Updated: 2020-12-13 09:02:21 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
Rhode Island 1.33 61004 1512 143.1
Ohio 1.20 555868 13455 115.6
North Dakota 1.18 87868 850 113.0
Arizona 1.17 404926 7137 102.7
Indiana 1.03 422167 6786 102.2
Idaho 1.09 121299 1714 101.6
Tennessee 1.18 430997 6599 99.2
Nevada 1.07 184864 2814 96.3
Utah 1.00 231239 2886 94.8
Kansas 1.08 189759 2695 92.7
Delaware 1.15 44718 869 91.5
South Dakota 0.96 88624 775 91.2
Pennsylvania 1.17 486494 11518 90.0
California 1.26 1555480 33358 85.2
New Mexico 1.02 118328 1761 84.2
Texas 1.40 1464960 23368 83.8
Alabama 1.15 292529 4022 82.7
Colorado 1.00 287876 4408 79.7
Montana 0.99 72703 825 79.2
Oklahoma 1.05 232566 3064 78.2
Arkansas 1.11 180960 2330 77.9
Kentucky 1.04 224086 3458 77.9
Connecticut 1.07 147286 2766 77.2
Mississippi 1.14 177541 2304 77.1
Wisconsin 1.01 465828 4405 76.2
Minnesota 0.85 375704 4195 75.9
Massachusetts 1.13 273998 5124 75.0
Illinois 1.01 843660 9408 73.4
Nebraska 0.86 148395 1393 73.1
Wyoming 0.87 39108 420 72.2
West Virginia 1.09 62171 1290 70.5
New Hampshire 1.25 29717 942 70.1
North Carolina 1.18 430472 6383 62.9
Iowa 0.98 254321 1898 60.6
South Carolina 1.16 248264 2956 59.6
Georgia 1.20 515255 6114 59.4
Michigan 0.86 462819 5767 57.9
Missouri 0.99 330318 3487 57.3
New Jersey 1.03 397321 5018 56.5
New York 1.10 770684 10747 54.8
Louisiana 0.98 265184 2474 53.0
Florida 1.08 1113010 10341 50.2
Maryland 1.09 232005 2977 49.6
Virginia 1.22 221050 3447 49.5
Washington 1.16 207683 3449 47.3
Oregon 1.01 92910 1480 36.3
Maine 1.26 15601 400 30.0
Vermont 0.98 5641 116 18.6

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 247.9 seconds to compute.
2020-12-13 09:06:28

version history

Today is 2020-12-13.
207 days ago: plots of multiple states.
199 days ago: include \(R_e\) computation.
196 days ago: created color coding for \(R_e\) plots.
191 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.
191 days ago: “persistence” time evolution.
184 days ago: “In control” mapping.
184 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.
176 days ago: Added census API functionality to compute per capita infection rates. Reduced spline spar = 0.65.
171 days ago: Added Per Capita US Map.
169 days ago: Deprecated national map. can be found here.
165 days ago: added state “Hot 10” analysis.
160 days ago: cleaned up county analysis to show cases and actual data. Moved “Hot 10” analysis to separate web page. Moved “Hot 10” here.
158 days ago: added per capita disease and mortality to state-level analysis.
146 days ago: changed to county boundaries on national map for per capita disease.
141 days ago: corrected factor of two error in death trend data.
137 days ago: removed “contained and uncontained” analysis, replacing it with county level control map.
132 days ago: added county level “baseline control” and \(R_e\) maps.
128 days ago: fixed normalization error on total disease stats plot.
121 days ago: Corrected some text matching in generating county level plots of \(R_e\).
115 days ago: adapted knot spacing for spline.
101 days ago:using separate knot spacing for spline fits of deaths and cases.
99 days ago: MAJOR UPDATE. Moved things around. Added per capita severity map.
71 days ago: improved national trends with per capita analysis.
70 days ago: added county level per capita daily cases map. testing new color scheme.
43 days ago: changed to daily mortaility tracking from ratio of overall totals.
36 days ago: added trend line to state charts.
8 days ago: decreased max value of Daily Cases per 100k State map.
1 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.