Ken Eames
Centre for the Mathematical Modelling of Infectious Diseases
London School of Hygiene and Tropical Medicine

Measuring networks:
• Direct measurement
• Proxy measures
Complications:
• Dynamics
• Influence of infection
• What we really want
Ongoing/future studies:
• Linking contact behaviour to infection
• Improved inference
• Low-tech and high-tech solutions

As far as we’re concerned, a network consists of a population and its interactions.
Conlan et al, Proc. R. Soc. B, 2011

Node attributes: age, gender, location, vaccination status...
Link attributes: duration, frequency, stability, proximity, timing…

• Contact tracing, linked to medical records.
• Reported sexual partnerships, and infection status.
Wylie & Jolly , Sex. Transm. Dis., 2001

• Observation : visual, video.
• Contact tracing : with or without infection information.
• Contact diaries : paper-based, interview-led, or electronic.
• Electronic tagging : radio, Bluetooth.

Contact diary
Please cut off this returning the form.
This questionnaire is for the person who has been given antiviral medication . If that person is a child then an adult column before can complete it on their behalf but should respond from the point -of-view of the child.
Today’s date ____________________ Day of the week____________________
Name (or description) of contact
Age
(or age range)
Gender
(Male or
Female)
Was there skin to skin contact
(Yes or
No)?
How long?
Over the day, for how long were you with this person (tick one)?
Where?
Where did you meet this person
(tick all that apply)?
How often?
How often do you normally meet this person (tick one)?
Edmunds et al, Proc. R. Soc. B, 1997; Mossong et al, PLoS Med, 2008
Please turn over if you need more space

Who?
Physical contact?
Contact diary
Duration Location
Frequency
Please cut off this column before returning the form.
This questionnaire is for the person who has been given antiviral medication . If that person is a child then an adult can complete it on their behalf but should respond from the point -of-view of the child.
Today’s date ____________________ Day of the week____________________
Name (or description) of contact
Age
(or age range)
Gender
(Male or
Female)
Was there skin to skin contact
(Yes or
No)?
How long?
Over the day, for how long were you with this person (tick one)?
Where?
Where did you meet this person
(tick all that apply)?
How often?
How often do you normally meet this person (tick one)?
• List of all contacts over the course of day(s).
• Collect information about participant, the people they meet, and the encounter.
• Low-tech, but lots of information.
Please turn over if you need more space

• If names are recorded accurately we can use contact diaries to reconstruct a social network.
• Only likely to be possible in a limited setting.
• 8661 encounters, 3528 different individuals.
• 49 participants.
• 310 shared contacts.
• 3218 one-off contacts.
Read, Eames, & Edmunds J. R. Soc. Interface, 2008

• If names are not recorded, we can still get useful data.
• Studies show high levels of like-with-like mixing by age.
• Largest amount of mixing is between school children.
• It’s useful and interesting, but it’s not a network.
Data: POLYMOD; Image: Rohani & King

• Might not need a network (i.e. named contacts) study at all.
• Depends on how much people know about those they interact with.
• Depends on what we want to do with the data.
young old
young old

• Familiar contact diary, plus clustering question.
• Aim to determine which contacts know each other.

Home
Work
Respondent
Social
• Information about clustering within egonet.
• Measure of clustering by age, social setting, etc.

• Bluetooth has the advantage that it’s commonly accessible.
• The disadvantage that it’s fairly long-range (& goes through walls).
• Custom-designed RFID tags can be tuned to record at a required distance, but are relatively expensive.
• Both approaches allow finer temporal resolution data to be collected.
Catutto et al, PLoS One, 2010

• Phone call/social network data : alterative network.
• Travel patterns : mass movements for spatial models (e.g. air-travel data); individual movements for networks (e.g. cattle movements, commuting data).
• Location & time-use data : inferring networks from location information.
Place Person
A
B
C
1
2
3
4
5
Time 1
Place Person
A
1
B
C
Time 2
5
2
3
4
5
4
Network
1
3
2

• Fatigue : reporting lots of contacts gets very boring.
• Recall : unless reporting is instant, contacts are forgotten.
• Accuracy : about the person: how old?
about the encounter: how long did we meet for?
• Matching contacts : how many John Smiths are there?
• Partial samples : if we only sample a small fraction of the population, is the network still meaningful?
• Boundaries : where should the study stop?
• Definition : how do we define a meaningful contact?
• Many of these are issues for any social contact data study, not just network studies.
• Automated data collection solves some problems, but only really suitable (currently) for small, specific, populations – a school, or a hospital.

• Networks constantly change:
• Natural dynamics – birth, death, ageing.
• Seasonal changes – school holidays, weekends.
• Day-to-day variation; predictable and chance encounters.
• The more dynamic a network is, the harder it is to measure.
• Population mixing becomes less “network” and more
“mass action”.
• Can return to betweengroup rather than betweenindividual models (maybe).
Participant

• Illness can have a large effect on social behaviour: time off work/school means fewer contacts, and a different agedistribution of contacts.
• Network likely to be reduced – for people who are heavily symptomatic – to “strong” home contacts.
100 ● 5.5
80
<5 min
5−10 min
10 min−1h
60
●
● 2.61
1−4 h
40
>4h
●
● 1.39
NA
20
● 0.73
●
●
0 ● ● 0.04
Home Leisure Other Work
Location of Contacts
• Impact of illness on the healthy: social distancing, from real or perceived risk.

• We want to know “how people interact”, but this is very woolly.
• What we really want to know is whom each person would infect if they were infectious with pathogen
Topical
.
• There are lots of factors we don’t understand, so instead try to determine whom they’ll meet when they’re ill (&, ideally, give each encounter a transmission probability).
• W e’re not going to be able to measure encounters when people are ill… so instead just measure normal mixing.
• How do we define “normal”? Let’s just measure mixing today.
• What do we mean by a contact? Let’s just measure what we can.

• Want to link contact behaviour (ideally, network position) to risk of infection.
• Combine social contact studies and swabbing/symptom surveillance.
• Which properties of an individual, or their network, matter?
• Do we really need to measure everything?
• Until we have measured “everything”, we can’t be sure.
• Is it going to be the same for every infection? Obviously not.
• Is it going to be the same in different populations or at different times? Probably not.
• Can we find robust proxies? Maybe.

Gardy et al, NEJM , 2011

• 762 survey participants in
Hong Kong.
• Social contact data and paired sera pre- and post-
2009 H1N1 epidemic.
Kucharski, Cowling, Lessler , Read, Cummings, Riley, …

Welch et al, Epidemics , 2011

• Fill in the low-tech gaps. Simple behavioural things we know very little about. Illness, seasonality, stability.
• Find out what matters, of the stuff we’re missing – modelling to exploit fully current data and guide future data collection.
• Match the model (& the data) to the intervention.
• Link to outbreak/illness data.
• Innovate (not forgetting to handle privacy and anonymity sensitively).

“It is essential to begin joint studies that involve epidemiologists, biostatisticians, and modellers. Maybe such an approach would make everyone hold hands, smile and produce something novel.”
Sally Blower, in Models for Infectious Human Diseases; their structure and relation to data