Estimating and Simulating a
SIRD Model of COVID-19 for
Many Countries, States, and Cities
Jesus Fernandez-Villaverde and Chad Jones
Extended results for Peru
Based on data through May 8, 2020
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Outline of Slides
• Basic data from Johns Hopkins CSSE (raw and smoothed)
• Brief summary of the model
• Baseline results (δ = 0.8%, γ = 0.2, θ = 0.1)
• Simulation of re-opening – possibilities for raising R0
◦ Baseline
◦ Alternative for δ = 0.3%
• Results with alternative parameter values:
◦ Lower mortality rate, δ = 0.3%
◦ Higher mortality rate, δ = 1.0%
◦ Infections last longer, γ = 0.1
◦ Cases resolve more quickly, θ = 0.2
◦ Cases resolve more slowly, θ = 0.05
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Underlying data from
Johns Hopkins CSSE
– Raw data
– Smoothed = 5 day centered moving average
– Later slides inflate deaths by 33% for “excess
deaths”
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Peru: Daily Deaths per Million People
03/20 03/27 04/03 04/10 04/17 04/24 05/01 05/08
2020
0
0.5
1
1.5
2
2.5
3
3.5D
aily
dea
ths
per
mil
lion p
eople
Peru
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Peru: Daily Deaths per Million People (Smoothed)
03/18 03/25 04/01 04/08 04/15 04/22 04/29 05/06
2020
0
0.5
1
1.5
2
2.5
3D
aily
dea
ths
per
mil
lion p
eople
(sm
ooth
ed)
Peru
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Brief Summary of Model
• See the paper for a full exposition
• A 5-state SIRDC model with a time-varying R0
Parameter Baseline Description
δ 0.8% Mortality rate from infections (IFR)
γ 0.2 Rate at which people stop being infectious
θ 0.1 Rate at which cases (post-infection) resolve
R0 ... Initial reproduction rate
R∗
0... Final reproduction rate
λ ... Speed at which R0 converges to R∗
0
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Guide to Graphs
• Warning: Results are often very uncertain; this can be seen by
comparing across multiple graphs. See the original paper.
• 7 days of forecasts: Rainbow color order!
ROY-G-BIV (old to new, low to high)
◦ Black=current
◦ Red = oldest, Orange = second oldest, Yellow =third oldest...
◦ Violet (purple) = one day earlier
• For robustness graphs, same idea
◦ Black = baseline (e.g. δ = 0.8%)
◦ Red = lowest parameter value (e.g. δ = 0.3%)
◦ Green = highest parameter value (e.g. δ = 1.0%)
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Repeated “Forecasts” from the
past 7 days of data
– After peak, forecasts settle down.
– Before that, very noisy!
– If the region has not peaked, do not trust
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Peru (7 days): Daily Deaths per Million People
Apr May Jun Jul
2020
0
10
20
30
40
50
60
70
80
Dai
ly d
eath
s per
mil
lion p
eople
Peru
R0=1.5/1.2/0.5 = 0.008 =0.01 =0.1 %Infect= 2/ 6/ 9
DATA THROUGH 08-MAY-2020
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Peru (7 days): Cumulative Deaths per Million (Future)
Mar Apr May Jun Jul
2020
0
200
400
600
800
1000
1200
1400
1600
Cu
mu
lati
ve
dea
ths
per
mil
lio
n p
eop
lePeru
R0=1.5/1.2/0.5 = 0.008 =0.01 =0.1 %Infect= 2/ 6/ 9
DATA THROUGH 08-MAY-2020
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Peru (7 days): Cumulative Deaths per Million, Log Scale
Mar Apr May Jun Jul
2020
1
2
4
8
16
32
64
128
256
512
1024
2048
4096
Cu
mu
lati
ve
dea
ths
per
mil
lio
n p
eop
lePeru
R0=1.5/1.2/0.5 = 0.008 =0.01 =0.1 %Infect= 2/ 6/ 9
New York City
Italy
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Robustness to Mortality Rate, δ
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Peru: Cumulative Deaths per Million (δ = .008/.003/.01)
