Figure 5.

Top: Ratio between maximum, $f_O^{\max }$, and minimum, $f_O^{\max }$, in the variation of the case distribution, i.e. in the fraction of infected individuals belonging to the old group, $f_O$, in time depending on the mixing rate between the groups, $\nu$, and the ratio of infection costs $T_Y/T_O$ (a). We also show the dependence on the infection cost in the young group, when the infection cost for the old group is fixed, $T_O=2000$, for four choices of the mixing rate (c). Bottom: Average between maximum, $f_O^{\max }$, and minimum, $f_O^{\min }$, in the variation of the case distribution, $f_O$ depending on the mixing rate between the groups, $\nu$, and the ratio of infection costs $T_Y/T_O$ (b). We also show how the maximal (solid) and minimal (dashed) fraction of cases belonging to the old group depends again on the infection cost of the young group $T_Y$, when the infection cost for the old group is fixed, $T_O=2000$, for the same choices of the mixing rate (d). All results are obtained by numerically integrating equations (2.5)–(2.9) using a standard ODE solver, with fixed $\mathrm{\Delta }t=0.005$, and, in both groups, $\alpha =0.50$, $\beta =0.6$, $\mu =0.2$, $\gamma =0.4$ and $c=1$, and initial conditions $I^{\mathit{\text{NP}}}(0)=0.0015$ in both groups. (Online version in colour.)