The coronavirus isn’t hitting us everywhere at the same time. The peak may yet vary by several weeks depending on location. Considering the economic costs of staying home, when is the right time to hole up, by the numbers?
The risk of infection probably depends on the population density and current infection rate in one’s local community, among other things. I’m also not sure how reliable the available data is due to lack of testing. One should also hole up some time before the peak so as not to risk developing pneumonia at a later time near the peak when hospital beds become unavailable. How long does an infection take to progress to pneumonia? How much does that vary? What about secondary infections for family members? Considering the logistic growth of cases, that pre-peak time depends on the growth rate, but by the time it looks bad, it’s too late.
If I’m monitoring e.g. the John’s Hopkins dashboard, how do I use that to time my isolation? What is the trigger point?
To answer my own question, I’ll try a Fermi estimate with what I know so far. These numbers are based on what I remember hearing and may be very inaccurate. It’s better to react too early than too late, so I’ll be using a more pessimistic model.
If anyone has better numbers, or spots an error or has a good reason to change the formula, please chime in with a comment, and I’ll consider edits.
There are about 3 hospital beds per 1000 people in the United States. Normally, about 2 of those are occupied, leaving 1 free per 1000 people to deal with the virus. Therefore, when the number of severe cases exceeds a “critical mass” of 0.1% of the population in your area, the medical system becomes overwhelmed, and cases become more deadly.
I think about 80% of cases are supposed to be mild, so 20% may require a hospital bed. Therefore, when the total number of cases in your area hits 0.5% of the population, we hit the critical 0.1% mark of severe cases.
Lukas_Gloor estimates that at best 5% of cases are diagnosed in the US. Therefore, we hit critical mass when the number of reported cases is projected to hit 0.025%. That’s about 250 confirmed cases per million people in your metro area.
But by that point it’s too late. You do not want to have a case of pneumonia when we hit critical mass. But it takes time for a case to progress that far. Lukas_Gloor estimates maybe 20 days for symptoms to progress to pneumonia, plus 7 days incubation, so you need to isolate 27 days before critical mass.
Lukas_Gloor estimates a doubling time of 2.5 days. That means about 11 doubling periods to add up to the 27 days. 11 doublings is 2^11 = 2048. Projecting 11 doubling periods backwards from 250/M, it should be about 27 days before critical mass, when there are about 250/2048 confirmed cases per million or about one confirmed case per ten million.
Conclusion: if your US metro area has less than ten million people, then isolate on the first confirmed case in your area. Otherwise, isolate when there is at least one confirmed case per ten million.
Am I being too pessimistic? This does seem too early, but so goes exponential growth. Catching the virus after this point would be very bad, but there would only be about 20 people per ten million who could actually give it to you that soon. What are the chances of catching it? Maybe they’re too small compared to risks you take every day (like driving a car to work) to warrant isolation that early.
When we hit the projected critical mass of confirmed cases, how many of them will have progressed to pneumonia? Maybe there’s a bit more time before the system is overwhelmed. On the other hand, at what stage of the disease do people get diagnosed? If they’re already severe by then, this might be moot.