modeling the ebola outbreak in west africa, november 7th 2014 update
DESCRIPTION
Researchers at the Network Dynamics and Simulation Science Laboratory have been using a combination of modeling techniques to predict the spread of the Ebola outbreak.TRANSCRIPT
DRAFT – Not for a.ribu2on or distribu2on
Modeling the Ebola Outbreak in West Africa, 2014
November 7th Update
Bryan Lewis PhD, MPH ([email protected]) Caitlin Rivers MPH, Eric Lofgren PhD, James Schli., Alex Telionis MPH, Meredith Wilson MPH
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 Barre. PhD
Technical Report #14-‐114
DRAFT – Not for a.ribu2on or distribu2on DRAFT – Not for a.ribu2on or distribu2on
Currently Used Data
● Data from WHO, MoH Liberia, and MoH Sierra Leone, available at h.ps://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.
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Cases Deaths Guinea 1906 997 Liberia 6454 2705 Sierra Leone 5235 1500 Total 13,617 5210
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Liberia – Case Loca2ons
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Liberia – County Case Incidence
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0
0.1
0.2
0.3
0.4
0.5
0.6
5/21/14 6/10/14 6/30/14 7/20/14 8/9/14 8/29/14 9/18/14 10/8/14 10/28/14 11/17/14
Percen
tage of C
ounty Po
pulaBo
n (%
)
Date
Percentage of County PopulaBon Infected with EVD Bomi County
Bong County
Gbarpolu County
Grand Bassa
Grand Cape Mount Grand Gedeh
Grand Kru
Lofa County
Margibi County
Maryland County
Montserrado County
Liberia – County Case Propor2ons
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Liberia – Contact Tracing
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Liberia Forecast – Original Model
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8/9/08 to
9/14
9/15 to
9/21
9/22 to
9/28
9/29 to
10/05
10/06 to
10/12
10/13 to
10/19
10/20 to
10/26
10/27 to
11/02
11/03 to
11/09
Reported 639 560 416 261 298 446 1604* -‐-‐ -‐-‐
Forecast (classic model)
697 927 1232 1636 2172 2883 3825 5070 6741
Reproduc2ve Number Community 1.3 Hospital 0.4 Funeral 0.5 Overall 2.2
52% of Infected are hospitalized
* Repor2ng change
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Learning from Lofa -‐ Summary
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Model fit to Lofa case with a change in behaviors resul2ng in reduced transmission sta2ng mid-‐Aug (blue), compared with observed data (green)
Fit reduc2on seen in Lofa
Model fit to Liberia case with a change in behaviors resul2ng in reduced transmission sta2ng Sept 21st (green), compared with observed data (blue)
Apply to Liberia
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Liberia Forecast – Prelim New Model
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9/16 to
9/21
9/22 to
9/28
9/29 to
10/05
10/06 to
10/12
10/13 to
10/19
10/20 to
10/26
10/27 to
11/02
11/03 to
11/09
11/10 to
11/16
Reported 560 416 261 298 446 1604* -‐-‐ -‐-‐ -‐-‐
Reported back log adjusted
396 251 245 490
New model 757 603 541 580 598 608 617 625 633
Reproduc2ve Number Community 0.5 Hospital 0.2 Funeral 0.2 Overall 1.0
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Prevalence of Cases – New model
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Date People in H+I 9/7/14 523 9/14/14 695 9/20/14 887 9/27/14 1051 10/4/14 1119 10/11/14 1152 10/18/14 1174 10/25/14 1192 11/1/14 1208 11/8/14 1224 11/15/14 1239 11/22/14 1255 11/29/14 1271 12/6/14 1288 12/13/14 1304 12/20/14 1320 12/27/14 1337
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Sierra Leone – County Data
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Sierra Leone – Contact A.ack Rate
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Sierra Leone Forecasts
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9/6 to
9/14
9/14 to
9/21
9/22 to
9/28
9/29 to
10/05
10/06 to
10/12
10/13 to
10/19
10/20 to
10/26
10/27 to
11/02
11/03 to
11/09
Reported 246 285 377 467 468 454 494
Forecast 256 312 380 464 566 690 841 1025 1250
35% of cases are hospitalized
ReproducBve Number Community 1.20 Hospital 0.29 Funeral 0.15 Overall 1.63
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Prevalence in SL
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10/6/14 456.6 10/13/14 556.7 10/20/14 678.8 10/27/14 827.5 11/3/14 1008.8 11/10/14 1229.8 11/17/14 1498.9 11/24/14 1826.8 12/1/14 2226.1 12/8/14 2712.2 12/15/14 3303.7 12/22/14 4023.3 12/29/14 4898.1
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Learning from Lofa
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Model fit to Lofa case series up Aug 18th (green) then from Aug 19 – Oct 21 (blue), compared with real data (red)
