Webinar 2011 10 Potter Slides
Modeling a Within-School Contact Network to Understand Influenza Transmission Gail E. Potter Fred Hutchinson Cancer Research Center
October 18, 2011
Manuscript available at: http://arxiv.org/PS_cache/arxiv/pdf/1109/1109.0262v2.pdf
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
1 / 37
Background
When a new strain of influenza virus emerges, we use large-scale simulation models to I I
Estimate epidemic impact Evaluate intervention strategies
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
2 / 37
Background
When a new strain of influenza virus emerges, we use large-scale simulation models to I I
Estimate epidemic impact Evaluate intervention strategies
Many influenza simulation models assume random mixing within mixing groups.
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
2 / 37
Background
When a new strain of influenza virus emerges, we use large-scale simulation models to I I
Estimate epidemic impact Evaluate intervention strategies
Many influenza simulation models assume random mixing within mixing groups. I I
Within school Within grade
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
2 / 37
Background
When a new strain of influenza virus emerges, we use large-scale simulation models to I I
Estimate epidemic impact Evaluate intervention strategies
Many influenza simulation models assume random mixing within mixing groups. I I
Within school Within grade
Schools are known to be a primary mechanism for influenza spread.
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
2 / 37
Scientific questions
1
What is the impact of the social network structure within schools on estimates of epidemic outcomes and intervention effectiveness?
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
3 / 37
Scientific questions
1
What is the impact of the social network structure within schools on estimates of epidemic outcomes and intervention effectiveness?
2
What is the direction of bias created by the random mixing assumption in estimates of epidemic outcomes and intervention effectiveness?
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
3 / 37
Scientific questions
1
What is the impact of the social network structure within schools on estimates of epidemic outcomes and intervention effectiveness?
2
What is the direction of bias created by the random mixing assumption in estimates of epidemic outcomes and intervention effectiveness?
3
Which network structures are important?
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
3 / 37
Scientific questions
1
What is the impact of the social network structure within schools on estimates of epidemic outcomes and intervention effectiveness?
2
What is the direction of bias created by the random mixing assumption in estimates of epidemic outcomes and intervention effectiveness?
3
Which network structures are important?
We create a detailed contact network model based on friendship and contact data and perform simulations to answer these questions.
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
3 / 37
The National Longitudinal Study of Adolescent Health (Add Health) Representative sample of 80 high schools and 52 feeder schools in U.S. during 1994-95 school year We analyze data from one high school+feeder school combination. Students were given a school roster and identified up to 5 best male friends and 5 best female friends. We assume two students are friends if an un-reciprocated or reciprocated nomination occurred. We treat the friendship network data as complete (n=1074). http://www.cpc.unc.edu/projects/addhealth Carolina Population Center, University of North Carolina
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
4 / 37
Friendship-based contact network model
Naive approach: Students only contact their friends, don’t contact non-friends. Simulate disease transmission over friendship network.
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
5 / 37
Friendship-based contact network model
Naive approach: Students only contact their friends, don’t contact non-friends. Simulate disease transmission over friendship network. More realistic approach: Students are more likely to transmit disease to their friends, but may also transmit it to other schoolmates. I I
Students are more likely to contact their friends. Students make longer social contacts with their friends.
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
5 / 37
Friendship-based contact network model
Naive approach: Students only contact their friends, don’t contact non-friends. Simulate disease transmission over friendship network. More realistic approach: Students are more likely to transmit disease to their friends, but may also transmit it to other schoolmates. I I
Students are more likely to contact their friends. Students make longer social contacts with their friends.
We supplement the Add Health data with a survey of contact behavior in schools to create a model capturing these two tendencies.
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
5 / 37
Social Contact Survey Data A Survey on Epidemics in High Schools Survey administered in two Virginia high schools (2009) I I
200 of 400 students surveyed 120 of 1,000 students surveyed
By a “contact,” we mean being in close proximity for more than roughly five minutes. I I I
Average number of contacts during each break between classes Average number of contacts during lunch break Percentage of contacts during school hours to friends
Huadong Xia, Jiangzhuo Chen, Madhav V. Marathe and Henning S. Mortveit, (2010). Synthesis & Embedding of Subnetworks for Individual-based Epidemic Models. NDSSL Technical Report 10-139.
