Michaelmas Term Overview

In term 1 (Michaelmas term) of this course, we will study a range of stochastic models that allow us to analyse populations of biological agents moving and interacting in both space and time. We will consider general individual-based models in the form of stochastic simulation algorithms accounting for reactions among chemical species, or interactions between individuals in a population. We show how these models can, in various limits, give rise to the same continuum-level descriptions obtained via conservation laws at the macroscale. However, we will also demonstrate novel features of stochastic individual-based models, such as stochastic resonance and noise-induced attractor switching, that are not present in the deterministic macroscale models.

A key focus will be on designing and understanding stochastic simulation algorithms to simulate various stochastic processes on a computer. Simultaneously, we will develop a toolkit of analytic approaches to studying these processes that will validate and complement direct numerical simulations. We begin by studying how to simulate spatially homogeneous reaction systems, before moving on to more complex spatially extended systems later in the course. Applications will include models from ecology, neuroscience, chemistry, genetics and cell biology.