This document summarizes modeling of the 2014 Ebola outbreak in West Africa conducted by researchers. It provides current case and death counts by country. Modeling is being done using official data and making assumptions to fill gaps. Forecasts presented predict continuing rapid growth in cases and infected individuals in the coming weeks in Liberia, Sierra Leone and overall across the affected countries, despite control efforts. The reproductive numbers used in the modeling suggest ongoing human-to-human transmission is driving the outbreak.

1. DRAFT
–
Not
for
a.ribu2on
or
distribu2on
Modeling
the
Ebola
Outbreak
in
West
Africa,
2014
Oct
21st
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-­‐112

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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
1519
862
Liberia
4068
2484
Nigeria
22
8
Sierra
Leone
3624
1200
Total
9233
4554

3. DRAFT
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distribu2on
Epi
Notes
• US
hospitals
are
being
built,
some
delays
due
to
rainy
season
NPR
3
• Good
news:
Nigeria
Ebola
free!!
Time
• Good
news:
Lofa,
Liberia
having
success
WHO
• Bad
news:
Surge
in
cases
in
Conakry,
Guinea
MSF
• Transmission
route
unclear
for
Nancy
Writebol
(interes2ng
interview)
Science
Mag

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distribu2on
Liberia
–
Case
Loca2ons
4

5. DRAFT
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or
distribu2on
Liberia
–
County
Case
Incidence
5

6. DRAFT
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or
distribu2on
Liberia
–
County
Case
Propor2ons
6
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
6/10/14
6/30/14
7/20/14
8/9/14
8/29/14
9/18/14
10/8/14
10/28/14
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
Nimba
County
River
Gee
County
RiverCess
County
Sinoe
County
Lofa
Margibi
Bomi
Montserrado

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distribu2on
Liberia
–
Contact
Tracing
7

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distribu2on
Liberia
–
Contact
tracing
8

9. DRAFT
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a.ribu2on
or
distribu2on
Liberia
–
Case
Confirma2on
9
Gives
an
idea
of
the
rela2ve
performance
and
case
management
in
the
different
coun2es.
Decreasing
rates
combined
with
number
of
lost
and
not
seen
contacts
(previous
slide),
indicate
the
response
efforts
are
overwhelmed.

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distribu2on
Liberia
Forecasts
10
8/9/08
-­‐9/14
9/15–
9/21
9/22–
9/28
9/29
–
10/05
10/06
–
10/12
10/13-­‐
10/19
10/20-­‐
10/26
Reported
639
560
416
261
119
-­‐-­‐
-­‐-­‐
Forecast
697
927
1232
1636
2172
2883
3825
Reproduc2ve
Number
Community
1.3
Hospital
0.4
Funeral
0.5
Overall
2.2
52%
of
Infected
are
hospitalized

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or
distribu2on
Prevalence
of
Cases
11
Week
People
in
H+I
9/28/2014
1228
10/05/2014
1631
10/12/2014
2167
10/19/2014
2878
10/26/2014
3821
11/02/2014
5071
11/16/2014
8911

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distribu2on
Sierra
Leone
Forecasts
12
41%
of
cases
are
hospitalized
9/6-­‐9
/14
9/14-­‐9
/21
9/22
–
9/28
9/29-­‐
10/05
10/06–
10/12
10/13-­‐
10/19
10/20-­‐
10/26
Reported
246
285
377
467
468
372
Forecast
413
512
635
786
973
1205
1491

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distribu2on
Prevalence
in
SL
13
Week
People
in
H+I
9/28/2014
668
10/05/2014
828
10/12/2014
1026
10/19/2014
1271
10/26/2014
1573
11/02/2014
1947
11/16/2014
2978

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distribu2on
All
Countries
Forecasts
14
8/18
–
8/24
8/25
–
8/31
9/1–
9/7
9/8
–
9/14
9/15-­‐
9/21
9/22
–
9/28
9/29
–
10/5
10/6
-­‐10/12
10/13-­‐
10/19
10/20-­‐
10/26
Actual
559
783
681
959
917
915
904
917
Forecast
483
578
693
830
994
1191
1426
1426
1708
2045
rI:
1.1
rH:0.4
rF:0.3
Overall:1.7

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or
distribu2on
Experiments
&
Research
• Exploring
the
reported
case
decline
in
Liberia
• Quick
look
at
“WHO
plan”
70%
hospitalized,
70%
safely
buried
in
60
days
• Analyzing
/
gathering
US
HCW
exposure
and
risk
in
case
we
need
to
address
more
US
spread
scenarios
15

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or
distribu2on
Liberia
underrepor2ng
16

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distribu2on
Control
with
70%
Hospitalized?
17
Star2ng
1
October,
70
percent
of
cases
are
diagnosed
and
treated,
the
efficacy
of
that
care
and
the
safety
of
burial
for
those
who
die
is
subject
to
the
exis2ng
efficacy
of
the
healthcare
system.
Liberia
-­‐
100
day
projec@on

