Not sure why insulin requirements increase so significantly during illness; although I'm normally very curious about such anomalies this is one that I just accept at face value, backed up by the meter of course! Someone with more brain power than me will be able to explain.
There ARE equations that can help calculate correction and insulin/carb ratios, but I've found them tricky to pin down and am currently stuck on just one set. It's therefore fortunate that my insulin profile matches the criteria for the formulae:
For a pump user with a basal insulin level at 50% of TDD, correction ratio calculates as 100 divided by TDD, insulin/carb ratio as 500 divided by TDD. These are surprisingly accurate for me, but I'm on a pump and my basal averages at almost exactly 50% of TDD, so a near perfect match for the numbers, which do change according to daily insulin profile. For example, someone with a basal at 35% of TDD would use 110 divided by TDD to get the correction ratio. And that's where my current knowledge of the formulae sadly ends.
I use the formulae to double-check the ratios against what I use in practice - they're a starting point only, but quite useful nonetheless. I've been trying for some times to find a reference that will tell me the different numbers to use in the calculations for different basal percentages, in order to further fine-tune my weekly checks, but without much success so far.