Updated: 2021-02-13 14:51:29 PDT

Original version created 2020-05-03. See below for revision history

Intro


The spread of the SARS-COV-19 viral disease defies description in terms of a single statistic. To be informed about personal risk we need to know more than how many people have been sick at a national level or even state level, we need information about how many people are currently sick in our communicty and how the number of sick people is changing is changing at a state and even county level. It can be hard to find this information.

This analysis seeks to fill partially that gap. It includes:
1. Several national pictures of disease trends to enable a “large pattern” view of how disease has and is evolving a on country-wide scale.
2. A per capita analysis of disease spread.
3. A more granular analysis of regions, states, and counties to shed light on local disease pattern evolution.
4. Details of the time evolution of growth statistics.


This computed document is part of a constantly evolving analysis, so please “refresh” for the latest updates. If you have suggestions or comments please reach out on twitter @WinstonOnData or facebook.


You are welcome to visit my code repository on Github.
You are also welcome to visit my analysis on the Politics of COVID
Finally, you can alway check my Rpubs for new documents and updates.

National Statistics

Total & Active Cases, and Deaths

These trend charts show the national disease statistics. Note that raw daily trends are systematically related to the M-F work week.

Mortality and \(R_e\)

Distribution of \(R_e\) Values

There is a wide distribution of \(R_e\) across regions and counties. The distributions in the graph below looks roughly symmetrical because the x-scale is logarithmic.

National Maps

State Level Data

There are several maps below. These include:

  • pandemic total cases (How many people have been sick?)
  • pandemic total cases per capita (What fraction of people have been sick?)
  • daily cases per capita (what fraction of people are getting sick?)
  • forecast short term cases per capita (based on \(R_e\)) (how fast is the disease growning or shrinking?)

Pandemic Totals

Computed Reproduction Rate \(R_e\).

County Data

While the State-Level Data tell as remarkable story, outbreaks tend to be highly localized to communities - County-level data can help decode this.


state R_e cases daily cases daily cases per 100k
South Carolina 0.94 480157 2938 59.3
Rhode Island 1.10 109120 608 57.5
New York 0.99 1523042 8737 44.5
New Jersey 1.02 739047 3794 42.7
Tennessee 1.16 729465 2838 42.7
Kentucky 0.93 390645 1860 41.9
Texas 0.82 2558176 11685 41.9
Oklahoma 0.82 410809 1546 39.5
North Carolina 0.80 819242 3992 39.3
Virginia 0.98 544250 3262 38.8
Delaware 1.00 82077 364 38.3
Arizona 0.84 794224 2530 36.4
Florida 0.93 1811027 7398 35.9
Georgia 0.88 930877 3655 35.5
Arkansas 0.76 308825 1048 35.0
Utah 0.97 358340 1060 34.8
Connecticut 0.97 266433 1236 34.5
Massachusetts 0.86 524002 2019 29.6
Pennsylvania 0.94 893359 3666 28.7
Louisiana 0.89 418188 1332 28.6
Kansas 0.94 289288 823 28.3
Mississippi 0.90 285648 820 27.4
Alabama 0.79 478735 1307 26.9
New Hampshire 0.98 69081 360 26.8
California 0.85 3469889 10367 26.5
Ohio 0.91 934810 2925 25.1
Montana 0.96 97162 256 24.6
West Virginia 0.88 126893 449 24.5
Colorado 0.97 414181 1274 23.0
Iowa 0.98 327434 708 22.6
Indiana 0.88 649610 1479 22.3
Idaho 1.02 167353 366 21.7
Nevada 0.83 287104 614 21.0
New Mexico 0.90 179716 434 20.7
District of Columbia 0.88 38670 139 20.3
Illinois 0.93 1161207 2501 19.5
Nebraska 0.95 195709 371 19.5
South Dakota 1.15 110075 168 19.4
Maryland 0.90 369156 1148 19.1
Wisconsin 0.89 605785 1014 17.5
Vermont 0.88 13407 107 17.1
Maine 0.86 42259 209 15.7
Missouri 0.88 466680 952 15.6
Washington 0.92 330427 1077 14.8
Minnesota 0.92 471440 781 14.1
Wyoming 0.84 53104 82 14.1
Michigan 0.88 627576 1303 13.1
Oregon 0.90 149577 509 12.5
North Dakota 0.90 98492 60 8.0
Hawaii 0.82 26671 60 4.2
Alaska 1.11 55755 189 NA
Northern Mariana Islands 0.00 132 0 NA
Virgin Islands 1.32 2525 12 NA

Regional Snapshots

Regional snapshots reveal the highly nuanced behavior of disease spread. Each snaphot includes multiple states and selected counties.

How to read the charts

There are four components:
1. State Maps show the number of active cases and with the Reproduction rate encoded as color.
2. State Graphs State-wide trend graphs.
3. Severity Ranking These is a table of counties where the highest number of new cases are expected. Severity is a compounded function \(f(R, cases(t))\). This is useful for finding new (often unexpected) “hot spots.” Added per capita rates.
4. County Graphs encode the R-value in the active number of cases. R is the Reproduction Rate.

