Modeling the Ebola Outbreak in West Africa, 2014
Sept 16th 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
● 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.
Cases DeathsGuinea 861
557Liberia 24071137Nigeria 22
8Sierra Leone 1603524Total 48932226
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Liberia- Case Locations
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Liberia – Health Care Workers
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Liberia – Contact Tracing
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Liberia – Community based cases
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Sierra Leone – Case Locations
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Sierra Leone – Case Finding
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Sierra Leone – Case FindingAssuming 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)
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Line Listing
• 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_location,legrand,exposure,hcw,source_id,identifying_notes,source
case_id exposure_date onset_date hospital_date death_date recovery_date age sex countrysub_location sub_sub_location legrand exposure hcw source_id identifying_notes ource
1 2013-12-02 2013-12-06 child GuineaGueckedou Meliandou c zoonotic N http://www.nejm.org/doi/full/10.1056/NEJMoa1404505
2 2013-12-13 adult F GuineaGueckedou Meliandou c family N 1 mother http://www.nejm.org/doi/full/10.1056/NEJMoa1404506
3 2013-12-25 2013-12-27 child F GuineaGueckedou Meliandou c family N 1 sister http://www.nejm.org/doi/full/10.1056/NEJMoa1404507
4 2014-01-01 elderly F GuineaGueckedou c family Y 1 grandmother http://www.nejm.org/doi/full/10.1056/NEJMoa1404508
5 2014-01-29 2014-01-31 adult F GuineaGueckedou h hcw Y 1 nurse http://www.nejm.org/doi/full/10.1056/NEJMoa1404509
6 2014-01-25 2014-02-02 adult F GuineaGueckedou h hcw Y 1 midwife http://www.nejm.org/doi/full/10.1056/NEJMoa1404510
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Line Listing - Epidemiology
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Line Listing – Exposure Type
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Line Listing – Transmission Trees
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Twitter TrackingMost common images:
Information about bushmeat, info about case locations, joke about soap cost, and dealing with Ebola patients,
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Liberia Forecasts
8/13 – 8/19
8/20 – 8/26
8/27 – 9/02
9/3 – 9/9
9/10 – 9/16
9/17-9/23
9/24 – 9/30
Actual 175 353 321 468 544 --Forecast 176 229 304 404 533 801 1064
Forecast performance Reproductive NumberCommunity 1.34Hospital 0.35Funeral 0.53Overall 2.22
52% of Infected arehospitalized
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Liberia Forecasts – Role of Prior Immunity
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Sierra Leone Forecasts
Reproductive NumberCommunity 1.22Hospital 0.23Funeral 0.24Overall 1.69
Forecast performance
59% of cases are hospitalized
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Prevalence of Cases
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All Countries Forecasts
rI:0.85rH:0.74rF:0.31Overal:1.90
Model Parameters'alpha':1/10'beta_I':0.200121'beta_H':0.029890'beta_F':0.1'gamma_h':0.330062'gamma_d':0.043827gamma_I':0.05'gamma_f':0.25'delta_1':.55'delta_2':.55'dx':0.6
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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
9/14-9/20
9/21 – 9/27
9/28 – 10/4
Actual 231 442 559 783 681 -- -- --Forecast 329 393 469 560 693 830 994 1191
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Synthetic Sierra Leone
Now integrated into the ISIS interface
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ISIS - based Calibration
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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
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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
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APPENDIXSupporting material describing model structure, and additional results
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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
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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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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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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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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Liberia model params
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Sierra Leone model params
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All Countries model params
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Long-term Operational Estimates
• Based on forced bend through extreme reduction in transmission coefficients, no evidence to support bends at these points– Long term projections are unstable
Turn from 8-26
End from 8-26
Total Case 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