Updated: 2020-11-27 10:17:23 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
North Dakota 0.90 76697 1086 144.4
Rhode Island 1.56 44874 1334 126.3
Wyoming 0.92 31300 724 124.4
New Mexico 1.05 90854 2427 116.0
Montana 0.96 59961 1137 109.2
Minnesota 0.91 293272 5952 107.7
Nebraska 0.96 121684 2034 106.8
South Dakota 0.83 75125 891 104.8
Wisconsin 0.92 398760 5802 100.4
Kansas 1.02 151777 2887 99.3
Iowa 0.88 223642 3098 98.9
Indiana 1.01 322292 6381 96.1
Nevada 1.21 145026 2645 90.5
Colorado 1.00 218114 4917 88.9
Illinois 0.96 698974 10873 84.8
Utah 0.83 186319 2540 83.4
Idaho 0.97 97762 1314 77.9
Oklahoma 1.02 186143 3037 77.5
Ohio 1.08 387690 8847 76.0
Missouri 0.95 275989 4092 67.2
Arkansas 1.09 149796 1869 62.5
Kentucky 0.96 171778 2708 61.0
Michigan 0.88 352227 5953 59.8
Pennsylvania 1.11 341056 7115 55.6
Arizona 1.09 315058 3858 55.5
West Virginia 1.05 44210 1011 55.3
Delaware 1.10 33466 474 49.9
Alabama 1.07 241702 2367 48.7
New Jersey 1.06 323451 4238 47.7
Texas 1.08 1227476 13218 47.4
Tennessee 0.83 345440 3108 46.7
Connecticut 0.93 109707 1614 45.1
Louisiana 0.82 226776 1833 39.3
Washington 1.15 162817 2792 38.3
Maryland 1.03 190846 2285 38.1
Mississippi 0.95 147236 1135 38.0
California 1.14 1178661 14385 36.7
Florida 0.93 963428 6880 33.4
North Carolina 0.99 349958 3350 33.0
Massachusetts 0.94 208009 2243 32.8
Oregon 1.13 70032 1338 32.8
Georgia 1.04 442884 3359 32.6
Virginia 1.19 180146 2236 32.1
New York 1.12 624324 6037 30.8
South Carolina 0.92 211799 1390 28.0
New Hampshire 0.93 18751 362 26.9
Maine 1.14 11251 235 17.6
Vermont 0.78 3897 71 11.4

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 259.9 seconds to compute.
2020-11-27 10:21:43

version history

Today is 2020-11-27.
191 days ago: plots of multiple states.
183 days ago: include \(R_e\) computation.
180 days ago: created color coding for \(R_e\) plots.
175 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.
175 days ago: “persistence” time evolution.
168 days ago: “In control” mapping.
168 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.
160 days ago: Added census API functionality to compute per capita infection rates. Reduced spline spar = 0.65.
155 days ago: Added Per Capita US Map.
153 days ago: Deprecated national map. can be found here.
149 days ago: added state “Hot 10” analysis.
144 days ago: cleaned up county analysis to show cases and actual data. Moved “Hot 10” analysis to separate web page. Moved “Hot 10” here.
142 days ago: added per capita disease and mortality to state-level analysis.
130 days ago: changed to county boundaries on national map for per capita disease.
125 days ago: corrected factor of two error in death trend data.
121 days ago: removed “contained and uncontained” analysis, replacing it with county level control map.
116 days ago: added county level “baseline control” and \(R_e\) maps.
112 days ago: fixed normalization error on total disease stats plot.
105 days ago: Corrected some text matching in generating county level plots of \(R_e\).
99 days ago: adapted knot spacing for spline.
85 days ago:using separate knot spacing for spline fits of deaths and cases.
83 days ago: MAJOR UPDATE. Moved things around. Added per capita severity map.
55 days ago: improved national trends with per capita analysis.
54 days ago: added county level per capita daily cases map. testing new color scheme.
27 days ago: changed to daily mortaility tracking from ratio of overall totals.
20 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.