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Mathematics Institute

MA256/MA356 Introduction to Mathematical Biology

Lecturer: Lukas Eigentler

Term(s): Term 1

Status for Mathematics students: List A (MA256 is for 2nd years, MA356 for 3rd years provided MA256 has not been taken in a previous year).

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:

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:

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



Additional Resources