Obviously, an epidemiological model with three interacting groups has a large number of associated parameters, making a comprehensive sweep of the entire parameter space impractical and difficult to visualize. Instead, we show results from a relatively restricted scenario, but comment that these results are representative of all plausible scenarios that have been considered. In particular, we constrain the number of individuals in the three groups to be N D ¼ N H ¼ 0.1 N and H G ¼ 0.8 N, and constrain the transmission rates between all groups, except within the epidemiologically important group, to be equal (b XY ¼ g, except when X ¼ Y ¼ D). We note that different forms and parameters within this transmission matrix can potentially lead to different optimizations of vaccine [22] .