Synthesizing Social Proximity Networks by Combining Subjective Surveys with Digital Traces Christopher Barrett*, Huadong Xia*, Jiangzhuo Chen*, Madhav V. Marathe*, Henning S. Mortveit* and Marcel Salathe # * The Network Dynamics and Simulation Science Laboratory, Virginia Bioinformatics Institute at Virginia Tech, USA # Center for Infectious Disease Dynamics, Penn State University, USA IEEE CSE2013

We thank our external collaborators and members of the Network Dynamics and Simulation Science Laboratory (NDSSL) for their suggestions and comments. This work has been partially supported by DTRA Grant HDTRA , DTRA CNIMS Contract HDTRA1-11-D , NIH MIDAS Grant 2U01GM , NSF PetaApps Grant OCI , NSF NetSE Grant CNS Acknowledgement

Close proximity relations between people are critical in understanding the diffusion of influenza-like epidemics. Those close proximity relations are modeled collectively as a social contact network. Existing solutions in constructing social contact networks: – Digital devices to detect proximity between people: RFID tags, cell phones, motes, etc. – Subjective assessment and survey information Background: Model Close Proximity Relations Between People Modeling Social contact network Social contact network

Solution 1: Digital Devices to Detect Proximity Between People Free of human error High quality Expensive Nontrivial to generalize 700-student contact Network => 1000-student contact Network?

Solution 2: Subjective Assessment and Survey Information Complete Graph G(n,p) Geometry Random Graph Subjective Assessment … Inexpensive Easy to generalize Sublocation interactions remains a black box

A hybrid methodology that combines both subjective surveys and digital traces: – Generic pattern exists in a very small location: conference room, class room, restaurant at different hours. As a Showcase: School networks New Solution: A Hybrid Methodology

Data sets Objective 1: understand In-class contact networks – Identifying class intervals – Extracting class networks Objective 2: generative network model that model the digital trace network Objective 3: comparison study on the impact of detailed sublocation structure Outline

Populations: – NRV population: 150K – High school population: 2.5K We collected class schedules for 3 schools in New River Valley Region Data Sets: Surveys

Digital trace data – Collected from an American high school – 788 participants, including 655 students, 73 teachers and 55 staff members, and 5 other people (94% of the school population) – Each participant carry a mote for an entire typical school day. – Their motes detect other motes within 3 meters for every 20 seconds, stored as CPRs in the data set CPR: close proximity records CPI: close proximity interaction, a continuous sequence of CPRs Contacts: a contact is the sum of all CPIs between two motes. – 2,148,991 CPRs, 762,868 CPIs and 118,291 contacts Data Sets: Digital Trace Data

Data sets Objective 1: understand In-class contact networks – Identifying class intervals – Extracting class networks Objective 2: generative network model that model the digital trace network Objective 3: comparison study on the impact of detailed sublocation structure Outline

Formation of school networks: Step to identify class networks: – Identify class periods – For each identified class period, identify within-class contact networks Structure of School Networks

Motes are anonymized and the class schedules are unknown. Mote Signals are highly volatile – Directional – Unstable device Challenges (1)

Classes and Breaks Reveal Quite Different Patterns

Use the Algorithm to Plot Time Zone for Class Breaks

Challenges (2): Isolate In-Class Contact Networks Interference exists for sensor Signals! – A very large Connected Component for any snapshot contact networks – Sensor Signals can traverse the wall (via windows/doors)?

Isolate In-Class Contact Networks CPIs within the same class interval comprise a relative stable contact network, even if CPIs are volatile --- foundation for us to analyze CPIs traverse across classrooms but we hypothesize: – CPIs between classrooms are short and unstable  An “test and try” algorithm to remove noises – CPIs between classrooms are sparser than within  Modularity based Community Detection Algorithm

Detect School Communities: Modularity Based Algorithm

 Alternative Slide

Students in the class typically form into one or multiple groups; students of the same group are highly connected. Duration of CPIs follow a power law like distribution Analyze In-class Contact Network 47 nodes 21 nodes 32 nodes

Data sets Objective 1: understand In-class contact networks – Identifying class intervals – Extracting class networks Objective 2: generative network model that model the digital trace network Objective 3: comparison study on the impact of detailed sublocation structure Outline

G(n,p) model is not appropriate: – Cannot: match degree, match clustering coefficients – Can: match n; match the sum of edge weights by adjusting p Chung-Lu model: match both degrees and edge weights – List of degree k v of each node v from a digital trace template – Chung-Lu model connect each node pair (v, u) with probability where m is the total edge number – We adjust the edge weight for each generated edge, so that the edge weight follow a power law distribution. ERGM model: – more powerful candidate – complex compared to Chung-Lu model Use Theoretic Graph Models to Fit Digital Trace Templates

Spectral Gap of a network: the difference between the largest two eigenvalues of the network adjacency matrix A larger spectral gap means the disease is easier to spread on the network. Compare Spectral Gaps between Digital Trace Templates and Graph Models

Data sets Objective 1: understand In-class contact networks – Identifying class intervals – Extracting class networks Objective 2: generative network model that model the digital trace network Objective 3: comparison study on the impact of detailed sublocation structures Outline

Aim: To compare three in-class models within a realistic context, we use the three models to construct three types of high school networks, and further embed school networks within the larger regional network Input: – High school populations in NRV region – The NRV population in NRV regions Output: – Three types school networks based on three in-class models respectively – Three types of NRV Network based on three in-class models respectively School Networks and the Region Network

The school network based on calibrated ChungLu model seems a good match to that based on digital trace templates, structurally. Structural Properties of School Networks Embedded with Different In-class Models

Disease Spread in a Social Network Within-host disease model: SEIR Between-host disease model: – probabilistic transmissions along edges of social contact network – from infectious people to susceptible people

Simulation to ILI without Intervention Vaccine high degree nodes Vaccine high degree nodes +social distance Epidemic Dynamics of School Networks Embedded with Different In-class Models

ANOVA peakday Sum of SquaresdfMean SquareFSignificance Between Groups * Within Groups Total Epicurve Difference with Different In-class Models Multiple Comparisons Dependent Variable: peakday Tukey HSD (I) groups(J) groupsMean Difference (I-J)Significance G(n,p) Digital trace *.022* ChungLu Digital trace G(n,p) *.022* ChungLu ChungLu G(n,p) Digital trace *. The mean difference is significant at the 0.05 level.

The digital trace based templates capture network structures that are critical in understanding the role of interventions, and not available in previous theoretic sublocation models such as G(n,p) It is possible to capture a faithful structural features or dynamics by tuning appropriate theoretic graph models like Chung-Lu to the real digital trace templates, at least under some limited scenarios. ERGM could possible serve as a good model, but Chung-Lu model seems like a reasonable fit for now. Summary of the Comparison Study

We show a hybrid methodology that combines subjective survey with digital trace data. In-class contact structure is important in understanding epidemics and intervention strategies. Our methodology is generic, applicable to other template networks – Office building – Military bases – Hospital rooms – … … Conclusions

Questions?

Extra slides

Similarity between Community Division

Types of classroom organization: teacher-centered or peer-based (internet source: Research Unit for Multilingualism and Cross-Cultural Communication)Research Unit for Multilingualism and Cross-Cultural Communication Illustration to Class Network Topology Structure

Construction of a High School Network

Embed School Networks Within a Larger Regional Network