## MA30047: Mathematical biology 1

[Page last updated: 23 October 2023]

Owning Department/School: Department of Mathematical Sciences
Credits: 6 [equivalent to 12 CATS credits]
Notional Study Hours: 120
Level: Honours (FHEQ level 6)
Period:
Semester 1
Assessment Summary: CW 25%, EX 75%
Assessment Detail:
• Coursework (CW 25%)
• Examination (EX 75%)
Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Requisites: Before taking this module you must take XX20231 OR take MA20221
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.

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.

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.

Course availability:

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

Department of Chemistry
• USSC-AFB01 : BSc(Hons) Natural Sciences (Biochemistry with Chemistry stream) (Year 3)
• USSC-AAB01 : BSc(Hons) Natural Sciences (Biochemistry with Chemistry stream) with Study year abroad (Year 4)
• USSC-AKB01 : BSc(Hons) Natural Sciences (Biochemistry with Chemistry stream) with Year long work placement (Year 4)
• USSC-AFB01 : BSc(Hons) Natural Sciences (Biochemistry with Environmental Science stream) (Year 3)
• USSC-AAB01 : BSc(Hons) Natural Sciences (Biochemistry with Environmental Science stream) with Study year abroad (Year 4)
• USSC-AKB01 : BSc(Hons) Natural Sciences (Biochemistry with Environmental Science stream) with Year long work placement (Year 4)
• USSC-AFB01 : BSc(Hons) Natural Sciences (Biochemistry with Pharmacology stream) (Year 3)
• USSC-AAB01 : BSc(Hons) Natural Sciences (Biochemistry with Pharmacology stream) with Study year abroad (Year 4)
• USSC-AKB01 : BSc(Hons) Natural Sciences (Biochemistry with Pharmacology stream) with Year long work placement (Year 4)
• USSC-AFB01 : BSc(Hons) Natural Sciences (Biology with Chemistry stream) (Year 3)
• USSC-AAB01 : BSc(Hons) Natural Sciences (Biology with Chemistry stream) with Study year abroad (Year 4)
• USSC-AKB01 : BSc(Hons) Natural Sciences (Biology with Chemistry stream) with Year long work placement (Year 4)
• USSC-AFB01 : BSc(Hons) Natural Sciences (Biology with Environmental Science stream) (Year 3)
• USSC-AAB01 : BSc(Hons) Natural Sciences (Biology with Environmental Science stream) with Study year abroad (Year 4)
• USSC-AKB01 : BSc(Hons) Natural Sciences (Biology with Environmental Science stream) with Year long work placement (Year 4)
• USSC-AFB01 : BSc(Hons) Natural Sciences (Biology with Pharmacology stream) (Year 3)
• USSC-AAB01 : BSc(Hons) Natural Sciences (Biology with Pharmacology stream) with Study year abroad (Year 4)
• USSC-AKB01 : BSc(Hons) Natural Sciences (Biology with Pharmacology stream) with Year long work placement (Year 4)
• USSC-AFB01 : BSc(Hons) Natural Sciences (Chemistry with Biochemistry stream) (Year 3)
• USSC-AAB01 : BSc(Hons) Natural Sciences (Chemistry with Biochemistry stream) with Study year abroad (Year 4)
• USSC-AKB01 : BSc(Hons) Natural Sciences (Chemistry with Biochemistry stream) with Year long work placement (Year 4)
• USSC-AFB01 : BSc(Hons) Natural Sciences (Chemistry with Biology stream) (Year 3)
• USSC-AAB01 : BSc(Hons) Natural Sciences (Chemistry with Biology stream) with Study year abroad (Year 4)
• USSC-AKB01 : BSc(Hons) Natural Sciences (Chemistry with Biology stream) with Year long work placement (Year 4)
• USSC-AFB01 : BSc(Hons) Natural Sciences (Chemistry with Environmental Science stream) (Year 3)
• USSC-AAB01 : BSc(Hons) Natural Sciences (Chemistry with Environmental Science stream) with Study year abroad (Year 4)
• USSC-AKB01 : BSc(Hons) Natural Sciences (Chemistry with Environmental Science stream) with Year long work placement (Year 4)
• USSC-AFB01 : BSc(Hons) Natural Sciences (Chemistry with Pharmacology stream) (Year 3)
• USSC-AAB01 : BSc(Hons) Natural Sciences (Chemistry with Pharmacology stream) with Study year abroad (Year 4)
• USSC-AKB01 : BSc(Hons) Natural Sciences (Chemistry with Pharmacology stream) with Year long work placement (Year 4)
• USSC-AFB01 : BSc(Hons) Natural Sciences (Environmental Science with Biochemistry stream) (Year 3)
• USSC-AAB01 : BSc(Hons) Natural Sciences (Environmental Science with Biochemistry stream) with Study year abroad (Year 4)
• USSC-AKB01 : BSc(Hons) Natural Sciences (Environmental Science with Biochemistry stream) with Year long work placement (Year 4)
• USSC-AFB01 : BSc(Hons) Natural Sciences (Environmental Science with Chemistry stream) (Year 3)
• USSC-AAB01 : BSc(Hons) Natural Sciences (Environmental Science with Chemistry stream) with Study year abroad (Year 4)
• USSC-AKB01 : BSc(Hons) Natural Sciences (Environmental Science with Chemistry stream) with Year long work placement (Year 4)
