At the moment, red squirrels still survive in reasonable numbers up in Scotland. It is not that grey squirrels out compete red ones, but that they carry an illness which kills red squirrels very fast.
So this is why research done recently is so encouraging. it is thought that there are about 20 areas in Scotland where red squirrels should survive even if greys fully colonize.
The report highlihgts havens within existing areas of non=native forests such as Eskdalemuir forest in Dumfries and Galloway. Oddly, the native red squirrel can survive in non-native plantations of species such as sitka spruce which grey squirrels cannot.
This is rightly considered a last resort, currently many organisations are still killing grey squirrels that cross a line in the country. DEFRA in the UK is looking at oral contraceptives for grey squirrels which might allow them to live out their lives and then die out. Another suggestion has been gene editing, though this seems dangerous.
Our great ally in this fight is the pine marten. Unfortunately a study done last year, showed that pine martens will not abandon their distaste for living near humans, which means that without humans eradicating the grey squirrels in our towns and cities, they will be able to hide out here and therefore remain longterm.