August 11, 2014 - Network Dynamics & Simulation Science Laboratory

Report
Modeling the Ebola
Outbreak in West Africa, 2014
August 11th Update
Bryan Lewis PhD, MPH ([email protected])
Caitlin Rivers MPH, Stephen Eubank PhD,
Madhav Marathe PhD, and Chris Barrett PhD
Goals
• Estimate future cases in Africa
• Offer any guidance on potential for
transmission in the United States
• Explore impact of various countermeasures
Data Sources
• Using case counts from WHO for Model Fitting
– Lots of variability from different sources, generally similar
– Challenging to estimate what proportion of infections are
captured
• Liberia’s Ministry of Health for Model
Selection and geographic resolution
Currently Used WHO Data
Cases
Deaths
Guinea
495
363
Liberia
516
282
Sierra Leone
691
286
Nigeria
13
2
1779
961
Total
●
●
●
Data reported by WHO on Aug 8 for
cases as of Aug 6
Sierra Leone case counts censored up
to 4/30/14.
Time series was filled in with missing
dates, and case counts were
interpolated.
Measure of Awareness?
Jul 29
Aug 8
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.
Legrand et al. Model Description
Susceptible
Exposed
not infectious
Infectious
Symptomatic
Hospitalized
Infectious
Funeral
Infectious
Removed
Recovered and immune
or dead and buried
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
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
Liberia Fitted Models
Assuming no impact from ongoing responses Assuming no impact from ongoing responses
and DRC parameter fit is correct:
and Uganda parameter fit is correct:
142 cases in next week
178 cases in next week
182 cases in the following week
235 cases in the following week
Liberia Fitted Models
Sources of Infections
Currently 14% of Liberian Infections among HCW
Supports use of “Uganda” parameter set
Liberia Forecasts over time
1. Model trained
on Liberian data,
using “Uganda”
parameters up to
specified date
2. Model projected
past “trained to”
date
3. Complete case
count data
provided for
reference
Sierra Leone Fitted Models
Assuming no impact from ongoing responses Assuming no impact from ongoing responses
and DRC parameter fit is correct:
and Uganda parameter fit is correct:
208 cases in next week
211 cases in next week
267 cases in the following week
273 cases in the following week
Sierra Leone Forecasts over time
Model trained on Sierra Leone data up to specified date, projected into future,
Complete case count data provided for reference
Explore Intervention Requirements
Vaccination of large swaths of population required to reduce txm, unless a targeted strategy
is used
Explore Intervention Requirements
This does not capture reduction in deaths, but shows nominal interruption of transmission
Notional US estimates
• Under assumption that Ebola case, arrives and doesn’t
seek care and avoids detection throughout illness
• CNIMS based simulations
– Agent-based models of populations with realistic social
networks, built up from high resolution census, activity,
and location data
• Assume:
– Reduced transmission Ebola 70% less likely to infect in
home and 95% less likely to infect outside of home than
respiratory illness
– Transmission calibrated to R0 of 3.5 if transmission is like
flu
Notional US estimates Approach
• Get disease parameters from fitted model in
West Africa
• Put into CNIMS platform
– ISIS simulation GUI
– Modify to represent US
• Example Experiment:
– 100 replicates
– One case introduction into Washington DC
– Simulate for 3 weeks
Notional US estimates Example
An Epi Plot
Cell=7187
3
0
1
2
Cumulative Infections
4
5
6
Replicate Mean
Overall Mean
0
5
10
Day
100 replicates
Mean of 1.8 cases
Max of 6 cases
Majority only one initial case
15
20
Conclusions
• Still need more information (though more is becoming
available) to remove uncertainty in estimates
• From available data and in the absence of significant
mitigation outbreak in Africa looks to continue to
produce significant numbers of cases in the coming
weeks
• Under current assumptions, Ebola transmission hard to
interrupt in Africa with “therapeutics” alone
• Expert opinion and preliminary simulations support
limited spread in US context
Next Steps
• Gather further data from news media and
reports to support model parameter selection
• Build patch model framework to incorporate
more geographic location information
• Build more detailed population of area to
support agent based simulations
ADDITIONAL SLIDES FOR MORE
DETAILS
Liberia Fitted Models
Model Parameters
Liberia Disease Parameters for Model Fitting
UgandaOut
Uganda_in DRCOut
DRC_in
beta_F
0.858
1.093
0.081
0.066
beta_H
0.091
0.113
0.003
0.002
beta_I
0.123
0.084
0.204
0.505
dx
0.585
0.650
0.867
0.670
gamma_I
0.050
0.100
0.079
0.100
gamma_d
0.084
0.125
0.050
0.104
gamma_f
0.665
0.500
0.512
0.500
gamma_h
0.335
0.238
0.153
0.200
Score
62370
NA
103596
NA
No behavioral Changes included
Sierra Leone Fitted Models
Model Parameters
Sierra LeoneDisease Parameters for Model Fitting
UgandaOut
Uganda_in DRCOut
DRC_in
beta_F
1.752
1.093
0.045
0.066
beta_H
0.260
0.113
0.001
0.002
beta_I
0.083
0.084
0.296
0.505
dx
0.323
0.650
0.300
0.670
gamma_I
0.247
0.100
0.149
0.100
gamma_d
0.211
0.125
0.159
0.104
gamma_f
0.330
0.500
0.814
0.500
gamma_h
0.247
0.238
0.333
0.200
Score
140931
NA
114419
NA
No behavioral Changes included
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
Parameters of two historical outbreaks
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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