MAS377 Mathematical Biology
|Semester 1, 2017/18||10 Credits|
|Lecturer:||Prof Nick Monk||uses MOLE||Reading List|
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.
- 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.
- To introduce students to the applications of mathematical techniques in deterministic models for the dynamics of biological populations.
20 lectures, no tutorials
One formal 2 hour written examination.
1. Population 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.
|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.