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Faculty Handbook 2022-2023

# Module Description

Please ensure you check the module availability box for each module outline, as not all modules will run each academic year.

## Department: Mathematical Sciences

### MATH3171: MATHEMATICAL BIOLOGY III

Type Level Credits Availability Module Cap Open 3 20 Available in 2022/23 Durham

#### Prerequisites

• Analysis in Many Variables II (MATH2031)

• None.

• None.

#### Aims

• Study of non-linear differential equations in biological models, building on level 1 and 2 Mathematics.

#### Content

• Introduction to application of mathematics to biological systems and environments.
• Core applied modelling techniques such as stability analysis, weakly non-linear analysis, travelling wave solutions.
• ODE models in biology.
• Reaction diffusion equations.
• Pattern formation in nature: Turing analysis.
• Examples taken from the following: diffusion of insects and other species; the formation of spiral wave patterns in nature; hyperbolic models of insect dispersal and migration of a school of fish; glia aggregation in the human brain and possible connection with Alzheimer's disease; enzyme kinetics; the chemostat for bacteria production; branching growth of organisms; modelling the life cycle of the cellular slime mold Dictyostelium discoideum, and the phenomenon of chemotaxis; epidermal and dermal wound healing; epidemic models and the spatial spread of infectious diseases.

#### Learning Outcomes

Subject-specific Knowledge:
• By the end of the module students will: be able to solve novel and/or complex problems in Mathematical Biology.
• have a systematic and coherent understanding of theoretical mathematics in the fields Mathematical Biology.
• have acquired coherent body of knowledge of these subjects demonstrated through one or more of the following topic areas:
• Models for diffusion of insect populations.
• Formation of spiral wave patterns.
• Mathematics of enzyme kinetics.
• Mathematics of the Chemostat.
• Chemostaxis and coalgulation of species.
• Pattern formation mechanisms.
Subject-specific Skills:
• In addition students will have specialised mathematical skills in the following areas which can be used with minimal guidance: Modelling.
Key Skills:

#### Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

• Lectures develop technical ideas and methodology and introduce motivating examples.
• Solution by students of problems in written assignments as part of formative assessment deepens and tests understanding of technical material and helps to develop modelling skills.
• Students will also be expected on occasion to find additional material from the Internet.
• Summative assessment by examination measures degree of technical mastery, grasp of basic ideas in modelling and skill carrying through necessary calculations.

#### Teaching Methods and Learning Hours

Activity Number Frequency Duration Total/Hours Lectures 42 2 per week for 20 weeks and 2 in term 3 1 Hour 42 Problems Classes 8 Four in each of terms 1 and 2 1 Hour 8 Preparation and Reading 150 Total 200

#### Summative Assessment

Component: Examination Component Weighting: 100%
Element Length / duration Element Weighting Resit Opportunity
Written examination 3 Hours 100%

#### Formative Assessment:

Eight written assignments to be assessed and returned. Other assignments are set for self-study and complete solutions are made available to students.

Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University