• USSC-AFB01 : BSc(Hons) Natural Sciences (Pharmacology with Biochemistry stream) (Year 3)
• USSC-AAB01 : BSc(Hons) Natural Sciences (Pharmacology with Biochemistry stream) with Study year abroad (Year 4)
• USSC-AKB01 : BSc(Hons) Natural Sciences (Pharmacology with Biochemistry stream) with Year long work placement (Year 4)
• USSC-AFB01 : BSc(Hons) Natural Sciences (Pharmacology with Biology stream) (Year 3)
• USSC-AAB01 : BSc(Hons) Natural Sciences (Pharmacology with Biology stream) with Study year abroad (Year 4)
• USSC-AKB01 : BSc(Hons) Natural Sciences (Pharmacology with Biology stream) with Year long work placement (Year 4)
• USSC-AFB01 : BSc(Hons) Natural Sciences (Pharmacology with Chemistry stream) (Year 3)
• USSC-AAB01 : BSc(Hons) Natural Sciences (Pharmacology with Chemistry stream) with Study year abroad (Year 4)
• USSC-AKB01 : BSc(Hons) Natural Sciences (Pharmacology with Chemistry stream) with Year long work placement (Year 4)
• USSC-AFM01 : MSci(Hons) Natural Sciences (Biochemistry with Chemistry stream) (Year 3)
• USSC-AAM01 : MSci(Hons) Natural Sciences (Biochemistry with Chemistry stream) with Study year abroad (Year 4)
• USSC-AKM01 : MSci(Hons) Natural Sciences (Biochemistry with Chemistry stream) with Professional Placement (Year 4)
• USSC-AFM01 : MSci(Hons) Natural Sciences (Biochemistry with Pharmacology stream) (Year 3)
• USSC-AAM01 : MSci(Hons) Natural Sciences (Biochemistry with Pharmacology stream) with Study year abroad (Year 4)
• USSC-AKM01 : MSci(Hons) Natural Sciences (Biochemistry with Pharmacology stream) with Professional Placement (Year 4)
• USSC-AFM01 : MSci(Hons) Natural Sciences (Biology with Chemistry stream) (Year 3)
• USSC-AAM01 : MSci(Hons) Natural Sciences (Biology with Chemistry stream) with Study year abroad (Year 4)
• USSC-AKM01 : MSci(Hons) Natural Sciences (Biology with Chemistry stream) with Professional Placement (Year 4)
• USSC-AFM01 : MSci(Hons) Natural Sciences (Biology with Pharmacology stream) (Year 3)
• USSC-AAM01 : MSci(Hons) Natural Sciences (Biology with Pharmacology stream) with Study year abroad (Year 4)
• USSC-AKM01 : MSci(Hons) Natural Sciences (Biology with Pharmacology stream) with Professional Placement (Year 4)
• USSC-AFM01 : MSci(Hons) Natural Sciences (Chemistry with Biochemistry stream) (Year 3)
• USSC-AAM01 : MSci(Hons) Natural Sciences (Chemistry with Biochemistry stream) with Study year abroad (Year 4)
• USSC-AKM01 : MSci(Hons) Natural Sciences (Chemistry with Biochemistry stream) with Professional Placement (Year 4)
• USSC-AFM01 : MSci(Hons) Natural Sciences (Chemistry with Biology stream) (Year 3)
• USSC-AAM01 : MSci(Hons) Natural Sciences (Chemistry with Biology stream) with Study year abroad (Year 4)
• USSC-AKM01 : MSci(Hons) Natural Sciences (Chemistry with Biology stream) with Professional Placement (Year 4)
• USSC-AFM01 : MSci(Hons) Natural Sciences (Chemistry with Pharmacology stream) (Year 3)
• USSC-AAM01 : MSci(Hons) Natural Sciences (Chemistry with Pharmacology stream) with Study year abroad (Year 4)
• USSC-AKM01 : MSci(Hons) Natural Sciences (Chemistry with Pharmacology stream) with Professional Placement (Year 4)
Department of Mathematical Sciences
• USMA-AFB15 : BSc(Hons) Mathematical Sciences (Year 3)
• USMA-AAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 4)
• USMA-AKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 4)
• USMA-AFB13 : BSc(Hons) Mathematics (Year 3)
• USMA-AAB14 : BSc(Hons) Mathematics with Study year abroad (Year 4)
• USMA-AKB14 : BSc(Hons) Mathematics with Year long work placement (Year 4)
• USMA-AFB01 : BSc(Hons) Mathematics and Statistics (Year 3)
• USMA-AAB02 : BSc(Hons) Mathematics and Statistics with Study year abroad (Year 4)
• USMA-AKB02 : BSc(Hons) Mathematics and Statistics with Year long work placement (Year 4)
• USMA-AFB20 : BSc(Hons) Mathematics, Statistics, and Data Science (Year 3)
• USMA-AAB06 : BSc(Hons) Statistics with Study year abroad (Year 4)
• USMA-AKB06 : BSc(Hons) Statistics with Year long work placement (Year 4)
• USMA-AFM14 : MMath(Hons) Mathematics (Year 3)
• USMA-AFM14 : MMath(Hons) Mathematics (Year 4)
• USMA-AAM15 : MMath(Hons) Mathematics with Study year abroad (Year 4)
• USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 4)
• USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 5)

 Notes: This unit catalogue is applicable for the 2023/24 academic year only. Students continuing their studies into 2024/25 and beyond should not assume that this unit will be available in future years in the format displayed here for 2023/24. Courses and units are subject to change 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. Find out more about these and other important University terms and conditions here.