# Infectious Disease Modelling: Mathematical Techniques

## Overview

Mathematical modelling is being increasingly used to inform public health decisions, with a recent example being the use of models during the COVID-19 pandemic to advise policy around what control measures were required and what the future epidemic trend might look like under different scenarios.

By dividing a population into categories, such as "susceptible" or "infectious", we can then consider the rate of movement of individuals from one category to another, based on factors like social contact patterns, risk of disease transmitting from one person to another, or time from infection to recovery. From this, we can write down equations that describe these movements on a population-scale, which can be analysed to draw conclusions to important questions, such as:

• If a new disease emerges in the population, will it take off or die out?
• What public health measures will be most effective?
• What level of vaccination is required to prevent an epidemic?

This course provides an introduction to the key mathematical concepts required for building and analysing mathematical models of infectious disease transmission.

## Programme details

Courses starts: 22 Jan 2025

Week 1: Introduction to infectious disease modelling

• Key concepts: prevalence, incidence, incubation period etc.
• Motivation and examples

Week 2: Key mathematical concepts

• Functions of time
• Exponentials
• Probabilities
• Matrices

Week 3: Understanding rates of change

• Rates of change
• Poisson processes
• Infection and recovery rates

Week 4: Building a model

• From assumptions to equations
• Common model types (SI, SIR, etc.)

Week 5: Predicting outbreaks

• The basic reproduction number, R
• Epidemic risk
• Growth rate

Week 6: Equilibrium behaviour

• Finding equilibria
• Assessing stability

Week 7: Including demographic processes

• Births and deaths
• Age structure
• Contact structure

Week 8: Immunity

• Acquired immunity
• Vaccination and herd immunity
• Waning immunity

Week 9: Controlling transmission

• Risk reduction, e.g. social distancing
• Pharmaceutical interventions
• Quarantine of cases

Week 10: Further topics

• Spatial meta-population models
• Mosquito-borne transmission, e.g. malaria
• Disease intensity versus prevalence

## Certification

Credit Application Transfer Scheme (CATS) points

To earn credit (CATS points) for your course you will need to register and pay an additional £30 fee for each course you enrol on. You can do this by ticking the relevant box at the bottom of the enrolment form or when enrolling online. If you do not register when you enrol, you have up until the course start date to register and pay the £30 fee.

Coursework is an integral part of all online courses and everyone enrolled will be expected to do coursework, but only those who have registered for credit will be awarded CATS points for completing work at the required standard. If you are enrolled on the Certificate of Higher Education, you need to indicate this on the enrolment form but there is no additional registration fee.

Digital credentials

All students who pass their final assignment, whether registered for credit or not, will be eligible for a digital Certificate of Completion. Upon successful completion, you will receive a link to download a University of Oxford digital certificate. Information on how to access this digital certificate will be emailed to you after the end of the course. The certificate will show your name, the course title and the dates of the course you attended. You will be able to download your certificate or share it on social media if you choose to do so.

Please note that assignments are not graded but are marked either pass or fail.

## Fees

Description Costs
Course Fee £310.00
Take this course for CATS points £30.00

## Funding

If you are in receipt of a UK state benefit, you are a full-time student in the UK or a student on a low income, you may be eligible for a reduction of 50% of tuition fees. Please see the below link for full details:

Concessionary fees for short courses

## Tutor

### Dr Emma Davis

Dr Emma Davis is an infectious disease epidemiologist and mathematical modeller, with a particular interest in the low prevalence dynamics that occur around the emergence of new outbreaks and the elimination of transmission.

She trained as a mathematician, with a PhD in mathematical modelling of neglected tropical diseases from the University of Warwick. Her work with the Neglected Tropical Disease Modelling Consortium and the JUNIPER Consortium has interfaced with global and UK health policy, including involvement with SPI-M (the modelling subgroup of UK policy advisory group SAGE) during the COVID-19 pandemic. She received a Rapid Assistive Modelling for the Pandemic Early Career Investigator Award from the Royal Society for her modelling work around COVID-19 contact tracing and isolation adherence.

She has experience teaching and mentoring both undergraduate and postgraduate students in mathematics, data science, infectious disease modelling and biomedical sciences. Aside from formal teaching, she is passionate about outreach, winning 1st place at the Smith Institute Take AIM Awards for articulating the impact of mathematics in 2018 and is the recipient of a Royal Society Outreach Innovation Award for developing popular science YouTube channel EpiWithEmma.

Webpage: www.emmalouisedavis.co.uk

## Course aims

The course demonstrates applications of mathematics to infectious disease control and surveillance.

### Course Objectives:

• Students will understand the core mathematical concepts required for mathematical modelling.
• Students will construct mathematical models of infectious disease transmission.
• Students will apply these lessons to model a real-world example and make recommendations for policy interventions.

## Teaching methods

The contact hours will be split into a one-hour pre-recorded lecture, to be viewed in advance of each one-hour interactive seminar per week.

## Learning outcomes

By the end of the course students should:

• understand the concept of rate of change and its applicability to time-dependent mathematical models;
• be able to construct and analyse models of infectious disease transmission based on the underlying biology of different diseases;
• be able to calculate the basic reproduction number, R, and other key epidemiological metrics;
• understand how models can be extended to include additional complexities.

## Assessment methods

You will be set two pieces of project work for the course, which will be in the format of reports (including mathematical equations). The first is due halfway through your course and does not count towards your final outcome but preparing for it, and the feedback you are given, will help you prepare for your assessed piece of work due at the end of the course. The assessed work is marked pass or fail.

There is no formal word limit on either piece of work, but a reasonable guideline would be 1-2 pages for the initial report and 3-5 pages for the final assessed report.

Students must submit a completed Declaration of Authorship form at the end of term when submitting your final piece of work. CATS points cannot be awarded without the aforementioned form - Declaration of Authorship form

## Application

We will close for enrolments 7 days prior to the start date to allow us to complete the course set up. We will email you at that time (7 days before the course begins) with further information and joining instructions. As always, students will want to check spam and junk folders during this period to ensure that these emails are received.

To earn credit (CATS points) for your course you will need to register and pay an additional £30 fee per course. You can do this by ticking the relevant box at the bottom of the enrolment form or when enrolling online.