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University of Limerick-led research team reveals approach behind calculation of ‘R-number’

Mon, 22 Nov 2021

A research team lead by University of Limerick has described the calculations behind the main model used to guide the Irish Government in its response to COVID-19.

In a new paper published today, UL’s Professor James Gleeson and his team describe one of the methods to estimate the now-famous reproduction or ‘R-number’ in COVID-19 cases, the results of which were reported in media briefings throughout the pandemic.

The paper, published in the journal Philosophical Transactions of the Royal Society A, details the modelling of COVID-19 by the Irish Epidemiological Modelling Advisory Group (IEMAG), which reports to the Irish National Public Health Emergency Team (NPHET).

Professor Gleeson, Professor of Industrial and Applied Mathematics at UL, is a member of IEMAG, which is tasked with providing mathematical and statistical modelling advice to NPHET through its chair Professor Philip Nolan.

“Since we were asked to join IEMAG in March 2020, we have been developing and running models to help provide advice to NPHET,” Professor Gleeson, lead author on the paper, explained.

“The models use a combination of mathematical and statistical techniques, some of which we created specifically for the IEMAG work, to help understand the trajectory of the virus to date, and the possible future scenarios,” added Professor Gleeson, who is co-director of the MACSI research group at UL and Director of the SFI Centre for Research Training in Foundations of Data Science.

One of the main models used by IEMAG is a ‘susceptible-exposed-infected-removed’ or SEIR model, which accounts for the number of people in the population who are currently in each state of the disease.

“Susceptible people are healthy, while exposed people have had recent contact with the virus, infected people can transmit the virus to others, and removed people are no longer infectious,” explained Professor Gleeson.

“Models of SEIR type are the standard choice for COVID-19 but there are a number of scientific challenges in applying these models that required us to combine statistical and mathematical techniques based on the expertise of several people in IEMAG and indeed in the wider mathematical sciences community in Ireland,” he added.

The paper, co-authored by researchers from UL and UCD, describes a technique that enables the level of contacts to be inferred from the observed data on confirmed cases.

This approach is one of the ways to estimate the R-number, Professor Gleeson explained.

“The model assumes a time-varying effective contact rate or a time-varying reproduction number, to model the effect of non-pharmaceutical interventions,” he said.

“There is a technical challenge in applying such models accurately to the observed data – for example the daily number of confirmed new cases, as the past history of the disease strongly affects predictions of future scenarios.

“We overcame this using an approach that inverts the SEIR equations in conjunction with statistical modelling and data analysis techniques to calibrate the model,” he added.

The team produced technical reports as the model was developed and improved, and these technical reports were made public on the Department of Health website, along with open-access computer code for running the model.

“We are delighted to have this work peer-reviewed and appearing in Philosophical Transactions of the Royal Society A,” said Professor Gleeson.

Professor Gleeson and his co-authors are members of the Insight Centre for Data Analytics and the Confirm Centre for Smart Manufacturing, both funded by Science Foundation Ireland.