Modeling the Ebola
Outbreak in West Africa, 2014
Sept 23rd 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
2712
22
1603
5198
Deaths
557
1137
8
524
2226
Data from WHO, MoH Liberia, and
MoH Sierra Leone, available at
https://github.com/cmrivers/ebola
MoH and WHO have reasonable agreement
Sierra Leone case counts censored up
to 4/30/14.
Time series was filled in with missing
dates, and case counts were
interpolated.
2
Epi Notes
• WHO reports results on case history analysis
providing clarity on some disease parameters
NEJM
• CDC releases their model with some dire
forecasts MMWR
• Sierra Leone not doing as well as they report
– More graves from Ebola patients than reported
cases – NY Times
3
Comparison of Parameters
4
Liberia- Case Locations
5
Liberia – Contact Tracing
6
Contact Tracing Metrics
7
Sierra Leone – Contact Tracing Efficiency
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
Twitter Tracking
Most common images:
Solidarity with Ebola affected countries, Jokes about
bushmeat, Ebola risk, and names, Positive health message
10
Liberia Forecasts
Forecast performance
8/13 –
8/19
8/20 –
8/26
8/27 –
9/02
9/3 –
9/9
9/10 –
9/16
9/179/23
9/24 –
9/30
175
353
321
468
544
--
--
Forecast 176
229
304
404
533
801
1105
Actual
52% of Infected are
hospitalized
Reproductive Number
Community 1.5
Hospital
0.1
Funeral
0.4
Overall
2.0
11
Liberia Forecasts – Role of Prior Immunity
12
Sierra Leone Forecasts
Forecast performance
41% of cases are
hospitalized
13
Prevalence of Cases
14
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
15
Combined Forecasts
Reproductive Number
Community 1.3
Hospital
0.1
Funeral
0.3
Overall
1.7
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
1007
1213
16
Learning from Lofa
• Lofa has experienced decreasing cases for several
weeks
– Exploring with contacts in MoH about whether these are
reporting artifact or reality and to understand what factors
are driving it
• The decrease starts at 0.13% of population infected
– Montserrado is currently at 0.101%, model predicts this
will occur on 9/19
• If we fit the decreased rate in Lofa what might
Monteserrado look like?
– Assuming equal decrease across all betas until more info
available
17
Learning from Lofa
18
Learning from Lofa
19
Hospital Beds – Prelim analysis
• Proposed scenario of 70% in hospital beds will
tip epidemic
• Explore using Compartmental Model
– Based on Liberia wide model
– Trigger change at a certain point in time (ie
instantaneously move up to 70%)
– Transmission in hospitals also assumed to be 90%
better than current fit
20
Hospital Beds – Prelim analysis
Impact in Liberia
Cases on Feb 1
Oct 1
155k
Nov 1
226k
Dec 1
352k
Jan 1
521k
No beds 669k
21
Hospital Beds – Discrete Rollout
• Using Stochastic model
– Monteserrado model fit (very high transmission
fit)
– 170 beds start arriving every week from midOctober on
– These beds are assumed to be 100% effective
– If beds are full, the current “hospitals” are
assumed to absorb
– No lower tier but better than current ECUs in
place
22
Hospital Beds – Discrete Rollout
23
Synthetic Liberia
Now integrated into the CNIMS interface
24
Agent-based Simulations
• Running simulations on two simulation
platforms
– EpiFast – Fast, integrated with CNIMS interface,
some interventions and behaviors can’t be
represented
– EpiSimdemics – Very flexible, can represent nearly
any conceivable behavior or intervention, slower,
and more cumbersome to execution
25
ABM of Monrovia
26
EpiSimdemics ABM running
27
Next steps
• Focus on agent-based model
– Incorporating regional travel
– Re-calibrate with WHO based parameters
– Set up to incorporate behaviors
• Address bed rollout in Stochastic
Compartmental model
– Sensitivity analysis to identify what capacities and
assumed reductions are necessary for turning the
epidemic down.
28
Supporting material describing model structure, and additional results
APPENDIX
29
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
30
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
31
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.
32
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
33
Parameters of two historical outbreaks
34
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
35
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
36
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
37
Liberia model params
38
Sierra Leone model params
39
All Countries model params
40
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
41