Updated: 2021-02-03 12:36:58 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
Texas 1.15 2429575 21545 77.3
South Carolina 0.91 449208 3384 68.3
Arizona 0.78 767688 4227 60.8
New York 0.93 1440465 11141 56.8
Oklahoma 0.91 392900 2184 55.7
North Carolina 0.95 769299 5477 53.9
Kentucky 0.91 371388 2301 51.8
New Jersey 0.93 703839 4511 50.8
Arkansas 0.90 295400 1472 49.2
Georgia 0.82 890985 5070 49.2
Delaware 0.89 78706 462 48.7
Florida 0.95 1735750 9875 47.9
Alabama 0.89 463511 2269 46.6
Connecticut 0.95 254691 1604 44.8
Louisiana 0.91 403941 2037 43.7
Virginia 0.83 511991 3628 43.1
Mississippi 0.83 277268 1260 42.2
Massachusetts 0.86 501945 2838 41.6
California 0.82 3356806 16217 41.4
Utah 0.83 347570 1244 40.8
Pennsylvania 0.97 857838 5154 40.3
West Virginia 0.88 122256 700 38.3
Tennessee 0.93 704661 2511 37.8
Ohio 0.86 903748 3952 33.9
Nevada 0.88 280299 971 33.2
New Mexico 0.91 175209 638 30.5
Indiana 0.85 633675 2019 30.4
Kansas 0.76 280237 847 29.1
New Hampshire 0.74 65356 389 29.0
Montana 0.94 94523 297 28.5
Maryland 0.88 357456 1635 27.2
Iowa 0.91 320175 838 26.8
Colorado 0.92 400502 1315 23.8
Illinois 0.80 1134710 2987 23.3
Wisconsin 0.86 594607 1347 23.3
Wyoming 0.88 52169 134 23.0
Idaho 0.83 163788 386 22.9
Maine 0.82 39986 304 22.8
Rhode Island 0.42 102654 240 22.7
Nebraska 0.79 191769 423 22.2
Vermont 1.03 12208 137 21.9
Missouri 0.84 456252 1296 21.3
Washington 0.95 319356 1514 20.8
Minnesota 0.89 463041 924 16.7
Michigan 0.88 612859 1597 16.0
Oregon 0.96 144009 631 15.5
South Dakota 0.77 108487 132 15.3
North Dakota 0.85 97829 100 13.3
Hawaii 0.90 25962 93 6.5

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 317.4 seconds to compute.
2021-02-03 12:42:15

version history

Today is 2021-02-03.
259 days ago: plots of multiple states.
251 days ago: include \(R_e\) computation.
248 days ago: created color coding for \(R_e\) plots.
243 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.
243 days ago: “persistence” time evolution.
236 days ago: “In control” mapping.
236 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.
228 days ago: Added census API functionality to compute per capita infection rates. Reduced spline spar = 0.65.
223 days ago: Added Per Capita US Map.
221 days ago: Deprecated national map. can be found here.
217 days ago: added state “Hot 10” analysis.
212 days ago: cleaned up county analysis to show cases and actual data. Moved “Hot 10” analysis to separate web page. Moved “Hot 10” here.
210 days ago: added per capita disease and mortality to state-level analysis.
198 days ago: changed to county boundaries on national map for per capita disease.
193 days ago: corrected factor of two error in death trend data.
189 days ago: removed “contained and uncontained” analysis, replacing it with county level control map.
184 days ago: added county level “baseline control” and \(R_e\) maps.
180 days ago: fixed normalization error on total disease stats plot.
173 days ago: Corrected some text matching in generating county level plots of \(R_e\).
167 days ago: adapted knot spacing for spline.
153 days ago:using separate knot spacing for spline fits of deaths and cases.
151 days ago: MAJOR UPDATE. Moved things around. Added per capita severity map.
123 days ago: improved national trends with per capita analysis.
122 days ago: added county level per capita daily cases map. testing new color scheme.
95 days ago: changed to daily mortaility tracking from ratio of overall totals.
88 days ago: added trend line to state charts.
60 days ago: decreased max value of Daily Cases per 100k State map.
53 days ago: increased max total state cases to 2,000,000 as California passes 1.5Million diagnosed cases.
30 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.
29 days ago: increased max total state cases to 3.0M as California passes 2.5Million diagnosed cases.
20 days ago: moved some graphs around.
8 days ago: changed scales of graphs. Total Deaths to 4,000,000 to accomdate California. Also, modified data analysis to not store stuf like lat lon and populations for county level data to reduce data storage requirements.

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.