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
6 / 37
Modeling the contact network
Proposal: Define a “contact” to be a 10-minute face-to-face social contact. I
If two students contact each other for an hour, that is 6 “contacts.”
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
7 / 37
Modeling the contact network
Proposal: Define a “contact” to be a 10-minute face-to-face social contact. I
If two students contact each other for an hour, that is 6 “contacts.”
Assume 7 classes (40 mins), 1 lunch break (50 mins), and 5 non-lunch breaks of 10 minutes each.
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
7 / 37
Modeling the contact network
Proposal: Define a “contact” to be a 10-minute face-to-face social contact. I
If two students contact each other for an hour, that is 6 “contacts.”
Assume 7 classes (40 mins), 1 lunch break (50 mins), and 5 non-lunch breaks of 10 minutes each. The maximum number of contacts between any pair is 38.
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
7 / 37
Modeling the contact network
1
Model the friendship network with an exponential family random graph model (ERGM).
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
8 / 37
Modeling the contact network
1
2
Model the friendship network with an exponential family random graph model (ERGM). Model the contact network conditional on the friendship network. I I
Break/lunch contact network Class contact network
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
8 / 37
Modeling break and lunch contacts Definition: degree = number of contacts a student makes Let Dbl denote the vector of break/lunch contact degrees. Let Ybl denote the sociomatrix of break/lunch contacts. P P(Ybl = ybl ) = dbl P(Ybl = ybl |Dbl = dbl )P(Dbl = dbl ) ●
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Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
9 / 37
Modeling break and lunch contacts Definition: degree = number of contacts a student makes Let Dbl denote the vector of break/lunch contact degrees. Let Ybl denote the sociomatrix of break/lunch contacts. P P(Ybl = ybl ) = dbl P(Ybl = ybl |Dbl = dbl )P(Dbl = dbl ) ●
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Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
10 / 37
Modeling break and lunch contacts
Model the break/lunch contact degree distribution by fitting negative binomial distributions to contact survey. Distribute 68% of contacts between friends We use a similar approach to model the class contact network, but 50% of contacts are to friends.
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
11 / 37
Model Selection
Dynamic contact network
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
12 / 37
Model Selection
Dynamic contact network Static contact network
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
12 / 37
Model Selection
Dynamic contact network Static contact network Friendship-only network
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
12 / 37
Model Selection
Dynamic contact network Static contact network Friendship-only network I
Calibrate so that total number of contacts is same as in static contact network.
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
12 / 37
Influenza Simulations Incubation period has 2, 3, or 4 days with probability 0.3, 0.5, and 0.2. Infectiousness is proportional to viral load (sampled from challenge study data). 67% of infected students become symptomatic. 75% of symptomatic cases withdraw to home: I I I
20% on first day 40% on second 15% on third
Chao, DE, Halloran, ME, Obenchain, VJ, and Longini, IM, (2010). “FluTE: a publicly available stochastic epidemic simulation model.” PLoS Computational Biology vol.6, no.1
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
13 / 37
Influenza Simulations
pti = per-10-minute transmission probability of person i on day t Yij = number of contacts between i and j on day t P(i infects j on day t) = 1 − (1 − pti )Yij
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
14 / 37
Comparison of three network models Estimated probability of epidemic
0.8
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0.6
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0.4
●
● ●
Dynamic Static Friendship−only
0.2
Estimated probability of epidemic
● ●
0.0
●
●
●
●
0.002
●
0.004
0.006
0.008
0.010
Probability of transmission in 10−min. contact
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
15 / 37
Model Selection
Dynamic contact network Static contact network Friendship-only network I
Calibrate so that total number of contacts is same as in static contact network.
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
16 / 37
Influenza Simulations: Random Mixing
Compare disease simulations over the contact network to those over a random mixing scenario. Calibrate so that the expected number of schoolmates contacted, as well as the total number of contacts, are the same in both models.
