1. Caveats and Comments
1
Overview:
This is my analysis, not Stanford’s. My goal is to understand the trajectory of COVID. It is not confidential and can be freely shared. The R program code is
available at https://github.com/StevenLShafer/COVID19/. The daily analysis are available at https://1drv.ms/u/s!AuOyHP_aTIy7rowrt2AjGpWm_frnEQ?e=KBcNbh.
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
ISR
BRA
ARG
ESP
USA
IRQ
BOL
CHL
HND
PRY
DOM
GTM
ECU
ZAF
FRA
IND
LBY
ROU
MEX
BEL
UKR
SAU
PHL
MAR
NLD
RUS
IRN
AUT
CHE
SLV
VEN
KGZ
CZE
NPL
SWE
GRC
PRT
BGR
POL
AZE
ETH
GBR
UZB
SRB
DNK
TUR
DEU
BGD
ZMB
ITA
BLR
KAZ
CAN
SVK
RWA
DZA
TUN
ZWE
IDN
AUS
NIC
KEN
SEN
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
2020-08-26 Summary: 9
12. Average daily deaths over past 7 days
BOL
COL
PER
ARG
BRA
MEX
ZAF
CHL
USA
ISR
IRQ
ECU
GTM
IRN
KAZ
HND
ROU
PRY
DOM
SAU
SLV
BGR
MAR
LBY
ESP
IND
RUS
UKR
AUS
BEL
BLR
SRB
PHL
SWE
IDN
ZWE
PRT
POL
NLD
DZA
TUR
BGD
VEN
NPL
KEN
ETH
CAN
FRA
UZB
CZE
AZE
NIC
ZMB
EGY
CHE
TUN
GBR
SYR
SEN
GHA
GRC
AGO
YEM
JPN
AFG
USA
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 56 61 66
Rank
Averagedeaths/day
Average daily deaths over past 7 days
Excludes countries with population < 5,000,000
2020-08-26 Summary: 12
14. 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 2020-08-26
2020-08-26 Summary: 14
15. 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
2020-08-26 Summary: 15
16. 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 2020-08-26
2020-08-26 Summary: 16
17. 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
2020-08-26 Summary: 17
18. Change in cases vs change in deaths
AL
AK
AZ
AR
CA
CO
CT
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
-3
0
3
6
-5 0 5
Change in cases (%/day)
Changeindeaths(%/day)
Change in cases vs change in deaths over last 14 days as of 2020-08-26
2020-08-26 Summary: 18
19. Total US COVID-19 Cases
CA
FL
TX
NY
GA
IL
AZ
NJ
NC
TN
LA
PA
MA
AL
OH
VA
SC
MI
MD
IN
MS
MO
WA
WI
MN
NV
IA
AR
CO
OK
CT
UT
KY
KS
NE
ID
OR
NM
RI
DE
DC
SD
ND
WV
NH
HI
MT
AK
ME
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 as of July 20, 2020: 0.42, p governor: 0.8. NB: association != causation.
2020-08-26 Summary: 19
20. Total US COVID-19 Cases
LA
FL
AZ
MS
GA
AL
NY
SC
NV
NJ
TN
TX
RI
DC
AR
MA
IA
IL
DE
MD
CA
ID
NE
UT
NC
CT
OK
VA
ND
KS
IN
SD
MO
MN
WI
NM
MI
PA
KY
OH
CO
WA
AK
WY
MT
OR
NH
WV
HI
ME
VT
None
1 in 200
1 in 100
1 in 67
1 in 50
1 in 40
1 in 33
1 in 29
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 as of July 20, 2020: 0.96, p governor: 0.15. NB: association != causation.
2020-08-26 Summary: 20
21. Average US COVID-19 cases over the past
7 days
MS
ND
GA
AL
TN
IA
TX
KS
NV
AR
ID
OK
FL
MO
CA
SD
SC
HI
IL
LA
NC
IN
KY
NE
WI
UT
MN
VA
MT
RI
AK
AZ
MD
OH
MI
DC
NM
WA
WY
OR
DE
WV
CO
PA
MA
NJ
NY
CT
ME
NH
VT
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 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 as of July 20, 2020: 0.014, p governor: 0.011. NB: association != causation.
2020-08-26 Summary: 21
22. Total US COVID-19 Deaths
NY
NJ
CA
TX
FL
MA
IL
PA
MI
GA
LA
AZ
CT
OH
MD
IN
NC
SC
VA
MS
AL
CO
WA
MN
TN
MO
NV
WI
IA
RI
KY
NM
OK
AR
DE
DC
KS
NH
OR
UT
NE
ID
WV
SD
ND
ME
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 as of July 20, 2020: 0.065, p governor: 0.22. NB: association != causation.
2020-08-26 Summary: 22
23. Total US COVID-19 Deaths
NJ
NY
MA
CT
LA
RI
DC
MS
MI
AZ
IL
DE
MD
PA
GA
FL
SC
IN
AL
TX
NV
NM
OH
IA
CO
MN
NH
CA
VA
WA
NC
MO
TN
AR
KY
NE
OK
WI
ID
SD
ND
KS
UT
WV
OR
ME
VT
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 as of July 20, 2020: 0.032, p governor: 0.23. NB: association != causation.
