[jrandm]

I believe you're focusing on the days aspect of that equation without considering what a lower T_double/p_detect could mean relative to hospitalizations.

If the real number of cases is doubling significantly faster than those detected -- say due to not testing them because their symptoms are mild enough to be missed entirely or to not seek treatment -- the calculations around things like mortality rate and severity of illness may yet change. As I understand it, scientists have already identified mutations of the virus that may also impact its ability to spread or injure infected hosts. I should note that these changes can swing both good and bad, I'm simply pointing out that there are more variables and that these variables changing may represent something not obvious from the equation.

I'm not an expert; I have fun reading about medical statistics. Most papers I've read take the time to examine these various confounding factors and what unexpected variations in their proposed equations might mean.

[trashtester]

If the number of real cases double every N days, the number of people needing hospitalization is also likely to double every N days. If not, it probably means that the infection rate spread at different rates in high risk vs low risk part of the population, but unless those populations are strongly segregated from each other, that is unlikely.

This could go in both directions. In both cases, though it would require that the high-risk subpopulation is primarily infected by each other (or staff) instead of being infected from the general population. If high-risk individuals are primarily infected by low-risk individuals, the doubling time for each group should be the same.

Note that such an effect could go in both directions. The high risk subpopulation could get it at a higher rate the rest if we let the infection spread like wildfire in hospitals and elderly housing centers, or it could spread at a lower rate if the risk patients are kept isolated.