When targeting a vaccination campaign (especially against the 2009 H1N1 influenza strain), there are often two competing priorities: minimization of transmission by immunizing those individuals that are most epidemiologically important; and minimization of the effects of the disease by immunizing those individuals that have the most severe health consequences when infected. (We note that for other infections these two groups may strongly overlap, in which case there is no conflict of priorities to resolve.) To tease apart these conflicting ideals, we extend the simple model above by having three groups [18, 19, 22, 23] : the dominant transmitter group (denoted by a subscript D), the group at highest risk of severe health complications if they become infected (denoted by a subscript H ) and the rest of the general population (denoted by a subscript G). These groups obey the basic equation (2.1) with two main modifications: firstly, the transmission dynamics are coupled through a 'who acquires infection from whom' matrix (b); and secondly, vaccination is prioritized so that either the dominant transmitter group (D) or the severe health risk group (H ) is vaccinated first, followed by the other group (either H or D), finally followed by the general population (G), (see electronic supplementary material). Here we have ignored the possibility that there is a group that are both dominant transmitters and at high risk of complications-obviously if such a group exists then it should be prioritized for vaccination before all others.