The spread of infectious diseases is highly determined by human decisions in regards to vaccination. The choice of whether to vaccinate or not may represent a conflict between group and private interests. If a large enough portion of the population is vaccinated, the disease can be contained or eradicated. However, there is a risk, perceived or real, to the individual for being vaccinated. Ostensibly, group beneficial behaviour is not supported in such social dilemmas. However, diseases have been eliminated in such situations. This seeming contradiction is assuaged by the introduction of a network model, which represents the structure of the population's social interactions. Outbreaks are quickly contained by means of the voluntary choice to vaccinate in a network below a threshold average edge degree. Such a network, however, does not represent changes in social interactions and mobility within the population, which would result in rearrangements of the network. In this thesis, we explore 4 dynamic network models, in which edges between nodes are created and dissolved. We observed many counterintuitive results, including that a relatively effective safe vaccine applied to a dangerous disease would result in less vaccinations than an ineffective unsafe vaccine applied to a benign disease. In addition, we were surprised by the overall strong similarities between each model examined. We observe the same qualitative results when we toggle the turnover rate for each model. Generally, a static network results in successful ring vaccination. However, as we make the network more dynamic, ring vaccination is no longer successful at containing the disease. We observed a criticality at which there is a high variability of possible outcomes. Within such a case it would be difficult for policy makers to predict what course an epidemic would take and whether a voluntary vaccination policy would be effective at containing the disease with few individuals being vaccinated. If we allow the network to become further dynamic, we observe that the model becomes more similar to the compartmental and other models that do no incorporate space.