focus of this talk will be Susceptible-Infected-Recovered (SIR) models on dense dynamic random graphs, in which the joint dynamics of vertices and edges are co-evolutionary, i.e., they influence each other bidirectionally. In particular, edges appear and disappear over time depending on the states of the two connected vertices, on how long they have been infected, and on the total density of susceptible and infected vertices. I will present our main results, which establish functional laws of large numbers for the densities of susceptible, infected, and recovered vertices, jointly with the underlying evolving random graphs in the graphon space. The talk will also include numerical illustrations showing that our model exhibits multiple epidemic peaks, as observed in real-world epidemics.

This talk is based on a joint work with P. Braunsteins, F. den Hollander and M. Mandjes.