1. Caveats and Comments
1
Overview:
This is my analysis, not Stanford’s. My plots and regressions are intended to understand the trajectory of COVID. It is not confidential and can be freely shared.
The R program code and PowerPoint files are available at https://github.com/StevenLShafer/COVID19/. Please contact me at steven.shafer@Stanford.edu if you
would like to be added or removed from the recipient list. Suggestions are most welcome! You are welcome to use the R code on GitHub for any purpose.
I am attempting to keep the analysis and commentary apolitical. I am now including partisan lean as a metric to help understand the epidemic. I occasionally point
out misrepresentations by government officials. I occasionally point out where government recommendations have placed Americans at increasing risk.
I try to provide a daily update in the morning, except Sundays. My analysis my be delayed by my clinical responsibilities as a Stanford anesthesiologist.
There is a lot of information on the figures. If something isn’t clear, please see the explanation on slide 2.
Data sources:
• USA Case Data: https://github.com/CSSEGISandData/COVID-19/raw/master/csse_covid_19_data/csse_covid_19_time_series/time_series_covid19_confirmed_US.csv
• USA Death Data: https://github.com/CSSEGISandData/COVID-19/raw/master/csse_covid_19_data/csse_covid_19_time_series/time_series_covid19_deaths_US.csv
• USA Testing and Hospitalization Data: https://raw.githubusercontent.com/COVID19Tracking/covid-tracking-data/master/data/states_daily_4pm_et.csv
• Global Case Data: https://github.com/CSSEGISandData/COVID-19/raw/master/csse_covid_19_data/csse_covid_19_time_series/time_series_covid19_confirmed_global.csv
• Global Death Data: https://github.com/CSSEGISandData/COVID-19/raw/master/csse_covid_19_data/csse_covid_19_time_series/time_series_covid19_deaths_global.csv
• Global Testing Data: https://raw.githubusercontent.com/owid/covid-19-data/master/public/data/owid-covid-data.csv
• Mobility Data: https://www.gstatic.com/covid19/mobility/Global_Mobility_Report.csv
• Partisan Lean: MIT Election Data and Science Lab: https://doi.org/10.7910/DVN/VOQCHQ/HEIJCQ
• Ensemble Model: https://github.com/reichlab/covid19-forecast-hub/raw/master/data-processed/COVIDhub-ensemble/2020-xx-xx-COVIDhub-ensemble.csv
Models:
1. Future projections of case numbers are based on the Gompertz function (https://en.wikipedia.org/wiki/Gompertz_function): log 𝑐𝑢𝑚𝑢𝑙𝑎𝑡𝑖𝑣𝑒 𝑐𝑎𝑠𝑒𝑠 =
𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝑐𝑎𝑠𝑒𝑠 + 𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑐𝑎𝑠𝑒𝑠 − 𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝑐𝑎𝑠𝑒𝑠 1 − 𝑒−𝑘 𝑡 . This is a naïve asymptotic model. k is the rate constant, such that log(2) / k = time to 50%
rise. t is the number of days. Wikipedia The Gompertz function is estimated from the last 3 weeks of data for cumulative cases (red dots in the figures).
Deaths are predicted from a log linear regression of deaths over the past 21 days. For the US, and individual states, I am also including the 98% prediction
interval from the COVID-19 Forecast Hub (https://covid19forecasthub.org/).
2. The rate of change in daily cases and deaths is the slope of delta cases / day over the last 14 days, divided by the average number of cases.
Locations
The locations for the modeling are where Pamela and I have family and friends, locations of interest to friends and colleagues, or countries in the news (e.g.,
China, South Korea, Sweden, Brazil) or with significant economic impact on the United States (e.g., Japan, Canada, Mexico). Locations are easy to add.
Stay safe, well, resilient, and kind.
