Updated: 2020-12-12 07:48:28 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

Current Status of Active Disease

Computed Reproduction Rate \(R_e\).

County Data

While the State-Level Data tell as remarkable story, outbreaks tend to be highly localized to communities - therefor it’s informative to look at County-level data


state R_e cases daily cases daily cases per 100k
Rhode Island 1.55 60162 1768 167.3
North Dakota 1.27 87191 912 121.2
Ohio 1.27 543860 13808 118.6
Idaho 1.18 119947 1844 109.3
Kansas 1.17 187758 2946 101.3
Indiana 1.02 415251 6611 99.6
Arizona 1.16 397364 6826 98.3
Tennessee 1.19 424415 6488 97.5
Nevada 1.09 182221 2832 96.9
Utah 0.98 228239 2799 91.9
South Dakota 0.94 87848 765 90.0
Delaware 1.15 43811 836 88.0
Connecticut 1.21 145479 3139 87.6
Pennsylvania 1.18 475067 11174 87.4
California 1.30 1522482 32678 83.5
New Mexico 0.99 116552 1723 82.4
Colorado 1.01 283773 4462 80.7
Nebraska 0.91 147366 1535 80.6
Wyoming 0.93 38810 468 80.4
Alabama 1.15 288328 3876 79.7
Montana 0.99 71910 827 79.4
Minnesota 0.85 371931 4344 78.6
Kentucky 1.02 220586 3371 75.9
Wisconsin 0.99 461328 4315 74.7
Arkansas 1.08 178410 2198 73.5
Illinois 1.01 834446 9369 73.1
Massachusetts 1.14 268806 4983 73.0
Oklahoma 0.99 229106 2846 72.6
Texas 1.32 1437264 20197 72.4
Mississippi 1.11 174997 2162 72.3
West Virginia 1.09 60894 1268 69.3
New Hampshire 1.27 28796 920 68.5
Michigan 0.90 458283 6247 62.7
North Carolina 1.21 424187 6314 62.2
Louisiana 1.09 263566 2810 60.3
Iowa 0.94 252375 1846 58.9
Georgia 1.21 508733 5841 56.7
South Carolina 1.15 244985 2778 56.1
Missouri 0.97 326695 3405 55.9
New Jersey 1.03 392234 4933 55.5
New York 1.11 759868 10527 53.7
Virginia 1.27 217676 3418 49.1
Florida 1.07 1102171 10006 48.6
Maryland 1.09 228927 2891 48.2
Washington 1.20 204414 3474 47.6
Oregon 1.01 91461 1471 36.0
Maine 1.28 15192 384 28.8
Vermont 1.01 5540 119 19.0

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 254.5 seconds to compute.
2020-12-12 07:52:42

version history

Today is 2020-12-12.
206 days ago: plots of multiple states.
198 days ago: include \(R_e\) computation.
195 days ago: created color coding for \(R_e\) plots.
190 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.
190 days ago: “persistence” time evolution.
183 days ago: “In control” mapping.
183 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.
175 days ago: Added census API functionality to compute per capita infection rates. Reduced spline spar = 0.65.
170 days ago: Added Per Capita US Map.
168 days ago: Deprecated national map. can be found here.
164 days ago: added state “Hot 10” analysis.
159 days ago: cleaned up county analysis to show cases and actual data. Moved “Hot 10” analysis to separate web page. Moved “Hot 10” here.
157 days ago: added per capita disease and mortality to state-level analysis.
145 days ago: changed to county boundaries on national map for per capita disease.
140 days ago: corrected factor of two error in death trend data.
136 days ago: removed “contained and uncontained” analysis, replacing it with county level control map.
131 days ago: added county level “baseline control” and \(R_e\) maps.
127 days ago: fixed normalization error on total disease stats plot.
120 days ago: Corrected some text matching in generating county level plots of \(R_e\).
114 days ago: adapted knot spacing for spline.
100 days ago:using separate knot spacing for spline fits of deaths and cases.
98 days ago: MAJOR UPDATE. Moved things around. Added per capita severity map.
70 days ago: improved national trends with per capita analysis.
69 days ago: added county level per capita daily cases map. testing new color scheme.
42 days ago: changed to daily mortaility tracking from ratio of overall totals.
35 days ago: added trend line to state charts.
7 days ago: decreased max value of Daily Cases per 100k State map.

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.