DRAFT – Not for a.ribu2on or distribu2on DRAFT – Not for a.ribu2on or distribu2on
Learning from Lofa
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Model fit to Lofa case with a change in behaviors resul2ng in reduced transmission sta2ng mid-‐Aug (blue), compared with observed data (green)
DRAFT – Not for a.ribu2on or distribu2on DRAFT – Not for a.ribu2on or distribu2on
Learning from Lofa
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Model fit to Liberian case data up to Sept 20th (current model in blue), reduc2on in transmissions observed in Lofa applied from Sept 21st on (green), and observed cases (red)
DRAFT – Not for a.ribu2on or distribu2on DRAFT – Not for a.ribu2on or distribu2on
Learning from Lofa
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Model fit to Liberia case with a change in behaviors resul2ng in reduced transmission sta2ng Sept 21st (green), compared with observed data (blue)
DRAFT – Not for a.ribu2on or distribu2on DRAFT – Not for a.ribu2on or distribu2on
Agent-‐based Model Progress
• Added Regional travel pa.erns • Rainy Season Adjustment • Agent-‐based parameter op2miza2on framework
• New GUI deployed for running ABM expts • Ini2al calibra2on with travel for all Liberia – Plausible base case determined – Ini2al a.empts with spa2al spread
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Regional Travel -‐ Liberia • Mobility data comes from flowminder.org
– Probability Matrix of county to county trips by week (15x15) – Number of trips probably high, ra2os be.er – Es2mates available for several model fits – Data converted to daily probabili2es
• Method: Make dynamic schedules for EpiSimdemics – Each person has a home county based on home loca2on – Each person is matched with a person in each non-‐home county, based on gender and age bin
– For each person and non-‐home county, a new schedule is created that shadows the schedule of the matched person
– A scenario file is created that contains rules for each source/des2na2on pair (15 x 14 = 210 for Liberia)
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Regional Travel -‐ Example
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# Travel from Grand_Kru (2042) to Maryland (2082) with prob 0.008036427trigger repeatable person.County = 2042 and person.isTraveling = -1 apply travel_to_2082 with prob=0.008036427
intervention travel_to_2008 set person.isTraveling = 2008 set person.daysLeft = 3 set tripsTo2008++ set traveling++ set trips++ schedule county2008 1
# return from travelintervention return unschedule 1 set person.isTraveling = -1 set person.daysLeft = -1 set traveling--
trigger repeatable person.daysLeft > 0 set person.daysLeft—
trigger repeatable person.daysLeft = 1 apply return
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Regional Travel -‐ Trips
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100000
100500
101000
101500
102000
102500
103000
103500
104000
104500
105000
10 20 30 40 50 60 70 80 90 100
Tra
velle
rs
Simulation Day
Travelers per day
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Regional Travel – Trips
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0
2000
4000
6000
8000
10000
12000
0 10 20 30 40 50 60 70 80 90 100
Tri
p S
tart
s
Simulation Day
MontserradoMargibi
BomiGrand_Bassa
BongGrand_Cape_Mount
NimbaGbarpolu
River_CessLofa
Grand_GedehMaryland
SinoeRiver_GeeGrand_Kru
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Rainy Season – Road Degrada2on
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Rainy Season – Road Degrada2on
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Bomi Bong Gbarpolu Grand Bassa
Grand Cape Mount Grand Gedeh Grand Kru Lofa Margibi Maryland Montserrado Nimba River Cess River Gee Sinoe Green 1
Bomi 0.55 0.5 1 0.5 0.425 0.425 0.1 1 0.425 1 0.55 0.1 0.425 0.3 Red 0.5
Bong 0.55 0.3 0.55 0.3 1 1 1 1 1 1 1 0.1 1 0.36666666
7 Black 0.1 Gbarpolu 0.5 0.3 0.5 0.5 0.425 0.425 0.1 0.5 0.425 0.5 0.3 0.1 0.425 0.3
Grand Bassa 1 0.55 0.5 0.5 0.3 0.3 0.4 1 0.3 1 0.55 0.1 0.3 0.3 Based on traveling from county capital to county capital
Grand Cape Mount 0.5 0.3 0.5 0.5 0.3 0.3 0.3 0.5 0.3 0.5 0.23333333
3 0.1 0.3 0.3 Based on 17SEPT2014 data Grand Gedeh 0.425 1 0.425 0.3 0.3 1 1 0.55 1 0.55 1 0.1 1 0.5
Grand Kru 0.425 1 0.425 0.3 0.3 1 1 0.53333333
3 1 0.533333333 1 0.1 1 0.5
Lofa 0.1 1 0.1 0.4 0.3 1 1 0.55 1 0.55 1 0.1 1 0.21428571
4
Margibi 1 1 0.5 1 0.5 0.55 0.53333333
3 0.55 0.53333333
3 1 1 0.1 0.53333333
3 0.3
Maryland 0.425 1 0.425 0.3 0.3 1 1 1 0.53333333
3 0.533333333 1 0.1 1 0.5
Montserrado 1 1 0.5 1 0.5 0.55 0.53333333
3 0.55 1 0.53333333
3 0.55 0.1 0.53333333
3 0.3
Nimba 0.55 1 0.3 0.55 0.233333333 1 1 1 1 1 0.55 0.1 1 0.23333333
