Pieter Trapman: Percolation and spatial epidemics

Abstract:
Percolation theory is a very rich body of mathematical theory and its development has been a catalyst for much interesting progress in probability theory.

The most basic percolation model is the following. Consider a connected graph G=G(V,E), with vertex/node set V and edge/bond set E. Then consider the random subgraph of G obtained by independently deleting edges of E with probability 1-p. In percolation theory, properties of this random subgraph are studied. Some questions of interest are: How does the distribution of the sizes of clusters depend on p and on G? If G is infinite, how many infinite clusters are there in the random sub-graph?

It turns out that percolation theory naturally leads to many easy to formulate questions, which are surprisingly hard to answer.  In this lecture, I will properly introduce some percolation models and discuss several natural questions and approaches to answer them.

In addition, I will  discuss how (variants of) percolation models can be used to study the spread of infectious diseases in a (spatially) structured population. I will show how this spatial spread differs from the most common models used in infectious disease epidemiology.

The docent-lecture will be accessible for MSc student in mathematical statistics.