That's an interesting idea, thanks for commenting. It's true that viruses depend on their host for survival, virus metabolism works by hijacking the cell's protein synthesis machinery.

However, a cell has the capacity for metabolic switching between sugar and ketones to perform normal metabolic processes like protein synthesis. So, I don't see how viruses can't replicate if the host is in ketosis state.

In essence, viruses don't live off the blood sugar (which stays constant even in a state of ketosis), but the cell's protein synthesis machinery. And even in ketosis, cells can still function and make proteins properly.