Grasping Reality on TypePad, by Brad DeLong

There were 2027 reported deaths in the U.S. from the novel coronavirus as of late on Mar 28—if our reporting systems have not yet broken down.

With a 1% death rate, and with 3 weeks between infection and death, that means that as of Mar 7 there were 202700 coronavirus cases in the United States.

Up through Mar 28 deaths have been doubling every three days, suggesting that before Mar 7 true cases were also doubling every three days:

1. If that that pace has continued since, by Mar 31 we will have had 8 further doublings: 52 million cases, 1/6 of the population.
2. If the curve bent to doubling every four days, by Mar 31 we will have had 6 further doublings: 13 million cases, 1/25 of the population, with an additional 30 million cases expected by April 7
3. If the curve bent to doubling every six days, by Mar 31 we will have had 4 further doublings: 3.2 million cases, 1/100 of the population, with an additional 3.8 million cases expected by April 7
4. If the curve bent to doubling every eight days, by Mar 31 we will have had 3 further doublings: 1.6 million cases, 1/200 of the population, with an additional 1.5 million cases expected by April 7
5. If the curve bent to doubling every twelve days, by Mar 31 we will have had 2 further doublings: 800,000 cases, 1/400 of the population, with an additional 600,000 cases expected by April 7
6. If the curve bent to doubling every twenty-four days, by Mar 31 we will have had 1 further doubling: 400,000 cases, 1/800 of the population, with an additional 200,000 cases expected by April 7

As of the morning of Mar 29, the U.S. had 125,000 reported cases

As of the evening of Mar 28, the U.S. had tested 650,000 people, with a 19% positive rate. Applying that to our six scenarios, in each scenario those we have tested are, respectively, 1, 5, 10, 20, 40, and 80 times more likely to have the disease than the average probability of having the disease.

Question: What is wrong with this analysis?