Corona Modeling: The Present as Past Projected Into Future

Yesterday I found out that my lease on ficticities.com was automatically extended for another year, and that my credit card was billed for the extension about 3 weeks ago. So I guess in celebration I’ll write a post…

As of right now the total number of confirmed coronavirus cases in the US stands at 356,653 (a palindrome!). But the actual number of cases is probably 10 million or more. Back-of-the-envelope math:

It takes an average of 5 days for a person newly infected by the virus to become symptomatic. Another week or so goes by before symptoms get bad enough for the infected person to go to the hospital, which is when the COVID diagnostic test is usually administered in this country. Maybe 5 more days go by before the test results come back from the lab. So the person who shows up as a confirmed case today likely got infected 5+7+5 = 17 days ago. The present total case count measures a reality that’s two and a half weeks in the past.

To arrive at today‘s actual number of corona cases, you have to take the 17-day-old past numbers and project them forward 17 days into the future. Lately the confirmed case rate has been doubling every 6 days. So, over a 17-day span, cases would be expected to increase nearly 2³ — let’s call it a seven-fold increase. Take the 357K confirmed case count from 17 days ago, multiply it by 7, and you get around 2.5 million cases.

But wait. The 2.5 million includes only those cases that are likely to progress to the point where symptoms become severe enough for testing a couple of weeks from now. My best estimate is that, for every case that eventually get tested, there are around 4.2 cases that never get tested. So: multiply 2.5 million by 4.2 and you get around 10.5 million total cases. That’s pretty close to rigorous epidemiological models., which forecast that 5 percent of the US population, or around 16 million people, will be infected during this first wave, expected to crest in the next week or so.