As students returned to their campuses for the start of the new academic year, many universities initially reported localised surges in the number of Covid-19 infections. This was partly due to students living together in small areas, such as halls of residence.

Now large numbers of students are expected to be soon travelling to see their families for the Christmas holidays.

Researchers at Cardiff University recently carried out a study to estimate how many secondary infections may be created by students returning home. The modelling was carried out by Thomas Woolley, Senior Lecturer in Applied Mathematics, Joshua Moore, PhD Candidate in Applied Mathematics, and Paul Harper, Professor of Operational Research and Director of the Data Innovation Research Institute.

Although the paper is yet to be peer reviewed and published in an academic journal, the researchers have presented it to task forces within the Welsh Government. It was also used to inform policy in relation to the firebreak lockdown that ran in Wales from October 23rd to November 8th, when students were asked to remain at their universities, rather than return home.

The data has also been communicated to the UK, Scottish and Northern Irish Governments, so it can inform the wider development of policy across the UK, including planning for the Christmas holidays.

The basis of the mathematical modelling comes down to estimating four variables; the percentage of students infected with the virus, the probability of an infected student transmitting the infection to another member of their household, the estimated number of occupants in a household, and the total number of students returning home from campus.

Specifying the percentage of students infected with the virus is difficult as it evolves over time and varies across the UK. To overcome this, the researchers have presented results for a variety of realistic values. Where they could, they used local data such as that from Cardiff University’s asymptomatic testing service.

Using the data the researchers estimate every infected student to infect on average 0.94 members of their household.

But while their equation provides a good single estimate of secondary infections, it ignores the possible variation in data. To capture this variability, the researchers ran the model over and over using different plausible values for the probability of a student infected someone in a household and the number of people in a household.

Writing in the Conversation, the researchers explain “For example, if 1.5% of students are infected (15 in every 1,000), we get a range of values for secondary cases, with the most probable being 15 infections. When 5% of students are infected (50 in every 1,000) the most probably outcome is 50 secondary infections….The results support the idea of each infected student generating roughly one more infection.

“In Wales, it is estimated that there are 99,900 households that contain at least one student in higher education. We do not readily have access to data on how many of these students live at home versus those who live away and will return home for the holidays. But, with 99,900 students, if 1.5% are infected we might expect around 1,400 new secondary infections from students returning home in Wales alone. If 5% are infected we could expect 4,700 new secondary infections.

“What’s more, 52.9% of all student households in Wales contain at least one other person with a diagnosed long-term illness. Such people are at greater risk of hospitalisation and death from COVID-19.

“With the potential movement of over 1 million UK students for the Christmas vacation, even at a modest 1% infection level (meaning 10 in 1,000 students are infected, perhaps many of them without symptoms at the time of travel) that would equate to 9,400 new secondary household cases across the entire country.”

Clearly this is a large number, but multiple strategies can be adopted to help reduce the number of students taking Covid-19 home. This includes strongly advising students not to mix in the days leading up to departure, implementing staggered departure times and facilitating mass testing of students before they head home.

Broadly speaking, these are the types of policies that the devolved UK nations have adopted, although mass testing of so many students during such a small window of departure will be hugely challenging.

Although the results are based on published UK data, the researchers have also developed a flexible online app that reproduces our results and can be adapted by an individual or institution to include data which is more accurate and/or specific to their location and needs. Ultimately, they hope their work can help by assessing risks caused by a large scale movement of students.