  Many fundamental concepts in network-based epidemic modeling depend on the
branching factor, which captures a sense of dispersion in the network
connectivity and quantifies the rate of spreading across the network. Moreover,
contact network information generally is available only up to some level of
error. We study the propagation of such errors to the estimation of the
branching factor. Specifically, we characterize the impact of network noise on
the bias and variance of the observed branching factor for arbitrary true
networks, with examples in sparse, dense, homogeneous and inhomogeneous
networks. In addition, we propose a method-of-moments estimator for the true
branching factor. We illustrate the practical performance of our estimator
through simulation studies and with contact networks observed in British
secondary schools and a French hospital.