Mar 22 Mar 29 Apr 05 Apr 12 Apr 19 Apr 26 May 03 May 10
2020
0
10
20
30
40
50
60
70
80
Cum
ula
tive
dea
ths
per
mil
lion p
eoplePeru
R0=1.5/1.2/0.5 = 0.008, =0.01, =0.1, %Infect= 2/ 6/ 9
DATA THROUGH 08-MAY-2020
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Peru: Daily Deaths per Million People (δ = .008/.003/.01)
Apr May Jun Jul
2020
0
2
4
6
8
10
12
14
Dai
ly d
eath
s per
mil
lion p
eople
Peru
R0=1.5/1.2/0.5 = 0.008, =0.01, =0.1, %Infect= 2/ 6/ 9
DATA THROUGH 08-MAY-2020
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Peru: Cumulative Deaths per Million (δ = .008/.003/.01)
Mar Apr May Jun Jul
2020
0
100
200
300
400
500
600
Cum
ula
tive
dea
ths
per
mil
lion p
eople
Peru
R0=1.5/1.2/0.5 = 0.008, =0.01, =0.1, %Infect= 2/ 6/ 9
= 0.008
= 0.003
= 0.01DATA THROUGH 08-MAY-2020
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Reopening and Herd Immunity
– Black: assumes R0(today) remains in place forever
– Red: assumes R0(suppress)= 1/s(today)
– Green: we move 25% of the way from R0(today)
back to initial R0 = “normal”
– Purple: we move 50% of the way from R0(today)
back to initial R0 = “normal”
NOTE: Lines often cover each other up
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Peru: Re-Opening (δ = 0.8%)
(Light bars = New York City, for comparison) 16 / 26
Peru: Re-Opening (δ = 0.3%)
(Light bars = New York City, for comparison) 17 / 26
Results for alternative
parameter values
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Peru: Daily Deaths per Million People (δ = 0.3%)
Apr May Jun Jul
2020
0
1
2
3
4
5
6
7
8
9
10
Dai
ly d
eath
s per
mil
lion p
eople
Peru
R0=1.5/1.2/0.5 = 0.003 =0.01 =0.1 %Infect= 5/14/19
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Peru: Cumulative Deaths per Million (δ = 0.3%)
Mar Apr May Jun Jul
2020
0
50
100
150
200
250
300
350
400
450
500
Cum
ula
tive
dea
ths
per
mil
lion p
eople
Peru
R0=1.5/1.2/0.5 = 0.003 =0.01 =0.1 %Infect= 5/14/19
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Peru: Daily Deaths per Million People (δ = 1.0%)
Apr May Jun Jul
2020
0
2
4
6
8
10
12
14
Dai
ly d
eath
s per
mil
lion p
eople
Peru
R0=1.5/1.2/0.5 = 0.010 =0.01 =0.1 %Infect= 1/ 5/ 7
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Peru: Cumulative Deaths per Million (δ = 1.0%)
Mar Apr May Jun Jul
2020
0
100
200
300
400
500
600
Cum
ula
tive
dea
ths
per
mil
lion p
eople
Peru
R0=1.5/1.2/0.5 = 0.010 =0.01 =0.1 %Infect= 1/ 5/ 7
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Peru: Daily Deaths per Million People (γ = .2/.1)
Apr May Jun Jul
2020
0
2
4
6
8
10
12
14
16
Dai
ly d
eath
s per
mil
lion p
eople
Peru
R0=1.5/1.2/0.5 = 0.008, =0.01, =0.1, %Infect= 2/ 6/ 9
DATA THROUGH 08-MAY-2020
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Peru: Cumulative Deaths per Million γ = .2/.1)
Mar Apr May Jun Jul
2020
0
100
200
300
400
500
600
Cum
ula
tive
dea
ths
per
mil
lion p
eople
Peru
R0=1.5/1.2/0.5 = 0.008, =0.01, =0.1, %Infect= 2/ 6/ 9
= 0.2
= 0.1
DATA THROUGH 08-MAY-2020
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Peru: Daily Deaths per Million People (θ = .1/.05/.2)
Apr May Jun Jul
2020
0
2
4
6
8
10
12
14
Dai
ly d
eath
s per
mil
lion p
eople
Peru
R0=1.5/1.2/0.5 = 0.008, =0.01, =0.1, %Infect= 2/ 6/ 9
DATA THROUGH 08-MAY-2020
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Peru: Cumulative Deaths per Million People (θ = .1/.05/.2)
Mar Apr May Jun Jul
2020
0
100
200
300
400
500
600
Cum
ula
tive
dea
ths
per
mil
lion p
eople
Peru
R0=1.5/1.2/0.5 = 0.008, =0.01, =0.1, %Infect= 2/ 6/ 9
= 0.1 = 0.05
= 0.2
DATA THROUGH 08-MAY-2020
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