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I'd carry on training just cut back for a couple of weeks. I think short sessions with some relatively hard but not super hard bits are what you need. So a run might be 4 miles with two at half mara pace in the middle, a bike ride you might do 20 miles with 5 at a good speed etc. In other words cut the volume right back for 2 weeks but leave a bit of moderately high intensity in there which will pretty much protect what you've gained so far and get the body used to working hard rather than just for a long time.
If you were actually suffering illness and really deep fatigue I'd say total rest but it sounds more like where you just need to let your capacity to recover exceed your training for a few weeks to make up for a deficit the other way. I've had the same recently playing catch up after enforced breaks and on Saturday any hill my quads were screaming right from the start and I couldn't stay with riders I'd normally ride away from but I know this weekend after a couple of hard chaingangs but little else I'll be ok.
You can do my swim for me if you like and I'll do your rest