That's a broad question that I don't have the answer to. If I did, I would have said it by now. That said, my sense is that the Public Health Agency of Canada definitely has a role to play, and I think it's trying to do that. The fact remains, however, that, at the provincial level, data also belong to the provinces.
I know all the parties have tried to reach agreements in the past, including the multi-lateral information sharing agreement, or MLISA for short. It doesn't seem to allow for data transfer, at least not in real time. Eventually they are transferred, but not until they've been validated, often nearly a year later. I'm not well versed enough in Canada's Constitution to say how a direct transfer should work. All I can tell you is that it doesn't work for those of us on the receiving end.