Steve Shafer
steven.shafer@Stanford.edu
2. 2,586,092
152,804
1
10
100
1,000
10,000
100,000
1,000,000
10,000,000
100,000,000
Actual(points)/Predicted(line)
Phase
Pre-Model
Modeled
Deaths
Tests
USA projection as of 2020-05-27
0
10,000
20,000
30,000
0
2,000
4,000
6,000
Cases/Day
Deaths/Day
Cases: 1,662,302 (32,123) -- Deaths: 98,220 (829) -- Case Mortality: 5.9% -- Daily Change in Cases: -0.5%
Explanation of the Figures
2
Brown dots:
cumulative tests
Red dots: cumulative cases
used to estimate Gompertz
function, presently set to last
3 weeks
Red line: predicted cumulative
cases based on the Gompertz
function estimated from the red
dots
Red number: total cases
on June 30th, based on
the Gompertz function
estimated from the red
dots
Black number: total
Deaths on July 31th,
based on log-linear
regression of the past
21 days
Black line: predicted
cumulative deaths, based
on a log linear regression
of deaths over past 21
days.
Axis for deaths / day, usually
1/10th of the axis for cases /
day on the left side of the
figure.
Green line: linear regression
over 8 days, used to calculate
percent increase / decrease
(see below)
Daily change in cases,
calculated as the slope of the
green line (above left) /
number of new cases
yesterday.
Case mortality:
cumulative deaths
/ cumulative cases.
Cases / day calculated
from cumulative cases
used to estimate the
Gompertz function
Cases / day calculated
from cumulative cases
not used to estimate the
Gompertz function
Deaths / day,
axis is on the left
Blue line: today
Blue dots: cumulative cases not
used to estimate Gompertz
function
Cumulative cases
(yesterday’s cases)
and cumulative deaths
(yesterday’s deaths)
Axis for cases / day.
Axis for deaths / day
appears to the right.
Geographic
location
Date of analysis,
also shown as
blue vertical line
below
Purple wedge: 98% ensemble
prediction interval from COVID-19
Forecast Hub (USA and US
States only)
9. Average new cases over past 7 days
PER
COL
BRA
ISR
USA
ARG
ZAF
BOL
CHL
DOM
IRQ
KGZ
ESP
HND
KAZ
ECU
SLV
BEL
ROU
GTM
SRB
MEX
IND
SAU
PHL
IRN
RUS
LBY
NLD
VEN
MAR
UKR
BGR
UZB
SWE
PRY
AZE
GHA
AUS
FRA
CZE
CHE
ZMB
POL
PRT
DNK
KEN
DZA
GBR
TUR
BGD
NPL
AUT
GRC
BLR
MDG
JPN
CAN
ZWE
DEU
SEN
IDN
GIN
ETH
SVK
USA
None
1 in 20,000
1 in 10,000
1 in 6,667
1 in 5,000
1 in 4,000
1 in 3,333
1 in 2,857
1 6 11 16 21 26 31 36 41 46 51 56 61 66
Rank
Averagecases/day
Average new cases over past 7 days
Excludes countries with population < 5,000,000
2020-08-10 Summary: 9
12. Average daily deaths over past 7 days
PER
BOL
COL
ZAF
MEX
BRA
CHL
ARG
USA
IRN
GTM
IRQ
KAZ
HND
ROU
DOM
KGZ
ECU
SLV
SRB
ISR
SAU
BGR
GBR
RUS
LBY
IND
ZMB
AUS
AZE
UKR
MAR
PRY
ZWE
BEL
BLR
PHL
DZA
POL
SWE
IDN
EGY
VEN
HTI
MDG
PRT
MWI
TUR
BGD
UZB
SEN
AGO
ETH
KEN
ESP
GHA
CAN
NIC
SDN
AFG
ITA
FRA
YEM
PAK
CZE
USA
None
1 in 500,000
