I've been fortunate that I haven't been sick enough for this issue to come up, so thanks for the post — it makes me think.
My birds' routines aren't very taxing, so if I'm well enough to take care of myself, I imagine I'll be well enough to take care of my birds.
During your recovery, is boarding your bird elsewhere possible? If you have a virus, it wouldn't be wise to have anyone come into your home to provide bird care.
Proactively, I will reach out to local bird stores to see if they would pick-up the birds for boarding if I was unavailable due to a short-term disability (accident, sickness, etc).
I hope you're feeling better soon.