# How Often Does a Child Get Sick?

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

He is now three, and in total, he has been sick 22 times in his life1 With an average duration of 4.4 days, meaning us parents lose about 16 % of our working time caring for him when he is sick. Since we share 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 can be frustrating!. If we plot this as a Kaplan–Meier survival curve, it looks like this.2 This is not actually using any real survival analysis (none of the samples in this set are censored), I’m just using the Kaplan–Meier curve as a convenient graphical device.

I feel like there are three sections on the curve:

• 0–30 days between illness: hazard rate 2.5 % per day.
• 30–55 days between illness: hazard rate 0.8 % 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. Once it’s time to start daycare there, it will be interesting to see if the hazard rate is lower (acquired immunity) or if what we’ve seen so far is just the background rate (natural mutations and loss of immunity against common colds and such.) If the data from my son is segmented into two halves, there seems to be no statistically significant reduction in hazard rate as he has grown older, so that makes me lean toward background rate.