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MA390 Topics in Mathematical biology

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).

Content:
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.

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, cancer and physiology; to consolidate basic mathematical techniques used in these approaches, such as ODEs, PDEs, probability theory, branching processes and Markov Chains.

Books.
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.

Additional Resources

Archived Pages: Pre-2011 2011 2012 2013 2014 2015 2016

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Year 1 regs and modules
G100 G103 GL11 G1NC

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Year 2 regs and modules
G100 G103 GL11 G1NC

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Year 3 regs and modules
G100 G103

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Year 4 regs and modules
G103

Archived Material
Past Exams
Core module averages