Figure 6

(a) Analysis of the optimal mean contact reduction \(u (t )\) during the critical period, where the number of simultaneously infected must be kept constant (the plot is for \(C_{0}=10\text{,}000\)). The numerically exact result is plotted along with the stability boundary \(\mathcal{R}_{0}^{-1}N (t )/S (t )\) (blue dashed line) and the analytical approximation (13) (red dotted line). The inset shows that the optimal control respects the stability requirement (14) during the critical period. (b) Plot of effective reproduction number \(\mathcal{R}_{\text{eff}} (t )\) corresponding to the optimal control. Throughout the critical period, \(\mathcal{R}_{\text{eff}} (t )\) is kept slightly below one