Content: Mathematical modelling of biological systems and processes is a growing field that uses multiple mathematical modelling and analysis techniques. This course will cover a range of these techniques, using examples from primarily medical systems. Topics include:
- Virus dynamics and mutation, including HIV/AIDS and basic immunology (ODEs, phase plane analysis - linearisation and stability analysis)
- Small gene circuits (bifurcations, stochastic modelling using master equations and solving them with method of characteristics (PDEs reduced to ODEs))
- Cancer modelling (branching processes, solutions with method of characteristics)
- Cancer treatment (possibly including game theory and control theory)
Aims: To introduce ideas and techniques of mathematical modelling (deterministic and stochastic) in biology
Objectives: To gain an insight into modelling techniques and principles in gene regulation, virus growth and cancer; to consolidate basic mathematical techniques used in these approaches, such as ODEs, PDEs, control theory, probability theory, branching processes and Markov Chains.
There is no dedicated text. A classic text (only deterministic modelling, I is predominantly ODEs and of more relevance to course, 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], Virus dynamics : mathematical principles of immunology and virology. Martin Nowak and Robert May. 2000. OUP, Methods and Models in Mathematical Biology, Müller, Johannes, Kuttler, Christina, Lecture Notes in Mathematical Modelling in the Life Sciences, Springer. ISBN 978-3-642-27251-6.