In this paper, we study the vaccination of graphs against the outbreak of infectious diseases, in the following natural model generalizing a model by Aspnes et al.: An infectious disease breaks out at a random node of the graph and propagates along the edges of the graph. Vaccinated nodes cannot be infected, nor pass on the infection, whereas all other nodes do. The decisions on which nodes get vaccinated must be made before the random outbreak location is known. There is a cost associated with vaccination and a different cost with getting infected. In this model, we provide two results. First, we improve the approximation guarantee for finding the best vaccination