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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