Developments in recombinant DNA technology have given researchers the ability to modify viruses so that they are highly selective towards cancer cells. Engineered viruses have successfully treated cancer in human trials. In an effort to better understand viral population dynamics in a temporal context, researchers have turned to mathematical models. Some of these viruses spread only by contact between virus-infected and uninfected tumor cells. Therefore, mathematical models that usually assume populations are well-mixed may not apply. This thesis describes a computational approach to modeling viral population dynamics that takes into account the spatial nature of viral spread by contact.