# MATHEMATICAL BIOLOGY AND PHYSIOLOGY - 2024/5

Module code: MATM040

## Module Overview

Mathematical biology is concerned with using mathematical techniques and models to shed light on the fundamental processes that underly biology. By abstracting biological detail into a formal mathematical setting, we can identify what the mechanisms are that drive the observed phenomena, and can make predictions about system behaviour. Looking at a concrete example in cancer biology, it can be shown that tumour growth can be well-described using a simple system of linear partial differential equations. From this system we can then ascertain that tumour growth is initially limited by the availability of nutrients and can predict the result of different treatment methodologies.

To work in this field the mathematical biologist must develop a broad library of models, techniques and experience and be willing to engage with biological detail. They must learn to be conversant with e.g. systems of ordinary differential equations, partial differential equations and discrete models, and to analyse these systems using techniques ranging from stability analysis to computational and asymptotic methods. A key aspect of the work is validating the derived models using experimental results.

### Module provider

Mathematics & Physics

DUNLOP Carina (Maths & Phys)

### Module cap (Maximum number of students): N/A

Workshop Hours: 11

Independent Learning Hours: 65

Lecture Hours: 22

Guided Learning: 30

Captured Content: 22

Semester 1

None.

## Module content

Indicative content includes:

• Introduction to mathematical modelling of biological and physiological problems. This will include basic modelling methodology, dimensional analysis and the need for data analysis and model validation.

• Models without spatial dependence including: discrete models for population genetics and signal-response dynamics and enzyme kinetics.

• Spatially dependent models. Diffusion and reaction-diffusion equations: derivation and interpretation. Application including some of morphogenesis, tumour modelling.

• Selection of advanced techniques such as parameter estimation, asymptotic analysis and modelling case studies.

## Assessment pattern

Assessment type Unit of assessment Weighting
Coursework ASSESSED COURSEWORK 20
Examination End-of-Semester Examination (2 hours) 80

N/A

## Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate:

• Understanding of the modelling process applied to biological problems.

• The ability to critically select and apply appropriate models and techniques.

• Subject knowledge through the discussion of standard models, their derivations and key parameters.

• Analytical ability through the solution of unseen problems.

Thus, the summative assessment for this module consists of:

• One coursework worth 20% of the module mark and corresponding to Learning Outcomes 1, 2 and 3.

• A synoptic examination (2 hours), worth 80% of the module mark, corresponding to Learning Outcomes 1 to 4.

Formative assessment
There are three formative unassessed courseworks over an 11 week period, designed to consolidate student learning.

## Module aims

• Introduce students to the application of mathematical techniques to biological and physiological problems, illustrating how such an approach can produce results that contribute significantly to biological understanding and thus enable the development of new therapies and technologies.
• To enable students to develop the necessary biological and physiological modelling skills for real-world situations.
• Introduce a range of biological models and techniques, enabling students to develop an understanding of their applicability in any given context.

## Learning outcomes

 Attributes Developed 001 Students will understand the process of modelling as applied to biological problems including model validation by comparison with experimental data. KCT 002 Given a biological application, students will be able to critically select an appropriate mathematical technique from a range of techniques covered. KCT 003 Students will be able to apply techniques such as dimensional analysis, asymptotic analysis and stability analysis to problems in biology. KC 004 Students will be able to analyse and solve a range of biological models including signal-response dynamics, discrete biologically inspired models, diffusion-based models, and models for tumour progression. KCT

Attributes Developed

C - Cognitive/analytical

K - Subject knowledge

T - Transferable skills

P - Professional/Practical skills

## Methods of Teaching / Learning

The learning and teaching strategy is designed to:

• Provide a detailed introduction to mathematical biological and physiological modelling.

• Develop the ability to critically select appropriate models and mathematical techniques for use in this field.

• Provide experience of applying advanced methods to analyse and solve biologically inspired models.

The learning and teaching methods include:

• Three contact hours per week for 11 weeks split between lectures and modelling classes. Typeset notes are provided to complement the lectures. The modelling classes form a structured learning environment in which students practice methods taught.

• There are three unassessed courseworks to provide students with further opportunity to consolidate learning. Students receive individual written feedback on these as guidance on their progress and understanding.

• Where possible, lectures are recorded. Lecture recordings are intended to give students the opportunity to review parts of the session that they might not have understood fully and should not be seen as an alternative to attendance at lectures.

Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.

Upon accessing the reading list, please search for the module using the module code: MATM040

## Other information

The School of Mathematics and Physics is committed to developing graduates with strengths in Digital Capabilities, Employability, Global and Cultural Capabilities, Resourceness and Resilience, and Sustainability. This module is designed to allow students to develop knowledge, skills and capabilities in the following areas:

Digital Capabilities: Students are encouraged to use online tools including NetLogo and VisualPDE to investigate biological simulations. Use of these platforms enable students to gain a deeper understanding of life sciences through exploration of simulations of intricate biological phenomena.

Employability: MATM040 forms a bridge between mathematical skills and the life sciences. The expertise that students gain in modelling biological processes are highly valued in pharmaceuticals, healthcare analytics, and biotechnology.

Global and Cultural Capabilities: The modelling sessions give students the opportunity to work together.  Student engagement in discussions naturally cultivates the sharing of the different cultures that the students originate from.

Resourcefulness and Resilience: Tackling the complexities of modelling biological systems instills resourcefulness, empowering students to address challenges at the intersection of mathematics and biology. Problems addressing intricate, real-world scenarios promote student resilience.

Sustainability: Students explore mathematical frameworks to understand population dynamics, biodiversity, and environmental impact. This interdisciplinary approach equips students with insights to address ecological challenges, promoting sustainable practices.

## Programmes this module appears in

Programme Semester Classification Qualifying conditions
Mathematics with Statistics MMath 1 Optional A weighted aggregate mark of 50% is required to pass the module

Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2024/5 academic year.