MAS377 Mathematical Biology

Semester 1, 2017/18 10 Credits
Lecturer: Prof Nick Monk uses MOLE Timetable Reading List
Aims Assessment Full Syllabus

The course provides an introduction to the mathematical modelling of the dynamics of biological populations. The emphasis will be on deterministic models based on systems of differential equations that encode population birth and death rates. Examples will be drawn from a range of different dynamic biological populations, from the species level down to the dynamics of molecular populations within cells. Central to the course will be the dynamic consequences of feedback interactions within the populations. In cases where explicit solutions are not readily obtainable, techniques that give a qualitative picture of the model dynamics (including numerical simulation) will be used.

Prerequisites: MAS222 (Differential Equations)
Not with: MAS323 (Differential Equations: A Case Study); MAS424 (Differential Equations (Advanced))
No other modules have this module as a prerequisite.


Outline syllabus

  • Population models: Deterministic models; birth and death processes; logistic growth; competition between populations.
  • Epidemic models: Compartment models; the SIR model.
  • Biochemical and Genetic Networks: Mass-action kinetics; simple genetic circuits; genetic switches and clocks.
  • Spatial Pattern Formation: Cellular models; lateral inhibition; reaction-diffusion; spatial pattern formation; the Turing mechanism.



Aims

  • To introduce students to the applications of mathematical techniques in deterministic models for the dynamics of biological populations.

20 lectures, no tutorials

Assessment

One formal 2 hour written examination.

Full syllabus

1. Population models

Deterministic models; birth and death processes; logistic growth; competition between populations.
2. Epidemic models
Compartment models; the SIR model.
3. Biochemical and Genetic Networks
Mass-action kinetics; simple genetic circuits; genetic switches and clocks.
4. Spatial Pattern Formation
Cellular models; lateral inhibition; reaction-diffusion; spatial pattern formation; the Turing mechanism.

Reading list

Type Author(s) Title Library Blackwells Amazon
B J.D.Murray Mathematical Biology 570.15118 (M) Blackwells Amazon
B S.P.Ellner and J.Guckenheimer Dynamic Models in Biology 570.15118 (E) Blackwells Amazon
C H.van den Berg Mathematical Models of Biological Systems 570.15118 (B) Blackwells Amazon

(A = essential, B = recommended, C = background.)

Most books on reading lists should also be available from the Blackwells shop at Jessop West.

Timetable

Mon 11:00 - 11:50 lecture   Hicks Lecture Theatre A
Thu 16:00 - 16:50 lecture   Hicks Lecture Theatre A