(NOTE: R < 1 implies a shrinking number of active cases, R > 1 implies a growing number of active cases. For R = 1, active cases are stable. ).


Washington and Oregon

California

Four Corners

Mid-Atlantic

Deep South

FL and GA

Texas & Oklahoma

Michigan & Wisconsin

Minnesota, North Dakota, and South Dakota

Connecticut, Massachusetts, and Rhode Island

New York

Vermont, New Hampshire, and Maine

Carolinas

North-Rockies

Midwest

Tennessee and Kentucky

Missouri and Arkansas

Conclusions

It’s in control some places, but not all places. And many places are completely out-of-control.

Stay Safe!
Be Diligent!
…and PLEASE WEAR A MASK



Built with R Version 4.0.3
This document took 680.4 seconds to compute.
2021-02-13 15:02:49

version history

Today is 2021-02-13.
269 days ago: plots of multiple states.
261 days ago: include \(R_e\) computation.
258 days ago: created color coding for \(R_e\) plots.
253 days ago: reduced \(t_d\) from 14 to 12 days. 14 was the upper range of what most people are using. Wanted slightly higher bandwidth.
253 days ago: “persistence” time evolution.
246 days ago: “In control” mapping.
246 days ago: “Severity” tables to county analysis. Severity is computed from the number of new cases expected at current \(R_e\) for 6 days in the future. It does not trend \(R_e\), which could be a future enhancement.
238 days ago: Added census API functionality to compute per capita infection rates. Reduced spline spar = 0.65.
233 days ago: Added Per Capita US Map.
231 days ago: Deprecated national map. can be found here.
227 days ago: added state “Hot 10” analysis.
222 days ago: cleaned up county analysis to show cases and actual data. Moved “Hot 10” analysis to separate web page. Moved “Hot 10” here.
220 days ago: added per capita disease and mortality to state-level analysis.
208 days ago: changed to county boundaries on national map for per capita disease.
203 days ago: corrected factor of two error in death trend data.
199 days ago: removed “contained and uncontained” analysis, replacing it with county level control map.
194 days ago: added county level “baseline control” and \(R_e\) maps.
190 days ago: fixed normalization error on total disease stats plot.
183 days ago: Corrected some text matching in generating county level plots of \(R_e\).
177 days ago: adapted knot spacing for spline.
163 days ago:using separate knot spacing for spline fits of deaths and cases.
161 days ago: MAJOR UPDATE. Moved things around. Added per capita severity map.
133 days ago: improved national trends with per capita analysis.
132 days ago: added county level per capita daily cases map. testing new color scheme.
105 days ago: changed to daily mortaility tracking from ratio of overall totals.
98 days ago: added trend line to state charts.
70 days ago: decreased max value of Daily Cases per 100k State map.
63 days ago: increased max total state cases to 2,000,000 as California passes 1.5Million diagnosed cases.
40 days ago: increased max total state cases to 2.5M as California passes 2Million diagnosed cases. Increased max cases/100k to 15k since ND passed 12k. Increased deaths / 100k to 250 as NJ passed 200.
39 days ago: increased max total state cases to 3.0M as California passes 2.5Million diagnosed cases.
30 days ago: moved some graphs around.

Appendix: Methods

Disease data are sourced from the NYTimes Github Repo. Population data are sourced from the US Census census.gov

Case growth is assumed to follow a linear-partial differential equation. This type of model is useful in populations where there is still very low immunity and high susceptibility.

\[\frac{\partial}{\partial t} cases(t, t_d) = a \times cases(t, t_d) \] \(cases(t)\) is the number of active cases at \(t\) dependent on recent history, \(t_d\). The constant \(a\) and has units of \(time^{-1}\) and is typically computed on a daily basis

Solution results are often expressed in terms of the Effective Reproduction Rate \(R_e\), where \[a \space = \space ln(R_e).\]

\(R_e\) has a simple interpretation; when \(R_e \space > \space 1\) the number of \(cases(t)\) increases (exponentially) while when \(R_e \space < \space 1\) the number of \(cases(t)\) decreases.

Practically, computing \(a\) can be extremely complicated, depending on how functionally it is related to history \(t_d\). And guessing functional forms can be as much art as science. To avoid that, let’s keep things simple…

Assuming a straight-forward flat time of latent infection \(t_d\) = 12 days, with \[f(t) = \int_{t - t_d}^{t}cases(t')\; dt' ,\] \(R_e\) reduces to a simple computation

\[R_e(t) = \frac{cases(t)}{\int_{t - t_d}^{t}cases(t')\; dt'} \times t_d .\]

Typical range of \(t_d\) range \(7 \geq t_d \geq 14\). The only other numerical treatment is, in order to reduce noise the data, I smooth case data with a reticulated spline to compute derivatives.


DISCLAIMER: Results are for entertainment purposes only. Please consult local authorities for official data and forecasts.