Updated: 2021-02-01 12:40:52 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.

## Per Capita


state R_e cases daily cases daily cases per 100k
South Carolina 0.97 443349 3853 77.7
Arizona 0.84 760753 5044 72.6
Oklahoma 1.00 389162 2521 64.3
New York 0.99 1420859 12481 63.6
Texas 0.98 2381384 17449 62.6
Georgia 0.92 883058 6217 60.4
Kentucky 0.97 367374 2575 58.0
New Jersey 1.02 696054 5149 58.0
Rhode Island 0.84 102814 610 57.7
Arkansas 0.96 292846 1667 55.7
Mississippi 1.00 275466 1657 55.4
North Carolina 0.94 758869 5630 55.4
Delaware 0.93 77880 516 54.3
Alabama 0.98 459629 2609 53.6
Virginia 0.94 506346 4493 53.4
Florida 1.01 1718376 10932 53.1
Louisiana 0.99 400438 2308 49.5
Utah 0.92 345570 1504 49.4
Massachusetts 0.92 497126 3294 48.2
California 0.85 3328770 18787 48.0
Pennsylvania 1.10 849214 6014 47.0
West Virginia 0.98 121139 839 45.9
Tennessee 0.96 700070 2746 41.3
Ohio 0.93 897022 4574 39.3
New Hampshire 0.86 64794 516 38.4
Nevada 0.93 278598 1099 37.6
New Mexico 1.00 174124 743 35.5
Indiana 0.90 630193 2323 35.0
Connecticut 0.71 250752 1196 33.4
Kansas 0.78 278694 969 33.3
Montana 1.04 94022 343 32.9
Maryland 0.97 354734 1938 32.3
Iowa 0.91 318618 888 28.3
Wisconsin 0.94 592403 1605 27.8
Maine 0.86 39485 354 26.6
Illinois 0.81 1128723 3251 25.4
Nebraska 0.80 191042 483 25.4
Idaho 0.84 163087 423 25.1
Wyoming 0.85 51912 142 24.4
Missouri 0.88 453987 1468 24.1
Colorado 0.89 397840 1317 23.8
Vermont 1.04 11947 140 22.4
Washington 0.98 316563 1614 22.1
Minnesota 0.95 461414 1047 18.9
South Dakota 0.83 108276 161 18.6
Michigan 0.87 609796 1687 16.9
North Dakota 0.96 97672 122 16.2
Oregon 0.96 142776 650 15.9
Hawaii 0.97 25799 105 7.4

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 1008.7 seconds to compute.
2021-02-01 12:57:41

version history

Today is 2021-02-01.
257 days ago: plots of multiple states.
249 days ago: include \(R_e\) computation.
246 days ago: created color coding for \(R_e\) plots.
241 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.
241 days ago: “persistence” time evolution.
234 days ago: “In control” mapping.
234 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.
226 days ago: Added census API functionality to compute per capita infection rates. Reduced spline spar = 0.65.
221 days ago: Added Per Capita US Map.
219 days ago: Deprecated national map. can be found here.
215 days ago: added state “Hot 10” analysis.
210 days ago: cleaned up county analysis to show cases and actual data. Moved “Hot 10” analysis to separate web page. Moved “Hot 10” here.
208 days ago: added per capita disease and mortality to state-level analysis.
196 days ago: changed to county boundaries on national map for per capita disease.
191 days ago: corrected factor of two error in death trend data.
187 days ago: removed “contained and uncontained” analysis, replacing it with county level control map.
182 days ago: added county level “baseline control” and \(R_e\) maps.
178 days ago: fixed normalization error on total disease stats plot.
171 days ago: Corrected some text matching in generating county level plots of \(R_e\).
165 days ago: adapted knot spacing for spline.
151 days ago:using separate knot spacing for spline fits of deaths and cases.
149 days ago: MAJOR UPDATE. Moved things around. Added per capita severity map.
121 days ago: improved national trends with per capita analysis.
120 days ago: added county level per capita daily cases map. testing new color scheme.
93 days ago: changed to daily mortaility tracking from ratio of overall totals.
86 days ago: added trend line to state charts.
58 days ago: decreased max value of Daily Cases per 100k State map.
51 days ago: increased max total state cases to 2,000,000 as California passes 1.5Million diagnosed cases.
28 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.
27 days ago: increased max total state cases to 3.0M as California passes 2.5Million diagnosed cases.
18 days ago: moved some graphs around.
6 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.