Updated: 2021-02-15 09:14:46 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
South Carolina 1.03 487293 3240 65.4
New York 1.01 1540127 8757 44.6
Tennessee 1.13 733856 2842 42.7
New Jersey 0.99 745005 3606 40.6
Delaware 1.03 82815 372 39.2
Virginia 0.98 550016 3196 38.0
Oklahoma 0.83 413535 1445 36.9
Texas 0.82 2570814 10205 36.6
North Carolina 0.81 825572 3686 36.3
Kentucky 0.87 393000 1604 36.1
Rhode Island 0.78 109120 375 35.5
Florida 0.96 1823982 7278 35.3
Georgia 0.88 936462 3434 33.3
Utah 0.94 359748 978 32.1
Arizona 0.78 797537 2076 29.9
Arkansas 0.72 310218 874 29.2
Massachusetts 0.89 527784 1972 28.9
Mississippi 0.98 287437 855 28.6
New Hampshire 1.04 69789 381 28.4
Pennsylvania 0.94 899476 3456 27.0
Alabama 0.82 480962 1214 25.0
Ohio 0.92 939414 2801 24.1
Louisiana 0.84 419489 1118 24.0
Nebraska 1.11 197668 456 23.9
California 0.83 3485019 9192 23.5
Colorado 0.98 415872 1271 23.0
West Virginia 0.89 127592 418 22.9
Nevada 0.92 288495 635 21.7
New Mexico 0.97 180562 445 21.3
Montana 0.88 97434 217 20.8
Indiana 0.87 652060 1376 20.7
Iowa 0.94 328126 639 20.4
Connecticut 0.66 266433 725 20.2
South Dakota 1.13 110323 172 19.9
Kansas 0.74 289303 573 19.7
District of Columbia 0.89 38918 132 19.3
Vermont 0.99 13669 120 19.2
Maryland 0.91 371163 1094 18.2
Illinois 0.90 1164754 2305 18.0
Idaho 0.87 167570 287 17.0
Wisconsin 0.90 607215 958 16.6
Minnesota 1.00 473145 842 15.2
Maine 0.82 42529 181 13.6
Missouri 0.82 467602 799 13.1
Michigan 0.84 628974 1152 11.6
Washington 0.81 331164 848 11.6
Wyoming 0.79 53168 67 11.5
Oregon 0.88 150282 467 11.4
North Dakota 1.09 98618 72 9.6
Hawaii 0.87 26771 60 4.2
Alaska 0.76 55755 118 NA
Northern Mariana Islands NaN 132 0 NA
Virgin Islands 1.07 2525 10 NA

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 318 seconds to compute.
2021-02-15 09:20:04

version history

Today is 2021-02-15.
271 days ago: plots of multiple states.
263 days ago: include \(R_e\) computation.
260 days ago: created color coding for \(R_e\) plots.
255 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.
255 days ago: “persistence” time evolution.
248 days ago: “In control” mapping.
248 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.
240 days ago: Added census API functionality to compute per capita infection rates. Reduced spline spar = 0.65.
235 days ago: Added Per Capita US Map.
233 days ago: Deprecated national map. can be found here.
229 days ago: added state “Hot 10” analysis.
224 days ago: cleaned up county analysis to show cases and actual data. Moved “Hot 10” analysis to separate web page. Moved “Hot 10” here.
222 days ago: added per capita disease and mortality to state-level analysis.
210 days ago: changed to county boundaries on national map for per capita disease.
205 days ago: corrected factor of two error in death trend data.
201 days ago: removed “contained and uncontained” analysis, replacing it with county level control map.
196 days ago: added county level “baseline control” and \(R_e\) maps.
192 days ago: fixed normalization error on total disease stats plot.
185 days ago: Corrected some text matching in generating county level plots of \(R_e\).
179 days ago: adapted knot spacing for spline.
165 days ago:using separate knot spacing for spline fits of deaths and cases.
163 days ago: MAJOR UPDATE. Moved things around. Added per capita severity map.
135 days ago: improved national trends with per capita analysis.
134 days ago: added county level per capita daily cases map. testing new color scheme.
107 days ago: changed to daily mortaility tracking from ratio of overall totals.
100 days ago: added trend line to state charts.
72 days ago: decreased max value of Daily Cases per 100k State map.
65 days ago: increased max total state cases to 2,000,000 as California passes 1.5Million diagnosed cases.
42 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.
41 days ago: increased max total state cases to 3.0M as California passes 2.5Million diagnosed cases.
32 days ago: moved some graphs around. 1 days ago: changed t-deaths_per_capita max to 300 to accomodate NJ, which now exceeds 250.

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.