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
17 / 37
Influenza Simulation Results Probability of Epidemic ●
0.8
● ● ● ●
Random Mixing Network Model
0.6
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●
0.4
●
●
0.2
Estimated probability of epidemic
●
0.0
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0.001
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●
0.002
0.003
0.004
0.005
0.006
0.007
Probability of transmission in 10−min. contact
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
18 / 37
Influenza Simulation Results Probability of Epidemic ●
0.8
● ● ● ●
Random Mixing Network Model
0.6
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●
0.4
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●
Factor of 2.1
0.2
Estimated probability of epidemic
●
0.0
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0.001
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●
0.002
0.003
0.004
0.005
0.006
0.007
Probability of transmission in 10−min. contact
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
19 / 37
Influenza Simulation Results Probability of Epidemic ●
0.8
● ● ● ●
Random Mixing Network Model
0.6
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●
Factor of 1.1
0.4
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Factor of 2.1
0.2
Estimated probability of epidemic
●
0.0
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0.001
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0.002
0.003
0.004
0.005
0.006
0.007
Probability of transmission in 10−min. contact
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
20 / 37
Influenza Simulation Results 1000
Final size
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Random Mixing Network Model
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600
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400
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200
Estimated expected final size
800
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0
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0.001
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0.002
0.003
0.004
0.005
0.006
0.007
Probability of transmission in 10−min. contact
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
21 / 37
Influenza Simulation Results 1000
Final size
●
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●
Random Mixing Network Model
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600
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400
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200
Estimated expected final size
800
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Factor of 2.3 0
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0.001
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0.002
0.003
0.004
0.005
0.006
0.007
Probability of transmission in 10−min. contact
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
22 / 37
Influenza Simulation Results 1000
Final size
●
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Random Mixing Network Model
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600
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Factor of 1.2 400
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200
Estimated expected final size
800
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Factor of 2.3 0
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0.001
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0.002
0.003
0.004
0.005
0.006
0.007
Probability of transmission in 10−min. contact
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
23 / 37
Influenza Simulation Results
25
Peak date
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20
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15
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10
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Random Mixing Network Model
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5
Estimated day of epidemic peak
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0
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0.001
0.002
0.003
0.004
0.005
0.006
0.007
Probability of transmission in 10−min. contact
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
24 / 37
Influenza Simulation Results
25
Peak date by final size
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20
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15
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10
●
5
Estimated day of epidemic peak
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Random Mixing Network Model
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0
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0
200
400
600
800
Final size
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
25 / 37
Intervention simulations
Reactive grade closure
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
26 / 37
Intervention simulations
Reactive grade closure I
Assume 67% of infected students are symptomatic.
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
26 / 37
Intervention simulations
Reactive grade closure I
Assume 67% of infected students are symptomatic.
Targeted antiviral prophylaxis
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
26 / 37
Intervention simulations
Reactive grade closure I
Assume 67% of infected students are symptomatic.
Targeted antiviral prophylaxis I
Symptomatic students receive 5 days of treatment; their contacts receive 10 days of prophylaxis.
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
26 / 37
Intervention simulations
Reactive grade closure I
Assume 67% of infected students are symptomatic.
Targeted antiviral prophylaxis I
I
Symptomatic students receive 5 days of treatment; their contacts receive 10 days of prophylaxis. Assume AV ES = 0.63, AV EI = 0.15, AV EP = 0.56
Halloran ME, Hayden FG, Yang Y, Longini, IM, Monto, AS (2007) Antiviral Effects on Influenza Viral Transmission and Pathogenicity: Observations from Household-based Trials. American Journal of Epidemiology 165(2): 212-221
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
26 / 37
TAP Intervention Results Estimated probability of epidemic with and without TAP intervention
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0.8
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0.6
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0.4
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0.0
Random mixing Random Mixing TAP Network Model Network Model TAP
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0.2
Estimated probability of epidemic
●
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0.002
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0.004
0.006
0.008
0.010
Probability of transmission given contact
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
27 / 37
TAP Intervention Results
0.0
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−0.5
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Random mixing Network Model
−1.0
Change in probability of epidemic
0.5
Estimated change in probability of epidemic due to TAP intervention
0.002
0.004
0.006
0.008
0.010
Probability of transmission given contact
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
28 / 37
TAP Intervention Results 1200
Estimated final size, with and without TAP
Random mixing Random Mixing TAP Network Model Network Model TAP
1000
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800
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600
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400
Estimated expected final size
●
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200
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0
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0.002
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●
0.004
0.006
0.008
0.010
Probability of transmission given contact
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
29 / 37
TAP Intervention Results
0
100
Estimated change in final size due to TAP intervention
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−100
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Random mixing Network Model
