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## MA30063: Mathematical biology 2

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 2
Assessment Summary: EX-TH 100%*
Assessment Detail:
• Open book Examination for duration of 24 hours* (EX-TH 100%)

*Assessment updated due to Covid-19 disruptions
Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Requisites: Before taking this module you must ( take MA20223 OR take PH20020 ) AND take MA30047
Description: Aims:
To introduce students to applications of partial differential equations to model problems arising in biology. Both mathematical modelling and mathematical analysis will be covered, and at all times the interplay between the mathematics and the underlying biological concepts will be emphasised.

Learning Outcomes:
At the end of this unit, students should be able to:
* Derive and interpret mathematical models of problems arising in biology using partial differential equations;
* Analyse models written in terms of partial differential 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 F A

Content:
Biological Motion
* Derivation of general conservation equation (macroscopic approach)
* Properties of a conservation equation
* Boundary conditions
* Derivation of the diffusion-advection equation (microscopic approach)
* Components of flux - diffusion, advection, chemotaxis
* Solution of the advection equation using method of characteristics
* Age structured problems
* Solutions of the diffusion equation using the fundamental solution
* Steady state distributions; transit times
Biological Invasions
* Wavefront and wavespeed calculations for exponentially growing populations
* Planar travelling waves; minimum wavespeed
Spatial Pattern Formation
* Critical domain size; scale and geometry effects
* Turing mechanisms
* Linear stability analysis; conditions for diffusion-driven instability; dispersion relation and Turing space.
Tumour Growth
* Formation of necrotic core
* Tumour size.
Programme availability:

#### MA30063 is Optional on the following programmes:

Department of Mathematical Sciences
• TSMA-AFM08 : MSc Modern Applications of Mathematics
• 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-AFB05 : BSc(Hons) Statistics (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)
Programmes in Natural Sciences
• UXXX-AFB01 : BSc(Hons) Natural Sciences (Biochemistry with Chemistry stream) (Year 3)
• UXXX-AAB02 : BSc(Hons) Natural Sciences (Biochemistry with Chemistry stream) with Study year abroad (Year 4)
• UXXX-AKB02 : BSc(Hons) Natural Sciences (Biochemistry with Chemistry stream) with Year long work placement (Year 4)
• UXXX-AFB01 : BSc(Hons) Natural Sciences (Biochemistry with Pharmacology stream) (Year 3)
• UXXX-AAB02 : BSc(Hons) Natural Sciences (Biochemistry with Pharmacology stream) with Study year abroad (Year 4)
• UXXX-AKB02 : BSc(Hons) Natural Sciences (Biochemistry with Pharmacology stream) with Year long work placement (Year 4)
• UXXX-AFB01 : BSc(Hons) Natural Sciences (Biology with Chemistry stream) (Year 3)
• UXXX-AAB02 : BSc(Hons) Natural Sciences (Biology with Chemistry stream) with Study year abroad (Year 4)
• UXXX-AKB02 : BSc(Hons) Natural Sciences (Biology with Chemistry stream) with Year long work placement (Year 4)
• UXXX-AFB01 : BSc(Hons) Natural Sciences (Biology with Pharmacology stream) (Year 3)
• UXXX-AAB02 : BSc(Hons) Natural Sciences (Biology with Pharmacology stream) with Study year abroad (Year 4)
• UXXX-AKB02 : BSc(Hons) Natural Sciences (Biology with Pharmacology stream) with Year long work placement (Year 4)
• UXXX-AFB01 : BSc(Hons) Natural Sciences (Chemistry with Biochemistry stream) (Year 3)
• UXXX-AAB02 : BSc(Hons) Natural Sciences (Chemistry with Biochemistry stream) with Study year abroad (Year 4)
• UXXX-AKB02 : BSc(Hons) Natural Sciences (Chemistry with Biochemistry stream) with Year long work placement (Year 4)
• UXXX-AFB01 : BSc(Hons) Natural Sciences (Chemistry with Biology stream) (Year 3)
• UXXX-AAB02 : BSc(Hons) Natural Sciences (Chemistry with Biology stream) with Study year abroad (Year 4)
• UXXX-AKB02 : BSc(Hons) Natural Sciences (Chemistry with Biology stream) with Year long work placement (Year 4)
• UXXX-AFB01 : BSc(Hons) Natural Sciences (Chemistry with Pharmacology stream) (Year 3)
• UXXX-AAB02 : BSc(Hons) Natural Sciences (Chemistry with Pharmacology stream) with Study year abroad (Year 4)
• UXXX-AKB02 : BSc(Hons) Natural Sciences (Chemistry with Pharmacology stream) with Year long work placement (Year 4)
• UXXX-AFB01 : BSc(Hons) Natural Sciences (Environmental Science with Biochemistry stream) (Year 3)
• UXXX-AAB02 : BSc(Hons) Natural Sciences (Environmental Science with Biochemistry stream) with Study year abroad (Year 4)
• UXXX-AKB02 : BSc(Hons) Natural Sciences (Environmental Science with Biochemistry stream) with Year long work placement (Year 4)
• UXXX-AFB01 : BSc(Hons) Natural Sciences (Pharmacology with Biochemistry stream) (Year 3)
• UXXX-AAB02 : BSc(Hons) Natural Sciences (Pharmacology with Biochemistry stream) with Study year abroad (Year 4)
• UXXX-AKB02 : BSc(Hons) Natural Sciences (Pharmacology with Biochemistry stream) with Year long work placement (Year 4)
• UXXX-AFB01 : BSc(Hons) Natural Sciences (Pharmacology with Biology stream) (Year 3)
• UXXX-AAB02 : BSc(Hons) Natural Sciences (Pharmacology with Biology stream) with Study year abroad (Year 4)
• UXXX-AKB02 : BSc(Hons) Natural Sciences (Pharmacology with Biology stream) with Year long work placement (Year 4)
• UXXX-AFM01 : MSci(Hons) Natural Sciences (Biochemistry with Chemistry stream) (Year 3)
• UXXX-AAM02 : MSci(Hons) Natural Sciences (Biochemistry with Chemistry stream) with Study year abroad (Year 4)
• UXXX-AKM02 : MSci(Hons) Natural Sciences (Biochemistry with Chemistry stream) with Professional Placement (Year 4)
• UXXX-AFM01 : MSci(Hons) Natural Sciences (Biochemistry with Pharmacology stream) (Year 3)
• UXXX-AAM02 : MSci(Hons) Natural Sciences (Biochemistry with Pharmacology stream) with Study year abroad (Year 4)
• UXXX-AKM02 : MSci(Hons) Natural Sciences (Biochemistry with Pharmacology stream) with Professional Placement (Year 4)
• UXXX-AFM01 : MSci(Hons) Natural Sciences (Biology with Chemistry stream) (Year 3)
• UXXX-AAM02 : MSci(Hons) Natural Sciences (Biology with Chemistry stream) with Study year abroad (Year 4)
• UXXX-AKM02 : MSci(Hons) Natural Sciences (Biology with Chemistry stream) with Professional Placement (Year 4)
• UXXX-AFM01 : MSci(Hons) Natural Sciences (Biology with Pharmacology stream) (Year 3)
• UXXX-AAM02 : MSci(Hons) Natural Sciences (Biology with Pharmacology stream) with Study year abroad (Year 4)
• UXXX-AKM02 : MSci(Hons) Natural Sciences (Biology with Pharmacology stream) with Professional Placement (Year 4)
• UXXX-AFM01 : MSci(Hons) Natural Sciences (Chemistry with Biochemistry stream) (Year 3)
• UXXX-AAM02 : MSci(Hons) Natural Sciences (Chemistry with Biochemistry stream) with Study year abroad (Year 4)
• UXXX-AKM02 : MSci(Hons) Natural Sciences (Chemistry with Biochemistry stream) with Professional Placement (Year 4)
• UXXX-AFM01 : MSci(Hons) Natural Sciences (Chemistry with Biology stream) (Year 3)
• UXXX-AAM02 : MSci(Hons) Natural Sciences (Chemistry with Biology stream) with Study year abroad (Year 4)
• UXXX-AKM02 : MSci(Hons) Natural Sciences (Chemistry with Biology stream) with Professional Placement (Year 4)
• UXXX-AFM01 : MSci(Hons) Natural Sciences (Chemistry with Pharmacology stream) (Year 3)
• UXXX-AAM02 : MSci(Hons) Natural Sciences (Chemistry with Pharmacology stream) with Study year abroad (Year 4)
• UXXX-AKM02 : MSci(Hons) Natural Sciences (Chemistry with Pharmacology stream) with Professional Placement (Year 4)
• UXXX-AAM02 : MSci(Hons) Natural Sciences (Chemistry with Physics stream) with Study year abroad (Year 4)

 Notes: This unit catalogue is applicable for the 2019/20 academic year only. Students continuing their studies into 2020/21 and beyond should not assume that this unit will be available in future years in the format displayed here for 2019/20. Programmes 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. Undergraduates: Find out more about these and other important University terms and conditions here. Postgraduates: Find out more about these and other important University terms and conditions here.