MA256 Introduction to Mathematical Biology
Lecturer: Lukas Eigentler
Term(s): Term 1
Status for Mathematics students: List A
Commitment: 30 one hour lectures
Assessment: 100% by 2 hour examination
Formal registration prerequisites: None
Assumed knowledge: Students should have a good knowledge of differential equations and matrix-vector manipulation. Some knowledge of stochastic modelling would be a plus. The following modules will provide a good background to this module:
- MA133 Differential Equations
- MA146 Methods of Mathematical Modelling 1
- MA144 Methods for Mathematical Modelling 2
- MA124 Maths by Computer
- ST111 Probability A
- ST112 Probability B
Useful background: A good understanding of mathematical models of biological systems will help students to follow the material in this course. The book listed below by Murray "Mathematical Biology, An Introduction" provides a guide to modelling biological systems with differential equations.
Synergies: The following year 2 modules will go well with this module:
Leads to: The following modules have this module listed as assumed knowledge or useful background:
- MA390 Topics in Mathematical Biology
- MA4E7 Population Dynamics: Ecology & Epidemiology
- MA4M1 Epidemiology by Example
- MA4M9 Mathematics of Neuronal Networks
Course content:
In this module, we will develop simple models of biological phenomena from basic principles. We will introduce analysis techniques to investigate model dynamics in order to deduce biologically significant results. We will use (systems of) ordinary differential equations, difference equations, and partial differential equations to study population dynamics, biochemical kinetics, epidemiological dynamics, evolution, and spatiotemporal phenomena. Throughout, we will discuss the biological implications of our results.
Aims:
Introduction to the fundamentals of Mathematical Biology.
Objectives:
- To develop simple models of biological phenomena from basic principles
- To analyse simple models of biological phenomena using mathematics to deduce biologically significant results
- To reproduce models and fundamental results for a range of biological systems
- To have a basic understanding of the biology of the biological systems introduced
Books:
H. Van den Berg, Mathematical Models of Biological Systems, Oxford Biology, 2011
James D. Murray, Mathematical Biology: I. An Introduction. Springer 2007
Keeling, M.J. and Rohani, P. Modeling Infectious Diseases in Humans and Animals, Princeton University Press, 2007
Anderson, R. and May, R. Infectious Diseases of Humans, Oxford University Press, 1992
Outline syllabus for publication
- Mean-field Population dynamics a. Single-species population models, b. Multi-species population models
- Models of biochemical kinetics
- Epidemiological models
- Models of evolution and game theory models
- Spatio-temporal models of population dynamics a. Travelling waves, b. Pattern formation
Reading list
- H. van den Berg, Mathematical Models of Biological Systems, Oxford Biology, 2011
- James D. Murray, Mathematical Biology: I. An Introduction Springer 2007
- Anderson, R. and May, R. Infectious Diseases of Humans, Oxford University Press, 1992
- Keeling, M.J. and Rohani, P. Modeling Infectious Diseases in Humans and Animals, Princeton University Press, 2007
Additional Resources