1 in 250,000
1 in 166,667
1 in 125,000
1 in 100,000
1 6 11 16 21 26 31 36 41 46 51 56 61 66
Rank
Averagedeaths/day
Average daily deaths over past 7 days
Excludes countries with population < 5,000,000
2020-08-10 Summary: 12
13. Case Mortality vs. Testing
LUX
AREBHR
MLT
DNK
ISL
RUS
ISR
LTU
AUS
USA
QAT
PRT
BEL
MDV
GBR
BLR
IRL
KWT
CAN
KAZ
LVA
SGP
SRB
SAU
AUT
NZL
DEU
ESP
CHE
CHLESTNOR
FINROU
ITA
CZE
SVN
NLD
GRC
TUR
POL
ZAF
PAN
SVK
BGR
SLVURY
HUN
COL
MARMYS
IRN
KOR
HRV
UKR
CUB
RWA
PRY
IND
CRI
ARGPHL
NPL
BOL
GHA
BRA
ECU
PER
JPN
PAK
TUN
FJI
MEX
BGD
SEN
UGA
KEN
TGO
THAZWE
CIV
IDN
TWN
ETH
VNM
MMR
NGA
USA
0
5
10
15
0 20 40 60
% Tested
%CaseMortality
Case Mortality vs. Testing as of 2020-08-10
ARE: United Arab Emirates, BHR:Bahrain, MLT: Malta, ISR: Israel, LTU: Lithuania, ISL: Iceland
2020-08-10 Summary: 13
15. Change in New Cases per Day
New cases are:
Increasing > +3%
Increasing between +1% and +3%
No Change (-1% to +1%)
Decreasing between -1% and -3%
Decreasing > -3%
New cases by state as of 2020-08-10
2020-08-10 Summary: 15
16. Cases as a Percent of Peak Cases
HI TX FL
OK LA MS AL GA
AZ NM KS AR TN NC SC DC
CA UT CO NE MO KY WV VA MD DE
OR NV WY SD IA IN OH PA NJ CT RI
WA ID MT ND MN IL MI NY MA
WI VT NH
AK ME
0
25
50
75
100
0
25
50
75
100
0
25
50
75
100
0
25
50
75
100
0
25
50
75
100
0
25
50
75
100
0
25
50
75
100
0
25
50
75
100
PercentofPeak
Daily Cases as a Percent of Peak Cases
2020-08-10 Summary: 16
17. Change in New Deaths per Day
New deaths are:
Increasing > +0.5%
Increasing between +0.1% and +0.5%
No Change (-0.1% to +0.1%)
Decreasing between -0.1% and -0.5%
Decreasing > -0.5%
New deaths by state as of 2020-08-10
2020-08-10 Summary: 17
18. Deaths as a Percent of Peak Deaths
HI TX FL
OK LA MS AL GA
AZ NM KS AR TN NC SC DC
CA UT CO NE MO KY WV VA MD DE
OR NV WY SD IA IN OH PA NJ CT RI
WA ID MT ND MN IL MI NY MA
WI VT NH
AK ME
0
25
50
75
100
0
25
50
75
100
0
25
50
75
100
0
25
50
75
100
0
25
50
75
100
0
25
50
75
100
0
25
50
75
100
0
25
50
75
100
PercentofPeak
Daily Deaths as a Percent of Peak Deaths
2020-08-10 Summary: 18
19. Change in cases vs change in deaths
AL
AK
AZ
AR
CA
COCT DE
DC
FL
GA
HI
ID
IL
IN
IA
KS
KY
LA
ME
MD
MA
MI
MN
MS
MO
MT
NE
NV
NHNJ
NM
NY
NC
ND
OH
OK
OR
PA
RI
SC
SD
TN
TX
UT
VT
VA
WA
WV
WI
WY
-6
-3
0
3
6
-10 -5 0 5
Change in cases (%/day)
Changeindeaths(%/day)
Change in cases vs change in deaths over last 14 days 2020-08-10
2020-08-10 Summary: 19
20. Total US COVID-19 Cases
CA
FL
TX
NY
GA
IL
AZ
NJ
NC
LA
PA
TN
MA
AL
OH
SC
VA
MI
MD
IN
MS
WA
MN
WI
MO
NV
CO
CT
AR
IA
UT
OK
KY
KS
NE
ID
NM
OR
RI
DE
DC
SD
WV
ND
NH
MT
ME
AK
HI
WY
VT
0
200,000
400,000
600,000
1 6 11 16 21 26 31 36 41 46 51
Rank
Totalcases
Masks
No
Yes
Governor
aa
Democratic
Republican
Total US COVID-19 Cases
p masks: 0.35, p governor: 0.67. NB: association != causation.