18. DRAFT
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or
distribu2on
Agent-­‐based
Model
Progress
• Construc2on
of
regional
travel
dynamic
social
network
• Framework
for
auto-­‐calibra2on
built
• New
version
of
SIBEL
deployed
– Enables
all
trained
analysts
to
run
Ebola
simula2ons
without
“behind
the
scenes”
manipula2on
– Auto-­‐modifica2on
possible
for
more
advanced
changes
18

19. DRAFT
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or
distribu2on
Regional
Travel
-­‐
Liberia
• Mobility
data
comes
from
flowminder.org
– Probability
Matrix
of
county
to
county
trips
by
week
(15x15)
– Number
of
trips
probably
high,
ra2os
be.er
– Es2mates
available
for
several
model
fits
– Data
converted
to
daily
probabili2es
• Method:
Make
dynamic
schedules
for
EpiSimdemics
– Each
person
has
a
home
county
based
on
home
loca2on
– Each
person
is
matched
with
a
person
in
each
non-­‐home
county,
based
on
gender
and
age
bin
– For
each
person
and
non-­‐home
county,
a
new
schedule
is
created
that
shadows
the
schedule
of
the
matched
person
– A
scenario
file
is
created
that
contains
rules
for
each
source/
des2na2on
pair
(15
x
14
=
210
for
Liberia)
19

20. DRAFT
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Regional
Travel
-­‐
Example
20
# Travel from Grand_Kru (2042) to Maryland (2082) with prob 0.008036427
trigger repeatable person.County = 2042 and person.isTraveling = -1
apply travel_to_2082 with prob=0.008036427
intervention travel_to_2008
set person.isTraveling = 2008
set person.daysLeft = 3
set tripsTo2008++
set traveling++
set trips++
schedule county2008 1
# return from travel
intervention return
unschedule 1
set person.isTraveling = -1
set person.daysLeft = -1
set traveling--
trigger repeatable person.daysLeft > 0
set person.daysLeft—
trigger repeatable person.daysLeft = 1
apply return

21. DRAFT
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distribu2on
Regional
Travel
-­‐
Trips
21
100000
100500
101000
101500
102000
102500
103000
103500
104000
104500
105000
10 20 30 40 50 60 70 80 90 100
Travellers
Simulation Day
Travelers per day

22. DRAFT
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distribu2on
Regional
Travel
–
Trips
22
0
2000
4000
6000
8000
10000
12000
0 10 20 30 40 50 60 70 80 90 100
TripStarts
Simulation Day
Montserrado
Margibi
Bomi
Grand_Bassa
Bong
Grand_Cape_Mount
Nimba
Gbarpolu
River_Cess
Lofa
Grand_Gedeh
Maryland
Sinoe
River_Gee
Grand_Kru

23. DRAFT
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a.ribu2on
or
distribu2on
Auto-­‐Calibra2on
of
ABM
• Agent-­‐based
model
is
harder
to
calibrate
than
compartmental
model
– More
poten2al
parameters
to
tweak
– More
randomness
to
outcomes
– Longer
run-­‐2mes
• Need
an
automated
process
to
push
the
model
out
23

24. DRAFT
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or
distribu2on
Auto-­‐Calibra2on
of
ABM
24

25. DRAFT
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a.ribu2on
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distribu2on
SIBEL
–
New
version
25

26. DRAFT
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for
a.ribu2on
or
distribu2on
SIBEL
–
New
features
• Generic
interven2on
supports
more
possible
interven2ons
• Dura2on
and
logis2cal
rates
of
interven2on
added
• Many
more…
26

27. DRAFT
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for
a.ribu2on
or
distribu2on
Agent-­‐based
Next
steps
• Hospital,
ECC,
home
care
kits
and
their
impact
at
different
levels
of
provision
/
efficacy
– Constrain
to
Monrovia
for
tractability
– Explore
use
of
auto-­‐calibra2on
to
establish
a
good
match
to
present
– Explore
behavioral
changes
and
details
of
care
(one
care
giver
only
at
home
vs.
several,
etc.)
• Calibra2ng
Regional
Travel
to
observed
spread
– Mul2-­‐dimensional
calibra2on
will
be
challenging
– Use
more
efficient
simula2on
plauorm
(EpiFast)
27

28. DRAFT
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or
distribu2on
APPENDIX
Suppor2ng
material
describing
model
structure,
and
addi2onal
results
28

29. DRAFT
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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.
29

30. DRAFT
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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.
30

31. 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
31

32. DRAFT
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for
a.ribu2on
or
distribu2on
Parameters
of
two
historical
outbreaks
32

33. 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
33

34. DRAFT
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for
a.ribu2on
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
34

35. DRAFT
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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
35

36. DRAFT
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or
distribu2on
Model
parameters
36
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