MA390 Topics in Mathematical Biology
Lecturer: 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:
- MA113 Differential Equations A: basic understanding of solving ODEs
- ST111 Probability A and ST112 Probability B: random variables, probability distributions
Useful background:
- MA256 Introduction to Mathematical Biology: all the assumed knowledge is rehearsed in this module
- MA250 Introduction to Partial Differential Equations: we will introduce the methods of characteristics from first principles but it is previously studied in this module
- MA254 Theory of ODEs: we will introduce phase planes, stability analysis and bifurcation theory from first principles but they are previously studied in this module
Synergies:
- MA261 Differential Equations: Modelling and Numerics
- ST202 Stochastic Processes
- MA3J3 Bifurcations, Catastrophes and Symmetry
- MA3J4 Mathematical Modelling with PDE
- MA3G1 Theory of Partial Differential Equations
- MA3H7 Control Theory
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, Müller, Johannes, Kuttler, Christina, Lecture Notes in Mathematical Modelling in the Life Sciences, Springer. ISBN 978-3-642-27251-6.