Updated: 2021-02-05 08:40:57 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
Rhode Island 1.23 105587 859 81.3
Texas 1.13 2470696 21644 77.6
North Carolina 1.13 784828 6731 66.3
South Carolina 0.87 454407 2988 60.3
Arkansas 1.05 299354 1757 58.7
Arizona 0.77 774136 3728 53.7
Oklahoma 0.91 396810 2085 53.2
Kentucky 0.93 375641 2244 50.5
Georgia 0.85 900374 4906 47.6
New York 0.82 1454918 9101 46.4
Louisiana 0.95 408249 2128 45.6
Alabama 0.90 467721 2206 45.3
Connecticut 0.94 257532 1527 42.6
Florida 0.89 1751016 8715 42.3
New Jersey 0.81 709394 3611 40.7
Utah 0.86 349930 1208 39.7
California 0.81 3384204 14751 37.7
Delaware 0.77 79234 357 37.6
Virginia 0.78 517178 3100 36.8
Massachusetts 0.82 506176 2468 36.1
Tennessee 0.90 708784 2295 34.5
Mississippi 0.74 278798 1004 33.6
Pennsylvania 0.84 864425 4175 32.6
Ohio 0.88 910963 3788 32.5
West Virginia 0.82 123229 595 32.5
Kansas 0.87 282259 921 31.7
Nevada 0.86 281886 880 30.1
Montana 0.99 95174 311 29.9
Iowa 0.99 322055 894 28.5
New Hampshire 0.80 66157 380 28.3
New Mexico 0.88 176283 584 27.9
Indiana 0.84 636895 1818 27.4
Colorado 0.97 403255 1360 24.6
Idaho 0.93 164654 412 24.4
Wyoming 0.96 52448 139 23.9
Nebraska 0.91 192692 445 23.4
Wisconsin 0.91 597312 1355 23.4
Vermont 1.05 12483 141 22.6
Illinois 0.85 1140290 2889 22.5
Maryland 0.79 359541 1331 22.2
Maine 0.86 40546 294 22.1
Missouri 0.87 458730 1273 20.9
Washington 0.95 322005 1462 20.0
Michigan 1.00 616679 1798 18.1
South Dakota 0.89 108794 143 16.5
Minnesota 0.89 464632 867 15.7
Oregon 0.98 145287 640 15.7
North Dakota 0.91 98042 104 13.8
Hawaii 0.86 26107 83 5.8

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 1368.9 seconds to compute.
2021-02-05 09:03:46

version history

Today is 2021-02-05.
261 days ago: plots of multiple states.
253 days ago: include \(R_e\) computation.
250 days ago: created color coding for \(R_e\) plots.
245 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.
245 days ago: “persistence” time evolution.
238 days ago: “In control” mapping.
238 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.
230 days ago: Added census API functionality to compute per capita infection rates. Reduced spline spar = 0.65.
225 days ago: Added Per Capita US Map.
223 days ago: Deprecated national map. can be found here.
219 days ago: added state “Hot 10” analysis.
214 days ago: cleaned up county analysis to show cases and actual data. Moved “Hot 10” analysis to separate web page. Moved “Hot 10” here.
212 days ago: added per capita disease and mortality to state-level analysis.
200 days ago: changed to county boundaries on national map for per capita disease.
195 days ago: corrected factor of two error in death trend data.
191 days ago: removed “contained and uncontained” analysis, replacing it with county level control map.
186 days ago: added county level “baseline control” and \(R_e\) maps.
182 days ago: fixed normalization error on total disease stats plot.
175 days ago: Corrected some text matching in generating county level plots of \(R_e\).
169 days ago: adapted knot spacing for spline.
155 days ago:using separate knot spacing for spline fits of deaths and cases.
153 days ago: MAJOR UPDATE. Moved things around. Added per capita severity map.
125 days ago: improved national trends with per capita analysis.
124 days ago: added county level per capita daily cases map. testing new color scheme.
97 days ago: changed to daily mortaility tracking from ratio of overall totals.
90 days ago: added trend line to state charts.
62 days ago: decreased max value of Daily Cases per 100k State map.
55 days ago: increased max total state cases to 2,000,000 as California passes 1.5Million diagnosed cases.
32 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.
31 days ago: increased max total state cases to 3.0M as California passes 2.5Million diagnosed cases.
22 days ago: moved some graphs around.
10 days ago: changed scales of graphs. Total Deaths to 4,000,000 to accomdate California. Also, modified data analysis to not store stuf like lat lon and populations for county level data to reduce data storage requirements.

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.