MAS377 Mathematical Biology
|Semester 1, 2019/20||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)
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.
- To introduce students to the applications of mathematical techniques in deterministic models for the dynamics of biological populations.
Learning outcomesBy the end of the unit, a candidate will be able to demonstrate a clear knowledge of: - Discrete time models without competition (Deterministic model, Galton-Watson branching process, multitype and age-structured model); - Continuous time models without competition (Deterministic model, pure birth, pure death and linear birth-death processes); - Models involving immigrations (Birth-death-immigrations process, equilibrium behaviour) - More general models (Deterministric models with density-dependent growth, general birth-death process with quasi-equilibrium); - Models with ineracting types (Competition, predator-prey and epidemic processes).
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; time delays.
|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.