Excelsior Statistics and Optimization

Is reopening causing a resurgence of coronavirus in your state?

Gordon Bower
04-05 June 2020

This series of posts will be updated weekly until the virus crisis subsides in the US. Previous posts are available for comparison: 28 May and 21 May.


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. States that had the virus only barely under control in April have to be very careful how far towards "business as usual" they go, and it looks like most of them went too far.

The states like New York and New Jersey that had huge caseloads in March and April are still recovering. As the situation improves in those states, still under significant restrictions, people looking only at the national totals were given the impression the virus was under control everywhere. Unfortunately, not so: more states are on the way up than on the way down. In fact a few states have yet to everget the epidemic under control, and even those states opted to relax some restrictions and let the rate of infection accelerate.

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, comparing new cases 28 May-03 June with new cases 21-27 May, sorted from best to worst. I will update this article with a new list each week; you can compare last week's version here. (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. In states with low numbers of cases, or where the number of reported test varies wildly day to day, it may take more than 14 days to prove a trend is meaningful.)

State28 May- 3 Jun21-27 MayRatioTrend
West Virginia 178 332 0.54
Delaware 616 902 0.68Decreasing
Illinois 9524 13888 0.69Decreasing
Connecticut 1668 2407 0.69
North Dakota 240 344 0.70Decreasing
Iowa 1931 2749 0.70
Minnesota 3406 4794 0.71Decreasing
District of Columbia 610 855 0.71
Wyoming 55 73 0.75
Pennsylvania 4223 5431 0.78Decreasing
Vermont 19 24 0.79
Oklahoma 576 697 0.83
Louisiana 2633 3177 0.83
Ohio 3353 4003 0.84Decreasing
South Dakota 452 533 0.85
New York 9120 10595 0.86Decreasing
Rhode Island 866 997 0.87Decreasing
Georgia 4256 4837 0.88
Maine 281 318 0.88Decreasing
Virginia 6152 6902 0.89
New Jersey 5440 5852 0.93
Michigan 2427 2599 0.93
Alabama 2819 2980 0.95
New Mexico 888 935 0.95
Wisconsin 2938 3049 0.96
Nebraska 1901 1862 1.02
Kansas 801 784 1.02
Indiana 3275 3163 1.04
Nevada 801 762 1.05
Mississippi 2272 2071 1.10
Missouri 1251 1121 1.12
Maryland 5812 5198 1.12
Colorado 2292 1957 1.17
Puerto Rico 626 531 1.18
Florida 6130 5163 1.19
California 18298 15053 1.22
New Hampshire 509 418 1.22
South Carolina 1792 1448 1.24
Idaho 263 193 1.36
Tennessee 3548 2599 1.37
North Carolina 6360 4654 1.37
Massachusetts 7372 5250 1.40
Arkansas 1790 1274 1.41
Washington 2078 1435 1.45
Kentucky 1333 910 1.46
Texas 10335 6869 1.50
Oregon 361 237 1.52Increasing
Utah 1791 996 1.80Increasing
Arizona 5038 2412 2.09Increasing
Alaska 93 10 9.30Increasing
Hawaii 10 110.00
Montana 44 314.67Increasing
Total150846145646 1.04 5 up; 9 down

What do we learn from this table?

This week's numbers are the first to reflect the impact of the Memorial Day and the start of summer travel season, as well as the relaxation of restrictions which mostly happened early in May. Some highlights:

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

About the same.

This week saw half the states going up and half going down. That's not a receipe for gaining a victory over the disease anytime soon — especially as many of the states going down are still recovering from massive outbreaks earlier in the spring. Very few states are maintaining the disease at a low level.

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, Pennsylvania and Rhode Island, great. Keep a close eye and make sure not to remove so many restrictions that progress halts.

If your state was doing well but isn't anymore, that means you might have gone too far with easing restrictions. Idaho and Missouri have had 3 weeks in a row of increases just like Florida has. Time to take social distancing seriously and regain control!

The start of tourist season might be very bad news, especially the wide-open spaces of the west. Montana, Alaska, Washington, Oregon, Colorado, and Utah have all just had their worst week in two months. I believe it was a grave mistake to lift the 14-day travel quarantine in my home state of Montana; any state that currently has a low infection rate compared to its neighbors should be looking hard at strictly limiting non-essential travel if it wishes to allow local business to reopen.

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 — Arizona, Arkansas, California, Mississippi, North Carolina, Texas —, you should be writing to your governor telling him you don't want him to reopen the state any more. Now is the time to rein it in. It's better to close early and lock down hard for a relatively short time. If you let the infection rate get high, or you only take half-measures to control it, it takes far longer to regain control.

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

This page last edited 05.06.20

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.