Module manager: Prof Martin Lopez-Garcia
Email: m.lopezgarcia@leeds.ac.uk
Taught: Semester 2 (Jan to Jun) View Timetable
Year running 2026/27
None
| MATH1000 | Core Mathematics |
MATH3565 Mathematical Biology
This module is not approved as a discovery module
Mathematical modelling is increasingly important in the biological and medical sciences. Mathematical and computational modelling can help to make sense of experimental data and to shed light into new biological phenomena. This module aims to introduce the student to some areas of mathematical biology and medicine, using tools from applied mathematics. Topics featured in this module range from mathematical ecology (modelling population dynamics in a variety of ecosystems) to mathematical immunology (modelling within-host infection dynamics and the immune response) and mathematical epidemiology (modelling the transmission of pathogens across individuals in a population).
On completion of this module, students should be able to model a wide range biological phenomena described by: - ordinary differential equations; - discrete and continuous time Markov processes - branching processes; - Brownian motion; - partial differential equations.
On successful completion of the module students will be able to: 1. Model biological systems using ordinary differential equations. 2. Determine the overall behaviour of these dynamical systems, including the identification of steady states and their stability. 3. Biologically interpret model parameters and their dimensions, and perform relevant change of variables to simplify the analysis of these systems. 4. Model biological systems using Markov processes. 5. Determine the overall behaviour of these dynamical systems, analysing long-term outcomes such as probability and time to extinction. 6. Use probability generating functions to study these systems. 7. Model biological systems in space and time using stochastic processes and partial differential equations. 8. Determine the overall behaviour of these dynamical systems, including asymptotic behaviour.
The module focuses on modelling biological phenomena from several areas of Biology and Medicine. Key covered topics are: · Ordinary differential equations to model biological systems and population dynamics. · Steady states and stability in one and multiple dimensions. · Random variables and probability generating functions. · Stochastic models in Biology, including birth-and-death and branching processes. · Spatial models and Brownian motion. Additional topics that build on these may be covered as time allows. Such topics may be drawn from the following, or similar: · Modelling the impact of harvesting on ecosystems. · Communicable diseases and infection transmission models. · Spatially extended systems. · Age-structured models.
| Delivery type | Number | Length hours | Student hours |
|---|---|---|---|
| Lecture | 44 | 1 | 44 |
| Private study hours | 156 | ||
| Total Contact hours | 44 | ||
| Total hours (100hr per 10 credits) | 200 | ||
Students will be given Example Sheets to practise during the semester. They will have the opportunity to submit their attempt for some questions (not to be marked) in order to receive feedback.
Check the module area in Minerva for your reading list
Last updated: 30/04/2026
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