−200
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−300
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−400
Estimated change in final size
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−500
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−600
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0.002
0.004
0.006
0.008
0.010
Probability of transmission given contact
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
30 / 37
TAP Intervention Results
●
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20
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15
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10
Estimated peak date of season
25
30
Estimated peak date with and without TAP intervention
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Random mixing Random Mixing TAP Network Model Network Model TAP
5
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0
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0.002
0.004
0.006
0.008
0.010
Probability of transmission given contact
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
31 / 37
TAP Intervention Results
0
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−5
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−10
Estimated change in peak date
5
10
Estimated change in peak date due to TAP intervention
●
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Random mixing Network Model
−20
−15
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0.002
0.004
0.006
0.008
0.010
Probability of transmission given contact
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
32 / 37
Grade Closure Intervention Results 1.0
Estimated probability of epidemic with and without grade intervention ● ●
Random Mixing Random Mixing grade Network Model Network Model grade
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0.8
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0.6
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0.4
Probability of epidemic
●
0.2
●
0.0
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0.001
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0.002
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0.003
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0.004
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0.005
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0.006
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0.007
Probability of transmission in 10−min. contact
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
33 / 37
Grade Closure Intervention Results
●
●
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−0.2
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Random Mixing Network Model
−0.4
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−0.6
Change in probability of epidemic
0.0
0.2
Change in probability of epidemic with grade intervention
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−0.8
● ●
● ●
−1.0
●
0.001
0.002
0.003
0.004
0.005
0.006
0.007
Probability of transmission in 10−min. contact
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
34 / 37
Limitations
Measurement error in reports of “average number of contacts.” Within-classroom contact frequencies not informed by data. We assumed perfect observation of symptoms and perfect reporting of contact behavior. We treated the Add Health friendship network data as a complete network. Model is for within-school contacts only. Friends may contact each other outside school.
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
35 / 37
Conclusions
We developed a data-driven model of contact behavior in a school. Model allows us to estimate epidemic parameters and estimate the effectiveness of interventions. Epidemic outcomes, with and without interventions, differ substantively from a random mixing scenario. The dynamic contact network model and static contact network model produced identical epidemic predictions. We recommend further exploration of contact network structure with the aim of improving existing simulation models.
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
36 / 37
Acknowledgments
Mark S. Handcock, Ira M. Longini Jr., M. Elizabeth Halloran CSQUID (Center for Statistics and Quantitative Infectious Disease) UW Social Network Modeling Group (Martina Morris and Steven Goodreau, PIs) Data: Stephen Eubank, Martina Morris Funding: National Institute of General Medical Sciences MIDAS grant U01-GM070749
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
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Grade Closure Intervention Results Estimated final size with and without grade intervention Random Mixing Random Mixing grade Network Model Network Model grade
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1000
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600
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400
Estimated final size
800
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200
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0
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0.001
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0.002
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0.003
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0.004
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0.005
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0.006
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0.007
Probability of transmission in 10−min. contact
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
38 / 37
Grade Closure Intervention Results
0
Change in final size with grade intervention
●
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−200
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−400
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−600
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−800
Change in final size
●
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Random Mixing Network Model
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−1200
−1000
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0.001
0.002
0.003
0.004
0.005
0.006
0.007
Probability of transmission in 10−min. contact
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
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Grade Closure Intervention Results
40
Estimated peak date with and without grade intervention
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30
Random Mixing Random Mixing grade Network Model Network Model grade
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20
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10
Estimated peak date of season
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0
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0.001
0.002
0.003
0.004
0.005
0.006
0.007
Probability of transmission in 10−min. contact
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
40 / 37
Grade Closure Intervention Results
0
5
Change in peak date with grade intervention
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−10
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−15
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−20
Change in peak date
−5
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Random Mixing Network Model
−30
−25
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0.001
0.002
0.003
0.004
0.005
0.006
0.007
Probability of transmission in 10−min. contact
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
41 / 37
October 18, 2011
Manuscript available at: http://arxiv.org/PS_cache/arxiv/pdf/1109/1109.0262v2.pdf
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
1 / 37
Background
When a new strain of influenza virus emerges, we use large-scale simulation models to I I
Estimate epidemic impact Evaluate intervention strategies
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
2 / 37
Background
When a new strain of influenza virus emerges, we use large-scale simulation models to I I
Estimate epidemic impact Evaluate intervention strategies
Many influenza simulation models assume random mixing within mixing groups.
