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. Modeling
the
Ebola
Outbreak
in
West
Africa,
2014
November
18th
Update
Bryan
Lewis
PhD,
MPH
(blewis@vbi.vt.edu)
presen2ng
on
behalf
of
the
Ebola
Response
Team
of
Network
Dynamics
and
Simula2on
Science
Lab
from
the
Virginia
Bioinforma2cs
Ins2tute
at
Virginia
Tech
Technical
Report
#14-­‐122
DRAFT
–
Not
for
a.ribu2on
or
distribu2on

2. NDSSL
Ebola
Response
Team
Staff:
Abhijin
Adiga,
Kathy
Alexander,
Chris
Barre.,
Richard
Beckman,
Keith
Bisset,
Jiangzhuo
Chen,
Youngyoun
Chungbaek,
Stephen
Eubank,
Sandeep
Gupta,
Maleq
Khan,
Chris
Kuhlman,
Eric
Lofgren,
Bryan
Lewis,
Achla
Marathe,
Madhav
Marathe,
Henning
Mortveit,
Eric
Nordberg,
Paula
Stretz,
Samarth
Swarup,
Meredith
Wilson,Mandy
Wilson,
and
Dawen
Xie,
with
support
from
Ginger
Stewart,
Maureen
Lawrence-­‐Kuether,
Kayla
Tyler,
Kathy
Laskowski,
Bill
Marmagas
Students:
S.M.
Arifuzzaman,
Aditya
Agashe,
Vivek
Akupatni,
Caitlin
Rivers,
Pyrros
Telionis,
Jessie
Gunter,
Elisabeth
Musser,
James
Schli.,
Youssef
Jemia,
Margaret
Carolan,
Bryan
Kaperick,
Warner
Rose,
Kara
Harrison
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
2

3. 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.
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
3
Cases
Deaths
Guinea
1919
1166
Liberia
6909
2836
Sierra
Leone
5586
1510
Total
14,436
5520

4. Liberia
–
Case
Loca2ons
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
4

5. Liberia
–
County
Case
Incidence
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
5

6. Liberia
Forecast
–
Original
Model
52%
of
Infected
are
hospitalized
Reproduc2ve
Number
Community
1.3
Hospital
0.4
Funeral
0.5
Overall
2.2
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
6
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*
227
298
Forecast
(classic
model)
697
927
1232
1636
2172
2883
3825
5070
6741
*
Repor2ng
change

7. Learning
from
Lofa
-­‐
Summary
Fit
reduc2on
seen
in
Lofa
Apply
to
Liberia
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
7
Model
fit
to
Lofa
case
with
a
change
in
behaviors
resul2ng
in
reduced
transmission
sta2ng
mid-­‐Aug
(blue),
compared
with
observed
data
(green)
Model
fit
to
Liberia
case
with
a
change
in
behaviors
resul2ng
in
reduced
transmission
sta2ng
Sept
21st
(green),
compared
with
observed
data
(blue)

8. Liberia
Forecast
–
Prelim
New
Model
Reproduc2ve
Number
Community
0.5
Hospital
0.2
Funeral
0.2
Overall
1.0
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
8
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
11/17
to
11/23
Reported
560
416
261
298
446
1604*
227
298
-­‐-­‐
-­‐-­‐
Reported
396
251
245
490
back
log
adjusted
New
model
757
603
541
580
598
608
617
625
633
638

9. Prevalence
of
Cases
–
New
model
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
9
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

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

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

12. Sierra
Leone
Forecasts
35%
of
cases
are
hospitalized
ReproducPve
Number
Community
1.20
Hospital
0.29
Funeral
0.15
Overall
1.63
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
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
11/10
to
11/16
11/17
to
11/23
Reported
246
285
377
467
468
454
494
486
580
-­‐-­‐
-­‐-­‐
Forecast
256
312
380
464
566
690
841
1025
1250
1523
1856

13. Prevalence
in
SL
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
13
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

14. Agent-­‐based
Model
Progress
• Synthe2c
Informa2on
Viewer
for
Ebola
affected
Countries
– Assist
in
troubleshoo2ng
simula2on
results
– Aid
in
calibra2on
issues
• Calibra2on
–
Rainy
Season
altera2on
• Considera2on
of
Mali
and
Senegal
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
14

15. Synthe2c
Informa2on
Viewer
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
15
Interface
for
exploring
details
of
the
popula2on
and
their
ac2vi2es

16. Synthe2c
Informa2on
Viewer
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
16
Zoom
down
to
the
household
level
to
see
rela2ve
densi2es
and
selected
details

17. Synthe2c
Informa2on
Viewer
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
17
Zoom
down
to
the
individual
and
look
at
their
ac2vity
pa.ern

