Updated: 2020-12-08 06:38:51 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 - therefor it’s informative to look at County-level data


state R_e cases daily cases daily cases per 100k
Indiana 1.17 390934 7414 111.7
Minnesota 1.01 356286 5848 105.8
Utah 1.12 217878 3182 104.5
South Dakota 0.98 85092 874 102.8
Nebraska 1.02 141714 1855 97.4
Nevada 1.14 171230 2758 94.4
Wyoming 0.94 37032 515 88.5
New Mexico 0.99 110184 1838 87.9
Colorado 1.07 267181 4836 87.4
Idaho 1.08 112445 1451 86.0
Montana 1.04 68806 896 86.0
Oklahoma 1.12 218782 3329 85.0
Kansas 1.06 176362 2466 84.8
Delaware 1.26 40526 790 83.2
Ohio 1.08 484758 9476 81.4
Pennsylvania 1.25 433266 10386 81.2
North Dakota 0.88 83555 598 79.5
Wisconsin 1.03 445079 4591 79.5
Kentucky 1.07 208216 3494 78.7
Michigan 1.06 435415 7724 77.6
Illinois 1.04 799208 9780 76.3
Arizona 1.09 369092 5277 76.0
Tennessee 1.06 398183 4899 73.7
Massachusetts 1.33 250284 4940 72.3
West Virginia 1.21 56106 1308 71.5
Arkansas 1.13 170058 2117 70.8
Connecticut 1.21 132692 2499 69.8
Alabama 1.15 273062 3295 67.7
Iowa 0.95 246163 2084 66.5
Mississippi 1.14 166748 1966 65.8
California 1.33 1393773 25575 65.3
Missouri 1.09 313473 3848 63.2
New Jersey 1.16 372988 5230 58.9
South Carolina 1.37 234180 2731 55.1
New Hampshire 1.27 25217 724 53.9
Louisiana 1.07 252608 2477 53.1
North Carolina 1.22 399385 5349 52.7
New York 1.21 718981 10123 51.6
Texas 1.10 1359938 13712 49.2
Maryland 1.18 217768 2884 48.0
Rhode Island 0.64 52625 506 47.9
Florida 1.09 1064149 9701 47.1
Georgia 1.21 485625 4725 45.9
Oregon 1.11 86033 1614 39.6
Virginia 1.23 203644 2675 38.4
Washington 1.06 190077 2671 36.6
Maine 1.35 13702 314 23.6
Vermont 1.29 5122 140 22.4

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 621.4 seconds to compute.
2020-12-08 06:49:12

version history

Today is 2020-12-08.
202 days ago: plots of multiple states.
194 days ago: include \(R_e\) computation.
191 days ago: created color coding for \(R_e\) plots.
186 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.
186 days ago: “persistence” time evolution.
179 days ago: “In control” mapping.
179 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.
171 days ago: Added census API functionality to compute per capita infection rates. Reduced spline spar = 0.65.
166 days ago: Added Per Capita US Map.
164 days ago: Deprecated national map. can be found here.
160 days ago: added state “Hot 10” analysis.
155 days ago: cleaned up county analysis to show cases and actual data. Moved “Hot 10” analysis to separate web page. Moved “Hot 10” here.
153 days ago: added per capita disease and mortality to state-level analysis.
141 days ago: changed to county boundaries on national map for per capita disease.
136 days ago: corrected factor of two error in death trend data.
132 days ago: removed “contained and uncontained” analysis, replacing it with county level control map.
127 days ago: added county level “baseline control” and \(R_e\) maps.
123 days ago: fixed normalization error on total disease stats plot.
116 days ago: Corrected some text matching in generating county level plots of \(R_e\).
110 days ago: adapted knot spacing for spline.
96 days ago:using separate knot spacing for spline fits of deaths and cases.
94 days ago: MAJOR UPDATE. Moved things around. Added per capita severity map.
66 days ago: improved national trends with per capita analysis.
65 days ago: added county level per capita daily cases map. testing new color scheme.
38 days ago: changed to daily mortaility tracking from ratio of overall totals.
31 days ago: added trend line to state charts.
3 days ago: decreased max value of Daily Cases per 100k State map.

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.