Blue arrows represent relevant flows in vaccination strata, dark red and purple in hospital pathways, and green in SARS-CoV-2 variant compartments. Seeappendix 1for the full diagram with flows describing SARS-CoV-2 variants, vaccination status, and hospital pathways (p 4), and definitions of all variables and parameters (pp 17, 35). S=susceptible. E=exposed. IA=infected, asymptomatic. IP=presymptomatic infectious. IC1=symptomatic, infectious. IC2=symptomatic, not infectious. H=hospitalised. GD=severe disease, leading to death (at home). D=deceased (as a result of COVID-19). R=recovered.i=age or care-home group (5-year age bands from 0-4 years to 75-79 years; >=80 years age group; care-home worker; and care-home resident).j=SARS-CoV-2 variant (alpha, delta, or alpha:delta [ie, infected with delta after a previous infection with alpha]).k=vaccination stratum (0, 1, 2, 3). Vk=in vaccination stratum k. (t)=force of infection at time t. =rate of disease progression. pC=probability of being symptomatic, given infected. pH=probability of severe disease requiring hospitalisation, given symptomatic disease. pGD=probability of death for severe symptomatic cases outside of hospital. p*=probability of COVID-19 diagnosis confirmed before admission to hospital. =probability of being protected against infection with the SARS-CoV-2 delta variant for those recovered from infection with the SARS-CoV-2 alpha variant. (t)= rate of movement between vaccination strata.