The National Parks and Wildlife Service of my Department has published a comprehensive review of the status of the mink in Ireland. This review also examined various management strategies for mink control and explored the feasibility of eradicating the species from the country. Based on experiences in other countries and taking into account developments in monitoring and management practises, it was estimated that eradicating mink in the wild from the island of Ireland would cost in the order of €100m over 5 years. The full report can be accessed here:
https://www.npws.ie/sites/default/files/publications/pdf/IWM40.pdf
For now, my Department's strategy prioritises the protection of important ground-nesting bird sites from predators, including invasive species such as mink.
As I understand it, the concerns about a mutated strain of Covid 19 in mink relate only to the farmed mink population.