Members of the Swiss army, hospital workers and civil servants can now install the SwissCovid app ahead of a planned wider rollout.
A Latvian coalition says it is running close behind.
But the US tech firms face criticism for their prescriptive approach.
Automated contact tracing involves using smartphones to detect when two people are close to each other for long enough that there is a significant risk of contagion, so that one can be warned if the other is later diagnosed with having the disease.