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
2 / 37
Background
When a new strain of influenza virus emerges, we use large-scale simulation models to I I
Estimate epidemic impact Evaluate intervention strategies
Many influenza simulation models assume random mixing within mixing groups. I I
Within school Within grade
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
2 / 37
Background
When a new strain of influenza virus emerges, we use large-scale simulation models to I I
Estimate epidemic impact Evaluate intervention strategies
Many influenza simulation models assume random mixing within mixing groups. I I
Within school Within grade
Schools are known to be a primary mechanism for influenza spread.
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
2 / 37
Scientific questions
1
What is the impact of the social network structure within schools on estimates of epidemic outcomes and intervention effectiveness?
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
3 / 37
Scientific questions
1
What is the impact of the social network structure within schools on estimates of epidemic outcomes and intervention effectiveness?
2
What is the direction of bias created by the random mixing assumption in estimates of epidemic outcomes and intervention effectiveness?
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
3 / 37
Scientific questions
1
What is the impact of the social network structure within schools on estimates of epidemic outcomes and intervention effectiveness?
2
What is the direction of bias created by the random mixing assumption in estimates of epidemic outcomes and intervention effectiveness?
3
Which network structures are important?
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
3 / 37
Scientific questions
1
What is the impact of the social network structure within schools on estimates of epidemic outcomes and intervention effectiveness?
2
What is the direction of bias created by the random mixing assumption in estimates of epidemic outcomes and intervention effectiveness?
3
Which network structures are important?
We create a detailed contact network model based on friendship and contact data and perform simulations to answer these questions.
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
3 / 37
The National Longitudinal Study of Adolescent Health (Add Health) Representative sample of 80 high schools and 52 feeder schools in U.S. during 1994-95 school year We analyze data from one high school+feeder school combination. Students were given a school roster and identified up to 5 best male friends and 5 best female friends. We assume two students are friends if an un-reciprocated or reciprocated nomination occurred. We treat the friendship network data as complete (n=1074). http://www.cpc.unc.edu/projects/addhealth Carolina Population Center, University of North Carolina
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
4 / 37
Friendship-based contact network model
Naive approach: Students only contact their friends, don’t contact non-friends. Simulate disease transmission over friendship network.
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
5 / 37
Friendship-based contact network model
Naive approach: Students only contact their friends, don’t contact non-friends. Simulate disease transmission over friendship network. More realistic approach: Students are more likely to transmit disease to their friends, but may also transmit it to other schoolmates. I I
Students are more likely to contact their friends. Students make longer social contacts with their friends.
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
5 / 37
Friendship-based contact network model
Naive approach: Students only contact their friends, don’t contact non-friends. Simulate disease transmission over friendship network. More realistic approach: Students are more likely to transmit disease to their friends, but may also transmit it to other schoolmates. I I
Students are more likely to contact their friends. Students make longer social contacts with their friends.
We supplement the Add Health data with a survey of contact behavior in schools to create a model capturing these two tendencies.
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
5 / 37
Social Contact Survey Data A Survey on Epidemics in High Schools Survey administered in two Virginia high schools (2009) I I
200 of 400 students surveyed 120 of 1,000 students surveyed
By a “contact,” we mean being in close proximity for more than roughly five minutes. I I I
Average number of contacts during each break between classes Average number of contacts during lunch break Percentage of contacts during school hours to friends
Huadong Xia, Jiangzhuo Chen, Madhav V. Marathe and Henning S. Mortveit, (2010). Synthesis & Embedding of Subnetworks for Individual-based Epidemic Models. NDSSL Technical Report 10-139.
