Updated: 2020-12-21 07:30:16 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 \(R_e\).

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
Tennessee 1.12 504191 9256 139.2
California 1.22 1893291 47292 120.8
Rhode Island 0.88 69116 1035 98.0
Oklahoma 1.14 259650 3693 94.3
Indiana 0.98 467348 5844 88.0
Arizona 0.93 456200 6104 87.9
Alabama 1.10 323107 4239 87.1
Nevada 0.98 204702 2509 85.8
Arkansas 1.12 199175 2549 85.2
Utah 0.99 250696 2533 83.2
Delaware 0.94 50670 729 76.8
Ohio 0.90 623625 8934 76.7
West Virginia 1.10 72484 1399 76.5
Pennsylvania 0.95 563284 9577 74.9
Mississippi 1.03 194469 2219 74.2
New Mexico 0.96 130379 1514 72.4
Massachusetts 1.03 310844 4835 70.8
Idaho 0.89 130536 1186 70.3
Kansas 0.91 205257 1992 68.5
South Carolina 1.09 273426 3317 66.9
Georgia 1.10 565170 6742 65.5
North Carolina 1.07 480049 6652 65.5
South Dakota 0.90 92989 553 65.1
Wisconsin 0.97 493422 3607 62.4
Kentucky 0.96 245509 2766 62.3
New Hampshire 0.99 35928 804 59.8
Wyoming 0.95 41791 346 59.5
Texas 0.90 1601350 16564 59.4
Illinois 0.93 903244 7498 58.5
Montana 0.93 77258 600 57.6
Iowa 1.05 267428 1796 57.3
Nebraska 0.92 156868 1078 56.6
Florida 1.10 1199826 11646 56.5
Louisiana 1.03 285848 2633 56.5
Colorado 0.91 311271 3071 55.5
New York 1.05 852203 10735 54.7
New Jersey 0.98 433510 4577 51.5
Missouri 0.94 355850 3068 50.4
Connecticut 0.77 164213 1795 50.1
Minnesota 0.83 397063 2643 47.8
Virginia 0.99 243954 2981 42.8
North Dakota 0.66 90117 305 40.5
Maryland 0.91 251456 2356 39.2
Michigan 0.85 492827 3775 37.9
Washington 0.97 228465 2749 37.7
Maine 1.12 19128 470 35.3
Oregon 1.03 103027 1364 33.4
Vermont 1.01 6442 105 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 631.6 seconds to compute.
2020-12-21 07:40:48

version history

Today is 2020-12-21.
215 days ago: plots of multiple states.
207 days ago: include \(R_e\) computation.
204 days ago: created color coding for \(R_e\) plots.
199 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.
199 days ago: “persistence” time evolution.
192 days ago: “In control” mapping.
192 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.
184 days ago: Added census API functionality to compute per capita infection rates. Reduced spline spar = 0.65.
179 days ago: Added Per Capita US Map.
177 days ago: Deprecated national map. can be found here.
173 days ago: added state “Hot 10” analysis.
168 days ago: cleaned up county analysis to show cases and actual data. Moved “Hot 10” analysis to separate web page. Moved “Hot 10” here.
166 days ago: added per capita disease and mortality to state-level analysis.
154 days ago: changed to county boundaries on national map for per capita disease.
149 days ago: corrected factor of two error in death trend data.
145 days ago: removed “contained and uncontained” analysis, replacing it with county level control map.
140 days ago: added county level “baseline control” and \(R_e\) maps.
136 days ago: fixed normalization error on total disease stats plot.
129 days ago: Corrected some text matching in generating county level plots of \(R_e\).
123 days ago: adapted knot spacing for spline.
109 days ago:using separate knot spacing for spline fits of deaths and cases.
107 days ago: MAJOR UPDATE. Moved things around. Added per capita severity map.
79 days ago: improved national trends with per capita analysis.
78 days ago: added county level per capita daily cases map. testing new color scheme.
51 days ago: changed to daily mortaility tracking from ratio of overall totals.
44 days ago: added trend line to state charts.
16 days ago: decreased max value of Daily Cases per 100k State map.
9 days ago: increased max total state cases to 2,000,000 as California passes 1.5Million diagnosed cases.

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.