I guess that’s what happens when you read a new, more pessimistic covid model just before going to bed. The realization came to mind at 3:30 am. Eventually I made myself go back to sleep, but I dreamed I was riding in an elevator that kept filling up with more people on every floor. Then I got out of the elevator and onto a bus: at every stop more people got on. Clearly it was time to get up and write this post.
My mistake was in the doubling. It’s not how long it takes for the number of people in the population who have ever been infected to double. It’s how long it takes for those currently infected to double their number.
Assume that a newly infected person is contagious for around ten days. If there were the same number of newly infected people 10 days ago as there are today, then that 10-days-ago cohort doubled its number before immunity or death dropped them from the ranks of the currently contagious. That’s the plateau, when the reproduction rate — the Rt — is 1. When Rt=1 the virus progresses through the population at a steady rate until it runs out of new bodies to infect. That’s herd immunity.
Rates of newly diagnosed cases are subject to testing bias: as more tests are conducted, the number of virus-positive results will increase even if the rate of infection stays the same or decreases. I’ve been using death rate as a lagging indicator of new infections. The mortality rate for the disease is estimated at 1%; assuming no change in demographics of those who contract the virus, then each person whose death is recorded today stands as a proxy for 100 people who got infected maybe 3 weeks ago. That proxy calc still seems valid enough.
So, total US covid deaths over the past 10 days, from May 12 to May 22 = 13,919. Deaths over the preceding 10 days, May 2 to May 12 = 16,274. Divide the first number by the second to get the Rt for 3 weeks ago = 0.85. That’s pretty good. How about the 10 days before that: Rt = 16,274/19,550 = 0.83. So the reproduction number is stable, based on the level of social distancing that’s been practiced in this country over the past month or so. Using the calcs I outlined in the last post, the viral wave would wash itself out by around the end of March 2021, with maybe 6 percent of the US population having been infected and 170,000 having died from the disease.
That fairly prolonged path to viral extinction is predicated on maintaining present levels of social distancing. But now the country is opening up again, and there’s not much wiggle room in the Rt. People are generally cautious, but they’re going back to work and they’re being encouraged to return to the shops and the churches. Will the Rt stay below 1, or will it shoot back up to the predistancing reproduction rate of around 2.5? Somewhere in between seems likely: let’s say Rt=1.5. Under that scenario new infections, and new deaths, will start going up 50% every 10 days.
At that rate, a year from now 80 percent of Americans will have been infected and 2.5 million will have died. Herd immunity.
Trump says that, even if new viral spikes pop up, the country will not shut down again. He asserts that we’ll be able to put out the fires. That’s a whole hell of a lot of fires. Herd immunity.
The new predictive model I read last night was published as a collaboration between Imperial College London and the World Health Organization. No wonder Trump cut off WHO funding. So far 100,000 Americans have died from covid; the CDC’s updated model shows the virus killing 500,000 Americans, and that’s assuming that current levels of social distancing are maintained — which they won’t be. No wonder Trump and his minions are throwing shade at the CDC. A number of prominent epidemiologists regard the CDC estimates as too optimistic.