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
6 / 37
Modeling the contact network
Proposal: Define a “contact” to be a 10-minute face-to-face social contact. I
If two students contact each other for an hour, that is 6 “contacts.”
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
7 / 37
Modeling the contact network
Proposal: Define a “contact” to be a 10-minute face-to-face social contact. I
If two students contact each other for an hour, that is 6 “contacts.”
Assume 7 classes (40 mins), 1 lunch break (50 mins), and 5 non-lunch breaks of 10 minutes each.
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
7 / 37
Modeling the contact network
Proposal: Define a “contact” to be a 10-minute face-to-face social contact. I
If two students contact each other for an hour, that is 6 “contacts.”
Assume 7 classes (40 mins), 1 lunch break (50 mins), and 5 non-lunch breaks of 10 minutes each. The maximum number of contacts between any pair is 38.
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
7 / 37
Modeling the contact network
1
Model the friendship network with an exponential family random graph model (ERGM).
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
8 / 37
Modeling the contact network
1
2
Model the friendship network with an exponential family random graph model (ERGM). Model the contact network conditional on the friendship network. I I
Break/lunch contact network Class contact network
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
8 / 37
Modeling break and lunch contacts Definition: degree = number of contacts a student makes Let Dbl denote the vector of break/lunch contact degrees. Let Ybl denote the sociomatrix of break/lunch contacts. P P(Ybl = ybl ) = dbl P(Ybl = ybl |Dbl = dbl )P(Dbl = dbl ) ●
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Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
9 / 37
Modeling break and lunch contacts Definition: degree = number of contacts a student makes Let Dbl denote the vector of break/lunch contact degrees. Let Ybl denote the sociomatrix of break/lunch contacts. P P(Ybl = ybl ) = dbl P(Ybl = ybl |Dbl = dbl )P(Dbl = dbl ) ●
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Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
10 / 37
Modeling break and lunch contacts
Model the break/lunch contact degree distribution by fitting negative binomial distributions to contact survey. Distribute 68% of contacts between friends We use a similar approach to model the class contact network, but 50% of contacts are to friends.
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
11 / 37
Model Selection
Dynamic contact network
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
12 / 37
Model Selection
Dynamic contact network Static contact network
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
12 / 37
Model Selection
Dynamic contact network Static contact network Friendship-only network
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
12 / 37
Model Selection
Dynamic contact network Static contact network Friendship-only network I
Calibrate so that total number of contacts is same as in static contact network.
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
12 / 37
Influenza Simulations Incubation period has 2, 3, or 4 days with probability 0.3, 0.5, and 0.2. Infectiousness is proportional to viral load (sampled from challenge study data). 67% of infected students become symptomatic. 75% of symptomatic cases withdraw to home: I I I
20% on first day 40% on second 15% on third
Chao, DE, Halloran, ME, Obenchain, VJ, and Longini, IM, (2010). “FluTE: a publicly available stochastic epidemic simulation model.” PLoS Computational Biology vol.6, no.1
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
13 / 37
Influenza Simulations
pti = per-10-minute transmission probability of person i on day t Yij = number of contacts between i and j on day t P(i infects j on day t) = 1 − (1 − pti )Yij
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
14 / 37
Comparison of three network models Estimated probability of epidemic
0.8
●
●
●
●
●
●
●
● ●
0.6
●
0.4
●
● ●
Dynamic Static Friendship−only
0.2
Estimated probability of epidemic
● ●
0.0
●
●
●
●
0.002
●
0.004
0.006
0.008
0.010
Probability of transmission in 10−min. contact
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
15 / 37
Model Selection
Dynamic contact network Static contact network Friendship-only network I
Calibrate so that total number of contacts is same as in static contact network.
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
16 / 37
Influenza Simulations: Random Mixing
Compare disease simulations over the contact network to those over a random mixing scenario. Calibrate so that the expected number of schoolmates contacted, as well as the total number of contacts, are the same in both models.
