Fig. 1.

Influence functions plotted as a function of the infected proportion, I, for the linear, saturating, fixed-order saturating, and reverse-order saturating cases given in Table 1. The thick/thin lines correspond to the influence of the more/less prophylactic subgroups (${\omega }_{-2}(I)$ and ${\omega }_2(I)$ solid, ${\omega }_{-1}(I)$ and ${\omega }_1(I)$ dashed). Influence is shown for $0\le I\le 0.5$, so that the behaviour near $I=0$ is more visible. Parameter values are given in Table 2, and the choice of influence functions is explained in the caption of Table 1. Note that the functions are symmetric about ${\omega }_0$ because we have used ${\omega }_{max}=1$. For ${\omega }_{max}>1$, the more prophylactic influence functions increase in magnitude, removing the symmetry