Updated: 2020-12-02 10:05:16 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 \(R_e\).

Mapped County Data

While the State-Level Data Tell as remarkable story, it is also interesting to look at County-level data


state R_e cases daily cases daily cases per 100k
Minnesota 1.05 323224 6436 116.4
South Dakota 0.89 79705 843 99.2
Wyoming 0.88 33845 572 98.3
North Dakota 0.74 80030 697 92.7
New Mexico 0.89 99521 1915 91.5
Nebraska 0.92 129636 1682 88.3
Indiana 0.93 347687 5378 81.0
Colorado 0.97 239377 4450 80.5
Utah 0.89 198288 2393 78.6
Montana 0.84 63388 801 76.9
Tennessee 1.29 368890 5102 76.7
Ohio 1.02 431408 8780 75.4
Nevada 0.96 155532 2186 74.8
Oklahoma 0.96 200553 2887 73.7
Michigan 1.05 389227 7181 72.1
Idaho 0.96 103538 1205 71.4
Kentucky 1.08 186672 3131 70.5
Kansas 0.84 161563 2048 70.4
Wisconsin 0.81 417035 4042 70.0
Illinois 0.90 740026 8772 68.4
Iowa 0.77 232596 2008 64.1
Arizona 1.11 334954 4285 61.7
Delaware 1.12 36187 555 58.5
West Virginia 1.04 48906 1004 54.9
Missouri 0.91 291034 3323 54.6
Pennsylvania 1.00 374452 6703 52.4
Arkansas 0.93 156749 1497 50.1
Mississippi 1.13 154418 1460 48.8
Connecticut 1.06 117497 1724 48.1
Alabama 1.05 252237 2315 47.6
New Jersey 1.01 342775 4048 45.6
Louisiana 0.96 235917 1875 40.2
California 1.09 1252373 15387 39.3
Florida 1.03 1005397 8054 39.1
New Hampshire 1.23 21141 526 39.1
Texas 0.97 1272815 10823 38.8
Maryland 0.99 201290 2178 36.3
New York 1.13 659943 7128 36.3
Massachusetts 1.01 220726 2468 36.1
North Carolina 1.02 368997 3666 36.1
Washington 1.03 174671 2575 35.3
Oregon 1.10 76769 1433 35.1
Rhode Island 0.48 46672 339 32.1
South Carolina 0.98 218962 1440 29.1
Virginia 0.97 189398 1923 27.6
Georgia 0.90 455963 2751 26.7
Maine 0.94 11933 173 13.0
Vermont 0.89 4237 70 11.2

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 941.9 seconds to compute.
2020-12-02 10:20:58

version history

Today is 2020-12-02.
196 days ago: plots of multiple states.
188 days ago: include \(R_e\) computation.
185 days ago: created color coding for \(R_e\) plots.
180 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.
180 days ago: “persistence” time evolution.
173 days ago: “In control” mapping.
173 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.
165 days ago: Added census API functionality to compute per capita infection rates. Reduced spline spar = 0.65.
160 days ago: Added Per Capita US Map.
158 days ago: Deprecated national map. can be found here.
154 days ago: added state “Hot 10” analysis.
149 days ago: cleaned up county analysis to show cases and actual data. Moved “Hot 10” analysis to separate web page. Moved “Hot 10” here.
147 days ago: added per capita disease and mortality to state-level analysis.
135 days ago: changed to county boundaries on national map for per capita disease.
130 days ago: corrected factor of two error in death trend data.
126 days ago: removed “contained and uncontained” analysis, replacing it with county level control map.
121 days ago: added county level “baseline control” and \(R_e\) maps.
117 days ago: fixed normalization error on total disease stats plot.
110 days ago: Corrected some text matching in generating county level plots of \(R_e\).
104 days ago: adapted knot spacing for spline.
90 days ago:using separate knot spacing for spline fits of deaths and cases.
88 days ago: MAJOR UPDATE. Moved things around. Added per capita severity map.
60 days ago: improved national trends with per capita analysis.
59 days ago: added county level per capita daily cases map. testing new color scheme.
32 days ago: changed to daily mortaility tracking from ratio of overall totals.
25 days ago: added trend line to state charts.

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.