(3/20/20) Evidence of social distancing not yet showing up in death rates, but still too soon to tell
Today we look at the death rates per day for key hot-bed countries. The Plots below show the death rate per day for the U.S., Italy, France, Spain, Iran, and U.K., all of which are showing acceleration. Also shown are the daily death rates for China, and Korea who show evidence of taming COVID-19.
Key observations are:
- The six aforementioned countries, including the U.S., continue to show an accelerated death rate (i.e., each day the death rate is trending up).
- China shows a clear deceleration of death rate (i.e., each day the death rate is trending down).
- Korea appears to trending neutral on death rate (i.e., each day is similar to the previous day).
So, let’s discuss different categories of rates, which we apply to the death rates above. The Table below shows a hypothetical relative case study for five different rate behaviors. Exponential would be the case for COVID-19 if nothing was done and every infected person infected a certain number of people who in turn infect a certain number of people. This infection rate is often referred to as R0 (e.g., for R = 3, 1 person infects 3 who infect 9 who infect 27, etc.). If some preventative measures are taken, we might expect exponential growth to slow down so we consider a binomial acceleration based on the number of cases being dependent on the square of the elapsed days. Linear is growing with every day and still not good, but at least better than the above. Constant would be achieving a R0 = 1, (i.e., 1 person infects 1 person infects 1 person) in which the infection and death rate stays constant and maybe controllable, but still not the desired outcome. Decline is what we are seeking corresponding to R0 < 1.
Based on the Plots above one can sort each country into these growth categories. Key observations are:
- France and Spain are still in full exponential growth; this is very troubling.
- Italy and Iran are in full acceleration, but maybe slowing down, but that may be because their numbers are already so big.
- The U.S. and U.K are in serious acceleration somewhere between exponential and binomial growth.
- China, if the numbers are to be believed, is in full retreat and I feel the numbers are more believable than unbelievable.
- Korea is an example of taming their problem, but in fact they never had a problem and just got ahead of any major outbreaks. This is noted by their never actually experiencing exponential growth.
- We should not be too alarmed at this point, since aggressive intervention in terms of quarantining and mandating social distancing really only started about a week or two ago. We expect the death rate to lag the incidence (infection) rate by about 3 weeks.
- This model predicts that if government intervention and social response are working then we should see a noticeable deceleration of the death rate in a 1-2 week time frame.
- It would be interesting to see how these levels of acceleration correlate with the fortitude of each country to exercise social distancing.