Mathematical Modelling in Biology and Medicine - 2023 entry

This is an advanced module in mathematical modelling applied to biology and medicine that focuses on modern applications of mathematical techniques to cutting-edge research in these areas. It will introduce you to advanced topics in biochemical networks, physiology, epidemiology and biomedical data analysis. The module is run as a combination of lectures and hands-on computational modelling sessions, and may also involve laboratory visits.

This module provides you with small-group teaching across a selection of advanced topics, reflecting the research interests of the staff involved. The syllabus consists of three short courses, each taught as a self-contained set comprising four lectures together with four workshops/tutorials. In order to take this module, you must ensure that you have completed module MTH2003 Differential Equations.

This is an optional module for Final Year students of MSci Natural Sciences, and is also an optional module for Third Year Mathematics, Computer Science and Physics undergraduates.

This module aims to introduce you to some of the advanced mathematical and computational modelling methods that are currently used in modern mathematical biology research. It will give you experience of hands-on modelling approaches, and develop an interdisciplinary viewpoint of biology. In this module, you will put into practice the knowledge you have acquired so far in your degree programme, and engage with modern scientific developments in an expanding and increasingly important field of study.

As part of this module, you will develop your skills in several of the following areas: literature review; project planning; experimentation and analysis; interpretation of results; and technical report writing.

On successful completion of this module, you should be able to:

Module Specific Skills and Knowledge:

1 Build computational/mathematical models that can capture biological phenomena and guide experimental studies (through hypothesis generation, experimental validation, etc.);

2 Analyse models and experimental data using appropriate tools/techniques;

3 Critically evaluate and analyse the module content within the context of wider reading to develop an overarching view of the interconnectedness of the subject and its interdisciplinary nature;

4 Recognise and exploit any connections between taught materials and project material;

5 Engage in targeted research and reading for personal development and future educational requirements, in addition to reading material primarily for assessment purposes;

Discipline Specific Skills and Knowledge:

6 Apply a range of computational and mathematical methods to model diverse biological phenomena;

7 Combine experimental and theoretical concepts, literature and ideas;

8 With reference to primary literature, evaluate how research developments in applied mathematics and computer science drive the subject forward and, where appropriate, the social, technological and commercial impacts they have;

9 Analyse in detail essential facts and theory in advanced areas of mathematical biology;

10 Analyse and evaluate independently a range of research-informed examples from the literature into written work;

11 With limited guidance, deploy established techniques of analysis and enquiry used in mathematical biology at the research level;

Personal and Key Transferable/ Employment Skills and Knowledge:

12 Communicate effectively with scientists possessing experimental backgrounds;

13 Think creatively and beyond traditional discipline boundaries;

14 Successfully communicate arguments, evidence and conclusions using written means in a manner appropriate to the intended audience;

15 Devise and sustain, with little guidance, a logical and reasoned argument with sound, convincing conclusions;

16 Analyse and evaluate appropriate data with very limited guidance.

Each topic is a self-contained short course lasting 8 hours, with its own specific syllabus available in separate documentation on the associated ELE page for this module. Three topics will run each academic year depending on demand and staffing. Topics may include the following:

• Mathematical modelling of gene-regulatory/metabolic networks;

• Mathematical modelling of excitable physiological systems;

• Uncertainty quantification in biomedical modeling;

• Disease dynamics on complex networks;

• Mathematical models of hormone signalling.

Deferral – if you miss an assessment deadline for certificated reasons judged acceptable by the Mitigation Committee, you will normally be either deferred in the assessment, or an extension may be granted. The mark given for a re-assessment taken as a result of deferral will not be capped and will be treated as if it were your first attempt at the assessment.

Referral – if you have failed the module overall (i.e. obtained a final overall module mark of less than 50%) you will be required to complete a further problem set. The mark given for a re-assessment taken as a result of referral will count for 100% of the final mark and will be capped at 50%.

Basic Reading:

ELE: http://vle.exeter.ac.uk/

Klipp E, Liebermeister W, Wierling C, Kowald A, Lehrach H, Herwig R. Systems Biology: A Textbook. Wiley (2009).

Alon U. An Introduction to Systems Biology: Design Principles of Biological Circuits. Chapman and Hall (2006).

Strogatz SH. Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering. Perseus Books (2000).

Britton NF. Essential Mathematical Biology. Springer (2005)

Web based and Electronic Resources:

More specialised reading lists will be provided at the start of each short course.

Supplementary electronic resources will be provided on the module ELE page http://vle.exeter.ac.uk/

Reading list for this module: