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Despite a rich foundation of epidemiological models for diseases propagating on networks, for SIS-type models few low-dimensional system have been proposed that manage to capture the complex dynamics induced by the network structure. We analyze one recently introduced model and derive results for the epidemic threshold and asymptotic approximations to the final size of the epidemic. Furthermore, we discuss possible generalizations of this model to match real-world contact networks and potential applications of these methods to metapopulation ecology.

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