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The accurate and efficient modeling of Internet worms is a particularly challenging task for network simulation tools. The atypical and aggressive behavior of these worms can easily consume excessive resources, both processing time and storage, within a typical simulator. In particular the selection of random IP addresses, and the sending of packets to the selected hosts, even if they are non-existent or not modeled in the simulation scenario, is challenging for existing network simulation tools. Further, the computation of routing information for these randomly chosen target addresses defeats most caching or on-demand routing methods, resulting in substantial overhead in the simulator. We discuss the design of our Internet worm models in the Georgia Tech Network Simulator, and show how we addressed these issues. We present some results from our Internet worm simulations that show the rate of infection spread for a typical worm under a variety of conditions.