A recently discovered population of the North American grey squirrel (Sciurus carolinensis), introduced to Ticino Park, Lombardy (N Italy), is likely to spread into continuous prealpine broadleaf forests of Lombardy and the south of Switzerland. We used Spatially Explicit Population Dynamics Models (SEPMs), successfully used to predict the spread of grey squirrels in England and Piedmont, Italy, to examine the effects of different control scenarios on grey squirrel expansion in a 20000 km2 area around Ticino Park. Without control, grey squirrels will invade Switzerland within the next two decades, and, concomitantly, the size and distribution of local populations of native red squirrels will be reduced. Simulating different grey squirrel control or removal scenarios suggests that: (i) efficient control is possible and mainly determined by the spatial distribution and woodland size of the ‘target’ control areas; and (ii) immediate actions must be taken, since delay in grey squirrel control will result in the population increasing and spreading, which makes the problems of successful containment more difficult. Model scenarios were based on surveys that may underestimate the real distribution range and current population size of grey squirrels. Therefore, a combination of hair–tube monitoring and a public participation survey to detect grey squirrel presence, which may also help to increase public awareness, is recommended. Successful containment of further grey squirrel spread will require local co-operation between Italian and Swiss authorities involved in wildlife management