Excelsior Statistics and Optimization

Is reopening causing a resurgence of coronavirus in your state?

Gordon Bower
28 May 2020

This post will be updated weekly until the virus crisis subsides in the US. Last week's version is still online for comparison.

Introduction

Short answer: Yes. It's just a question of how soon and how fast. Before states started to reopen, only Alaska, Hawaii, Montana, and Vermont had it solidly under control. A month into reopening, those are still the only states maintaining a consistently low level of cases, though there is hope that some of the states with large early outbreaks will soon join them. A few states have yet to everget the epidemic under control; many others had it only barely under control, and are very likely to tip themselves back intoR>1 territory as they ease restrictions on movement.

I wrote before, in a longer and more technical article, about how the key to stopping the spread of an epidemic is to reduce the virus's reproduction number, R, below 1: If each contagious person infects an average of less than one healthy person, the spread of the disease grinds to a halt. If each contagious person infects more than one healthy person, the disease spreads faster and faster.

In the USA, the number of recorded cases rose very rapidly through the month of March. This was partly due to expanded testing capability, partly due to the virus's rapid spread. In April the virus's spread was slowed, and reasonable access to testing was established, in most states.

If you want to precisely model the spread of the virus, you need to take into account a lot of factors: how long it takes to become contagious, how many people are asymptomatic, how widely available testing is. Our purpose in this article isn't to get into that level of detail. To learn how detailed models work, you can go to rt.live and scroll to the "Learn More" links at the bottom of the page; read about what goes in to the Institute for Health Metrics and Evaluation's model; or read a fun little comic strip about pandemic modeling by Zach Weinersmith, the author of the Saturday Morning Breakfast Cereal daily comic.

What we're going to do here is talk about a simple and fairly stable way for you to keep tabs on how well your state is doing, without making you do a lot of math. Here's our simple shortcut:

  1. How many new cases did your state report this week?
  2. How many new cases did your state report last week?
  3. Divide the first by the second.

If the quotient is less than one, that is good: your number of cases is going down, and is likely to continue to go down about this same rate next week if nothing changes. If the quotient is greater than one, that is bad: your number of cases is going up and is likely to keep going up unless your state takes action to limit the spread.

We take weekly totals rather than daily totals for two reasons. First, this avoids hiccups in the data caused by what time of day a state updates its official tally, or fails to update it on a Sunday and has twice as many cases as usual to add on Monday. Second, the incubation time for the infection averages around five days (see this article for instance.) If you have symptoms, you may have spread the disease for a day or so before you first had symptoms; if you are asymptomatic you might spread the disease for several days after you contract it. One week corresponds very roughly to the average length of time elapsed between Person A testing positive and Person B testing positive after being infected by person A. This means that this quotient is a rough estimate of R — subject, of course, to all those extra factors about testing, how many asymptomatic carriers there are, and so on, that the people building complicated models are worrying about.

How is your state doing this week?

Here's a list of all 50 states, plus the District of Columbia and Puerto Rico, that I made today, comparing new cases 21-27 May with new cases 14-20 May, sorted from best to worst. I will update this article with a new list each week. (View last week's version.) The "trend" column is from a more complicated analysis to see if the increase or decrease in number of cases over this 14-day period was statistically significant.

State21-27 May14-20 MayRatioTrend
Montana 3 16 0.19
Hawaii 1 5 0.20
Connecticut 2271 4162 0.55Decreasing
Alaska 10 18 0.56
Michigan 2599 4618 0.56Decreasing
Oregon 237 385 0.62
Massachusetts 5250 8473 0.62Decreasing
New Jersey 5852 9216 0.63Decreasing
Rhode Island 997 1521 0.66
Delaware 902 1242 0.73Decreasing
New Hampshire 418 569 0.73
Wyoming 73 99 0.74
Maryland 5198 6835 0.76Decreasing
North Dakota 344 448 0.77
New York 10595 13709 0.77Decreasing
Kansas 784 989 0.79
Texas 6869 8653 0.79
Kentucky 910 1128 0.81
Indiana 3163 3801 0.83Decreasing
Nevada 762 912 0.84
Nebraska 1862 2210 0.84
Colorado 1957 2322 0.84Decreasing
Illinois 13888 15724 0.88Decreasing
District of Columbia 855 967 0.88
Arizona 2412 2690 0.90
Pennsylvania 5431 6025 0.90
Utah 996 1090 0.91
New Mexico 935 953 0.98
Washington 1435 1459 0.98
Puerto Rico 531 537 0.99
Minnesota 4794 4753 1.01
Florida 5163 5069 1.02
Oklahoma 697 674 1.03
Maine 318 304 1.05
Idaho 193 184 1.05
Ohio 4003 3715 1.08
Alabama 2598 2352 1.10Increasing
Georgia 4837 4374 1.11
Mississippi 2071 1868 1.11
Tennessee 2599 2317 1.12
California 15053 13199 1.14
Missouri 1121 978 1.15
Iowa 2749 2331 1.18
Virginia 6902 5801 1.19
North Carolina 4654 3910 1.19
South Dakota 533 445 1.20
Louisiana 3177 2652 1.20
Wisconsin 3049 2511 1.21
South Carolina 1448 1145 1.26
Vermont 24 18 1.33
Arkansas 1274 767 1.66
West Virginia 332 169 1.96
Total145129160312 0.91 1 up; 10 down

What do we learn from this table?

Are things better or worse now than they were a few weeks ago?

About the same.

This week was a good week, with only 21 states showing ratios above 1.00. I hope that's not just a lucky anomaly. This was only the second week (the other was May 8-13) in the past two months that more than half of states reported declines. If we want to only hear about 100 deaths per day instead of 1000 per day on the evening news, we need about six weeks in a row of solid progress.

The chart below shows the week-by-week history of these ratios in nine representative states:

Ratios for last 9 weeks in selected states (click to enlarge)

What do we learn from this graph?

How is your state doing? If yours isn't on the graph, you can download a complete list and look. If your state is still below 1.00 even after easing some restrictions like New York has, great. Maybe Pennsylvania and Rhode Island can cautiously ease a little and keep a close eye to make sure nothing bad happens in the next two weeks.

If your state was doing well but isn't anymore, that means you might have gone too far with easing restrictions. Wyoming might be in for a very bad summer after removing their travel restrictions and allowing tourists from all over the country into Yellowstone Park again.

And finally, if your state has yet to maintain a ratio below 1.00, you have a problem, that's going to turn into an emergency if you don't fix it. If you live in a state showing consistent week-over-week rises like Alabama, Arkansas, Maine, Minnesota, and North Carolina, you should be writing to your governor telling him you don't want him to reopen the state any more — he needs to do a better job shutting it down!

Stay tuned for an update from me next week, and stay safe!

This page last edited 28.05.20

Coronavirus resources

For immediate health concerns, call your local doctor or hospital. (Yes, call first, don't just show up!)

For statistics on the spread of the disease, Domo's coronavirus tracker has been my preferred set of charts to look at.

The projections published by Institute for Health Metrics and Evaluation at the University of Washington were very influential in US policy choices in late March and April 2020. Their projections for number of deaths weeks in advance proved remarkably accurate, and unlike some modelers, they discuss their methods and assumptions at some length.

If you want to play with the data yourself, this GitHub site provided by the Johns Hopkins University Center for Systems Science and Engineering is being updated daily with downloadable .csv files.

Your local state probably publishes daily updates on the progress of the pandemic in your area: here are links to Montana's and Alaska's.