Department of Mathematical Sciences, Unit Catalogue 2009/10 |
MA50179: Mathematical biology 1 |
 Credits:
| 6 |
| Level:
| Masters |
| Period: | Semester 1 |
| Assessment:
| CW 25%, EX 75% |
| Supplementary Assessment: | Like-for-like 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 in-depth 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, first-order 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. Age-structured populations *: models in discrete time; models in continuous time. Harvesting: maximum sustainable yield; yield effort curves. Population dynamics of interacting species: host-parasitoid interactions: Nicholson-Bailey model; Jury conditions and Naimark-Sacker bifurcations. Predator-prey models: Lotka-Volterra model; phase plane analysis; Routh-Hurwitz conditions and Hopf bifurcations; Poincare-Bendixon 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. Vector-borne diseases and sexually transmitted diseases. Infectious diseases in age-structured populations *. * Topics to be covered by independent directed reading. |