# MATHEMATICAL ECOLOGY AND EPIDEMIOLOGY - 2024/5

Module code: MAT3040

## Module Overview

This module provides an introduction to the applications of ordinary, delay and partial differential equations to ecology and epidemiology.

### Module provider

Mathematics & Physics

SKELDON Anne (Maths & Phys)

### Module cap (Maximum number of students): N/A

Independent Learning Hours: 69

Lecture Hours: 33

Guided Learning: 15

Captured Content: 33

Semester 1

None.

## Module content

Indicative content includes:

• Review of simple ODE models in ecology such as the logistic and Lotka-Volterra models. Extensions of such models such as the use of the Holling functional responses. Phase plane analysis of such models.

• ODE models in epidemiology. The Kermack McKendrick model. Higher dimensional models that include, for example, an exposed compartment, or which incorporate treatment, vaccination or quarantining. Analytical techniques useful in the linearised analysis of high dimensional systems, such as the Routh Hurwitz conditions. The calculation of the basic reproduction number and its importance in epidemiological modelling.

• Age structured models and their reformulation into delay differential equations or renewal integral equations. The study of the characteristic equations resulting from the linear stability analysis of such models. Use of such equations in ecology and epidemiology, to include the Ross Macdonald model of malaria transmission. The basic reproduction number for models with delay.

• Reaction-diffusion equations. Travelling wave solutions; applications to ecology and epidemiology.

## Assessment pattern

Assessment type Unit of assessment Weighting
School-timetabled exam/test In-Semester Test (50 min) 20
Examination End-of-Semester Examination (2 hrs) 80

N/A

## Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate:

• Understanding of how to model real life ecological and epidemiological scenarios, and an understanding of the meaning of the terms in a given model.

• Knowledge of appropriate mathematical techniques to analyse the models.

• Ability to make predictions.

Thus, the summative assessment for this module consists of:

• One in-semester test (50 minutes), worth 20% of the module mark, corresponding to Learning Outcomes 1 to 3.

• A synoptic examination (2 hours), worth 80% of the module mark, corresponding to Learning Outcomes 1 to 3.

Formative assessment
There are two formative unassessed courseworks over an 11 week period, designed to consolidate student learning.

Feedback
Students receive individual written feedback on the formative unassessed coursework and the in-semester test. The feedback is timed so that feedback from the first unassessed coursework assists students with preparation for the in-semester test. The feedback from both unassessed courseworks and the in-semester test assists students with preparation for the end-of-semester examination. This written feedback is complemented by verbal and written feedback given in tutorials. Students also receive verbal and written feedback in office hours.

## Module aims

• Introduce students to basic principles involved in mathematical modelling in ecology and epidemiology.
• Give students an appreciation of how ordinary differential equations, delay differential equations and partial differential equations can apply in various ecological and epidemiological scenarios.
• Teach students appropriate analytical techniques for studying such mathematical models.
• Give students an appreciation of how to interpret the results of the analysis and how to make predictions.

## Learning outcomes

 Attributes Developed 001 Students will gain an understanding of how to model ecological and epidemiological problems using differential equations (ordinary, partial and delay). KCT 002 Students will develop an understanding of appropriate analytical techniques for the study of such problems. KC 003 Students will demonstrate how to interpret the results of the analysis and how to make predictions. KCT

Attributes Developed

C - Cognitive/analytical

K - Subject knowledge

T - Transferable skills

P - Professional/Practical skills

## Methods of Teaching / Learning

The learning and teaching strategy is designed to:

Equip students with skills in modelling ecological and epidemiological phenomena mathematically.

Cover mathematical techniques appropriate to the study of those problems.

Enable students to develop skills in the interpretation of the results of analytical techniques and to make ecological or epidemiological predictions as appropriate.

The learning and teaching methods include:

• Three one-hour lectures per week for eleven weeks, with typeset notes to complement the lectures. The lectures provide a structured learning environment with opportunities for students to ask questions and to practice methods taught.

• There are two unassessed courseworks to provide students with further opportunity to consolidate learning. Students receive individual written feedback on these as guidance on their progress and understanding.

• Lectures may be recorded. Lecture recordings are intended to give students the opportunity to review parts of the session that they might not have understood fully and should not be seen as an alternative to attendance at lectures.

Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.

Upon accessing the reading list, please search for the module using the module code: MAT3040

## Other information

The School of Mathematics and Physics is committed to developing graduates with strengths in Digital Capabilities, Employability, Global and Cultural Capabilities, Resourcefulness and Resilience and Sustainability. This module is designed to allow students to develop knowledge, skills, and capabilities in the following areas:

Digital Capabilities: The SurreyLearn page for MAT3040 features a dynamic discussion forum where students can pose questions and engage with others using e.g. LaTeX and MathML tools. This enhances their digital competencies while facilitating collaborative learning and information sharing.

Employability: Students taking MAT3040 develop skills in model evaluation and prediction. These skills are transferable to employment in many sectors including: Data Science and Analytics; Finance and Banking; Healthcare; Environmental Science and Marketing.

Global and Cultural Capabilities: Students enrolled in MAT3040 originate from various countries and possess a wide range of cultural backgrounds. During problem solving sessions in lectures, student engagement in discussions naturally cultivates the sharing of different cultures.

Resourcefulness and Resilience: The model evaluation and prediction techniques encountered by students on MAT3040 cultivate student resourcefulness and resilience by fostering problem-solving abilities and adaptability. This training empowers students to approach real-world issues with confidence and persistence, qualities vital for personal and professional growth.

Sustainability: Mathematical models in ecology covered in MAT3040 can be used to predict environmental consequences, aiding sustainable conservation by simulating population dynamics and human impact on biodiversity. In epidemiology, models manage disease spread, guiding resource allocation and supporting public health sustainability. These models offer vital insights, preserving ecosystems and long-term well-being.

## Programmes this module appears in

Programme Semester Classification Qualifying conditions
Financial Mathematics BSc (Hons) 1 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics with Statistics BSc (Hons) 1 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics BSc (Hons) 1 Optional A weighted aggregate mark of 40% is required to pass the module
Economics and Mathematics BSc (Hons) 1 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics with Statistics MMath 1 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics with Music BSc (Hons) 1 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics MMath 1 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics MSc 1 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics and Physics BSc (Hons) 1 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics and Physics MPhys 1 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics and Physics MMath 1 Optional A weighted aggregate mark of 40% is required to pass the module

Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2024/5 academic year.