# MA256 Introduction to Mathematical Biology

**Lecturer: **Magnus Richardson

**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:**

Following a general introduction to mathematical modelling for biology, the module will cover topics from the sub-cellular level to interacting populations. Subjects included are: enzyme dynamics, gene expression, electrophysiology, excitable cells, cellular communication, tissue-level and models of whole-body physiology, population dynamics, interacting populations and epidemiology.

**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**

Following a general introduction to mathematical modelling for biology, the module will cover topics from the sub-cellular level to interacting populations. Subjects included are: enzyme dynamics, gene expression, electrophysiology, excitable cells, cellular communication, tissue-level and models of whole-body physiology, population dynamics, interacting populations and epidemiology.

**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**