# MA390 Topics in Mathematical Biology

Lecturer: Professor Nigel Burroughs

Term(s): Term 1

Status for Mathematics students: List A

Commitment: Up to 30 lectures over the term and support classes.

Assessment: 100% 3 hour examination

Formal registration prerequisites: None

Assumed knowledge:

Useful background:

Synergies:

Leads to: The following modules have this module listed as assumed knowledge or useful background:

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.

Books:
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, MÃ¼ller, Johannes, Kuttler, Christina, Lecture Notes in Mathematical Modelling in the Life Sciences, Springer. ISBN 978-3-642-27251-6.