  Models of spread processes over non-trivial networks are commonly motivated
by modeling and analysis of biological networks, computer networks, and human
contact networks. However, identification of such models has not yet been
explored in detail, and the models have not been validated by real data. In
this paper, we present several different spread models from the literature and
explore their relationships to each other; for one of these processes, we
present a sufficient condition for asymptotic stability of the healthy
equilibrium, show that the condition is necessary and sufficient for uniqueness
of the healthy equilibrium, and present necessary and sufficient conditions for
learning the spread parameters. Finally, we employ two real datasets, one from
John Snow's seminal work on cholera epidemics in London in the 1850's and the
other one from the United States Department of Agriculture, to validate an
approximation of a well-studied network-dependent
susceptible-infected-susceptible (SIS) model.