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
17 / 37
Influenza Simulation Results Probability of Epidemic ●
0.8
● ● ● ●
Random Mixing Network Model
0.6
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0.4
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●
0.2
Estimated probability of epidemic
●
0.0
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0.001
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●
0.002
0.003
0.004
0.005
0.006
0.007
Probability of transmission in 10−min. contact
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
18 / 37
Influenza Simulation Results Probability of Epidemic ●
0.8
● ● ● ●
Random Mixing Network Model
0.6
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0.4
●
●
Factor of 2.1
0.2
Estimated probability of epidemic
●
0.0
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0.001
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●
0.002
0.003
0.004
0.005
0.006
0.007
Probability of transmission in 10−min. contact
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
19 / 37
Influenza Simulation Results Probability of Epidemic ●
0.8
● ● ● ●
Random Mixing Network Model
0.6
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●
Factor of 1.1
0.4
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●
Factor of 2.1
0.2
Estimated probability of epidemic
●
0.0
● ●
0.001
●
●
0.002
0.003
0.004
0.005
0.006
0.007
Probability of transmission in 10−min. contact
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
20 / 37
Influenza Simulation Results 1000
Final size
●
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Random Mixing Network Model
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600
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400
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200
Estimated expected final size
800
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0
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0.001
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0.002
0.003
0.004
0.005
0.006
0.007
Probability of transmission in 10−min. contact
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
21 / 37
Influenza Simulation Results 1000
Final size
●
●
●
Random Mixing Network Model
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600
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400
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200
Estimated expected final size
800
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Factor of 2.3 0
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0.001
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0.002
0.003
0.004
0.005
0.006
0.007
Probability of transmission in 10−min. contact
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
22 / 37
Influenza Simulation Results 1000
Final size
●
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Random Mixing Network Model
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600
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Factor of 1.2 400
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200
Estimated expected final size
800
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Factor of 2.3 0
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0.001
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0.002
0.003
0.004
0.005
0.006
0.007
Probability of transmission in 10−min. contact
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
23 / 37
Influenza Simulation Results
25
Peak date
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20
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15
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10
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Random Mixing Network Model
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5
Estimated day of epidemic peak
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0
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0.001
0.002
0.003
0.004
0.005
0.006
0.007
Probability of transmission in 10−min. contact
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
24 / 37
Influenza Simulation Results
25
Peak date by final size
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20
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15
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10
●
5
Estimated day of epidemic peak
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Random Mixing Network Model
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0
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0
200
400
600
800
Final size
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
25 / 37
Intervention simulations
Reactive grade closure
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
26 / 37
Intervention simulations
Reactive grade closure I
Assume 67% of infected students are symptomatic.
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
26 / 37
Intervention simulations
Reactive grade closure I
Assume 67% of infected students are symptomatic.
Targeted antiviral prophylaxis
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
26 / 37
Intervention simulations
Reactive grade closure I
Assume 67% of infected students are symptomatic.
Targeted antiviral prophylaxis I
Symptomatic students receive 5 days of treatment; their contacts receive 10 days of prophylaxis.
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
26 / 37
Intervention simulations
Reactive grade closure I
Assume 67% of infected students are symptomatic.
Targeted antiviral prophylaxis I
I
Symptomatic students receive 5 days of treatment; their contacts receive 10 days of prophylaxis. Assume AV ES = 0.63, AV EI = 0.15, AV EP = 0.56
Halloran ME, Hayden FG, Yang Y, Longini, IM, Monto, AS (2007) Antiviral Effects on Influenza Viral Transmission and Pathogenicity: Observations from Household-based Trials. American Journal of Epidemiology 165(2): 212-221
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
26 / 37
TAP Intervention Results Estimated probability of epidemic with and without TAP intervention
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0.8
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0.4
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Random mixing Random Mixing TAP Network Model Network Model TAP
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0.2
Estimated probability of epidemic
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0.002
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0.006
0.008
0.010
Probability of transmission given contact
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
27 / 37
TAP Intervention Results
0.0
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Random mixing Network Model
−1.0
Change in probability of epidemic
0.5
Estimated change in probability of epidemic due to TAP intervention
0.002
0.004
0.006
0.008
0.010
Probability of transmission given contact
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
28 / 37
TAP Intervention Results 1200
Estimated final size, with and without TAP
Random mixing Random Mixing TAP Network Model Network Model TAP
1000
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800
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600
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400
Estimated expected final size
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200
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0
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0.002
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0.004
0.006
0.008
0.010
Probability of transmission given contact
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
