Orateur
Description
Some models of discrete-time epidemics can be studied in the larger setting of first-passage percolation in multitype directed configuration models, where edges have an integer length representing transmission delays. Through directed breadth-first explorations and coupling with multitype branching processes on countable state spaces, we study the distribution of geodesics between several random points, as the population tends to infinity. Under general conditions, we show convergence of the (shifted) length of geodesics to the first points of Cox processes with given intensities. Going back to our application, this allows us to obtain scaling limits for the "epidemic curve", extending previous works [Barbour and Reinert, 2013] to a discrete-time setting, under minimal assumptions. This is an ongoing joint work with Mathilde André.
