$S[1]=9.9$ million, $R[1]=0$ and $D[1]=0$. We set $\chi_{\textrm{max}}=100$. Referring back to Figure \[fig\_results0\], it can be seen that the three MTL specifications $\varphi_{\textrm{S}}^1$, $\varphi_{\textrm{S}}^2$ and $\varphi_{\textrm{S}}^3$ are all violated without any control strategies. Now we investigate the hypothetical scenario where isolation measures are replaced by shield immunity control.

Figures \[fig\_results\_shield1\], \[fig\_results\_shield2\] and \[fig\_results\_shield3\] show the simulation results for shield immunity control of the COVID-19 SEIR model with MTL specifications $\varphi_{\textrm{S}}^1$, $\varphi_{\textrm{S}}^2$ and $\varphi_{\textrm{S}}^3$, respectively. The results show that the MTL specifications $\varphi_{\textrm{S}}^1$, $\varphi_{\textrm{S}}^2$ and $\varphi_{\textrm{S}}^3$ are satisfied with the synthesized shield immunity control inputs respectively. We observe that with the three MTL specifications, the synthesized shield immunity control inputs all increase to a peak at approximated 20 days after the outbreak and then gradually decrease. These observations are consistent with the claim that shield immunity at early phases of the outbreak can mitigate the spread of SARS-CoV-2 in the most efficient manner. The results also show that the control effort for satisfying $\varphi_{\textrm{S}}^1$ is less than that for satisfying $\varphi_{\textrm{S}}^2$, which is still less than that for satisfying $\varphi_{\textrm{S}}^3$. This is consistent with the fact that $\varphi_{\textrm{S}}^2$ implies $\varphi_{\textrm{S}}^1$, and $\varphi_{\textrm{S}}^3$ implies both $\varphi_{\textrm{S}}^1$ and $\varphi_{\textrm{S}}^2$. For all three specifications, 