Mathematical model tested on mink predicts the end of virus variants

The model has been tested on the Cluster-5 variant at mink farms in North Jutland. Illustration: Dzīvnieku Brīvība, CC BY 2.0

How long and how many people to test to be sure whether a virus is extinct or not?

This is the big question that researchers from Aalborg University (AAU) now expect to be able to help authorities answer both in Denmark and abroad. When the next pandemic strikes, restrictions and reopening can be carried out with greater certainty and make the isolation strategy more effective,

The new model from AAU can provide a more accurate picture of when individual mutations of a virus can be considered to have been defeated.

“Isolation strategies carry many financial, social and human costs for well-being, public health, and personal freedom. Therefore, it’s important to lift restrictions as soon as possible. We have now provided a basis of calculation for that,” says Jakob Stoustrup, professor at the Technical Faculty of IT and Design, in the university's press release on the model.

How long to maintain the lockdown and how many people to test

Behind the model is a group of researchers from the Faculty of Medicine and the Technical Faculty of IT and Design at Aalborg University. Based on data from coronavirus mutations in the North Jutland mink in the autumn of 2020, they have prepared a model that shows when one can be sure that a virus variant no longer exists in society.

“The model shows how long an area needs to be in lockdown and how many people need to be tested over a period of time before one can be reasonably sure that the mutation has been eradicated,” explains Professor Martin Bøgsted from the Faculty of Medicine at AAU.

The model can be freely used by everyone

The scientific article on the model is published in Nature as a scientific report with open access: Mathematical modelling of SARS-CoV-2 variant outbreaks reveals their probability of extinction.

“Now the model is part of the preparedness that nations and authorities around the world have available in their arsenal. We hope that it will be widely used,” says Jakob Stoustrup, member of the expert reference group that has advised the Danish Parliament on the treatment of the coronavirus pandemic since the autumn of 2020.

Model tested on the mink variant

The article describes how the model has been tested in retrospect on the Cluster-5 variant of SARS-CoV-19, which was discovered in North Jutland in the autumn of 2020. Due to the fear of vaccine resistance, several municipalities were isolated, 17 million mink was culled, and the mink industry was shut down.

Due to the severe consequences for the mink industry, there has since been political pressure to determine whether the variant was in fact a threat, or whether it could with a certain degree of probability have become extinct with fewer restrictions.

The modelling shows that the probability of the extinction of the variant was 0.22 before restrictions were introduced, and 0.37 when the restrictions were lifted. The researchers found that the model generally shows that a lockdown increases the time to certainty of extinction of a virus variant. Therefore, they recommend that lockdowns always be supplemented by a massive testing strategy, which should ensure the necessary data to increase certainty.

Longer restrictions increase certainty

In the case of the Cluster-5 variant, the probability of extinction was still quite low when the restrictions were lifted at the beginning of October 2020. The certainty of extinction would have been greater if the restrictions had been lifted four weeks later, when the probability of extinction was calculated to be 0.52.

When the article was written in March 2021, so much time had passed that one could be 95 percent sure that the variant was extinct. However, the researchers point out that they have not had access to detailed data from the authorities, which could have ensured more reliable calculations earlier in the process.

Using birth and death data to model the extinction of species is not new, but this is the first time that the probability of extinction was modelled on the basis of hidden information.