2020-08-10 Summary: 20
21. Total US COVID-19 Cases
LA
AZ
FL
MS
NY
NJ
AL
GA
SC
RI
NV
DC
TN
MA
TX
AR
DE
MD
IA
IL
NE
CA
CT
ID
UT
NC
VA
IN
OK
SD
MN
NM
KS
WI
ND
MI
MO
PA
CO
OH
WA
KY
WY
AK
OR
NH
MT
WV
ME
HI
VT
None
1 in 200
1 in 100
1 in 67
1 in 50
1 in 40
1 in 33
1 6 11 16 21 26 31 36 41 46 51
Rank
TotalCases
Masks
No
Yes
Governor
aa
Democratic
Republican
Total US COVID-19 Cases
p masks: 0.84, p governor: 0.26. NB: association != causation.
2020-08-10 Summary: 21
22. Average US COVID-19 cases over the past
7 days
LA
GA
FL
MS
AL
NV
TN
AR
TX
ID
SC
OK
AZ
CA
ND
MO
NC
IA
WI
VA
IL
IN
UT
NE
KS
MD
MN
KY
HI
SD
MT
AK
DC
OH
WA
NM
DE
RI
CO
OR
MI
WV
WY
PA
MA
NJ
NY
NH
CT
ME
VT
None
1 in 10,000
1 in 5,000
1 in 3,333
1 in 2,500
1 6 11 16 21 26 31 36 41 46 51
Rank
NewCases/Day
Masks
No
Yes
Governor
aa
Democratic
Republican
Average US COVID-19 cases over the past 7 days
p masks: 0.039, p governor: 0.013. NB: association != causation.
2020-08-10 Summary: 22
23. Total US COVID-19 Deaths
NY
NJ
CA
TX
MA
FL
IL
PA
MI
CT
LA
GA
AZ
OH
MD
IN
VA
NC
SC
MS
CO
AL
MN
WA
MO
TN
RI
WI
NV
IA
KY
NM
OK
DE
DC
AR
NH
KS
OR
NE
UT
ID
SD
WV
ME
ND
MT
VT
HI
WY
AK
0
10,000
20,000
30,000
1 6 11 16 21 26 31 36 41 46 51
Rank
TotalDeaths
Masks
No
Yes
Governor
aa
Democratic
Republican
Total US COVID-19 Deaths
p masks: 0.052, p governor: 0.17. NB: association != causation.
2020-08-10 Summary: 23
24. Total US COVID-19 Deaths
NJ
NY
MA
CT
RI
LA
DC
MI
MS
IL
DE
MD
PA
AZ
IN
GA
SC
FL
AL
NM
CO
TX
OH
NV
NH
MN
IA
VA
CA
WA
MO
NC
AR
TN
NE
KY
WI
SD
OK
ND
ID
KS
UT
ME
VT
OR
WV
MT
WY
AK
HI
None
1 in 2,000
1 in 1,000
1 in 667
1 in 500
1 6 11 16 21 26 31 36 41 46 51
Rank
TotalDeaths
Masks
No
Yes
Governor
aa
Democratic
Republican
Total US COVID-19 Deaths
p masks: 0.028, p governor: 0.18. NB: association != causation.
2020-08-10 Summary: 24
25. Average US COVID-19 deaths over the past
7 days
MS
LA
AZ
TX
SC
FL
NV
GA
AL
AR
CA
TN
ID
NC
IA
NM
MA
OK
SD
OH
MT
MD
VA
WV
WA
ND
IL
IN
MO
MN
WI
DC
UT
KS
KY
OR
PA
NE
MI
RI
DE
NJ
NY
HI
WY
AK
CT
CO
NH
VT
ME
None
1 in 500,000
1 in 250,000
1 in 166,667
1 in 125,000
1 6 11 16 21 26 31 36 41 46 51
Rank
Deaths/Day
Masks
No
Yes
Governor
aa
Democratic
Republican
Average US COVID-19 deaths over the past 7 days
p masks: 0.47, p governor: 0.023. NB: association != causation.
2020-08-10 Summary: 25
27. Percent of Positive COVID Tests
AZ
MS
FL
AL
SC
TX
ID
GA
NV
KS
NE
IA
MD
MA
RI
IN
PA
AR
CO
LA
VA
NJ
SD
DE
UT
MO
TN
NC
MN
NY
IL
CA
OK
WA
WI
OH
DC
CT
KY
WY
OR
MI
ND
NH
NM
MT
WV
HI
ME
AK
VT
0.0
5.0
10.0
15.0
20.0
1 6 11 16 21 26 31 36 41 46 51
Rank
PercentofPositiveTests
Masks
No
Yes
Governor
aa
Democratic
Republican
Percent of Positive COVID Tests
p masks: 0.25, p governor: 0.022. NB: association != causation.
