Low-dimensional representations of stochastic dynamics on discrete structures

Last modified: 2014-06-09

#### Abstract

Many biological systems of interest are inhomogeneous but not purelyspatial, meaning that the interactions between individuals i and j is notsimply a function of Euclidian distance, but are instead well modelled by amore general matrix element A_{ij}. This has led to frequent adoption of anetwork paradigm, where individuals are placed on vertices of a graph. Suchdiscrete structures pose particular challenges due to the high dimensionalityof any stochastic process defined on them, motivating attempts to providelow-dimensional limits or approximations to the general dynamics. This talkwill consider some promising techniques for addressing these challenges,mainly in the context of disease transmission models, including random graphmodels, motif-based expansion, and non-commutative algebra.

#### Keywords

epidemic model; network; algebra