A ‘contact network’ modeling infection transmission comprises of nodes (or individuals) that are linked when they are in contact that possibly transmits an infection. We here studied infection transmission on contact networks of various degree distributionsscale-free, exponential and constantunder SIRV model assuming susceptible, infected, removed and vaccinated statuses of nodes. Aiming for infectious disease containment within the very early stage of spreading, we computed the minimum transmissibility at which an infectious disease epidemic begins to emerge, and its change according to mass preventive and ring post-outbreak vaccination. In the most degree-heterogeneous scale-free network, the ‘super-spreading’ by the hubs, or high-degree nodes, allowed epidemics even for low transmissibility. In compensation, vaccination was much more efficient for the scale-free network. We also found that basic reproductive number R0 defines a measurement of epidemic emergence univers...