Modeling the Ebola
Outbreak in West Africa, 2014
Sept 16th Update
Bryan Lewis PhD, MPH (blewis@vbi.vt.edu)
Caitlin Rivers MPH, Eric Lofgren PhD, James Schlitt, Katie 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 Barrett PhD
Currently Used Data
Guinea
Liberia
Nigeria
Sierra Leone
Total
●
Cases
861
2407
22
1603
4893
Deaths
557
1137
8
524
2226
Data from WHO, MoH Liberia, and
MoH Sierra Leone, available at
https://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.
2
Liberia- Case Locations
3
Liberia – Health Care Workers
4
Liberia – Contact Tracing
5
Liberia – Community based cases
6
Sierra Leone – Case Locations
7
Sierra Leone – Case Finding
8
Sierra Leone – Case Finding
Assuming all cases are followed to the same degree, this what the
“observed” Re would be based on cases found from contacts (using time
lagged 7,10,12 day reported cases as denominator)
9
Line Listing
case_id
exposure_date onset_date
hospital_date
1
2013-12-02
http://www.nejm.org/doi/full/10.1056/NEJMoa1404505
2
http://www.nejm.org/doi/full/10.1056/NEJMoa1404506
3
2013-12-25
http://www.nejm.org/doi/full/10.1056/NEJMoa1404507
4
http://www.nejm.org/doi/full/10.1056/NEJMoa1404508
5
2014-01-29
http://www.nejm.org/doi/full/10.1056/NEJMoa1404509
6
2014-01-25
http://www.nejm.org/doi/full/10.1056/NEJMoa1404510
death_date
recovery_date
age
country
sub_location
sub_sub_location
legrand
exposure
Guinea
Gueckedou
Meliandou
c
zoonotic
N
F
Guinea
Gueckedou
Meliandou
c
family
F
Guinea
Gueckedou
Meliandou
c
family
elderly
F
Guinea
Gueckedou
c
2014-01-31
adult
F
Guinea
Gueckedou
2014-02-02
adult
F
Guinea
Gueckedou
2013-12-06
child
2013-12-13
adult
2013-12-27
child
2014-01-01
sex
hcw
source_id
N
1
mother
N
1
sister
family
Y
1
grandmother
h
hcw
Y
1
nurse
h
hcw
Y
1
midwife
identifying_notes
ource
• Gathered 50 case descriptions from media reports
• Tried to piece together all info we’d like access to from
“comprehensive source”
case_id,exposure_date,onset_date,hospital_date,death_date
,recovery_date,age,sex,country,sub_location,sub_sub_locati
on,legrand,exposure,hcw,source_id,identifying_notes,source
10
Line Listing - Epidemiology
11
Line Listing – Exposure Type
12
Line Listing – Transmission Trees
13
Twitter Tracking
Most common images:
Information about bushmeat, info about case locations,
joke about soap cost, and dealing with Ebola patients,
14
Liberia Forecasts
Forecast performance
Reproductive Number
Community 1.34
Hospital
0.35
Funeral
0.53
Overall
2.22
52% of Infected are
hospitalized
8/13 –
8/19
8/20 –
8/26
8/27 –
9/02
9/3 –
9/9
9/10 –
9/16
9/179/23
175
353
321
468
544
--
Forecast 176
229
304
404
533
801
Actual
9/24 –
9/30
1064
15
Liberia Forecasts – Role of Prior Immunity
16
Sierra Leone Forecasts
Forecast performance
Reproductive Number
Community 1.22
Hospital
0.23
Funeral
0.24
Overall
1.69
59% of cases are
hospitalized
17
Prevalence of Cases
18
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
rI:0.85
rH:0.74
rF:0.31
Overal:1.90
19
Combined Forecasts
8/10 –
8/16
8/17 –
8/23
8/24 –
8/30
8/31–
9/6
9/8 –
9/13
9/149/20
9/21 –
9/27
9/28 –
10/4
Actual
231
442
559
783
681
--
--
--
Forecast
329
393
469
560
693
830
994
1191
20
Synthetic Sierra Leone
Now integrated into the ISIS interface
21
ISIS - based Calibration
22
Next Steps - Compartmental
• Interventions under way
– More hospital beds in urban areas
– More “home-care” kits in rural areas
– Arrival of therapeutics
• Inform the agent-based model
– Geographic disaggregation
– Parameter estimation
– Intervention comparison
23
Next Steps – Agent-based
• Implement new disease mapping
– Has been
• Add regional mobility
• ABM stochastic space larger than
compartmental, how to accommodate?
• Integrating data to assist in logistical questions
– Locations of ETCs, lab facilities from OCHA
– Road network
– Capacities of existing support operations
24
Supporting material describing model structure, and additional results
APPENDIX
25
Further evidence of endemic Ebola
• 1985 manuscript finds ~13% sero-prevalence of Ebola in remote Liberia
– Paired control study: Half from epilepsy patients and half from healthy volunteers
– Geographic and social group sub-analysis shows all affected ~equally
26
Legrand et al. Model Description
Susceptible
Exposed
not infectious
Infectious
Symptomatic
Hospitalized
Infectious
Funeral
Legrand, J, R F Grais, P Y Boelle, A J Valleron, and A
Flahault. “Understanding the Dynamics of Ebola
Epidemics” Epidemiology and Infection 135 (4). 2007.
Cambridge University Press: 610–21.
doi:10.1017/S0950268806007217.
Infectious
Removed
Recovered and immune
or dead and buried
27
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 Infection 135 (4). 2007. Cambridge
University Press: 610–21.
doi:10.1017/S0950268806007217.
28
Legrand et al. Approach
• Behavioral changes to reduce
transmissibilities at specified
days
• Stochastic implementation fit
to two historical outbreaks
– Kikwit, DRC, 1995
– Gulu, Uganda, 2000
• Finds two different “types” of
outbreaks
– Community vs. Funeral driven
outbreaks
29
Parameters of two historical outbreaks
30
NDSSL Extensions to Legrand Model
• Multiple stages of behavioral change possible
during this prolonged outbreak
• Optimization of fit through automated
method
• Experiment:
– Explore “degree” of fit using the two different
outbreak types for each country in current
outbreak
31
Optimized Fit Process
• Parameters to explored selected
– Diag_rate, beta_I, beta_H, beta_F, gamma_I, gamma_D,
gamma_F, gamma_H
– Initial values based on two historical outbreak
• Optimization routine
– Runs model with various
permutations of parameters
– Output compared to observed case
count
– Algorithm chooses combinations that
minimize the difference between
observed case counts and model
outputs, selects “best” one
32
Fitted Model Caveats
• Assumptions:
– Behavioral changes effect each transmission route
similarly
– Mixing occurs differently for each of the three
compartments but uniformly within
• These models are likely “overfitted”
– Many combos of parameters will fit the same curve
– Guided by knowledge of the outbreak and additional
data sources to keep parameters plausible
– Structure of the model is supported
33
Liberia model params
34
Sierra Leone model params
35
All Countries model params
36
Long-term Operational Estimates
Turn
from 8-26
End
Total Case
from 8-26 Estimate
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
• Based on forced bend through extreme reduction in transmission
coefficients, no evidence to support bends at these points
– Long term projections are unstable
37
