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.

This course combines online study with a weekly 1-hour live webinar led by your tutor. Find out more about how our short online courses are taught.

Programme details

This course begins on the 17 Sep 2025 which is when course materials are made available to students. Students should study these materials in advance of the first live meeting which will be held on 24 Sep 2025, 3:30-4:30pm (UK time).

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 

Coursework is an integral part of all online courses and everyone enrolled will be expected to do coursework. All those enrolled on an online courses are registered for credit and will be awarded CATS points for completing work at the required standard.

See more information on CATS points

Digital credentials

All students who pass their final assignment 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 £360.00

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: https://warwick.ac.uk/fac/sci/statistics/staff/academic-research/davis/

Publications: https://scholar.google.com/citations?user=47c4aMsAAAAJ&hl=en

Course aims

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

Learning takes place on a weekly schedule. At the start of each weekly unit, students are provided with learning materials on our online platform, including one hour of pre-recorded video, often supplemented by guided readings and educational resources. These learning materials prepare students for a one-hour live webinar with an expert tutor at the end of each weekly unit which they attend in small groups. Webinars are held on Microsoft Teams, and provide the opportunity for students to respond to discussion prompts and ask questions. The blend of weekly learning materials that can be worked through flexibly, together with a live meeting with a tutor and their peers, maximise learning and engagement through interaction in a friendly, supportive environment.

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 independent formative and summative work for this course. Formative work will be submitted for informal assessment and feedback from your tutor, but has no impact on your final grade. The summative work will be formally assessed as pass or fail.

Application

Please use the 'Book' or 'Apply' button on this page. Alternatively, please complete an Enrolment form for short courses | Oxford University Department for Continuing Education

Level and demands

The Department's short online courses are taught at FHEQ Level 4, i.e. first year undergraduate level. FHEQ level 4 courses require approximately 10 hours study per week, therefore a total of about 100 study hours.

English Language Requirements

We do not insist that applicants hold an English language certification, but warn that they may be at a disadvantage if their language skills are not of a comparable level to those qualifications listed on our website. If you are confident in your proficiency, please feel free to enrol. For more information regarding English language requirements please follow this link: https://www.conted.ox.ac.uk/about/english-language-requirements

 

Terms & conditions for applicants and students

Information on financial support