Fig. 16.

Scenarios allowing transmissibility to increase beyond initial${\mathcal{R}}_0$. Simulations of the COVID-19 pandemic in England with epidemiological parameters estimated in Section 5.1. Larger panels show daily COVID-19 deaths in England while shallow panels underneath show the corresponding controlled reproduction numbers as introduced in Section 2.1. (a,b) heterogeneous susceptibility model: without vaccination (red); and with cumulative vaccination as per blue dots (green curve); (c,d) homogeneous model: without vaccination (black); and with vaccination (green curve). Dashed curves represent cumulative percentage infected in the respective colours. Reported COVID-19 deaths are represented by green dots. Two scenarios are considered for VE against infection: $30\%$ (a,c); and $70\%$ (b,d). VE against death is fixed at $90\%$. Curves generated by running model (31)-(39).