In a nutshell: we know how to manage third-party generated personal data (such as driving licenses, health care records, passports, ...) in a private but verifiable way using blockchain. This technology should be expanded as much as possible.
However, we do not yet have the technology to handle user generated personal data (for example location data) in the same way. This is key to be able to do automated, digital contact tracing in a private but verifiable way. I propose some ideas on how this could be done, again using blockchain.
https://knowledge.insead.edu/blog/insead-blog/safeguarding-privacy-in-a-pandemic-13956