2020-08-10 Summary: 27
28. Positive fraction trends
HI TX FL
OK LA MS AL GA
AZ NM KS AR TN NC SC DC
CA UT CO NE MO KY WV VA MD DE
OR NV WY SD IA IN OH PA NJ CT RI
WA ID MT ND MN IL MI NY MA
WI VT NH
AK ME
min
max
min
max
min
max
min
max
min
max
min
max
min
max
min
max
Fractionpositivefrommintomax
Positive fraction trends from min to max
2020-08-10 Summary: 28
29. Change in positive tests over past 14 days
HI
MN
MT
MO
ND
NV
OK
MS
ID
AR
WA
AL
OR
TX
KY
FL
WY
TN
WV
AK
KS
UT
SC
GA
IA
WI
SD
IN
NE
CA
VA
AZ
NC
LA
NM
OH
CO
RI
DE
NH
PA
IL
MD
VT
MI
MA
NJ
NY
ME
CT
DC
0.0
2.0
4.0
1 6 11 16 21 26 31 36 41 46 51
Rank
Changeinpositivetests(%/day)
Masks
No
Yes
Governor
aa
Democratic
Republican
Change in positive tests over past 14 days
p masks: 0.029, p governor: 0.042. NB: association != causation.
2020-08-10 Summary: 29
30. Current hospitalizations as a percent of peak
since FebruaryAL
AR
HI
KS
KY
MO
MT
ND
WV
WY
TN
MS
ID
OK
AK
NC
GA
UT
NV
OH
SC
VA
CA
NE
FL
OR
TX
WA
LA
NM
IN
IA
MN
SD
WI
AZ
CO
MD
IL
RI
PA
DC
MI
ME
NH
VT
DE
MA
NJ
CT
NY
0
30
60
90
1 6 11 16 21 26 31 36 41 46 51
Rank
Hospitalizations(%ofpeak)
Masks
No
Yes
Governor
aa
Democratic
Republican
Current hospitalizations as a percent of peak since February
p masks: 0.098, p governor: 0.044. NB: association != causation.
2020-08-10 Summary: 30
31. Hospitalizations trends
HI TX FL
OK LA MS AL GA
AZ NM KS AR TN NC SC DC
CA UT CO NE MO KY WV VA MD DE
OR NV WY SD IA IN OH PA NJ CT RI
WA ID MT ND MN IL MI NY MA
WI VT NH
AK ME
min
max
min
max
min
max
min
max
min
max
min
max
min
max
min
max
Hospitalizationsfrommintomax
Hospitalizations trends from min to max
2020-08-10 Summary: 31
32. Change in hospitalizations over past 14
days
HI
MT
KS
WV
NE
WI
RI
ND
KY
IN
MN
WY
SD
VA
IL
WA
AR
MO
AL
MA
MI
IA
TN
ID
NM
MS
MD
AK
DC
OK
NH
NC
GA
CT
UT
OR
CO
NV
LA
PA
OH
SC
NY
CA
ME
FL
TX
NJ
AZ
DE
VT
-4.0
0.0
4.0
1 6 11 16 21 26 31 36 41 46 51
Rank
Changeinhospitalizations(%/day)
Masks
No
Yes
Governor
aa
Democratic
Republican
Change in hospitalizations over past 14 days
p masks: 0.57, p governor: 0.86. NB: association != causation.
2020-08-10 Summary: 32
33. Case Mortality vs. Testing
AL
AK
AZ
AR
CA
CO
CT
DE
DC
FL
GA
HI ID
ILIN
IA
KS
KY
LA
ME
MD
MA
MI
MNMS
MO
MT
NE
NV
NH
NJ
NM
NY
NC
ND
OH
OK
OR
PA
RI
SC
SD
TN
TX
UT
VT
VA
WA
WV
WI
WY
2.5
5.0
7.5
10 20 30
% Tested
%Mortality
Mortality vs. Testing as of 2020-08-10
2020-08-10 Summary: 33