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

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  • Estimating and Simulating a

    SIRD Model of COVID-19 for

    Many Countries, States, and Cities

    Jesús Fernández-Villaverde and Chad Jones

    Extended results for New Hampshire

    Based on data through May 28, 2020

    0 / 38

  • Outline of Slides

    • Basic data from Johns Hopkins CSSE (raw and smoothed)

    • Brief summary of the model

    • Baseline results (δ = 1.0%, γ = 0.2, θ = 0.1)

    • Simulation of re-opening – possibilities for raising R0

    • Results with alternative parameter values:

    ◦ Lower mortality rate, δ = 0.8%

    ◦ Higher mortality rate, δ = 1.2%

    ◦ Infections last longer, γ = 0.15

    ◦ Cases resolve more quickly, θ = 0.2

    ◦ Cases resolve more slowly, θ = 0.07

    • Data underlying estimates of R0(t)

    1 / 38

  • Underlying data from

    Johns Hopkins CSSE

    – Raw data

    – Smoothed = 5 day centered moving average

    – Later slides inflate deaths by 33% for “excess

    deaths”

    2 / 38

  • New Hampshire: Daily Deaths per Million People

    03/23 04/06 04/20 05/04 05/18

    2020

    -5

    0

    5

    10

    15

    20

    25

    30

    35

    40

    45 D

    ai ly

    d ea

    th s

    p er

    m il

    li o

    n p

    eo p

    le New Hampshire

    3 / 38

  • New Hampshire: Daily Deaths per Million People (Smoothed)

    03/21 04/04 04/18 05/02 05/16

    2020

    -1

    0

    1

    2

    3

    4

    5

    6

    7

    8

    9 D

    ai ly

    d ea

    th s

    p er

    m il

    li o

    n p

    eo p

    le (

    sm o

    o th

    ed )

    New Hampshire

    4 / 38

  • 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 1.0% 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

    α 0.05 Rate at which R0(t) decays with daily deaths

    R0 ... Initial base reproduction rate

    R0(t) ... Base reproduction rate at date t (βt/γ)

    5 / 38

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

  • Estimates of Time-Varying R0

    – Inferred from daily deaths, and

    – the change in daily deaths, and

    – the change in (the change in daily deaths)

    (see end of slide deck for this data)

    6 / 38

  • New Hampshire: Estimates of R0(t)

    Apr 21 Apr 24 Apr 27 Apr 30 May 03 May 06 May 09 May 12 May 15 May 18

    2020

    0

    0.5

    1

    1.5

    2

    2.5

    3

    3.5 R

    0 (t

    ) New Hampshire

    = 0.010 =0.10 =0.20

    7 / 38

  • New Hampshire: Percent Currently Infectious

    Apr 21 Apr 24 Apr 27 Apr 30 May 03 May 06 May 09 May 12 May 15 May 18

    2020

    0.2

    0.25

    0.3

    0.35

    0.4

    0.45

    0.5

    0.55 P

    er ce

    n t

    cu rr

    en tl

    y i

    n fe

    ct io

    u s,

    I /N

    ( p

    er ce

    n t)

    New Hampshire

    Peak I/N = 0.53% Final I/N = 0.23% = 0.010 =0.10 =0.20

    8 / 38

  • Notes on Intepreting Results

    9 / 38

  • 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 = 1.0%)

    ◦ Red = lowest parameter value (e.g. δ = 0.8%)

    ◦ Green = highest parameter value (e.g. δ = 1.2%)

    10 / 38

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

  • How does R0 change over time?

