  Network-based models of epidemic spread have become increasingly popular in
recent decades. Despite a rich foundation of such models, few low-dimensional
systems for modeling SIS-type diseases have been proposed that manage to
capture the complex dynamics induced by the network structure. We analyze one
recently introduced model and derive important epidemiological quantities for
the system. We derive the epidemic threshold and analyze the bifurcation that
occurs, and we use asymptotic techniques to derive an approximation for the
endemic equilibrium when it exists. We consider the sensitivity of this
approximation to network parameters, and the implications for disease control
measures are found to be in line with the results of existing studies.
