# How Often Does a Child Get Sick?

Our first child was born mere weeks before covid-19 came to our part of the world. As a result, they were effectively locked down for the first 1.5 years of their life until they started going to daycare. This had the effect that for those 1.5 years, they were not sick a single time.

At some point they turned three, and in total, had been sick 22 times until
then^{1} With an average duration of 4.4 days, meaning us parents lost about 16
% of our working time caring for them when they were sick. Since we shared that
burden fairly evenly, that’s 8 % for each person, or in practise only getting 37
hours of work out of a 40 hour work week. It was frustrating at times!. If we
plot this as a survival curve, it looks like this.

I feel like there are three sections on the curve:

- 0–30 days between illness: hazard rate 2.4 % per day.
- 30–55 days between illness: hazard rate 1 % per day.
- 55–100 days between illness: hazard rate < 0.1 % per day.

The last one is definitely a separate phenomenon: that was over the summer break. I suspect the first two are periods with more and less infections going around in society, so e.g. early winter will have a 2.5 % daily probability of getting sick, while mid-spring has an 0.8 % daily probability. These are of course very unscientific observations, but they may serve as a good starting point for inquiry.

Our second child has not grown up as secluded, and already been sick multiple times before starting daycare. I was curious whether their hazard rate would be lower when they started daycare (because acquired immunities) or if the curve above is sort of the background rate.

Here is the corresponding (significantly less dense) data for the second child.

This also seems to show regions of higher and lower activity^{2} Maybe hazard
rates of 4 % and 2 % respectively?. We can plot these together to make it
more clear how they relate:

Perhaps surprisingly, the pre-exposed child has been sick *more* frequently than
the isolated one!

This difference is nowhere near significant.^{3} The log-odds difference is
0.27, but the standard error is a whopping 0.40! but if it was, it would be an interesting
cue as to how much genetics affects hazard rate – two siblings, meaning virtually
the same genetics and upbringing, still have a hazard rate difference of about
one percentage point. That would translate to one being sick 16 more days of the
year than the other!