Fig. 4: Best vaccination strategy for each possible starting day before the second peak.

a Illustrates the proportion of infectious individuals over time in the baseline scenario, i.e., without vaccination. The vertical dashed lines indicate the peaks of the epidemic and act as reference points in the subsequent panels. b The variation in the height of the subsequent largest peak relative to the baseline (vertical axis) due to the most effective vaccination strategy initiated on each day (horizontal axis). Here, the term “best” strategy refers to the approach that results in the greatest reduction in the height of the subsequent largest peak. The color of each bar indicates the vaccination rate of that strategy. c The same quantities as (b) but, instead of using a constant vaccination rate α, we have used a vaccination rate α(t, S) ∝ Θ(S − S^*), i.e., a vaccination that is only active when the susceptible compartment exceeds its stationary value. The horizontal black dashed lines in panels b) and c) correspond to the maximum possible reduction, obtained when the second peak is just as tall as the equilibrium value. In this case, the strategy that comes closer to achieve the optimal value is the one in panel b) that starts on day 89 with speed α = 0.002.