Estimating and Simulating a [-3pt] SIRD Model of COVID-19 ... chadj/Covid/PER- آ 

  • View
    0

  • Download
    0

Embed Size (px)

Text of Estimating and Simulating a [-3pt] SIRD Model of COVID-19 ... chadj/Covid/PER- آ 

  • Estimating and Simulating a

    SIRD Model of COVID-19 for

    Many Countries, States, and Cities

    Jesús Fernández-Villaverde and Chad Jones

    Extended results for Peru

    Based on data through May 8, 2020

    0 / 26

  • 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

    1 / 26

  • Underlying data from

    Johns Hopkins CSSE

    – Raw data

    – Smoothed = 5 day centered moving average

    – Later slides inflate deaths by 33% for “excess

    deaths”

    2 / 26

  • 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

    3.5 D

    ai ly

    d ea

    th s

    p er

    m il

    li o n p

    eo p le

    Peru

    3 / 26

  • 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

    3 D

    ai ly

    d ea

    th s

    p er

    m il

    li o n p

    eo p le

    ( sm

    o o th

    ed )

    Peru

    4 / 26

  • 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

    5 / 26

    https://web.stanford.edu/~chadj/sird-paper.pdf

  • 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%)

    6 / 26

    https://web.stanford.edu/~chadj/sird-paper.pdf

  • 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

    7 / 26

  • Peru (7 days): Daily Deaths per Million People

    Apr May Jun Jul

    2020

    0

    10

    20

    30

    40

    50

    60

    70

    80

    D ai

    ly d

    ea th

    s p er

    m il

    li o n p

    eo p le

    Peru

    R 0 =1.5/1.2/0.5 = 0.008 =0.01 =0.1 %Infect= 2/ 6/ 9

    DATA THROUGH 08-MAY-2020

    8 / 26

  • Peru (7 days): Cumulative Deaths per Million (Future)

    Mar Apr May Jun Jul

    2020

    0

    200

    400

    600

    800

    1000

    1200

    1400

    1600

    C u

    m u

    la ti

    v e

    d ea

    th s

    p er

    m il

    li o

    n p

    eo p

    le Peru

    R 0 =1.5/1.2/0.5 = 0.008 =0.01 =0.1 %Infect= 2/ 6/ 9

    DATA THROUGH 08-MAY-2020

    9 / 26

  • 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

    C u

    m u

    la ti

    v e

    d ea

    th s

    p er

    m il

    li o

    n p

    eo p

    le Peru

    R 0 =1.5/1.2/0.5 = 0.008 =0.01 =0.1 %Infect= 2/ 6/ 9

    New York City

    Italy

    10 / 26

  • Robustness to Mortality Rate, δ

    11 / 26

  • 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

    C u m

    u la

    ti v e

    d ea

    th s

    p er

    m il

    li o n p

    eo p le Peru

    R 0 =1.5/1.2/0.5 = 0.008, =0.01, =0.1, %Infect= 2/ 6/ 9

    DATA THROUGH 08-MAY-2020

    12 / 26

  • Peru: Daily Deaths per Million People (δ = .008/.003/.01)

    Apr May Jun Jul

    2020

    0

    2

    4

    6

    8

    10

    12

    14

    D ai

    ly d

    ea th

    s p er

    m il

    li o n p

    eo p le

    Peru

    R 0 =1.5/1.2/0.5 = 0.008, =0.01, =0.1, %Infect= 2/ 6/ 9

    DATA THROUGH 08-MAY-2020

    13 / 26

  • Peru: Cumulative Deaths per Million (δ = .008/.003/.01)

    Mar Apr May Jun Jul

    2020

    0

    100

    200

    300

    400

    500

    600

    C u m

    u la

    ti v e

    d ea

    th s

    p er

    m il

    li o n p

    eo p le

    Peru

    R 0 =1.5/1.2/0.5 = 0.008, =0.01, =0.1, %Infect= 2/ 6/ 9

    = 0.008

    = 0.003

    = 0.01 DATA THROUGH 08-MAY-2020

    14 / 26

  • 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

    15 / 26

  • 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

    18 / 26

  • 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

    D ai

    ly d

    ea th

    s p er

    m il

    li o n p

    eo p le

    Peru

    R 0 =1.5/1.2/0.5 = 0.003 =0.01 =0.1 %Infect= 5/14/19

    19 / 26

  • 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

    C u m

    u la

    ti v e

    d ea

    th s

    p er

    m il

    li o n p

    eo p le

    Peru

    R 0 =1.5/1.2/0.5 = 0.003 =0.01 =0.1 %Infect= 5/14/19

    20 / 26

  • Peru: Daily Deaths per Million People (δ = 1.0%)

    Apr May Jun Jul

    2020

    0

    2

    4

    6

    8

    10

    12

    14

    D ai

    ly d

    ea th

    s p er

    m il

    li o n p

    eo p le

    Peru

    R 0 =1.5/1.2/0.5 = 0.010 =0.01 =0.1 %Infect= 1/ 5/ 7

    21 / 26

  • Peru: Cumulative Deaths per Million (δ = 1.0%)

    Mar Apr May Jun Jul

    2020

    0

    100

    200

    300

    400

    500

    600

    C u m

    u la

    ti v e

    d ea

    th s

    p er

    m il

    li o n p

    eo p le

    Peru

    R 0 =1.5/1.2/0.5 = 0.010 =0.01 =0.1 %Infect= 1/ 5/ 7

    22 / 26

  • Peru: Daily Deaths per Million People (γ = .2/.1)

    Apr May Jun Jul

    2020

    0

    2

    4

    6

    8

    10

    12

    14

    16

    D ai

    ly d

    ea th

    s p er

    m il

    li o n p

    eo p le

    Peru

    R 0 =1.5/1.2/0.5 = 0.008, =0.01, =0.1, %Infect= 2/ 6/ 9

    DATA THROUGH 08-MAY-2020

    23 / 26

  • Peru: Cumulative Deaths per Million γ = .2/.1)

    Mar Apr May Jun Jul

    2020

    0

    100

    200

    300

    400

    500

    600

    C u m

    u la

    ti v e

    d ea

    th s

    p er

    m il

    li o n p

    eo p le

    Peru

    R 0 =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

    24 / 26

  • Peru: Daily Deaths per Million People (θ = .1/.05/.2