    • Inferred from death data when we have it

    • For future, two approaches:

    1 Alternatively, we fit this equation:

    logR0(t) = a0 − α(Daily Deaths)

    ⇒α ≈ .05

    R0 declines by 5 percent for each new daily death,

    or rises by 5 percent when daily deaths decline

    • Robustness: Assume R0(t) = final empirical value. Constant in

    future, so no α adjustment → α = 0 11 / 38

  • 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

    – With α = .05 (see robustness section for α = 0)

    12 / 38

  • New Hampshire (7 days): Daily Deaths per Million People (α = .05)

    May Jun Jul Aug Sep Oct Nov

    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

    New Hampshire

    R 0 =2.1/1.3/1.2 = 0.010 =0.1 =0.2 %Infect= 3/ 8/19

    13 / 38

  • New Hampshire (7 days): Cumulative Deaths per Million (Future, α = .05

    Apr May Jun Jul Aug Sep Oct Nov

    2020

    0

    200

    400

    600

    800

    1000

    1200

    1400

    1600

    1800

    C u m

    u la

    ti v e

    d ea

    th s

    p er

    m il

    li o n p

    eo p le

    New Hampshire

    R 0 =2.1/1.3/1.2 = 0.010 =0.1 =0.2 %Infect= 3/ 8/19

    14 / 38

  • New Hampshire (7 days): Cumulative Deaths per Million, Log Scale (α =

    15 / 38

  • Robustness to Mortality Rate, δ

    16 / 38

  • New Hampshire: Cumulative Deaths per Million (δ = .01/.008/.012)

    Apr 21 Apr 28 May 05 May 12 May 19 May 26 Jun 02

    2020

    0

    20

    40

    60

    80

    100

    120

    140

    160

    180

    200

    C u

    m u

    la ti

    v e

    d ea

    th s

    p er

    m il

    li o

    n p

    eo p

    le New Hampshire

    R 0 =2.1/0.5/0.6 = 0.010 =0.05 =0.1 %Infect= 2/ 2/ 2

    DATA THROUGH 28-MAY-2020

    17 / 38

  • New Hampshire: Daily Deaths per Million People (δ = .01/.008/.012)

    May Jun Jul Aug Sep Oct Nov

    2020

    0

    2

    4

    6

    8

    10

    12

    D ai

    ly d

    ea th

    s p er

    m il

    li o n p

    eo p le

    New Hampshire

    R 0 =2.1/0.5/0.6 = 0.010 =0.05 =0.1 %Infect= 2/ 2/ 2

    DATA THROUGH 28-MAY-2020

    18 / 38

  • New Hampshire: Cumulative Deaths per Million (δ = .01/.008/.012)

    Apr May Jun Jul Aug Sep Oct Nov

    2020

    0

    50

    100

    150

    200

    250

    C u

    m u

    la ti

    v e

    d ea

    th s

    p er

    m il

    li o

    n p

    eo p

    le New Hampshire

    R 0 =2.1/0.5/0.6 = 0.010 =0.05 =0.1 %Infect= 2/ 2/ 2

    = 0.01 = 0.008 = 0.012 DATA THROUGH 28-MAY-2020

    19 / 38

  • 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

    20 / 38

  • New Hampshire: Re-Opening (α = .05)

    (Light bars = New York City, for comparison) 21 / 38

  • New Hampshire: Re-Opening (α = 0)

    (Light bars = New York City, for comparison) 22 / 38

  • Results for alternative

    parameter values

    23 / 38

  • New Hampshire (7 days): Daily Deaths per Million People (α = 0)

    May Jun Jul Aug Sep Oct Nov

    2020

    0

    10

    20

    30

    40

    50

    60

    70

    80

    90

    100

    D ai

    ly d

    ea th

    s p

    er m

    il li

    o n

    p eo

    p le

    New Hampshire

    R 0 =2.1/1.4/1.4 = 0.010 =0.1 =0.2 %Infect= 3/20/54

    24 / 38

  • New Hampshire (7 days): Cumulative Deaths per Million (Future, α = 0)

    Apr May Jun Jul Aug Sep Oct Nov

    2020

    0

    1000

    2000

    3000

    4000

    5000

    6000

    C u m

    u la

    ti v e

    d ea

    th s

    p er

    m il

    li o n p

    eo p le

    New Hampshire

    R 0 =2.1/1.4/1.4 = 0.010 =0.1 =0.2 %Infect= 3/20/54

    25 / 38

  • New Hampshire (7 days): Cumulative Deaths per Million, Log Scale (α =

    26 / 38

  • New Hampshire: Daily Deaths per Million People (δ = 0.8%)

    May Jun Jul Aug Sep Oct Nov

    2020

    0