Opening university campuses to staff and students under the shadow of Covid-19 is a huge challenge. KTN and its partners in the Virtual Forum for Knowledge Exchange in the Mathematical Sciences (V-KEMS) have been working hard to convene mathematical modellers, university leadership and policy makers to explore potential mathematical interventions for universities and government to consider. 

 The challenge of sending students back to university is complex; perhaps even more so than opening schools. Universities are like mini-cities with people living and studying in close proximity to and with considerable links to the communities in which they are based. With many students now classing themselves as ‘customers’ and many university staff furloughed, pressure on universities to safely open their doors whilst providing a good student experience is mounting.

V-KEMS, which includes KTN, the Isaac Newton Institute, the International Centre for Mathematical Sciences and the Newton Gateway to Maths, convened a group of 40 mathematical scientists, behavioural scientists, public health experts and representatives from universities to examine the core problems and how mathematical modelling could be potentially applied to mitigate them. The resulting principles and illustrative calculations, after further work and consultation, could help universities and policy makers formulate coherent and consistent guidelines.

Challenges considered during a three-day study group ranged from those at building level to those at community level. Topics considered included the access and flow of people through buildings, the impact of aerosol transmission and cleaning strategies in lecture halls, the role of shared services such as food outlets and leisure facilities, and the interaction between the university and the local community including public transport.

The use of lecture spaces brings the potential for surface transmission of the virus as well as aerosol spreading. The group therefore modelled how different cleaning strategies might mitigate some of the associated risks from surfaces in addition to social distancing. For example, how do we use maths to assess the risk of transmission when students are using alternate seating rows and being asked to clean their desks pre and post lecture?

Modelling the layouts and scheduling of lecture halls this way allowed the group to explore such vital questions as what size of class would help to minimise airborne transmission, and given these reduced class sizes is it possible for universities to commit to offering students face-to-face time before safe capacity is reached?

The group also considered how this insight should inform timetabling by modelling the impact of students moving between buildings with the aim to avoid bottlenecks in corridors and shared spaces. By timetabling to avoid mass exit onto campus and linking bus schedules it is suggested student movements can be streamlined.

The insight from the group has been utilised by Warwick University in their planning. Dr Martine Barons Director of the Applied Statistics and Risk Unit at the University of Warwick commented: “The VKEMS event itself was key to getting university planners around the table with relevant researchers; it can be hard to identify who has exactly the expertise you need, even when they are colleagues at the same institution. Aside from the obvious COVID risks associated with various ways of grouping students, transport and learning events, one of the great unknowns is how students will respond.  Will they all go to their rooms between classes, even if that means taking the bus, or will additional dwell space be required so they can stay on campus in a distanced manner? Mathematical modelling had helped to visualise student movements between lectures looking for study space to help identify pinch points and capacity needs.”

The participants considered whether access to campus for student bubbles based on geography, age group or hierarchy could reduce the transmission of disease compared to allowing everyone on at the same time? Whether those bubbles could be extended to cover social activities as well as academic ones?  What should the size of the bubbles be?  Could transmission be minimised if each bubble could be housed and taught together? What is the effect on non-compliance? How much non-compliance is needed before the bubble system breaks down?

Fundamental to this are continuing conversations with staff and students to ensure that campuses are not only safe for those on and around them, but also provide an environment and experience which students have come to expect from their time in higher education.

Universities are intrinsic parts of the community in which they are based and minimising transmission of any outbreak on campus to the wider community was a key element of the group’s discussion.  Introducing student shopping hours in supermarkets, minimising student and staff interaction with the local community and the importance of communications were all considered, with a focus on what factors are in the university’s control.

The mathematical models are useful tools for planning around building layouts and capacities, timetables and accommodation, but it was also recognised that testing will play a significant role in the control of outbreaks. Follow up sessions led by Professor Julia Gog (Cambridge) and Professor Chris Budd OBE (Bath) involved the Department for Education, Universities UK and NHS Test and Trace where some of the ideas introduced in the V-KEMS Study Group are being developed.

Professor Chris Budd OBE, University of Bath commented: “As students return to Higher Education from all over the country, and beyond, Universities are facing numerous challenges to reopening in the face of the COVID-19 pandemic. In particular developing ways of teaching and learning that are both safe for students and staff, yet preserve as much of the student experience as is possible. The leaders of the universities also need to know how best to test their students and staff for the virus, and under what circumstances they may have to go to full on-line teaching, or even to shut down. Mathematical modelling is playing a vital role in helping Universities to plan for this return. KTN has played a vital role in engaging the efforts of the whole of the mathematical community across the country to do this, in close collaboration with epidemiologists, social scientists, university and student leaders, and policy makers. KTN has initiated, facilitated and amplified this effort so that it is able to be a powerful asset in the fight against COVID-19, and the whole community owes them a great debt for doing this.”

Mathematical modelling cannot provide solutions to all the challenges, but it can be one of many tools available to help universities develop strategies and scenarios for everything from cleaning to timetabling.


The working paper from the group, “Unlocking Higher Education Spaces
– What Might Mathematics Tell Us?” is now available – click here to access it (PDF, 56 pages).

To learn more about V-KEMS, click here or contact our Industrial Mathematics expert, Matt Butchers. You can also follow V-KEMS on Twitter.