Academic Year:
| 2013/4 |
Owning Department/School:
| Department of Mathematical Sciences |
Credits:
| 6 |
Level:
| Honours (FHEQ level 6) |
Period: |
Semester 1
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Assessment:
| CW 25%, EX 75% |
Supplementary Assessment: |
MA30047 Mandatory Extra Work (where allowed by programme regulations)
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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; yield-effort curves.
* Spruce budworm model: hysteresis effect.
Population dynamics of interacting species:
* Host-parasitoid interactions: Nicholson-Bailey model; Jury conditions and Neimark-Sacker bifurcations.
* Predator-prey models: Lotka-Volterra model; nonlinear functional responses; Rosenzweig-MacArthur model; paradox of enrichment.
* Competition: Gause's principle of competitive exclusion.
Infectious diseases:
* SIS disease: contact rates and density- vs. frequency-dependent disease transmission; basic reproductive ratio R0; threshold theorem.
* SIR epidemics and endemics: final size of the epidemic; disease eradication and control; host regulation and disease-induced extinction.
* Vector-borne diseases and sexually transmitted diseases.
Parts of the content include using computer packages (e.g. using and adapting MATLAB programs) as introduced in the pre-requisites.
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Programme availability: |
MA30047 is Optional on the following programmes:
Programmes in Natural Sciences
- UXXX-AFB01 : BSc (hons) Natural Sciences (Full-time) - Year 3
- UXXX-AKB02 : BSc (hons) Natural Sciences with Industrial Placement (Full-time with Thick Sandwich Placement) - Year 4
- UXXX-AAB02 : BSc (hons) Natural Sciences with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
- UXXX-AFM01 : MSci (hons) Natural Sciences (Full-time) - Year 3
- UXXX-AKM02 : MSci (hons) Natural Sciences with Professional Placement (Full-time with Thick Sandwich Placement) - Year 4
- UXXX-AAM02 : MSci (hons) Natural Sciences with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
Department of Mathematical Sciences
- USMA-AFB15 : BSc (hons) Mathematical Sciences (Full-time) - Year 3
- USMA-AKB16 : BSc (hons) Mathematical Sciences (Full-time with Thick Sandwich Placement) - Year 4
- USMA-AAB16 : BSc (hons) Mathematical Sciences with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
- USMA-AFB13 : BSc (hons) Mathematics (Full-time) - Year 3
- USMA-AKB14 : BSc (hons) Mathematics (Full-time with Thick Sandwich Placement) - Year 4
- USMA-AFB01 : BSc (hons) Mathematics and Statistics (Full-time) - Year 3
- USMA-AKB02 : BSc (hons) Mathematics and Statistics (Full-time with Thick Sandwich Placement) - Year 4
- USMA-AAB02 : BSc (hons) Mathematics and Statistics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
- USMA-AAB14 : BSc (hons) Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
- USMA-AFB05 : BSc (hons) Statistics (Full-time) - Year 3
- USMA-AKB06 : BSc (hons) Statistics (Full-time with Thick Sandwich Placement) - Year 4
- USMA-AAB06 : BSc (hons) Statistics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
- USMA-AFM14 : MMath Mathematics (Full-time) - Year 3
- USMA-AFM14 : MMath Mathematics (Full-time) - Year 4
- USMA-AAM15 : MMath Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
- TSMA-AFM09 : MSc Mathematical Sciences (Full-time)
- TSMA-APM09 : MSc Mathematical Sciences (Part-time)
- TSMA-AFM08 : MSc Modern Applications of Mathematics (Full-time)
- TSMA-AWM14 : MSc Modern Applications of Mathematics (Full-time incorporating placement)
- TSMA-AFL02 : PG Dip Modern Applications of Mathematics (Full-time)
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