Research Fellows Directory
Dr Tim Rogers
University of Bath
The purpose of my research is to analyse mathematical models to help predict the behaviour of complicated natural processes, such as the chemical reactions taking place in a cell, or evolution of micro-organisms. The major challenge in this area is to make robust predictions about processes which are both sparse, meaning that most elements of a system only interact with a handful of others, and highly random.
One important example is the spread of disease. We know that infections are passed from person to person via a network of social interactions, but who falls ill and who does not seems to be random. Classical epidemic models have the advantage of being mathematically solvable, but they do not capture the full effect of the network structure. An alternative, and currently very popular, approach is to build a computer simulation and wait and see what emerges. Unfortunately, the predictions of the computer often do not agree with those of the mathematical model. So which should we believe?
My work aims to bridge the gap between over-simplified equations and over-complicated computer simulations, giving new insights into the behaviour of complex random processes. To achieve this, I develop mathematical methods to extract the key mechanisms at work in a model, for example by separating the fast and slow parts of a process to get a clearer picture. This research draws on ideas and techniques from probability, applied mathematics, and statistical physics.