This document provides updates on modeling the Ebola outbreak in West Africa from October 2014. It summarizes current case and death counts in Guinea, Liberia, and Sierra Leone. Forecasts for new Ebola cases in Liberia and Sierra Leone over the next month are presented, with reproductive numbers reported for different transmission settings. County-level data on cases and proportions are shown for Liberia and Sierra Leone.

1. DRAFT
–
Not
for
a.ribu2on
or
distribu2on
Modeling
the
Ebola
Outbreak
in
West
Africa,
2014
Halloween
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-­‐115

2. DRAFT
–
Not
for
a.ribu2on
or
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
6248
2705
Sierra
Leone
5235
1500
Total
13411
5210

3. DRAFT
–
Not
for
a.ribu2on
or
distribu2on
Liberia
–
Case
Loca2ons
3

4. DRAFT
–
Not
for
a.ribu2on
or
distribu2on
Liberia
–
County
Case
Incidence
4

5. DRAFT
–
Not
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
–
Not
for
a.ribu2on
or
distribu2on
Liberia
–
Contact
Tracing
6

7. DRAFT
–
Not
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
**
-­‐-­‐
-­‐-­‐
Forecast
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
–
Not
for
a.ribu2on
or
distribu2on
Prevalence
of
Cases
8
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

9. DRAFT
–
Not
for
a.ribu2on
or
distribu2on
Liberia
Repor2ng
Jump
9
Treat
recent
large
case
report
as
a
backlog
evenly
distributed
over
the
last
month

10. DRAFT
–
Not
for
a.ribu2on
or
distribu2on
Sierra
Leone
–
County
Data
10

11. DRAFT
–
Not
for
a.ribu2on
or
distribu2on
Sierra
Leone
–
Contact
A.ack
Rate
11

12. DRAFT
–
Not
for
a.ribu2on
or
distribu2on
Sierra
Leone
Forecasts
12
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
Forecast
413
512
635
786
973
1205
1491
1844
2278
41%
of
cases
are
hospitalized

13. DRAFT
–
Not
for
a.ribu2on
or
distribu2on
Sierra
Leone
Forecasts
–
New
Model
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
–
Not
for
a.ribu2on
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
–
Not
for
a.ribu2on
or
distribu2on
Learning
from
Lofa
15
Model
fit
to
Lofa
case
series
up
Aug
18th
(green)
then
from
Aug
19
–
Oct
21
(blue),
compared
with
real
data
(red)

16. DRAFT
–
Not
for
a.ribu2on
or
distribu2on
Learning
from
Lofa
16
Model
fit
to
Lofa
case
with
a
change
in
behaviors
resul2ng
in
reduced
transmission
sta2ng
mid-­‐Aug
(blue),
compared
with
observed
data
(green)

17. DRAFT
–
Not
for
a.ribu2on
or
distribu2on
Learning
from
Lofa
17
Model
fit
to
Liberian
case
data
up
to
Sept
20th
(current
model
in
blue),
reduc2on
in
transmissions
observed
in
Lofa
applied
from
Sept
21st
on
(green),
and
observed
cases
(red)

18. DRAFT
–
Not
for
a.ribu2on
or
distribu2on
Learning
from
Lofa
18
Model
fit
to
Liberia
case
with
a
change
in
behaviors
resul2ng
in
reduced
transmission
sta2ng
Sept
21st
(green),
compared
with
observed
data
(blue)

19. DRAFT
–
Not
for
a.ribu2on
or
distribu2on
Agent-­‐based
Model
Progress
• Added
Regional
travel
pa.erns
• Agent-­‐based
parameter
op2miza2on
framework
• New
GUI
deployed
for
running
ABM
expts
• Ini2al
calibra2on
with
travel
for
all
Liberia
– Plausible
base
case
determined
– Search
parameter
space
for
transmissions
that
match
na2onal
aggregate
– Assess
regional
travel
• Timing,
total
cases,
case
incidence
at
“present”
• Variability
with
same
parameter
sets
19

20. DRAFT
–
Not
for
a.ribu2on
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)
20

21. DRAFT
–
Not
for
a.ribu2on
or
distribu2on
Regional
Travel
-­‐
Example
21
# 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

22. DRAFT
–
Not
for
a.ribu2on
or
distribu2on
Regional
Travel
-­‐
Trips
22
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

23. DRAFT
–
Not
for
a.ribu2on
or
distribu2on
Regional
Travel
–
Trips
23
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

24. DRAFT
–
Not
for
a.ribu2on
or
distribu2on
Auto-­‐Calibra2on
of
ABM
24

25. DRAFT
–
Not
for
a.ribu2on
or
distribu2on
SIBEL
–
New
version
25

26. DRAFT
–
Not
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
–
Not
for
a.ribu2on
or
distribu2on
Plausible
Base
Case
27
• Hospital
isola2on
for
50%
-­‐
reduces
txm
by
80%
• Proper
burial
for
50%
-­‐
reduces
txm
by
80%
• Ebola
Mode:
Transmission
in
household
3x
more
likely
than
outside
the
household

28. DRAFT
–
Not
for
a.ribu2on
or
distribu2on
Transmission
calibra2on
28

29. DRAFT
–
Not
for
a.ribu2on
or
distribu2on
Transmission
calibra2on
29
4665
cases
Day
158
Day
27
22
cases
131
days
Burn
in
period

30. DRAFT
–
Not
for
a.ribu2on
or
distribu2on
Regional
Spread
–
Reaches
all
coun2es
30

31. DRAFT
–
Not
for
a.ribu2on
or
distribu2on
Regional
Spread
–
Variability
within
coun2es
31

32. DRAFT
–
Not
for
a.ribu2on
or
distribu2on
Regional
Spread
–
Variability
within
coun2es
32
Lofa
county
example
Cumula2ve
cases
for
two
different
replicates
(same
parameters)

33. DRAFT
–
Not
for
a.ribu2on
or
distribu2on
Agent
based
Next
Steps
• Spa2al
spread
calibra2on
– Incorporate
degraded
road
network
to
help
guide
fiqng
to
current
data
– Guide
with
more
spa2ally
explicit
ini2al
infected
seeds
• Experiments:
– Impact
of
hospitals
with
geo-­‐spa2al
disease
– Vaccina2on
campaign
effec2veness
33

34. DRAFT
–
Not
for
a.ribu2on
or
distribu2on
APPENDIX
Suppor2ng
material
describing
model
structure,
and
addi2onal
results
34

35. DRAFT
–
Not
for
a.ribu2on
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.
35

36. 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.
36

37. 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
37

38. DRAFT
–
Not
for
a.ribu2on
or
distribu2on
Parameters
of
two
historical
outbreaks
38

39. DRAFT
–
Not
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
39

40. DRAFT
–
Not
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
40

41. DRAFT
–
Not
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
41

42. DRAFT
–
Not
for
a.ribu2on
or
distribu2on
Model
parameters
42
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