Department of Mathematical Sciences, Unit Catalogue 2011/12 

Credits:  6 
Level:  Masters UG & PG (FHEQ level 7) 
Period: 
Semester 1 
Assessment:  CW 25%, EX 75% 
Supplementary Assessment:  Likeforlike reassessment (where allowed by programme regulations) 
Requisites:  
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: Students should be familiar with mathematical modelling issues for problems in population biology. They should be able to 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. They will be able to demonstrate an indepth understanding of the topic. Skills: Mathematical modelling in biology, including the ability to extend and interpret a model published in the research literature. Ordinary differential equations, difference equations, firstorder partial differential equations. Content: Single species population dynamics: Models in discrete and continuous time: basic reproductive ratio R_0; compensatory and depensatory competition; transcritical, tangent and period doubling bifurcations, chaos. Agestructured populations*: models in discrete time; models in continuous time. Harvesting: maximum sustainable yield; yield effort curves. Population dynamics of interacting species: hostparasitoid interactions: NicholsonBailey model; Jury conditions and NaimarkSacker bifurcations. Predatorprey models: LotkaVolterra model; phase plane analysis; RouthHurwitz conditions and Hopf bifurcations; PoincareBendixon theorem, Dulac condition; Lyapunov functions; Volterra's principle. Nonlinear functional responses *. Competition: Gause's principle of competitive exclusion. Infectious diseases: SIS disease: basic reproductive ratio R_0; threshold theorem. SIR epidemics and endemics: threshold theorem; size of the epidemic; eradication and control. Vectorborne diseases and sexually transmitted diseases. Infectious diseases in agestructured populations *. * Topics to be covered by independent directed reading. 
Programme availability: 
MA50179 is Optional on the following programmes:Department of Biology & Biochemistry
