The Rate of Contagion is Accelerating

I’ve been using a US age-adjusted mortality rate of 0.6 percent as the basis for estimating infections. The formula is simple: divide deaths by .006. So, for the US, 148K deaths divided by .006 = about 24.6 million Americans who have been infected by the coronavirus. That’s 24.6/328 = 7.5 percent of the US population.

Of course the people who’ve been infected don’t stay infected forever. Fewer than 1 percent die; the rest recover. On average, how long does an infected person remain contagious? I’ve been assuming ten days — a number recently confirmed by the CDC.

Yesterday 1.150 people died from covid in the US. Divide by .006: that’s nearly 200 thousand people who got infected on roughly the same day as those who died yesterday. Assume a steady rate of deaths over a consecutive ten day span: 200K x 10 = 2 million people currently infected and contagious. That doesn’t seem like a lot compared to 328 million people who live in this country.

But the law of large numbers eventually prevails over the law of infrequent events. A steady rate of deaths and new infections is a flattened curve. It’s an Rt of 1.0, where on average each newly infected person in turn infects one other person. The rate of contagion doesn’t escalate, nor does it diminish. Every ten days 2 million infected people recover or die from covid, replaced by a cohort of 2 million newly infected people who carry the virus forward, and so on, continuing the spread until nearly everyone has been infected, at which point herd immunity is “achieved.”

The objective of epidemiological intervention is to suppress contagion before things go that far — to drive the Rt below 1.0 and keep it there until the epidemic extinguishes itself. Here are the Rt scores over the past several ten-day intervals, calculated as the most recent 10-day average daily death rate divided by the average death rate for the preceding 10 days:

  • July 12 — July 22:   843/633 = 1.33
  • July 2 — July 12:   633/630 = 1.00
  • June 22 —  July 2:    630/599 = 1.05
  • June 12 —  June 22:   599/853 = 0.70
  • June 2 –  June 12:   853/940 = 0.91
  • May 23 –  June 2:   940/1,316 = 0.71
  • May 13 –  May 23:   1,316/1,700 = 0.77

Things were going pretty well. The Rt stayed consistently below 1; daily death rates — and, by inference, daily infection rates — had decreased by 70 percent in a month and a half. Another three weeks with Rt kept at 0.7 and covid deaths would have dropped to around 200 per day, daily new infections to 30 thousand — still a lot, but possibly manageable even after lifting lockdown via widespread community testing, case quarantining and contact tracing. But then, in late June, the  Rt went back up to 1, and now in mid-July it’s jumped substantially above 1. Instead of improving to 30K infections per day we’ve now regressed to nearly 200K per day. So even if the Rt restabilizes at 1, the plateau will be far higher than before, with far more work to do just to recapture the earlier hard-earned level of containment.

Lately I’ve become intrigued by the percentage of test-positives as possibly another proxy for infection rates. Here are Rt values calculated as the most recent 10-day average daily test-positive rate divided by the average test-positive rate for the preceding 10 days:

  • July 12 — July 22:   8.7%/7.9% = 1.10
  • July 2 — July 12:   7.9%/6.6% = 1.20
  • June 22 —  July 2:    6.6%/4.7% = 1.40
  • June 12 —  June 22:   4.7%/4.6% = 1.02
  • June 2 –  June 12:   4.6%/5.4% = 0.85
  • May 23 –  June 2:   5.4%/6.6% = 0.82
  • May 13 –  May 23:   6.6%/9.8% = 0.67

The Rt trends are similar for both methods of estimation, with the test-positive trend about 20 days ahead of the death trend. That makes sense: while recovery typically takes about 10 days from initial infection, those who die from covid typically do so about 20 days after they’ve been diagnosed. Death is a lagging indicator; test-positives might offer a more contemporaneous view.

Based on test-positives, the Rt has been trending upward since mid-June. That’s when many states began phase 3 of reopening, exposing far more people to the virus in larger gatherings and for longer durations, without the ability to identify and isolate infected individuals before they can spread the disease to others. It’s been a deadly failure.


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