1. Modeling
the
Ebola
Outbreak
in
West
Africa,
2014
Sept
9th
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-­‐101
DRAFT
–
Not
for
a.ribu2on
or
distribu2on

2. Currently
Used
Data
Cases
Deaths
Guinea
771
494
Liberia
1915
871
Sierra
Leone
1297
910
Nigeria
21
7
Total
4004
2282
● Data
from
WHO,
MoH
Liberia,
and
MoH
Sierra
Leone,
available
at
h.ps://github.com/cmrivers/ebola
● 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

3. Epi
Notes
• Nigeria
reports
2ndary
spread
in
Port
Harcourt
– One
of
the
ini2ally
exposed
people
in
quaran2ne
broke
it,
sought
care
in
Port
Harcourt,
treated
by
doc,
who
then
treated
others
200+
contacts
60
as
“high
risk”
–
WHO
• Liberian
situa2on
requires
non-­‐conven2onal
interven2ons
-­‐
WHO
– In
Monrovia,
es2mate
1000
beds
are
needed
now,
only
have
240
beds,
with
260
beds
planned/arriving
– ETCs
fill
instantly
when
opened,
poin2ng
to
a
high
“invisible
caseload”
– Need
roughly
3
workers
per
case
to
safely
manage,
thus
there
is
a
huge
demand
for
HCW,
not
available
locally
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
3

4. Twi.er
Tracking
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
4
Most
common
images:
Jokes
about
bushmeat,
panic,
and
dealing
with
Ebola
pa2ents,
protest,
and
fear
of
entry
to
South
Africa
Most
common
links:
Ebola
song,
Nega2ve
test
result
in
Nigeria,
Screening
of
School
exam
takers
,
US
military
help

5. Liberia
Forecasts
rI:
0.95
rH:
0.65
rF:
0.61
R0
total:
2.22
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
5
8/13
–
8/19
8/20
–
8/26
8/27
–
9/02
9/3
–
9/9
9/10
–
9/16
9/16-­‐
9-­‐22
Actual
175
353
321
468
-­‐-­‐
-­‐-­‐
Forecast
176
229
304
404
533
705
Model
Parameters
'alpha':1/12,
'beta_I':0.17950,
'beta_H':0.062036,
'beta_F':0.489256,
'gamma_h':0.308899,
'gamma_d':0.075121,
'gamma_I':0.050000,
'gamma_f':0.496443,
'delta_1':.5,
'delta_2':.5,
'dx':0.510845
Forecast
performance

6. Sierra
Leone
Forecasts
rI:0.85
rH:0.74
rF:0.31
R0
total:
1.90
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
6
8/6
–
8/12
8/13
–
8/19
8/20
–
8/26
8/27
–
9/02
9/3
–
9/9
9/10
–
9/16
Actual
143
93
100
-­‐-­‐
-­‐-­‐
-­‐-­‐
Forecast
135
168
209
260
324
405
Model
Parameters
'alpha':1/10
'beta_I':0.164121
'beta_H':0.048990
'beta_F':.16
'gamma_h':0.296
'gamma_d':0.044827
'gamma_I':0.055
'gamma_f':0.25
'delta_1':.55
delta_2':.55
'dx':0.58
Forecast
performance

7. All
Countries
Forecasts
Model
Parameters
'alpha':1/10
'beta_I':0.200121
'beta_H':0.029890
'beta_F':0.1
'gamma_h':0.330062
'gamma_d':0.043827
gamma_I':0.05
'gamma_f':0.25
'delta_1':.55
'delta_2':.55
'dx':0.6
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
7
rI:0.85
rH:0.74
rF:0.31
Overal:1.90

8. Combined
Forecasts
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
8
8/10
–
8/16
8/17
–
8/23
8/24
–
8/30
8/31–
9/6
9/8
–
9/13
9/14-­‐
9-­‐20
Actual
231
442
559
502
-­‐-­‐
-­‐-­‐
Forecast
329
393
469
560
669
798

9. Forecas2ng
Resource
Demand
• Accoun2ng
for
prevalent
cases
in
the
model
– Can
include
their
modeled
state:
community,
hospital,
or
burial
• Help
with
logis2cal
planning
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
9

10. Exhaus2ng
Health
Care
System
-­‐
Liberia
• Model
adjusted
to
have
limited
capacity
“be.er”
health
compartment
(sized:
300,
500,
1000,
2000
beds)
added
to
exis2ng
“degraded”
health
compartment
(previous
fit)
• Those
in
new
health
compartment
assumed
to
be
– Well
isolated
and
the
dead
are
buried
properly
(ie
once
in
the
health
system,
very
limited
transmission
to
community
90%
less
than
original
fit)
• More
beds
have
a
measurable
impact
in
total
cases
at
2
months,
but
does
not
halt
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
transmission
alone
10
S E I
H
HD
F R

11. Exhaus2ng
Health
Care
System
–
Sierra
Leone
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
11
S E I
H
HD
F R
• Model
adjusted
to
have
limited
capacity
“be.er”
health
compartment
(sized:
300,
500,
1000,
2000
beds)
added
to
exis2ng
“degraded”
health
compartment
(previous
fit)
• Those
in
new
health
compartment
assumed
to
be
– Well
isolated
and
the
dead
are
buried
properly
(ie
once
in
the
health
system,
very
limited
transmission
to
community
90%
less
than
original
fit)
• More
beds
have
a
measurable
impact
in
total
cases
at
2
months,
but
does
not
halt
transmission
alone

12. 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
are
for
unstable
a.ribu2on
or
distribu2on
12
Turn
from
8-­‐26
End
from
8-­‐26
Total
Case
EsFmate
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

13. Synthe2c
Sierra
Leone
Popula2on
Network,
first
drap
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
13
Now
integrated
into
the
ISIS
interface

14. Agent-­‐based
Sierra
Leone
Calibra2on
• 100
replicates,
seeded
with
1
ini2al
infec2on,
disease
model
similar
to
fi.ed
ODE
parameters
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
14
Epidemic
sizes
Epidemic
curves

15. Next
Steps
-­‐
Compartmental
• Further
refinement
of
to
look
at
health-­‐care
system
and
non-­‐conven2onal
interven2ons
– Impact
of
increased
/
decreased
effec2veness
– What
will
it
take
to
slow
things
down
• Inform
the
agent-­‐based
model
– Geographic
disaggrega2on
– Parameter
es2ma2on
– Interven2on
comparison
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
15

16. Next
Steps
–
Agent-­‐based
• Refining
disease
model
– Mapping
fit
disease
parameters
into
computa2onally
efficient
ABM
representa2on
– Calibra2on
– Representa2on
of
interven2ons
(proper
burial)
• Add
regional
mobility
• ABM
stochas2c
space
larger
than
compartmental,
how
to
accommodate?
• Integra2ng
data
to
assist
in
logis2cal
ques2ons
– Loca2ons
of
ETCs,
lab
facili2es
from
OCHA
– Road
network
– Capaci2es
of
exis2ng
support
opera2ons
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
16

17. Suppor2ng
material
describing
model
structure,
and
addi2onal
results
APPENDIX
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
17

18. Further
evidence
of
endemic
Ebola
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
18
• 1985
manuscript
finds
~13%
sero-­‐prevalence
of
Ebola
in
remote
Liberia
– Paired
control
study:
Half
from
epilepsy
pa2ents
and
half
from
healthy
volunteers
– Geographic
and
social
group
sub-­‐analysis
shows
all
affected
~equally

19. 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
19

20. 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
20

21. 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
21

22. Parameters
of
two
historical
outbreaks
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
22

23. 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
23

24. 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
24

25. 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
25