The ratio for delta at its peak was lower than the current ratio for omicron? I suspect you are seeing some relative of the effect I was talking about, then. I think you probably need the integrals of the total cases and total hospitalisations, otherwise it will be affected by how close you are to the inflection point.I didnt do any maths to the case numbers. I took the actual recorded case numbers, and checked how many more times that amount has already been reached in London at its highest Omicron point seen in the data so far. Then I took peak hospital rates from Delta wave for London and multiplied them by the same factor. Then I divided them to account for the decrease mentioned in the aforementioned study. Number came out significantly lower than a number already seen in the London hospital data in this Omicron wave.
Reasons why I would not have expected this crude attempt to match the actual figures at all includes the need to take into account age of cases, hospital infections, and those who went to hospital for other reasons but were already infected before admission as discussed in previous post. I only did this exercise briefly, mostly so I could then warn others not to base their expectations on this simplified method or how many hospital admissions there were at peak in London in the delta wave.
Mind you, it's been a long time since I needed to think about calculus things, so I could be well off.