Researchers at the Network Dynamics and Simulation Science Laboratory have been using a combination of modeling techniques to predict the spread of the Ebola outbreak.

1. DRAFT
–
Not
for
a.ribu2on
or
distribu2on
Modeling
the
Ebola
Outbreak
in
West
Africa,
2014
Nov
4th
Update
Bryan
Lewis
PhD,
MPH
(blewis@vbi.vt.edu)
Caitlin
Rivers
MPH,
Eric
Lofgren
PhD,
James
Schli.,
Alex
Telionis
MPH,
Henning
Mortveit
PhD,
Dawen
Xie
MS,
Samarth
Swarup
PhD,
Hannah
Chungbaek,
Keith
Bisset
PhD,
Maleq
Khan
PhD,
Chris
Kuhlman
PhD,
Stephen
Eubank
PhD,
Madhav
Marathe
PhD,
and
Chris
Barre.
PhD
Technical
Report
#14-­‐113

2. DRAFT
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distribu2on
Currently
Used
Data
● Data
from
WHO,
MoH
Liberia,
and
MoH
Sierra
Leone,
available
at
h.ps://github.com/cmrivers/ebola
● MoH
and
WHO
have
reasonable
agreement
● Sierra
Leone
case
counts
censored
up
to
4/30/14.
● Time
series
was
filled
in
with
missing
dates,
and
case
counts
were
interpolated.
2
Cases
Deaths
Guinea
1906
997
Liberia
6454
2705
Sierra
Leone
5235
1500
Total
13,617
5210

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or
distribu2on
Liberia
–
Case
Loca2ons
3

4. DRAFT
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for
a.ribu2on
or
distribu2on
Liberia
–
County
Case
Incidence
4

5. DRAFT
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for
a.ribu2on
or
distribu2on
0
0.1
0.2
0.3
0.4
0.5
0.6
5/21/14
6/10/14
6/30/14
7/20/14
8/9/14
8/29/14
9/18/14
10/8/14
10/28/14
11/17/14
Percentage
of
County
Popula:on
(%)
Date
Percentage
of
County
Popula:on
Infected
with
EVD
Bomi
County
Bong
County
Gbarpolu
County
Grand
Bassa
Grand
Cape
Mount
Grand
Gedeh
Grand
Kru
Lofa
County
Margibi
County
Maryland
County
Montserrado
County
Liberia
–
County
Case
Propor2ons
5

6. DRAFT
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for
a.ribu2on
or
distribu2on
Liberia
–
Contact
Tracing
6

7. DRAFT
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for
a.ribu2on
or
distribu2on
Liberia
Forecasts
7
8/9/08
to
9/14
9/15
to
9/21
9/22
to
9/28
9/29
to
10/05
10/06
to
10/12
10/13
to
10/19
10/20
to
10/26
10/27
to
11/02
11/03
to
11/09
Reported
639
560
416
261
298
446
1604*
-­‐-­‐
-­‐-­‐
Forecast
(classic
model)
697
927
1232
1636
2172
2883
3825
5070
6741
Reproduc2ve
Number
Community
1.3
Hospital
0.4
Funeral
0.5
Overall
2.2
52%
of
Infected
are
hospitalized
*
Massive
increase

8. DRAFT
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for
a.ribu2on
or
distribu2on
Learning
from
Lofa
-­‐
Summary
8
Model
fit
to
Lofa
case
with
a
change
in
behaviors
resul2ng
in
reduced
transmission
sta2ng
mid-­‐Aug
(blue),
compared
with
observed
data
(green)
Fit
reduc2on
seen
in
Lofa
Model
fit
to
Liberia
case
with
a
change
in
behaviors
resul2ng
in
reduced
transmission
sta2ng
Sept
21st
(green),
compared
with
observed
data
(blue)
Apply
to
Liberia

