The first approach looked at vaccine take-up and Covid deaths 31 days later in three age groups (60-69, 70-79 and over-80s), and estimated how many more people would have died up to the end of March 2021 had nobody been vaccinated. This basic analysis considers only the direct effects of vaccination on mortality, but vaccines also have indirect effects through dampening transmission. The PHE/MRC (Medical Research Council) Biostatistics Unit model is a more complex “transmission dynamics” model, expressing in mathematics how the virus progresses through populations. They use extensive data such as Covid-19 deaths by age and region, and antibody samples, and their model simulates the numbers of infections and deaths without any vaccinations. Up to 19 June, they estimate a reduction in 7.2m infections and 27,200 deaths. Of course, these are comparisons with a rather unreal parallel world – if no vaccines were available, government policies and social reactions would have been different. It’s worth noting that other models estimated locking down a week earlier in March 2020 would have saved more than 20,000 lives.