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
Sept
30th
Update
Bryan
Lewis
PhD,
MPH
(blewis@vbi.vt.edu)
Caitlin
Rivers
MPH,
Eric
Lofgren
PhD,
James
Schli.,
Ka2e
Dunphy,
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-­‐104
DRAFT
–
Not
for
a.ribu2on
or
distribu2on

2. 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
2
Cases
Deaths
Guinea
1074
648
Liberia
3362
1830
Nigeria
22
8
Sierra
Leone
2208
605
Total
6666
3091

3. Epi
Notes
• Reports
of
efficacy
of
HIV
drug
“”
lowering
mortality
CNN
• Two
other
physicians
infected
with
Ebola
back
in
US,
one
at
NIH
enrolled
in
vax
trial
Poli2co
• Suspect
cases
con2nue
to
be
iden2fied
in
the
US,
currently
a
pa2ent
in
Dallas
(previous
nega2ves
from
CA,
NY,
NM,
FL)
WaPo
• Sierra
Leone’s
repor2ng
s2ll
inconsistent
Crawford
Killian
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
3

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

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

6. Liberia
Forecasts
Forecast
performance
52%
of
Infected
are
hospitalized
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
6
8/18-­‐
8/24
8/25
–
8/31
9/01–
9/07
9/08
–
9/14
9/15
–
9/21
9/22
–
9/29
9/30-­‐1
0/6
Actual
431
368
421
620
558
-­‐-­‐
-­‐-­‐
Forecast
314
417
555
738
981
1304
1733
Reproduc2ve
Number
Community
1.3
Hospital
0.4
Funeral
0.5
Overall
2.2

7. Prevalence
of
Cases
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
7
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

8. Sierra
Leone
Forecasts
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
8
Forecast
performance
41%
of
cases
are
hospitalized
8/25
–
8/31
9/01–
9/07
9/08
–
9/14
9/15
–
9/21
9/22-­‐
9/28
9/29
–
10/06
10/06-­‐
10/12
Actual
196
219
194
274
332
-­‐-­‐
-­‐-­‐
Forecast
267
333
413
512
635
786
974

9. Prevalence
in
SL
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
9
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

10. All
Countries
Forecasts
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
10
rI:
1.1
rH:0.4
rF:0.3
Overall:1.7

11. Combined
Forecasts
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
11
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
Actual
559
783
681
959
917
-­‐-­‐
-­‐-­‐
-­‐-­‐
Forecast
483
578
693
830
994
1191
1426
1426

12. Experiments
• Hospital
bed
es2mate
calcula2ons
• Reduc2on
in
2me
to
hospitaliza2on
• Improvements
in
2me
from
symptom
onset
to
hospitaliza2on
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
12

13. Hospital
Beds
–
Prelim
analysis
Impact
in
Liberia,
beds
only
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
13
Cases
on
Feb
1
Oct
1
245k
Nov
1
312k
Dec
1
391k
Jan
1
475k
No
beds
533k
16%
hospitaliza2on
ra2o
-­‐>
70%
Beta_H
reduc2on
by
90%

14. Hospital
Beds
–
Prelim
analysis
Impact
in
Liberia,
beds
and
proper
burial
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
14
Cases
on
Feb
1
Oct
1
73k
Nov
1
135k
Dec
1
230k
Jan
1
375k
No
beds
533k
16%
hospitaliza2on
ra2o
-­‐>
70%
Beta_H
reduc2on
by
90%
Beta_F
reduc2on
by
90%

15. Hospital
beds
–
Prelim
analysis
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
15
Impact
in
Liberia,
beds
+
proper
burial
+
shortened
2me
to
hospitaliza2on

16. Hospital
beds
–
Prelim
analysis
5
days
3
days
1
days
Oct
1
52k
25k
10k
Nov
1
108k
65k
31k
Dec
1
206k
152k
92k
Jan
1
358k
318k
2506
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
16
Cumula2ve
cases
in
Liberia
on
Feb
1
with
reduced
beta_H,
reduced
beta_F,
and
shortened
2me
to
hospitaliza2on

17. Op2mal
center
placement
Preliminary
op2miza2on
using
road
networks
and
popula2on
centers
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
17

18. Agent-­‐based
Simula2ons
Progress
• Regional
travel
method,
developed
– Implementa2on
working
this
week
• Interven2onal
support
designed
for
– Increasing
hospitaliza2on
level
– Be.er
burial
– Decreasing
2me
to
hospitaliza2on
• Capacity
monitoring
at
ETU/ECU
designed
– Need
some
bounds
on
experimental
design
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
18

19. Suppor2ng
material
describing
model
structure,
and
addi2onal
results
APPENDIX
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
19

20. 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
20

21. 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
21

22. 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
22

23. Parameters
of
two
historical
outbreaks
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
23

24. 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
24

25. 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
25

26. 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
26

27. Liberia
model
params
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
27

28. Sierra
Leone
model
params
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
28

29. All
Countries
model
params
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
29

30. Long-­‐term
Opera2onal
Es2mates
• Based
on
forced
bend
through
extreme
reduc2on
in
transmission
coefficients,
no
evidence
to
support
bends
at
these
points
– Long
DRAFT
term
–
projecNot
2ons
for
are
unstable
a.ribu2on
or
distribu2on
30
Turn
from
8-­‐26
End
from
8-­‐26
Total
Case
EsXmate
1
month
3
months
13,400
1
month
6
months
15,800
1
month
18
months
31,300
3
months
6
months
64,300
3
months
12
months
91,000
3
months
18
months
120,000
6
months
12
months
682,100
6
months
18
months
857,000