Epidemic risk from friendship network data: an equivalence with a   non-uniform sampling of contact networks
  Contacts between individuals play an important role in determining how infectious diseases spread. Various methods to gather data on such contacts co-exist, from surveys to wearable sensors. Comparisons of data obtained by different methods in the same context are however scarce, in particular with respect to their use in data-driven models of spreading processes. Here, we use a combined data set describing contacts registered by sensors and friendship relations in the same population to address this issue in a case study. We investigate if the use of the friendship network is equivalent to a sampling procedure performed on the sensor contact network with respect to the outcome of simulations of spreading processes: such an equivalence might indeed give hints on ways to compensate for the incompleteness of contact data deduced from surveys. We show that this is indeed the case for these data, for a specifically designed sampling procedure, in which respondents report their neighbors with a probability depending on their contact time. We study the impact of this specific sampling procedure on several data sets, discuss limitations of our approach and its possible applications in the use of data sets of various origins in data-driven simulations of epidemic processes. 
Julie Fournet and Alain Barrat
physics.soc-ph cs.SI q-bio.PE