18. Calibra2on
–
Previous
Steps
• Disease
Model
representa2on
• Flowminder
data
used
for
travel
• Ini2alize
simula2on
in
Lofa
• Road
map
with
travel
status
used
for
prelim
es2mate
of
travel
altera2on
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
18
Bomi
Bong
Gbarpolu
Grand
Bassa
Grand
Cape
Mount
Grand
Gedeh
Grand
Kru
Lofa
Margibi
Maryland
Montserrado
Nimba
River
Cess
River
Gee
Sinoe
Green
1
Bomi
0.55
0.5
1
0.5
0.425
0.425
0.1
1
0.425
1
0.55
0.1
0.425
0.3
Red
0.5
Bong
0.55
0.3
0.55
0.3
1
1
1
1
1
1
1
0.1
1
0.366666667
Black
0.1
Gbarpolu
0.5
0.3
0.5
0.5
0.425
0.425
0.1
0.5
0.425
0.5
0.3
0.1
0.425
0.3
Grand
Bassa
1
0.55
0.5
0.5
0.3
0.3
0.4
1
0.3
1
0.55
0.1
0.3
0.3
Based
on
traveling
from
county
capital
to
county
capital
Grand
Cape
Mount
0.5
0.3
0.5
0.5
0.3
0.3
0.3
0.5
0.3
0.5
0.233333333
0.1
0.3
0.3
Based
on
17SEPT2014
data
Grand
Gedeh
0.425
1
0.425
0.3
0.3
1
1
0.55
1
0.55
1
0.1
1
0.5
Grand
Kru
0.425
1
0.425
0.3
0.3
1
1
0.533333333
1
0.533333333
1
0.1
1
0.5
Lofa
0.1
1
0.1
0.4
0.3
1
1
0.55
1
0.55
1
0.1
1
0.214285714
Margibi
1
1
0.5
1
0.5
0.55
0.533333333
0.55
0.533333333
1
1
0.1
0.533333333
0.3
Maryland
0.425
1
0.425
0.3
0.3
1
1
1
0.533333333
0.533333333
1
0.1
1
0.5
Montserrado
1
1
0.5
1
0.5
0.55
0.533333333
0.55
1
0.533333333
0.55
0.1
0.533333333
0.3
Nimba
0.55
1
0.3
0.55
0.233333333
1
1
1
1
1
0.55
0.1
1
0.233333333
River
Cess
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
River
Gee
0.425
1
0.425
0.3
0.3
1
1
1
0.533333333
1
0.533333333
1
0.1
0.5
Sinoe
0.3
0.366666667
0.3
0.3
0.3
0.5
0.5
0.2142857
14
0.3
0.5
0.3
0.233333333
0.1
0.5

19. Calibra2on
–
Spa2al
Spread
Simula2on
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
19

20. Calibra2on
–
Spa2al
Spread
MoH
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
20

21. Simula2on
Comparison
–
spread
from
Lofa
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
21
Cases
per
100k
popula2on
Mean
simula2on
Normal
Travel
Ministry
of
Health
Data

22. Simula2on
Comparison
–
Rainy
Season
Travel
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
22
Cases
per
100k
popula2on
Mean
simula2on
Rainy
Travel
Ministry
of
Health
Data

23. Simula2on
Comparison
–
spread
from
Lofa
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
23
Total
Cases
Single
Simula2on
result
–
Normal
Travel
Ministry
of
Health
Data

24. Simula2on
Comparison
–
spread
from
Lofa
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
24
Total
Cases
Single
Simula2on
result
–
Rainy
Travel
Ministry
of
Health
Data

25. Calibra2on
Next
Steps
• Determine
“right”
2me
of
rainy
travel
– Pursue
more
real-­‐2me
and
comprehensive
data
• Combine
all
condi2ons
and
a.empt
calibra2on
– Lofa-­‐based
introduc2on
– Lofa
and
other
county
temporal
changes
in
txm
– Regional
travel
–
affected
by
rainy
season
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
25

26. Agent-­‐based
Next
Steps
• Planned
Experiments:
– Impact
of
hospitals
with
geo-­‐spa2al
disease
• Study
design
/
implementa2on
under
construc2on
– Vaccina2on
campaign
effec2veness
• Framework
under
development
– Es2ma2on
of
surveillance
coverage
requirements
• Simulate
zoono2c
and
human
introduc2on
scenarios,
look
at
“gold
standard”
transmission
trees
with
varying
level
of
completeness
to
represent
different
levels
of
surveillance
• Address
ques2on
of
needed
resources
for
eventual
final
stages
of
“stamp
out”
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
26

27. Suppor2ng
material
describing
model
structure,
and
addi2onal
results
APPENDIX
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
27

28. Legrand
et
al.
Model
Descrip2on
Susceptible
Exposed
not infectious
Infectious
Symptomatic
Hospitalized
Infectious
Funeral
Infectious
Removed
Recovered and immune
or dead and buried
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.
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
28

29. 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.
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
29

30. 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
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
30

31. Parameters
of
two
historical
outbreaks
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
31

32. 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
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
32

33. 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
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
33

34. 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
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
34

35. Model
parameters
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
35
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

36. Learning
from
Lofa
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
36
Model
fit
to
Lofa
case
series
up
Aug
18th
(green)
then
from
Aug
19
–
Oct
21
(blue),
compared
with
real
data
(red)

37. Learning
from
Lofa
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
37
Model
fit
to
Lofa
case
with
a
change
in
behaviors
resul2ng
in
reduced
transmission
sta2ng
mid-­‐Aug
(blue),
compared
with
observed
data
(green)

38. Learning
from
Lofa
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
38
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)

39. Learning
from
Lofa
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
39
Model
fit
to
Liberia
case
with
a
change
in
behaviors
resul2ng
in
reduced
transmission
sta2ng
Sept
21st
(green),
compared
with
observed
data
(blue)