FIGURE 5.

Optimal vaccination rollout for different velocity of loss of partial immunity. The figure illustrates the optimal solutions obtained via the model predictive control for the AstraZeneca vaccine (see Table 2), by assuming (A) a faster loss of immunity that occurs on average in 6 weeks ($\alpha =1/6$), and (B) a slower loss of immunity that occurs on average in 24 weeks ($\alpha =1/24$). On the left panels, we illustrates the number of first doses (green) and second doses (red) that should be performed each week, according to the optimal solution. On the right panes, we illustrate the temporal evolution of the number of individuals for which the second dose is being delayed