3 River Cess 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
River Gee 0.425 1 0.425 0.3 0.3 1 1 1 0.53333333
3 1 0.533333333 1 0.1 0.5
Sinoe 0.3 0.36666666
7 0.3 0.3 0.3 0.5 0.5 0.214285
714 0.3 0.5 0.3 0.23333333
3 0.1 0.5
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Auto-‐Calibra2on of ABM
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SIBEL – New version
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SIBEL – New features
• Generic interven2on supports more possible interven2ons
• Dura2on and logis2cal rates of interven2on added
• Many more…
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Plausible Base Case
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• Hospital isola2on for 50% -‐ reduces txm by 80% • Proper burial for 50% -‐ reduces txm by 80% • Ebola Mode: Transmission in household 3x more likely than
outside the household
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Transmission calibra2on
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4665 cases
Day 158 Day 27 22 cases
131 days Burn in period
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Calibra2on – Spa2al Spread
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Simula2on Comparison
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Cases per 100k popula2on
Mean simula2on results Ministry of Health Data
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Simula2on Comparison
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Total Cases
Single Simula2on result Ministry of Health Data
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Agent-‐based Next Steps • Spa2al spread calibra2on – Incorporate degraded road network to help guide finng to current data
– Guide with more spa2ally explicit ini2al infected seeds and intervenBons
– Incorporate road degrada2on for rainy season • Planned Experiments: – Impact of hospitals with geo-‐spa2al disease
• Study design / implementa2on under construc2on – Vaccina2on campaign effec2veness
• Framework under development
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APPENDIX Suppor2ng material describing model structure, and addi2onal results
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Legrand et al. Model Descrip2on
Exposednot infectious
InfectiousSymptomatic
RemovedRecovered and immune
or dead and buried
Susceptible
HospitalizedInfectious
FuneralInfectious
Legrand, J, R F Grais, P Y Boelle, A J Valleron, and A Flahault. “Understanding the Dynamics of Ebola Epidemics” Epidemiology and Infec1on 135 (4). 2007. Cambridge University Press: 610–21. doi:10.1017/S0950268806007217.
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DRAFT – Not for a.ribu2on or distribu2on DRAFT – Not for a.ribu2on or distribu2on
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 Infec1on 135 (4). 2007. Cambridge University Press: 610–21. doi:10.1017/S0950268806007217.
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Legrand et al. Approach
• Behavioral changes to reduce transmissibili2es at specified days
• Stochas2c implementa2on 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
• Mul2ple stages of behavioral change possible during this prolonged outbreak
• Op2miza2on 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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Op2mized Fit Process • Parameters to explored selected – Diag_rate, beta_I, beta_H, beta_F, gamma_I, gamma_D, gamma_F, gamma_H
– Ini2al values based on two historical outbreak • Op2miza2on rou2ne
– Runs model with various permuta2ons of parameters
– Output compared to observed case count
– Algorithm chooses combina2ons that minimize the difference between observed case counts and model outputs, selects “best” one
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Fi.ed Model Caveats
• Assump2ons: – Behavioral changes effect each transmission route similarly
– Mixing occurs differently for each of the three compartments but uniformly within
• These models are likely “overfi.ed” – Many combos of parameters will fit the same curve – Guided by knowledge of the outbreak and addi2onal data sources to keep parameters plausible
– Structure of the model is supported
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Model parameters
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Sierra&Leonealpha 0.1beta_F 0.111104beta_H 0.079541beta_I 0.128054dx 0.196928gamma_I 0.05gamma_d 0.096332gamma_f 0.222274gamma_h 0.242567delta_1 0.75delta_2 0.75
Liberiaalpha 0.083beta_F 0.489256beta_H 0.062036beta_I 0.1595dx 0.2gamma_I 0.066667gamma_d 0.075121gamma_f 0.496443gamma_h 0.308899delta_1 0.5delta_2 0.5
All Countries Combined