Mathematical models attempt to capture the essence of a biological system in the form of equations. The construction and analysis of such models allow us both to interrogate the biological system in ways which are not possible using experimentation alone, and to make quantitative predictions about the behaviour we expect the system to support. In contrast to the, perhaps more well-known, statistical approaches, mathematical models attempt to illuminate the mechanisms driving specific phenomena and to simplify the analysis of the overall system by identifying the key components of such mechanisms.

Mathematical models can be used to describe systems of any scale, from the genetic up to the ecosystem level and typically are used in situations in which the variables of interest are time-dependent. The beauty of mathematics is that it exposes universal properties that are preserved across biological systems, even when their scales vary greatly. By studying the geometry of the mathematical equations, we can make concrete statements about how the system should behave as well as how perturbations to it affect the resulting dynamics.


Workshop Aims:

- Introduction to developing mathematical models

- Simulation of mathematical models

- Phase-space analysis and prediction

- Code development to solve mathematical models


Knowledge of basic programming desired but not essential


Day 1

- Defining mathematical models

- Contrasting mathematical with statistical models

- Developing a first model - worked example of the Brusselator system

- Simulating mathematical models using xppaut/MATLAB

Day 2

- Writing mathematical models in MATLAB/xppaut

- Introduction to phase-space analysis

- Using phase-space analysis to predict behaviour

Day 3

- Further analysis of mathematical models

- Introduction to bifurcation theory

- Using xppaut to predict dynamic behaviour

- Short introduction to parameter estimation (time allowing)


Workshop files


If you have any queries regarding this course, please contact Danny Galvis.


Dates: 10/07, 17/07, 24/07, 13:30-16:30
Instructors:  Dr Danny Galvis
Location: Hatherly B12