Maybe there is a way to do virus contact tracing, such as that for Covid-19, on a voluntary basis with a reduced need for health officials involvement. This probably isn’t it 
but say…
People encrypt their WebId using their private key and send them to an AP inbox on a regional pod. Assume for this simple example that the user stays in one region and none of this is complicated by bluetooth data about where exactly a person is indoors, etc. When encrypting they use the public key of that regional pod.
That pod puts them in SafeNet according to GPS location. That pod sends back to the user’s inbox the SafeNet address, but its encrypted so the user can’t go there. The SafeNet address represents a list of the encrypted WebId’s and inboxes of the people at that location at that time.
The user’s app does this throughout the day and the user’s route along with the encrypted SafeNet address for each location is kept locally by each user for 28 days. So every one has locally their route including encrypted SafeNet addresses, each of which represents a group of people who were in proximity at that place and time.
So then someone tests positive. They send their WebId and public key to the regional server along with proof that they were tested positive (?), as well as their 28 day list of routes with the encrypted SafeNet addresses back to the regional pod, which decrypts those addresses and looks at those to find all the encrypted WebId’s of people who were in proximity and should be tested. It sends notifications that they should be tested to their inboxes including their encrypted WebId as proof.