COVID-19: Update on Stay-at-Home Effectiveness

Two weeks after my previous post, there are now more data available and it's pretty clear that the stay-at-home measures result in a significant flattening of the exponential growth of infections. Even areas with less-restrictive measures (like Iowa or Arkansas) show some flattening of infection growth, which presumably means that every little bit of action people take helps to reduce the transmission of this virus.

I updated my charts with the latest data from the COVID Tracking Project and added fits to a 2-piece exponential with a bend in the middle at some date.  I thought it would be interesting to see what conclusions one could draw from these fits, but it's not clear that there are any really definitive trends.  Still, I thought it worth posting in case someone else might spot some insights in these data.

Methodology

As discussed in the previous post, fitting the positive case rate is not ideal, since there could well be trends caused by changes in the testing rates or testing schemes. There is much less ambiguity in the death-rate trends, but these lag by a week or two and they often have much more statistical noise (making for harder fits). Some states are reporting hospitalization rates and those could potentially be a more solid statistic to fit, but the reporting on this is still very spotty (as you can see). Therefore, I have stuck with fitting the case-rate, while plotting the other two numbers so that one can see how well they track one another. If you see the case-rate and death-rate diverge (not simply due to the time-lag), then you have good reason to suspect changes in the testing regime.

I have used a 4-parameter piece-wise function and fit minimizing the least-squares of the difference in logs of the data and fit function. Not all of the data yielded good fits, but I haven't noted this (although you can see the problematic ones in the charts). In some cases this is due to shapes not fitting the model, like states that haven't yet flattened out or ones like PA (and perhaps IL) that may have more of a 3-legged-exponential shape. The charts below label the inflection point as "m", the doubling-time of the earlier exponential as "b", and the doubling-time of the latter exponential as "v".

Observations

From these charts, one can see that the infection slope has generally been reduced significantly in most states sometime around the latter half of March. Many states now have slopes that are nearly flat (you should consider any fit with v > 20 as flat), but some are still growing at doubling-times of 7-14 days (GA, MD, AL, KY, MS, NM). Those still growing are a mix of states with strict stay-at-home policies and ones with laxer policies, so there must be other factors at play (e.g. population density and cultural behavior). In addition, there are states that haven't yet flattened but are still growing relatively slowly (DE, SD, PR, NE, and perhaps RI).

The only states showing a decline in case-rate are WA and LA. It makes sense that WA had the earliest infections, so they might be the first to see a decline. The LA curve has an unusual shape that perhaps indicates changes in how many tests are administered, but the death-rate does seem to have flattened out so perhaps the decline is real. There are hints of a decline in NY, PA, and IN, but too few data points that don't quite make a clear trend yet. The NY data looked like a decline until today's (Apr 15) data point showed up.

At present, COVID Tracking has no data for AS (American Somoa) and very little for MP, GU, VI. In addition, the statistics on the 8 smallest states (AK, ND, MT, HI, ME, WV, VT, WY) are probably too low for good confidence in any fit parameters. It might be helpful to chart all these data normalized by state population (to see the true prevalence of infection), but that would not help the statistical challenge of these small states.

Another interesting question is whether states in warmer climates have lower infection rates, which might have an implication for whether COVID-19 will show significant seasonality. In particular, the rapid flattening in FL (despite lax shelter-in-place policies) and the relatively quick downward trend in case-rate in LA in comparison to the mid-atlantic states suggested this hypothesis. However, I think the high growth rate in MS and the slower growth rates in many colder-climate states argue against this idea.

Fits by state

State	b	m	v	State Name
AK	3.726	24.7	1.056e+08	Alaska
AL	2.578	25.0	12.56	Alabama
AR	2.708	20.4	15.9	Arkansas
AS	0.000	0.0	0	American Somoa
AZ	2.674	26.0	61.4	Arizona
CA	3.428	28.0	69.16	California
CO	3.071	26.0	1623	Colorado
CT	2.089	26.8	19.17	Connecticut
DC	3.994	31.7	69.85	District of Columbia
DE	3.711	26.0	6.014	Delaware
FL	2.484	27.0	70.47	Florida
GA	2.485	23.9	13.74	Georgia
GU	11.780	24.0	89.11	Guam
HI	3.913	24.3	2.513e+07	Hawaii
IA	3.651	29.0	14.16	Iowa
ID	2.972	28.5	1.537e+08	Idaho
IL	1.879	21.5	10.04	Illinois
IN	2.486	29.2	2.502e+07	Indiana
KS	3.397	29.3	3.515e+05	Kansas
KY	3.660	28.0	10.54	Kentucky
LA	2.129	25.0	276.3	Louisiana
MA	3.066	28.5	15.03	Massachusetts
MD	2.870	28.0	10.25	Maryland
ME	2.963	20.3	26.41	Maine
MI	2.486	15.4	23.57	Michigan
MN	2.767	21.3	21.61	Minnesota
MO	1.951	26.6	191.5	Missouri
MP	0.000	0.0	0	Northern Mariana Islands
MS	1.672	20.9	13.66	Mississippi
MT	3.954	26.0	123.9	Montana
NC	2.791	26.6	44.33	North Carolina
ND	2.923	19.6	15.91	North Dakota
NE	9.018	15.0	5.8	Nebraska
NH	4.239	31.0	942.3	New Hampshire
NJ	1.881	25.5	43.08	New Jersey
NM	4.514	29.9	12.6	New Mexico
NV	3.081	27.5	2.2e+07	Nevada
NY	1.963	22.6	34.56	New York
OH	2.240	24.8	29.2	Ohio
OK	2.615	27.6	80.67	Oklahoma
OR	4.097	26.0	528.7	Oregon
PA	2.403	28.7	26.71	Pennsylvania
PR	9.094	72.2	10.13	Puerto Rico
RI	4.086	30.0	5.703	Rhode Island
SC	2.875	28.2	5.332e+07	South Carolina
SD	23.811	16.0	4.543	South Dakota
TN	2.769	25.7	1032	Tennessee
TX	2.831	31.2	65.69	Texas
UT	2.454	23.4	87.3	Utah
VA	3.280	30.3	20.3	Virginia
VI	2.627	20.0	4761	Virgin Islands
VT	3.090	24.0	2470	Vermont
WA	4.443	21.3	1.646e+08	Washington
WI	1.654	18.7	21.41	Wisconsin
WV	2.180	27.1	36.02	West Virginia
WY	5.308	31.0	110.3	Wyoming

Notes

As before, my Jupyter notebook file for this analysis is available for anyone who might be interested. Please send me comments and suggestions that occur to you.