Figure 4.

Effective reproductive number 30 days after seeding an outbreak ($r_{\mathrm{eff}}^{30}$), as a function of vaccine effectiveness (infection blocking) and vaccine coverage (fraction of the eligible population vaccinated, shown along the top axes). The fraction of the total population vaccinated is shown along the bottom axes. Outlined areas indicate values of vaccine coverage over which herd immunity is reached as per the definition given in §2f for those vaccine effectiveness values at which herd immunity is achieved at all. We have clipped the colour scale such that $r_{\mathrm{eff}}^{30}\in$ [0.5, 1.5] to better see the zone near $r_{\mathrm{eff}}^{30}=1$. (a) Alpha variant, ages $16+\hspace{0.17em}\mathrm{eligible}$; (b) Alpha variant, ages $12+\hspace{0.17em}\mathrm{eligible}$; (c) Delta variant, ages $16+\hspace{0.17em}\mathrm{eligible}$; (d) Delta variant, ages $12+\hspace{0.17em}\mathrm{eligible}$; (e) Omicron variant, ages $16+\hspace{0.17em}\mathrm{eligible}$; (f) Omicron variant, ages $12+\hspace{0.17em}\mathrm{eligible}$. Initial number of imported infections is 20, and other simulation parameters are summarized in the electronic supplementary material, table S6. (Online version in colour.)