Mathematical Models of Biological Systems

Cod y Modiwl
MA34920
Teitl y Modiwl
Mathematical Models of Biological Systems
Blwyddyn Academaidd
2026/2027
Semester
Semester 2
Cyd-gysylltydd y Modiwl
Professor Simon Cox
Rhestr Ddarllen
Gweld ar Aspire
Rhagofynion
MA21410 neu MT21410
MA21410 or MT21410
Staff Eraill sy'n Cyfrannu

Dulliau Asesu

Math o Asesiad

Manylion Asesiad

Cyfran
Asesiad Semester Semester Assessment: 20 Awr Selected exercises from three problem sheets and a report on a computer investigation 40%
Arholiad Semester Semester Exam: 2 Awr 60%
Asesiad Ailsefyll Supplementary Assessment: Supplementary problem sheet. 40%
Arholiad Ailsefyll Supplementary Exam: 2 Awr 60%

Canlyniadau Dysgu

Wedi cwblhau'r modiwl dylai'r myfyrwyr fedru:

  1. Explain the biological relevance of parameters in a mathematical model of a complex system
  2. Calculate the stability of the steady-state solutions to a mathematical model of a biological system.
  3. Find travelling wave solutions of a differential equation.
  4. Use a computer to explore the dynamics of a complex system.

Disgrifiad cryno

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.

Nod

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.

Cynnwys

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.

Sgiliau Modiwl

Math o Sgiliau

Manylion Sgiliau
Addasrwydd a gwydnwch Students are expected to develop their own approach to time-management and to use the feedback from marked work to support their learning.
Cydlynu ag erail Students will be encouraged to work in groups to solve problems.
Cyfathrebu proffesiynol Students will be expected to submit clearly written solutions to set exercises.
Datrys Problemau Creadigol The assignments will give the students opportunities to show creativity in finding solutions and develop their problem solving skills.
Gallu digidol Use of the internet, Blackboard, and mathematical packages will be encouraged to enhance their understanding of the module content and examples of application
Sgiliau Pwnc-benodol Develop mathematical skills in developing and solving models

Nodau

Mae'r modiwl hwn yn cydymffurfio a FfCChC Lefel 6