Teaching Responsibility
LJMU Schools involved in Delivery:
Computer Science and Mathematics
Learning Methods
Lecture
Tutorial
Module Offerings
6110MATHS-JAN-CTY
Aims
This course will teach the application of mathematical models to a variety of problems in biology and medicine. The aims of the course are:
To introduce mathematical models of biological systems and techniques for analysing them.
To enable students to appreciate and understand how mathematics can be used to model biological systems.
Learning Outcomes
1.
Recognise the importance of applications to real biological problems and be able to interpret the biological significance of terms in the mathematical models.
2.
Develop simple models based upon particular biological systems.
3.
Analyse the behaviour of solutions to the differential equations that arise in models for biological systems.
4.
Determine steady states, their stability and produce phase plane portraits.
5.
Understand and analyse simple infectious disease models and the concepts of epidemic, endemic and disease-free states.
6.
Analyse travelling wave solutions of PDEs.
7.
Analyse pattern forming solutions of PDEs.
Module Content
Outline Syllabus:Single species population models
Multi species population models
Mathematical models of ecological systems
Epidemiological models
Evolution and evolutionary game theory
ODE models in biology and medicine Reaction kinetics
Biological movement and pattern formation
Travelling waves
Delay differential equations
Module Overview:
This module will teach the application of mathematical models to a variety of problems in biology and medicine. The aims of the module are to introduce mathematical models of biological systems and techniques for analysing them.
This module will teach the application of mathematical models to a variety of problems in biology and medicine. The aims of the module are to introduce mathematical models of biological systems and techniques for analysing them.
Additional Information:It will show the application of differential and difference equations to simple biological, ecological and medical problems. It will provide an understanding of the mathematical modelling methods that describe population dynamics, epidemiological processes and evolutionary processes in ecological systems. It will also show the use of mathematical modelling in biochemical reactions, the application of partial differential equations in describing spatial processes such as cancer growth and pattern formation in embryonic development, and the use of delay-differential equations in physiological processes.