Determining whether a class of random graphs is consistent with an observed contact network. (7th March 2018) - Nath, Madhurima; Ren, Yihui; Khorramzadeh, Yasamin; Eubank, Stephen
Highlights: The paper discusses the transmission of infectious diseases modeled as a diffusive process on networks. The epidemic potential and epidemic curves for different networks are compared. These measures depend on both the global structure of the contact network and the dynamics on the network. The probability of transmission is treated as a free parameter to re-calibrate the network models such that the epidemic potential remains the same. Networks with matching local statistics do not necessarily yield similar outcomes for the spread of infectious diseases. This extends to the response of the networks to various time-dependent intervention measures. Interventions that change network structure spoil the re-calibration. Hence, reasoning about the effects of interventions using a constrained random graph model for the network is unreliable. Abstract: 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.