## The Annals of Applied Statistics

- Ann. Appl. Stat.
- Volume 6, Number 1 (2012), 1-26.

### Estimating within-school contact networks to understand influenza transmission

Gail E. Potter, Mark S. Handcock, Ira M. Longini, and M. Elizabeth Halloran

#### Abstract

Many epidemic models approximate social contact behavior by assuming random mixing within mixing groups (e.g., homes, schools and workplaces). The effect of more realistic social network structure on estimates of epidemic parameters is an open area of exploration. We develop a detailed statistical model to estimate the social contact network within a high school using friendship network data and a survey of contact behavior. Our contact network model includes classroom structure, longer durations of contacts to friends than nonfriends and more frequent contacts with friends, based on reports in the contact survey. We performed simulation studies to explore which network structures are relevant to influenza transmission. These studies yield two key findings. First, we found that the friendship network structure important to the transmission process can be adequately represented by a dyad-independent exponential random graph model (ERGM). This means that individual-level sampled data is sufficient to characterize the entire friendship network. Second, we found that contact behavior was adequately represented by a static rather than dynamic contact network. We then compare a targeted antiviral prophylaxis intervention strategy and a grade closure intervention strategy under random mixing and network-based mixing. We find that random mixing overestimates the effect of targeted antiviral prophylaxis on the probability of an epidemic when the probability of transmission in 10 minutes of contact is less than 0.004 and underestimates it when this transmission probability is greater than 0.004. We found the same pattern for the final size of an epidemic, with a threshold transmission probability of 0.005. We also find random mixing overestimates the effect of a grade closure intervention on the probability of an epidemic and final size for all transmission probabilities. Our findings have implications for policy recommendations based on models assuming random mixing, and can inform further development of network-based models.

#### Article information

**Source**

Ann. Appl. Stat. Volume 6, Number 1 (2012), 1-26.

**Dates**

First available in Project Euclid: 6 March 2012

**Permanent link to this document**

https://projecteuclid.org/euclid.aoas/1331043386

**Digital Object Identifier**

doi:10.1214/11-AOAS505

**Mathematical Reviews number (MathSciNet)**

MR2951527

**Zentralblatt MATH identifier**

1236.91117

**Keywords**

Contact network epidemic model influenza simulation model social network

#### Citation

Potter, Gail E.; Handcock, Mark S.; Longini, Ira M.; Halloran, M. Elizabeth. Estimating within-school contact networks to understand influenza transmission. Ann. Appl. Stat. 6 (2012), no. 1, 1--26. doi:10.1214/11-AOAS505. https://projecteuclid.org/euclid.aoas/1331043386

#### Supplemental materials

- Supplementary material A: Model validation and descriptive
analyses of simulated contact networks. We compare our fitted degree distribution to that
from an alternate data source, the POLYMOD study. We
compare marginal and joint distributions of variables from
contact networks simulated from our model to the empirical
marginal and joint distributions in the epidemic survey,
which was used to estimate model input
parameters.Digital Object Identifier: doi:10.1214/11-AOAS505SUPPA
- Supplementary material B: Sensitivity analysis for targeted
antiviral prophylaxis intervention. We perform sensitivity analysis to assess the
impact of the assumption of perfect reporting of contacts
in the targeted antiviral prophylaxis intervention.
Simulations are performed with 90% and 75% of contacts
reported.Digital Object Identifier: doi:10.1214/11-AOAS505SUPPB