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## MA50179: Mathematical biology 1

Owning Department/School: Department of Mathematical Sciences
Credits: 6
Level: Masters UG & PG (FHEQ level 7)
Period: Semester 1
Assessment Summary: CW 25%, EX 75%
Assessment Detail:
• Coursework (CW 25%)
• Examination (EX 75%)
Supplementary Assessment: MA50179 Mandatory extra work (where allowed by programme regulations)
Requisites: Before taking this module you must take MA20221 OR take MA20202 or equivalent.
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;
* demonstrate an in-depth understanding of the topic.

Skills:
Mathematical modelling in biology T/F A
Problem solving T/F A
Written communication F A

Content:
Single species population dynamics:
* Models in discrete and continuous time: basic reproductive ratio R0; compensatory and depensatory competition (Allee effects);
* Delay 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.
* Global bifurcations
*
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.
* Macroparasitic diseases
*
Parts of the content include using computer packages (e.g. using and adapting MATLAB programs) as introduced in the pre-requisites.
* = Topics to be covered by independent directed reading.
Programme availability:

#### MA50179 is Optional on the following programmes:

Department of Biology & Biochemistry
Department of Mathematical Sciences

Notes:
* This unit catalogue is applicable for the 2015/16 academic year only. Students continuing their studies into 2016/17 and beyond should not assume that this unit will be available in future years in the format displayed here for 2015/16.
* Programmes and units are subject to change at any time, in accordance with normal University procedures.
* Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules.