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 Schlitt, Katie Dunphy,

Stephen Eubank PhD, Madhav Marathe PhD, and Chris Barrett PhD

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Currently Used DataCases 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:● 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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Liberia Forecasts

rI: 0.95rH: 0.65rF: 0.61R0 total: 2.22

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

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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 logisitical planning

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Exhausting Health Care System

• 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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Next Steps

• Agent-based modeling:– Initial version of Sierra Leone constructed– Need more work on mixing estimates– Initial look at sublocation modeling required a re-

adjustment– Gathering data to assist in logistical questions

• Further refinement of compartmental model to look at health-care system questions– Impact of increased / decreased effectiveness

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APPENDIXSupporting material describing model structure, and additional results

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Epi Notes

• Case identified in Senegal– Guinean student, sought care in Dakar, identified

and quarantined 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 after recovering from the virus, according to the World Health Organization. CNN

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Epi Notes

• Guinea riot in Nzerekore (2nd city) on Aug 29– Market area “disinfected,” angry residents attack

HCW and hospital, “Ebola is a lie” BBC• India quarantines 6 “high-risk” Ebola suspects

on Monday in New Delhi– Among 181 passengers who arrived in India from

the affected western African countries HealthMap

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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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Twitter TrackingMost common images:

Risk map, lab work (britain), joke cartoon, EBV rally

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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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Sierra Leone Forecasts

rI:0.85rH:0.74rF:0.31R0 total: 1.90

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':.55delta_2':.55'dx':0.58

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All Countries Forecasts

rI:0.85rH:0.74rF:0.31Overal:1.90

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Exhausting Health Care System

• 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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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 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