No, there you go again - I'm not missing it, I'm referring to omicron cases, surely that's obvious. We are told omicron would double every 2-3 days. Delta has been fairly static numbers for a while.
Assuming we're testing a repsentative sample of the pop, we would see the doubling. We aren't testing as well, relatively, so we're guessing how widespread it is in the community.
you mean, if 1,000 people are infected today, 50 of them go to hospital today?
No.
Of course not.
If they were infected today, none would go to hospital today.
Of course each has a different delay, but each individual still has the same 5% (say) chance overall.
The number who go to hosp is still a multiple of the number infected. Some will take longer than others, so if you want an instantaneous figure you have to add some stats with a known distribution function. That would give a smeared-hump shaped graph which would come down again when the peaking function constraint took over. But the time integral would still be a multiple/divisor of the original cases.
The accumulating number who will go to hosp is an integral of the exponential function. For the number in hosp at one time you'd have to know the statistical function for how long people stay in, incorporate that into the admissions expression and integrate the lot. For large numbers/times you have to incorporate factors like reinfection and the reducing exponent as the feedstock gets used up, which is apart of the limiting function.
A common way to run the numbers is not to build one expression, but put stages of calculation for each function into Matlab which is good at chuntering through an array of functions. Or you can of course use a spreadsheet like excel. The incidental numbers go across, and you just total up the columns to integrate. Then you add your confidence limits on your functions and decide how well you want to cover the extremes of risk, for things like peak hospital occupancy.
Hence tents in car parks, even if they DO only cover an extra 4%. HMG will be able to claim they're not at fault, it'll be that unfotunate shortage of staff...
There are some good/simple pdfs on modeling, on the net.
For functions and integrals you'd need remember your school maths - A level or so, but a spreadsheet needs less knowledge to implement.