Modeling the Ebola Outbreak in West Africa, November 7th 2014 update

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.

2

Cases Deaths Guinea 1906 997 Liberia 6454 2705 Sierra Leone 5235 1500 Total 13,617 5210


Liberia – Case Loca2ons

3


Liberia – County Case Incidence

4


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

5


Liberia – Contact Tracing

6


Liberia Forecast – Original Model

7

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


Learning from Lofa -‐ Summary

8

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


Liberia Forecast – Prelim New Model

9

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


Prevalence of Cases – New model

10

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


Sierra Leone – County Data

11


Sierra Leone – Contact A.ack Rate

12


Sierra Leone Forecasts

13

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


Prevalence in SL

14

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


Learning from Lofa

15

Model fit to Lofa case series up Aug 18th (green) then from Aug 19 – Oct 21 (blue), compared with real data (red)


Learning from Lofa

16

Model fit to Lofa case with a change in behaviors resul2ng in reduced transmission sta2ng mid-‐Aug (blue), compared with observed data (green)


Learning from Lofa

17

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)


Learning from Lofa

18

Model fit to Liberia case with a change in behaviors resul2ng in reduced transmission sta2ng Sept 21st (green), compared with observed data (blue)


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

19


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)

20


Regional Travel -‐ Example

21

# 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


Regional Travel -‐ Trips

22

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


Regional Travel – Trips

23

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


Rainy Season – Road Degrada2on

24


Rainy Season – Road Degrada2on

25

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


Auto-‐Calibra2on of ABM

26


SIBEL – New version

27


SIBEL – New features

•  Generic interven2on supports more possible interven2ons

•  Dura2on and logis2cal rates of interven2on added

•  Many more…

28


Plausible Base Case

29

•  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


Transmission calibra2on

30

4665 cases

Day 158 Day 27 22 cases

131 days Burn in period


Calibra2on – Spa2al Spread

31


Simula2on Comparison

32

Cases per 100k popula2on

Mean simula2on results Ministry of Health Data


Simula2on Comparison

33

Total Cases

Single Simula2on result Ministry of Health Data


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

34

DRAFT – Not for a.ribu2on or distribu2on

APPENDIX Suppor2ng material describing model structure, and addi2onal results

35


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.

36


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.

37


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

38


Parameters of two historical outbreaks

39


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

40


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

41


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

42


Model parameters

43

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

Science

Modeling the Ebola Outbreak in West Africa, November 7th 2014 update