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## MA30047: Mathematical biology 1

Credits: 6
Level: Honours (FHEQ level 6)
Period: Semester 1
Assessment: CW 25%, EX 75%
Supplementary Assessment: MA30047 Mandatory Extra Work (where allowed by programme regulations)
Requisites: Before taking this unit you must 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:
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.

Skills:
Mathematical modelling in biology, ordinary differential equations, difference equations.

Content:
Single species population dynamics: Models in discrete and continuous time: basic reproductive ratioR_0; compensatory and depensatory competition; transcritical, tangent and period doubling bifurcations, chaos. 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. 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.
Programme availability:

#### MA30047 is Optional on the following programmes:

Department of Biology & Biochemistry
• RSBB-AFM07 : Integrated PhD Postgenomic Biosciences (Biosciences Route) (Full-time) - Year 1
• TSBB-AFM03 : MRes Biosciences (Full-time) - Year 1
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) - Year 1
• TSMA-APM09 : MSc Mathematical Sciences (Part-time) - Year 1
• TSMA-APM09 : MSc Mathematical Sciences (Part-time) - Year 2
• TSMA-AFM08 : MSc Modern Applications of Mathematics (Full-time) - Year 1
• TSMA-AFL02 : PG Dip Modern Applications of Mathematics (Full-time) - Year 1

NB. Programmes and units are subject to change at any time, in accordance with normal University procedures.