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Determining whether a class of random graphs is consistent with an observed contact network

Nath, Madhurima; Ren, Yihui; Khorramzadeh, Yasamin; & Eubank, Stephen. (2018). Determining whether a class of random graphs is consistent with an observed contact network. Journal of Theoretical Biology, 440, 121-132.

Nath, Madhurima; Ren, Yihui; Khorramzadeh, Yasamin; & Eubank, Stephen. (2018). Determining whether a class of random graphs is consistent with an observed contact network. Journal of Theoretical Biology, 440, 121-132.

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We demonstrate a general method to analyze the sensitivity of attack rate in a network model of infectious disease epidemiology to the structure of the network. We use Moore and Shannon’s “network reliability” statistic to measure the epidemic potential of a network. A number of networks are generated using exponential random graph models based on the properties of the contact network structure of one of the Add Health surveys. The expected number of infections on the original Add Health network is significantly different from that on any of the models derived from it. Because individual-level transmissibility and network structure are not separately identifiable parameters given population-level attack rate data it is possible to re-calibrate the transmissibility to fix this difference. However, the temporal behavior of the outbreak remains significantly different. Hence any estimates of the effectiveness of time dependent interventions on one network are unlikely to generalize to the other. Moreover, we show that in one case even a small perturbation to the network spoils the re-calibration. Unfortunately, the set of sufficient statistics for specifying a contact network model is not yet known. Until it is, estimates of the outcome of a dynamical process on a particular network obtained from simulations on a different network are not reliable.


Network reliability
Epidemic modeling
Network structure
ERGM
Epidemic potential


JOUR



Nath, Madhurima
Ren, Yihui
Khorramzadeh, Yasamin
Eubank, Stephen



2018


Journal of Theoretical Biology

440


121-132


December 29, 2017




0022-5193

10.1016/j.jtbi.2017.12.021



7242