September 9, 2014

Report
Modeling the Ebola
Outbreak in West Africa, 2014
Sept 9th Update
Bryan Lewis PhD, MPH ([email protected])
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
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Currently Used Data
Cases
Deaths
Guinea
771
494
Liberia
1915
871
Sierra Leone
1297
910
21
7
4004
2282
Nigeria
Total
●
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.
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2
Epi Notes
• Nigeria reports 2ndary spread in Port Harcourt
– One of the initially exposed people in quarantine broke it,
sought care in Port Harcourt, treated by doc, who then
treated others 200+ contacts 60 as “high risk” – WHO
• Liberian situation requires non-conventional
interventions - WHO
– In Monrovia, estimate 1000 beds are needed now, only
have 240 beds, with 260 beds planned/arriving
– ETCs fill instantly when opened, pointing 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
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Twitter Tracking
Most common images:
Jokes about bushmeat, panic, and dealing with Ebola
patients, protest, and fear of entry to South Africa
Most common links:
Ebola song, Negative test result in Nigeria,
Screening of School exam takers , US
military help
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Liberia Forecasts
Forecast performance
rI: 0.95
rH: 0.65
rF: 0.61
R0 total: 2.22
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
8/13 –
8/19
8/20 –
8/26
8/27 –
9/02
9/3 –
9/9
9/10 –
9/16
9/169-22
175
353
321
468
--
--
Forecast 176
229
304
404
533
705
Actual
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Sierra Leone Forecasts
Forecast performance
rI:0.85
rH:0.74
rF:0.31
R0 total: 1.90
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
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
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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
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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
231
442
559
502
--
--
Forecast 329
393
469
560
669
798
Actual
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Forecasting Resource Demand
• Accounting for
prevalent cases in the
model
– Can include their
modeled state:
community, hospital, or
burial
• Help with logistical
planning
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Exhausting Health Care System - Liberia
•
•
Model adjusted to have limited capacity “better” health compartment (sized: 300, 500,
1000, 2000 beds) added to existing “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
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10
Exhausting Health Care System – Sierra Leone
•
•
Model adjusted to have limited capacity “better” health compartment (sized: 300, 500,
1000, 2000 beds) added to existing “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
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11
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
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12
Synthetic Sierra Leone Population Network,
first draft
Now integrated into the ISIS interface
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13
Agent-based Sierra Leone Calibration
Epidemic sizes
Epidemic curves
• 100 replicates, seeded with 1 initial infection,
disease model similar to fitted ODE parameters
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14
Next Steps - Compartmental
• Further refinement of to look at health-care
system and non-conventional interventions
– Impact of increased / decreased effectiveness
– What will it take to slow things down
• Inform the agent-based model
– Geographic disaggregation
– Parameter estimation
– Intervention comparison
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Next Steps – Agent-based
• Refining disease model
– Mapping fit disease parameters into computationally
efficient ABM representation
– Calibration
– Representation of interventions (proper burial)
• 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
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Supporting material describing model structure, and additional results
APPENDIX
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17
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
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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
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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.
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20
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
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Parameters of two historical outbreaks
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22
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
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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
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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
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25

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