[STAT/AP] Marco Seiler: Spread of an infection in a dynamical graph structure

04 September 2023 15:45 till 16:45 - Location: Lecture Hall G | Add to my calendar

Spread of an infection in a dynamical graph structure:
We study a contact process, which is one of the most popular interacting particle systems to model the spread of an infection in a spatially structured population given through a graph. For infinite graphs one is typically interested in the phase transition of survival and the associated critical infection rate. Below the critical rate the infection goes almost surely extinct and above there is a positive probability to survive.
The aim of this talk is to discuss how a dynamical graph structure affects the critical behaviour compared to a static graph. We will in particular focus on the special case of a dynamical version of the Galton-Watson tree. To be precise the edges between two vertices x and y are updated independently after an exponential time with rate v{x,y} and are declared to be open with proba- bility p{x,y} or closed otherwise. On top of this dynamical random graph we define a contact process, where the infection can only spread via open edges. In this setting we study the phase transition and provide conditions which imply either non-triviality or triviality of the phase transition. Here triviality means that for every infection rate the survival probability is strictly positive. As a consequence, we find that in contrast to the static case it is not always trivial.