In another thread Rich Davis mocked me using the following statement, posted by Russ on March 12:
"The number of cases has been doubling every two days in the US for a few weeks. If that continues, we will go from 1500 cases today, to 1,000,000 by or just after the end of this month! It is simple math. We need to arrest the progression of the illness and realize it is not an over-reaction. Frankly, your response surprises me given the simple math of the problem.
1000,2000,4000,8000, 16000, 32000...every 2 days! Exponential growth is a bitch."
Not surprisingly, Rich foolishly missed the point of Russ's accurate and early prediction. Rich conveniently overlooked the clauses, "If that continues," and "We need to arrest the progression of the illness and realize it is not an over-reaction." So, how have we done at arresting the progression so far? Consider the following:
An infection will propagate through a population at an exponential rate. The propagation rate is affected by many factors, like the inherent infectiousness of the disease and the mechanism of transfer. It is obviously very complex. In addition, any closed system, whether it is a Petri dish or the planet earth places constraints on the propagation of the infection. These constraints always cause the unconstrained rate of exponential growth to slow. Eventually, in a real system, exponential growth slows to a point where it levels off and stops. The disease models all take this into account.
With Covid-19, all of humanity is also placing artificial constraints on the propagation of the disease. These artificial constraints are the whole package of exceptionally burdensome business closures, stay-at-home orders, personal isolation efforts, masks and so on. Flattening the curve is all about constraining the exponential growth of the infection through social action.
So, are our efforts to flatten the curve working? Or, in the words of Russ Carroll, are we, "arrest(ing) the progression of the illness?" I think the answer is yes. Of course I can not, to the satisfaction of Rich Davis, prove that the effect shown below is caused in large part by social distancing. I believe however, that the data graphed below amply demonstrates that our efforts to flatten the curve are working quickly.
The graph below is similar to those posted earlier in another thread, but I have broken the total infection data (for dates after March 14) into one-week chunks. Excel will fit a nice exponential tend-line curve to each chunk, and extend it for any subsequent period, I selected five extra days. You will see that the actual infection curve always falls below the trend line for the previous period. That is good, the growth rate is slowing. Excel also conveniently provides the equation for each trend line in the format N=N0ert . This is nice, because it makes it easy to calculate a doubling rate for each period. The doubling rate is the the number of days it takes the number of Americans testing positive for Covid-19 to double. Russ was absolutely correct that as of March 12 and for several days thereafter, the doubling rate was 2.
According to the calculations below the doubling rate for each one week period is:
March 15-21: 2 days
March 22-28: 3.2 days
March 29- April 4: 5.3 days
All of this data and analysis is available elsewhere, but sometimes it is hard to find and interpret. Given that the social distancing measures started in earnest in a lot of places between March 15-21, I think that this analysis shows pretty well that these efforts have had a rapid effect. Yes, Rich, maybe the infection rate would have slowed just as rapidly through natural causes, I doubt it though. Will the social distancing etc. efforts be enough to avoid overwhelming the health care system? For most places, I personally remain optimistic.
Jim
