Lecturer: Professor Nigel Burroughs
Term(s): Term 1
Status for Mathematics students: List A
Commitment: 30 one hour lectures
Assessment: 3 hour examination (100%)
Prerequisites: There are no prerequisites but the following is advised: Probability A & B (ST111), Introduction to partial differential equations (MA250), Theory of ODEs (MA254), Introduction to Systems Biology (MA256).
Mathematical modelling of biological systems and processes is a growing field that uses multiple mathematical techniques. This course will cover a range of these techniques, using examples from primarily medical systems. Topics include:
1. Small gene circuits (bifurcations, phase plots, linearization analysis, stochastic analogues through master equations).
2. Virus dynamics (ODEs) and mutation, including HIV/AIDS and basic immunology.
3. Cancer modelling (branching processes). Therapy.
4. Waves in biology (excitable systems, neurobiology).
This course leads on to MA4J6, Mathematics and Biophysics of Cell dynamics.
To introduce ideas and techniques of mathematical modelling (deterministic and stochastic) in biology.
To gain an insight into modelling techniques and principles in gene regulation, virus growth, cancer and physiology; to consolidate basic mathematical techniques used in these approaches, such as ODEs, PDEs, probability theory, branching processes and Markov Chains.
There is no dedicated text. A classic text (only deterministic modelling, I is predominantly ODEs, II is PDEs) is Mathematical Biology I & II. James Murrey. Springer. Useful texts for specific topics are: Branching process models of cancer. Richard Durrett. 2015. Springer. [https://0-link-springer-com.pugwash.lib.warwick.ac.uk/book/10.1007/978-3-319-16065-8], Mathematical Physiology I: Cellular Physiology and II: Systems physiology. James Keener, James Sneyd. 2009. Springer. Virus dynamics : mathematical principles of immunology and virology. Martin Nowak and Robert May. 2000. OUP.