2020-08-26 Summary: 23
24. Average US COVID-19 deaths over the past
7 days
MS
LA
TX
GA
NV
FL
SC
AZ
AR
TN
ID
CA
AL
IA
NC
OK
MA
KY
NM
ND
IN
RI
WV
MT
OH
VA
IL
WY
WA
MN
DE
AK
MD
NE
UT
PA
DC
OR
WI
MI
SD
MO
KS
HI
CO
NH
NJ
NY
ME
CT
VT
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
Rank
Deaths/Day
Masks
No
Yes
Governor
aa
Democratic
Republican
Average US COVID-19 deaths over the past 7 days
p masks as of July 20, 2020: 0.53, p governor: 0.018. NB: association != causation.
2020-08-26 Summary: 24
25. Daily testing 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
Dailytestingfrommintomax
Daily testing trends from min to max
Line = Friedman's supersmoother
2020-08-26 Summary: 25
26. Change in daily tests over past 14 days
MA
HI
MT
NC
WV
ME
NJ
MI
CT
OK
IL
AR
TN
IN
KS
NY
WY
VT
MD
KY
ND
GA
RI
IA
DC
SD
OH
MN
NM
VA
NH
CA
AK
LA
WI
ID
TX
PA
DE
AZ
OR
SC
MO
NV
MS
UT
FL
WA
AL
NE
CO
-4.0
-2.0
0.0
1 6 11 16 21 26 31 36 41 46 51
Rank
Changeindailytests(%/day)
Masks
No
Yes
Governor
aa
Democratic
Republican
Change in daily tests over past 14 days
p masks as of July 20, 2020: 0.11, p governor: 0.34. NB: association != causation.
2020-08-26 Summary: 26
28. Percent of Positive COVID Tests
AZ
MS
FL
AL
SC
ID
TX
GA
NV
KS
IA
NE
IN
CO
AR
MD
SD
MO
RI
PA
LA
UT
MA
VA
DE
NC
NJ
TN
WA
MN
OK
WI
CA
IL
KY
OH
NY
ND
WY
DC
OR
CT
MI
HI
NH
NM
MT
WV
ME
AK
VT
0.0
5.0
10.0
15.0
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 as of July 20, 2020: 0.09, p governor: 0.0093. NB: association != causation.
2020-08-26 Summary: 28
29. 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
2020-08-26 Summary: 29
30. Change in positive tests over past 14 days
HI
ND
WA
MT
MS
KY
MO
SD
AK
NV
OK
WI
ID
IA
KS
TX
WY
UT
OR
MN
FL
NE
CA
CO
IN
GA
SC
NC
TN
WV
DE
LA
NM
VA
AL
OH
IL
PA
AR
AZ
NH
MI
RI
MD
VT
ME
NJ
NY
MA
DC
CT
-1.0
0.0
1.0
2.0
3.0
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 as of July 20, 2020: 0.01, p governor: 0.29. NB: association != causation.
2020-08-26 Summary: 30
31. Change in tests vs change in positive tests
AL
AK
AZ AR
CACO
CT
DE
DC
FL
GA
HI
ID
IL
IN
IA KS
KY
LA
ME
MD
MA
MI
MN
MS
MO
MT
NE
NV
NH
NJ
NM
NY
NC
ND
OH
OK
OR
PA
RI
SC
SD
TN
TXUT
VT
VA
WA
WV
WI
WY
-1
0
1
2
-4 -2 0
Change in tests (%/day)
Changeinpositivetests(%/day)
Change in tests vs change in positive tests last 14 days as of 2020-08-26
2020-08-26 Summary: 31
32. Current hospitalizations as a percent of peak
since FebruaryAK
HI
KS
MT
WV
WY
MO
AR
ND
OK
ID
KY
NC
MS
NE
VA
TN
OH
GA
IA
AL
NV
CA
IN
WA
SD
SC
UT
WI
MN
OR
FL
TX
LA
IL
NM
RI
MD
CO
AZ
VT
PA
DC
MI
DE
ME
NH
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 as of July 20, 2020: 0.018, p governor: 0.053. NB: association != causation.
2020-08-26 Summary: 32
33. 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
2020-08-26 Summary: 33
34. Change in hospitalizations over past 14
days
HI
WY
MT
KS
DE
AK
IA
WV
OK
SD
MO
AR
MN
RI
WI
DC
NE
IN
ID
IL
ND
MI
VA
WA
CT
NC
KY
PA
VT
NY
CA
MD
OH
MS
GA
CO
TN
MA
NV
AL
SC
FL
TX
ME
LA
OR
UT
NJ
AZ
NH
NM
-6.0
-4.0
-2.0
0.0
2.0
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 as of July 20, 2020: 0.36, p governor: 0.9. NB: association != causation.
2020-08-26 Summary: 34