Updated: 2020-12-04 08:51:39 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
Rhode Island 1.35 50890 1263 119.5
Minnesota 1.01 334053 6024 109.0
South Dakota 0.97 81515 890 104.7
Wyoming 0.98 35075 609 104.7
Nebraska 1.03 134320 1888 99.1
Utah 1.09 204908 2943 96.7
Indiana 1.05 360507 6094 91.8
New Mexico 0.93 103021 1876 89.7
Colorado 1.03 248426 4638 83.9
Montana 0.97 65196 874 83.9
Idaho 1.09 106573 1397 82.8
North Dakota 0.76 81089 622 82.7
Tennessee 1.27 379804 5381 80.9
Kentucky 1.18 194323 3589 80.8
Nevada 1.00 160104 2288 78.3
Arizona 1.25 347052 5331 76.7
Kansas 0.92 166130 2177 74.8
Michigan 1.08 403896 7443 74.7
Illinois 1.00 759896 9567 74.6
Wisconsin 0.92 425776 4293 74.3
Ohio 1.00 447467 8598 73.9
Iowa 0.93 237569 2290 73.1
Connecticut 1.36 123514 2503 69.9
Oklahoma 0.89 204888 2526 64.5
Arkansas 1.11 160939 1854 62.0
Alabama 1.24 259275 3001 61.7
Delaware 1.11 37293 570 60.0
Mississippi 1.26 158469 1784 59.7
Pennsylvania 1.09 390272 7593 59.4
West Virginia 1.09 50996 1058 57.8
Louisiana 1.26 242605 2688 57.6
Missouri 0.98 297865 3432 56.4
Massachusetts 1.28 229080 3475 50.9
Texas 1.18 1305280 13960 50.1
New Jersey 1.06 351594 4314 48.6
New Hampshire 1.30 22411 605 45.0
California 1.16 1289836 17526 44.8
Florida 1.10 1024355 8922 43.3
New York 1.18 677138 8072 41.1
North Carolina 1.08 377270 3997 39.4
Maryland 1.03 205789 2252 37.5
Washington 1.07 180238 2736 37.5
Georgia 1.17 465180 3794 36.8
Oregon 1.07 79504 1423 34.9
South Carolina 1.10 222562 1653 33.4
Virginia 0.96 192984 1876 26.9
Vermont 1.36 4544 118 18.9
Maine 1.17 12440 224 16.8

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 628.1 seconds to compute.
2020-12-04 09:02:07

version history

Today is 2020-12-04.
198 days ago: plots of multiple states.
190 days ago: include \(R_e\) computation.
187 days ago: created color coding for \(R_e\) plots.
182 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.
182 days ago: “persistence” time evolution.
175 days ago: “In control” mapping.
175 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.
167 days ago: Added census API functionality to compute per capita infection rates. Reduced spline spar = 0.65.
162 days ago: Added Per Capita US Map.
160 days ago: Deprecated national map. can be found here.
156 days ago: added state “Hot 10” analysis.
151 days ago: cleaned up county analysis to show cases and actual data. Moved “Hot 10” analysis to separate web page. Moved “Hot 10” here.
149 days ago: added per capita disease and mortality to state-level analysis.
137 days ago: changed to county boundaries on national map for per capita disease.
132 days ago: corrected factor of two error in death trend data.
128 days ago: removed “contained and uncontained” analysis, replacing it with county level control map.
123 days ago: added county level “baseline control” and \(R_e\) maps.
119 days ago: fixed normalization error on total disease stats plot.
112 days ago: Corrected some text matching in generating county level plots of \(R_e\).
106 days ago: adapted knot spacing for spline.
92 days ago:using separate knot spacing for spline fits of deaths and cases.
90 days ago: MAJOR UPDATE. Moved things around. Added per capita severity map.
62 days ago: improved national trends with per capita analysis.
61 days ago: added county level per capita daily cases map. testing new color scheme.
34 days ago: changed to daily mortaility tracking from ratio of overall totals.
27 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.