Analysis, Estimation, and Validation of Discrete-Time Epidemic Processes

Models of spreading processes over nontrivial networks are commonly motivated by modeling and analysis of biological networks, computer networks, and human contact networks. However, learning the spread parameters 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 estimating the spread parameters. Finally, we employ two real data sets, one from John Snow's seminal work on cholera epidemics in London in the 1850s and the other one from the United States Department of Agriculture, to validate an approximation of a well-studied network-dependent susceptible-infected-susceptible model.