29 / 37
TAP Intervention Results
0
100
Estimated change in final size due to TAP intervention
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−100
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Random mixing Network Model
−200
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−300
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−400
Estimated change in final size
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−500
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−600
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0.002
0.004
0.006
0.008
0.010
Probability of transmission given contact
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
30 / 37
TAP Intervention Results
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20
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15
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10
Estimated peak date of season
25
30
Estimated peak date with and without TAP intervention
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Random mixing Random Mixing TAP Network Model Network Model TAP
5
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0
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0.002
0.004
0.006
0.008
0.010
Probability of transmission given contact
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
31 / 37
TAP Intervention Results
0
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−5
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−10
Estimated change in peak date
5
10
Estimated change in peak date due to TAP intervention
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Random mixing Network Model
−20
−15
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0.002
0.004
0.006
0.008
0.010
Probability of transmission given contact
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
32 / 37
Grade Closure Intervention Results 1.0
Estimated probability of epidemic with and without grade intervention ● ●
Random Mixing Random Mixing grade Network Model Network Model grade
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0.8
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0.6
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0.4
Probability of epidemic
●
0.2
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0.0
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0.001
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0.002
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0.003
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0.004
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0.005
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0.006
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0.007
Probability of transmission in 10−min. contact
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
33 / 37
Grade Closure Intervention Results
●
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−0.2
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Random Mixing Network Model
−0.4
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−0.6
Change in probability of epidemic
0.0
0.2
Change in probability of epidemic with grade intervention
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−0.8
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−1.0
●
0.001
0.002
0.003
0.004
0.005
0.006
0.007
Probability of transmission in 10−min. contact
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
34 / 37
Limitations
Measurement error in reports of “average number of contacts.” Within-classroom contact frequencies not informed by data. We assumed perfect observation of symptoms and perfect reporting of contact behavior. We treated the Add Health friendship network data as a complete network. Model is for within-school contacts only. Friends may contact each other outside school.
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
35 / 37
Conclusions
We developed a data-driven model of contact behavior in a school. Model allows us to estimate epidemic parameters and estimate the effectiveness of interventions. Epidemic outcomes, with and without interventions, differ substantively from a random mixing scenario. The dynamic contact network model and static contact network model produced identical epidemic predictions. We recommend further exploration of contact network structure with the aim of improving existing simulation models.
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
36 / 37
Acknowledgments
Mark S. Handcock, Ira M. Longini Jr., M. Elizabeth Halloran CSQUID (Center for Statistics and Quantitative Infectious Disease) UW Social Network Modeling Group (Martina Morris and Steven Goodreau, PIs) Data: Stephen Eubank, Martina Morris Funding: National Institute of General Medical Sciences MIDAS grant U01-GM070749
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
37 / 37
Grade Closure Intervention Results Estimated final size with and without grade intervention Random Mixing Random Mixing grade Network Model Network Model grade
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1000
●
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600
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400
Estimated final size
800
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200
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0
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0.001
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0.002
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0.003
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0.004
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0.005
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0.006
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0.007
Probability of transmission in 10−min. contact
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
38 / 37
Grade Closure Intervention Results
0
Change in final size with grade intervention
●
●
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−200
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−400
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−600
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−800
Change in final size
●
● ●
Random Mixing Network Model
● ●
−1200
−1000
●
0.001
0.002
0.003
0.004
0.005
0.006
0.007
Probability of transmission in 10−min. contact
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
39 / 37
Grade Closure Intervention Results
40
Estimated peak date with and without grade intervention
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30
Random Mixing Random Mixing grade Network Model Network Model grade
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20
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10
Estimated peak date of season
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0
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0.001
0.002
0.003
0.004
0.005
0.006
0.007
Probability of transmission in 10−min. contact
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
40 / 37
Grade Closure Intervention Results
0
5
Change in peak date with grade intervention
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−10
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−15
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● ●
●
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−20
Change in peak date
−5
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Random Mixing Network Model
−30
−25
●
0.001
0.002
0.003
0.004
0.005
0.006
0.007
Probability of transmission in 10−min. contact
Gail Potter (FHCRC)
A Within-School Contact Network
October 18, 2011
41 / 37