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for
a.ribu2on
or
distribu2on
Liberia
Forecast
–
New
Model
9
9/16
to
9/21
9/22
to
9/28
9/29
to
10/05
10/06
to
10/12
10/13
to
10/19
10/20
to
10/26
10/27
to
11/02
11/03
to
11/09
11/10
to
11/16
Reported
560
416
261
298
446
1604*
-­‐-­‐
-­‐-­‐
-­‐-­‐
Reported
back
log
adjusted
396
251
245
490
New
model
757
603
541
580
598
608
617
625
633
Reproduc2ve
Number
Community
0.5
Hospital
0.2
Funeral
0.2
Overall
1.0
*
Massive
increase

10. DRAFT
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for
a.ribu2on
or
distribu2on
Prevalence
of
Cases
–
New
model
10
Date
People
in
H+I
9/7/14
523
9/14/14
695
9/20/14
887
9/27/14
1051
10/4/14
1119
10/11/14
1152
10/18/14
1174
10/25/14
1192
11/1/14
1208
11/8/14
1224
11/15/14
1239
11/22/14
1255
11/29/14
1271
12/6/14
1288
12/13/14
1304
12/20/14
1320
12/27/14
1337

11. DRAFT
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or
distribu2on
Sierra
Leone
–
County
Data
11

12. DRAFT
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or
distribu2on
Sierra
Leone
–
Contact
A.ack
Rate
12

13. DRAFT
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for
a.ribu2on
or
distribu2on
Sierra
Leone
Forecasts
13
9/6
to
9/14
9/14
to
9/21
9/22
to
9/28
9/29
to
10/05
10/06
to
10/12
10/13
to
10/19
10/20
to
10/26
10/27
to
11/02
11/03
to
11/09
Reported
246
285
377
467
468
454
494
Forecast
256
312
380
464
566
690
841
1025
1250
35%
of
cases
are
hospitalized
Reproduc:ve
Number
Community
1.20
Hospital
0.29
Funeral
0.15
Overall
1.63

14. DRAFT
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or
distribu2on
Prevalence
in
SL
14
10/6/14
456.6
10/13/14
556.7
10/20/14
678.8
10/27/14
827.5
11/3/14
1008.8
11/10/14
1229.8
11/17/14
1498.9
11/24/14
1826.8
12/1/14
2226.1
12/8/14
2712.2
12/15/14
3303.7
12/22/14
4023.3
12/29/14
4898.1

15. DRAFT
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distribu2on
Experiments
and
Research
• US
Health
care
worker
Exposure
15

16. DRAFT
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for
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or
distribu2on
US
cases
per
exposure
hour
by
exposure
type
2
/
48
=
0.042
0
/
3432
=
0.0
Transmission
probability
per
triage
hour
of
exposure*
Transmission
probability
per
ICU
hour
of
exposure*
*
Assuming
that
during
the
triage
period
HCWs
do
not
u2lize
full
protec2ve
gear
and
isola2on
protocol
while
wai2ng
for
Ebola
test
results.
*
Assuming
that
during
the
ICU
period
HCWs
do
u2lize
full
protec2ve
gear
and
isola2on
protocol
while
trea2ng
Ebola
pa2ents.

17. DRAFT
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for
a.ribu2on
or
distribu2on
US
overall
experience
to
date
1
transmission
for
every
1716
exposure
hours
(71.5
days)
US Healthcare System

18. DRAFT
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for
a.ribu2on
or
distribu2on
Agent-­‐based
Model
Progress
• Calibra2on
progress
– Spa2al
spread
guided
by
seeding
18

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distribu2on
Calibra2on
–
Spa2al
Spread
19

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or
distribu2on
Simula2on
Comparison
20
Cases
per
100k
popula2on
Mean
simula2on
results
Ministry
of
Health
Data

21. DRAFT
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for
a.ribu2on
or
distribu2on
Simula2on
Comparison
21
Total
Cases
Single
Simula2on
result
Ministry
of
Health
Data

22. DRAFT
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for
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or
distribu2on
Agent
based
Next
Steps
• Spa2al
spread
calibra2on
– Incorporate
degraded
road
network
to
help
guide
filng
to
current
data
– Guide
with
more
spa2ally
explicit
ini2al
infected
seeds
and
interven:ons
• Experiments:
– Impact
of
hospitals
with
geo-­‐spa2al
disease
• Configura2on
s2ll
being
set
up
– Vaccina2on
campaign
effec2veness
• Framework
under
development
22

