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Coronavirus epidemic: The end of the beginning?

April 7th, 2020, 6:30am by Sam Wang


Mathematical models of the disease are useful for state/national-level decisionmaking. But they don’t seem to address what we need as individuals. So Lucas Manning, Ben Deverett, and I calculated some simpler things. Basically, I think we’re at or slightly past the point of maximum personal risk. We just have to shelter for another…month!

Yesterday I visited friends by standing outside their houses, talking at 3-4 meters. We’re also getting good at Zoom dinner parties – distance socializing. By continuing to shelter in place, we are all doing our part.

Are you tired of the sheltering? I have bad news…and good news. My focus is New Jersey. What I say also applies to New York City and state. I will give information about other states along the way.

First, the bad news. Our state just passed 1,000 deaths. The total number of deaths has doubled in the last 3.9 days, according to our analysis. At this speed, the total number of people currently infected in N.J. is, in all likelihood, the highest it has ever been in this epidemic. Take care, now more than ever. Postpone even necessary errands for a few days.

And now, the good news: the infection rate may be starting to creep down a little – all across the nation! Even with uncertainties of counting and testing, the available evidence supports this conclusion.

Coronavirus appears to spread equally effectively in a wide variety of states, whether sparsely or densely populated. If you look by region, doubling times are generally in the 3-4 day range. Potentially, this is frightening. Unchecked, doubling and redoubling would infect pretty much all of us by May.

However, notice a general trend: the U.S. as a whole, and pretty much every region, are trending upward. This slowing is good news. To make an analogy to compound interest, the “interest rate of death” is decreasing.

Some regions are doing very well. In Pacific states, the doubling-time is 5 to 10 days.

These states are on a par with nations that have controlled their doubling time, including China, South Korea, and now Italy and Spain.

In those states, not only are deaths slowing, the number of infected people has probably been decreasing for at least a week. How do we know that?

The rate at which people die of covid-19 is proportional to the number of people who are infected (at least, until intensive care units start to overflow and we run out of ventilators). So if total deaths are doubling, so is the number of total cumulative infected.

But people don’t stay infective forever. For example, if the period of being infectious is 2 weeks, then the average time of being infections is 1 week, or 7 days. If this is true, then once the doubling time gets above 7 days, more people are getting over their infection than the number of people becoming newly infected.

In other words, Washington and Oregon have maxed out on the number of infected. Their risk is now decreasing. In fact, they hit that break-even point a while ago, since deaths are a lagging indicator of new infection. Three cheers for Governor Jay Inslee and his government! They might be a few weeks away from the next stage of recovery: testing, tracking, and maybe easing of restrictions.

California and Rocky Mountain states are close behind.

Before we get too excited about this, let’s pause to think about possible problems with this analysis. The number of deaths from coronavirus may be underestimated. But as long as the fraction of missed deaths stays about the same, doubling time estimates are not affected. As a worst-case scenario, even if that fraction increases by a factor of 1.5 over two weeks, in a fast-spreading state like New Jersey the doubling time would increase by only 0.3 days. In contrast, tracking the number of confirmed cases is far worse because of limited testing and aggressive triaging. For these reasons, in my view the number of deaths is an accurate readout, albeit a slow one.

Back to the analysis.

What about the eastern part of the nation? We’re not there yet. However, the overall trend is clear – doubling times are getting longer in nearly every state. Here are the top ten by number of deaths:
However, in all cases the doubling time is still less than 7 days. That means that as of two weeks ago (about when these people got infected), the number of infected people was still rising. But with two more weeks of sheltering, it is likely that last week was the moment of highest individual risk of infection. We may be past the halfway mark of this whole hellish experience. (Or more accurately, we may be at least halfway this phase of our hellish experience.)

But the risk is still high. Here in New Jersey, I estimate that as many as 1 in 30 people has coronavirus. As a number of us scientists and medical leaders wrote a few weeks ago, New Jersey has to shelter in place at least through the end of April. Do not falter now. Reduce the risk to you as an individual and to everyone you meet.

Stay Jersey Strong!

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3 Comments so far ↓

  • Steve Garmire

    Governor Jay Inslee of Washington has done well. May I recognize an even earlier pioneer, Michelle Reid, the Superintendent of a north King County school district who closed her schools on March 5th? Many people thought at the time that she was a nervous nanny. Below are excerpts from her letter to parents on March 4th, eight days before Inslee closed schools in the three county east Puget Sound area.
    “I have spent the past few weeks researching and monitoring the rapidly changing COVID-19 coronavirus health issue in our region and across the world … Now, I believe that the time has come for our district community to make an important shift,” Northshore School District superintendent Michelle Reid said in a Wednesday letter to families.
    In her lengthy announcement, she further explained her rationale. “We are taking this strategic approach not because we think by doing so, we will stop an epidemic; we are simply trying to do our part to slow the spread of COVID-19,” she wrote. “We are no longer able to provide quality instruction and maintain an environment that is safe.”
    What I hope is happening now, although I have not seen many signs of it yet, is that we are preparing to aggressively test and make contact traces and impose spot quarantines when we do restart the economy. Will we be ready to do what the South Koreans did so brilliantly?

  • Partha Neogy

    I am struck by the fact that chain reactions in a nuclear reactor provide a pretty good analogue of sars-cov-2 infections. Both are exponential processes. Even R0 for the virus is close to the 2.4 neutrons, on average, for thermal fission of U-235. The time scales for the two processes, of course, are vastly different. Sequestration is analogous to a control rod in a reactor isolating nuclei from neutrons coming from the fission of other nuclei. The one important difference is that people carrying the virus cease to be infectious after a period of tme. Fissionable nuclei, of course, do not lose their ability to fission.

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