Degree dependent contact process

In this talk we consider a novel version of the contact process, which is one of the simplest model for individual based modelling of epidemic spread. There is a graph that describes who knows who. Then contact process is a random process on this graph that evolves as follows: Each node (person) of the graph is either healthy or infected. Infected nodes heal randomly at rate 1, and while they are infected, they transmit the infection to their neighbors in the graph at some rate r(e) across each edge. In this talk we set the transmission rate across an edge depend on the degrees (number of neighbors) of the two endpoints of the edge, i.e., of the form r(u,v)= lambda/ f(deg(u), deg(v)) so that higher degree vertices transmit the disease through an individual edge less frequently than lower degree vertices, but the total number of transmissions they make on average still grows with their degree, as a polynomial of their degree with an exponent less than one. We study the conditions for survival of the infection process till eternity, when the underlying graph is a simple random tree. On a finite random graph mimicking social networks, called the configuration model, we study the length of time until the infection goes extinct. We find the power of superspreaders and also how we can control them. Joint work with Zsolt Bartha (TU/e) and Daniel Valesin (Warwick).