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This article considers the effects of Internet worms on persistently unpatched hosts and hosts for which vulnerabilities are refreshed. Previous models have been homogeneous; that is, all hosts transitioned through the same set of states. The model considered in this article is heterogeneous and more realistic in that subpopulations of hosts are assumed to have inherently different characteristics. Equilibrium conditions are obtained for which an Internet worm will self-propagate indefinitely, which lead to thresholds below which worms will become extinct.