Viruses remain a significant threat to modern networked computer systems. Despite the best efforts of those who develop anti-virus systems, new viruses and new types of virus that are not dealt with by existing protection schemes appear regularly. In addition, the rate at which a virus can spread has risen dramatically with the increase in connectivity. Defenses against infections by known viruses rely at present on immunization yet, for a variety of reasons, immunization is often only effective on a subset of the nodes in a network and many nodes remain unprotected. Little is known about either the way in which a viral infection proceeds in general or the way that immunization affects the infection process. We present the results of a simulation study of the way in which virus infections propagate through certain types of network and of the effect that partial immunization has on the infection. The key result is that relatively low levels of immunization can slow an infection significantly.