Internet worms, which spread in computer networks without human mediation, pose a severe threat to computer systems today. The rate of propagation of worms has been measured to be extremely high and they can infect a large fraction of their potential hosts in a short time. We study two different methods of patch dissemination to combat the spread of worms. We first show that using a fixed number of patch servers performs inadequately against Internet worms. We then show that by exploiting the exponential data dissemination capability of P2P systems, the spread of worms can be halted effectively. We compare the two methods by using fluid models to compute two quantities of interest: the time taken to effectively combat the progress of the worm, and the maximum number of infected hosts. We validate our models using simulations.