I sometimes let my muscles recover for 5 days before a long ride. As for cardio, I have just recently started to track my progress. Going by perception, it seems I lose fitness in about a week off. Age, health, and stress all effect performance and training.
To answer your question, my CTS book states an athlete will lose fitness in 9 - 12 days off of training. Since training is their specialty, I will assume this is correct.
Family amd health should come before training, so get well first.

To a speedy recovery!