This document summarizes modeling work done to forecast the Ebola outbreak in West Africa in 2014. It presents compartmental models fitted to case count data from Guinea, Liberia, and Sierra Leone. The models are extensions of previous work and include adjustments for limited healthcare capacity. Forecasts are generated for each country through September 2014, with the overall trend expected to continue rising without significant behavioral changes or other interventions.

1. Modeling
the
Ebola
Outbreak
in
West
Africa,
2014
Sept
5th
Update
Bryan
Lewis
PhD,
MPH
(blewis@vbi.vt.edu)
Caitlin
Rivers
MPH,
Eric
Lofgren
PhD,
James
Schli.,
Ka2e
Dunphy,
Stephen
Eubank
PhD,
Madhav
Marathe
PhD,
and
Chris
Barre.
PhD
Technical
Report
#14-­‐100
DRAFT
–
Not
for
a.ribu2on
or
distribu2on

2. Currently
Used
Data
Cases
Deaths
Guinea
749
489
Liberia
1839
907
Sierra
Leone
1297
910
Nigeria
21
7
Total
3069
1563
● Data
from
WHO,
MoH
Liberia,
and
MoH
Sierra
Leone,
available
here:
● 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. Liberia
Forecasts
rI:
0.95
rH:
0.65
rF:
0.61
R0
total:
2.22
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
3
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
163
232
296
296
-­‐-­‐
-­‐-­‐
Forecast
133
176
234
310
410
543
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

4. Forecas2ng
Resource
Demand
• Accoun2ng
for
prevalent
cases
in
the
model
– Can
include
their
modeled
state:
community,
hospital,
or
burial
• Help
with
logisi2cal
planning
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
4

5. Exhaus2ng
Health
Care
System
• 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
5
S E I
H
HD
F R

6. Next
Steps
• Agent-­‐based
modeling:
– Ini2al
version
of
Sierra
Leone
constructed
– Need
more
work
on
mixing
es2mates
– Ini2al
look
at
subloca2on
modeling
required
a
re-­‐
adjustment
– Gathering
data
to
assist
in
logis2cal
ques2ons
• Further
refinement
of
compartmental
model
to
look
at
health-­‐care
system
ques2ons
– Impact
of
increased
/
decreased
effec2veness
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
6

7. Suppor2ng
material
describing
model
structure,
and
addi2onal
results
APPENDIX
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
7

8. Epi
Notes
• Case
iden2fied
in
Senegal
– Guinean
student,
sought
care
in
Dakar,
iden2fied
and
quaran2ned
though
did
not
report
exposure
to
Ebola,
thus
HCWs
were
exposed.
BBC
• Liberian
HCWs
survival
credited
to
Zmapp
– Dr.
Senga
Omeonga
and
physician
assistant
Kynda
Kobbah
were
discharged
from
a
Liberian
treatment
center
on
Saturday
aoer
recovering
from
the
virus,
according
to
the
World
Health
Organiza2on.
CNN
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
8

9. Epi
Notes
• Guinea
riot
in
Nzerekore
(2nd
city)
on
Aug
29
– Market
area
“disinfected,”
angry
residents
a.ack
HCW
and
hospital,
“Ebola
is
a
lie”
BBC
• India
quaran2nes
6
“high-­‐risk”
Ebola
suspects
on
Monday
in
New
Delhi
– Among
181
passengers
who
arrived
in
India
from
the
affected
western
African
countries
HealthMap
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
9

10. Further
evidence
of
endemic
Ebola
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
10
• 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

11. Twi.er
Tracking
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
11
Most
common
images:
Risk
map,
lab
work
(britain),
joke
cartoon,
EBV
rally

12. 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
12

13. 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
13

14. 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
14

15. Parameters
of
two
historical
outbreaks
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
15

16. 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
16

17. 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
17

18. 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
18

19. Sierra
Leone
Forecasts
rI:0.85
rH:0.74
rF:0.31
R0
total:
1.90
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
19
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

20. All
Countries
Forecasts
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
20
rI:0.85
rH:0.74
rF:0.31
Overal:1.90

21. Exhaus2ng
Health
Care
System
DRAFT
–
Not
for
a.ribu2on
or
distribu2on
21
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

22. 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
22
Turn
from
8-­‐26
End
from
8-­‐26
Total
Case
EsJmate
1
month
6
months
15,800
1
month
18
months
31,300
3
months
6
months
64,300
3
months
18
months
120,000
6
months
9
months
599,000
6
months
18
months
857,000