
Academic Year:  2014/5 
Owning Department/School:  Department of Mathematical Sciences 
Credits:  6 
Level:  Honours (FHEQ level 6) 
Period: 
Semester 1 
Assessment Summary:  CW 25%, EX 75% 
Assessment Detail: 

Supplementary Assessment: 
MA30047 Mandatory Extra Work (where allowed by programme regulations) 
Requisites:  Before taking this unit you must take MA20202 or take MA20221 
Description:  Aims: To introduce students to problems arising in population biology that can be tackled using applied mathematics. Both mathematical modelling and mathematical analysis will be covered, and at all times the interplay between the mathematics and the underlying biology will be emphasised. Learning Outcomes: At the end of this unit, students should be able to: * handle mathematical modelling issues for problems in population biology, * analyse models written in terms of ordinary differential equations or difference equations, * give a qualitative and quantitative account of their solution, and * interpret the results in terms of the original biological problem. Skills: Mathematical modelling in biology T/F A Problem solving T/F A Written communication and group work F A Content: Single species population dynamics: * Models in discrete and continuous time: basic reproductive ratio R0; compensatory and depensatory competition (Allee effects). * Harvesting: constant yield and constant effort strategies; maximum sustainable yield; yieldeffort curves. * Spruce budworm model: hysteresis effect. Population dynamics of interacting species: * Hostparasitoid interactions: NicholsonBailey model; Jury conditions and NeimarkSacker bifurcations. * Predatorprey models: LotkaVolterra model; nonlinear functional responses; RosenzweigMacArthur model; paradox of enrichment. * Competition: Gause's principle of competitive exclusion. Infectious diseases: * SIS disease: contact rates and density vs. frequencydependent disease transmission; basic reproductive ratio R0; threshold theorem. * SIR epidemics and endemics: final size of the epidemic; disease eradication and control; host regulation and diseaseinduced extinction. * Vectorborne diseases and sexually transmitted diseases. Parts of the content include using computer packages (e.g. using and adapting MATLAB programs) as introduced in the prerequisites. 
Programme availability: 
MA30047 is Optional on the following programmes:Programmes in Natural Sciences
