# Gwybodaeth Modiwlau

Module Identifier
MA34920
Module Title
Mathematical Models of Biological Systems
2022/2023
Co-ordinator
Semester
Semester 2
Pre-Requisite
MA21410 or MT21410 MA21410 or MT21410

#### Assessment

Assessment Type Assessment length / details Proportion
Semester Assessment Computer prac  Report on a computer investigation  10%
Semester Assessment Problem Sheets  Three assessed problem sheets.  30%
Semester Exam 2 Hours   Exam  Semester Examination  60%
Supplementary Exam 2 Hours   Resit  Resit  100%

### Learning Outcomes

On successful completion of this module students should be able to:

Explain the biological relevance of parameters in a mathematical model of a complex system

Calculate the stability of the steady-state solutions to a mathematical model of a biological system.

Find travelling wave solutions of a differential equation.

Use a computer to explore the dynamics of a complex system.

### Brief description

Mathematical Biology is the application of mathematics to predict the response of biological systems. With a little knowledge of biology, mathematicians are now able to develop appropriate models of biological phenomena which are also of mathematical interest.
The course aims to develop students' ability to identify the key parameters in a complex system and create and solve a comparatively simple model, the results of which can then be related back to the original system. Examples will include chaotic population models and waves in reaction-diffusion systems which lead to pattern formation.

### Aims

Mathematical Biology is an area of interest that is growing rapidly in popularity; with a little knowledge of biology, mathematicians are now able to develop appropriate models of biological phenomena which are also of mathematical interest in their own right. Mathematicians who are familiar with rigorous biological modelling have extremely attractive employment prospects in this and related areas such as medicine.

### Content

Continuous and Discrete Single Species Population Models; Logistic Map; Fixed points; Linear Stability Analysis; Transition to Chaos.
Two species population models; Lotka Volterra; Predator Prey.
Spread of Epidemics; Cellular automata.
Reaction Diffusion Equations; Propagating Wave Solutions; Travelling Fronts; Spatial Pattern Formation; Animal Coat Patterns.

### Module Skills

Skills Type Skills details
Adaptability and resilience Students are expected to develop their own approach to time-management and to use the feedback from marked work to support their learning.
Co-ordinating with others Students will be encouraged to work in groups to solve problems.
Creative Problem Solving The assignments will give the students opportunities to show creativity in finding solutions and develop their problem solving skills.
Digital capability Use of the internet, Blackboard, and mathematical packages will be encouraged to enhance their understanding of the module content and examples of application
Professional communication Students will be expected to submit clearly written solutions to set exercises.
Subject Specific Skills Develop mathematical skills in developing and solving models

### Notes

This module is at CQFW Level 6