23. DRAFT
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for
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or
distribu2on
APPENDIX
Suppor2ng
material
describing
model
structure,
and
addi2onal
results
23

24. DRAFT
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for
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or
distribu2on
Legrand
et
al.
Model
Descrip2on
Exposed
not infectious
Infectious
Symptomatic
Removed
Recovered and immune
or dead and buried
Susceptible
Hospitalized
Infectious
Funeral
Infectious
Legrand,
J,
R
F
Grais,
P
Y
Boelle,
A
J
Valleron,
and
A
Flahault.
“Understanding
the
Dynamics
of
Ebola
Epidemics”
Epidemiology
and
Infec1on
135
(4).
2007.
Cambridge
University
Press:
610–21.
doi:10.1017/S0950268806007217.
24

25. DRAFT
–
Not
for
a.ribu2on
or
distribu2on
Compartmental
Model
• Extension
of
model
proposed
by
Legrand
et
al.
Legrand,
J,
R
F
Grais,
P
Y
Boelle,
A
J
Valleron,
and
A
Flahault.
“Understanding
the
Dynamics
of
Ebola
Epidemics”
Epidemiology
and
Infec1on
135
(4).
2007.
Cambridge
University
Press:
610–21.
doi:10.1017/S0950268806007217.
25

26. DRAFT
–
Not
for
a.ribu2on
or
distribu2on
Legrand
et
al.
Approach
• Behavioral
changes
to
reduce
transmissibili2es
at
specified
days
• Stochas2c
implementa2on
fit
to
two
historical
outbreaks
– Kikwit,
DRC,
1995
– Gulu,
Uganda,
2000
• Finds
two
different
“types”
of
outbreaks
– Community
vs.
Funeral
driven
outbreaks
26

27. DRAFT
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for
a.ribu2on
or
distribu2on
Parameters
of
two
historical
outbreaks
27

28. DRAFT
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for
a.ribu2on
or
distribu2on
NDSSL
Extensions
to
Legrand
Model
• Mul2ple
stages
of
behavioral
change
possible
during
this
prolonged
outbreak
• Op2miza2on
of
fit
through
automated
method
• Experiment:
– Explore
“degree”
of
fit
using
the
two
different
outbreak
types
for
each
country
in
current
outbreak
28

29. DRAFT
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for
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or
distribu2on
Op2mized
Fit
Process
• Parameters
to
explored
selected
– Diag_rate,
beta_I,
beta_H,
beta_F,
gamma_I,
gamma_D,
gamma_F,
gamma_H
– Ini2al
values
based
on
two
historical
outbreak
• Op2miza2on
rou2ne
– Runs
model
with
various
permuta2ons
of
parameters
– Output
compared
to
observed
case
count
– Algorithm
chooses
combina2ons
that
minimize
the
difference
between
observed
case
counts
and
model
outputs,
selects
“best”
one
29

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for
a.ribu2on
or
distribu2on
Fi.ed
Model
Caveats
• Assump2ons:
– Behavioral
changes
effect
each
transmission
route
similarly
– Mixing
occurs
differently
for
each
of
the
three
compartments
but
uniformly
within
• These
models
are
likely
“overfi.ed”
– Many
combos
of
parameters
will
fit
the
same
curve
– Guided
by
knowledge
of
the
outbreak
and
addi2onal
data
sources
to
keep
parameters
plausible
– Structure
of
the
model
is
supported
30

31. DRAFT
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or
distribu2on
Model
parameters
31
Sierra&Leone
alpha 0.1
beta_F 0.111104
beta_H 0.079541
beta_I 0.128054
dx 0.196928
gamma_I 0.05
gamma_d 0.096332
gamma_f 0.222274
gamma_h 0.242567
delta_1 0.75
delta_2 0.75
Liberia
alpha 0.083
beta_F 0.489256
beta_H 0.062036
beta_I 0.1595
dx 0.2
gamma_I 0.066667
gamma_d 0.075121
gamma_f 0.496443
gamma_h 0.308899
delta_1 0.5
delta_2 0.5
All
Countries
Combined