Transcript September 5, 2014

Modeling the Ebola
Outbreak in West Africa, 2014
Sept 5th Update
Bryan Lewis PhD, MPH ([email protected])
Caitlin Rivers MPH, Eric Lofgren PhD, James Schlitt, Katie Dunphy,
Stephen Eubank PhD, Madhav Marathe PhD,
and Chris Barrett PhD
Currently Used Data
Cases
Deaths
Guinea
749
489
Liberia
1839
907
Sierra Leone
1297
910
21
7
3069
1563
Nigeria
Total
●
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.
2
Liberia Forecasts
Forecast performance
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
rI: 0.95
rH: 0.65
rF: 0.61
R0 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
3
Forecasting Resource Demand
• Accounting for
prevalent cases in the
model
– Can include their
modeled state:
community, hospital, or
burial
• Help with logisitical
planning
4
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
5
Next Steps
• Agent-based modeling:
– Initial version of Sierra Leone constructed
– Need more work on mixing estimates
– Initial look at sublocation modeling required a readjustment
– Gathering data to assist in logistical questions
• Further refinement of compartmental model
to look at health-care system questions
– Impact of increased / decreased effectiveness
6
Supporting material describing model structure, and additional results
APPENDIX
7
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
8
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
9
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
10
Twitter Tracking
Most common images:
Risk map, lab work (britain), joke cartoon, EBV rally
11
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
12
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.
13
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
14
Parameters of two historical outbreaks
15
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
16
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
17
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
18
Sierra Leone Forecasts
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
19
All Countries Forecasts
rI:0.85
rH:0.74
rF:0.31
Overal:1.90
20
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
21
Long-term Operational Estimates
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
3 months
18 months 120,000
6 months
9 months
6 months
18 months 857,000
64,300
599,000
• Based on forced bend through extreme reduction in transmission
coefficients, no evidence to support bends at these points
– Long term projections are unstable
22