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We consider the spread of infectious disease through contact networks ofConfiguration Model type. We assume that the disease spreads through contactsand infected individuals recover into an immune state. We discuss a number ofexisting mathematical models used to investigate this system, and showrelations between the underlying assumptions of the models. In the process weoffer simplifications of some of the existing models. The distinctions betweenthe underlying assumptions are subtle, and in many if not most cases thissubtlety is irrelevant. Indeed, under appropriate conditions the models areequivalent. We compare the benefits and disadvantages of the different models,and discuss their application to other populations (\emph{e.g.,} clusterednetworks). Finally we discuss ongoing challenges for network-based epidemicmodeling.

Epidemic spread in networks: Existing methods and current challenges