Theoretically quantifying the direct and indirect benefits of vaccination against SARS-CoV-2 in terms of avoided deaths.

The Coronavirus Disease 2019 (COVID)-19 pandemic has placed unprecedented pressures on societies around the world. Successful vaccines, developed against the spike protein of the Severe Acute Respiratory Syndrome Virus 2 (SARS-CoV-2) virus, offer hope that new hospitalisations and new deaths will subside. However, vaccination takes place in a dynamic environment. For example, new variants of the disease may occur where the effectiveness of a vaccine lies below that of the original target of the vaccine, while changes in the behaviour of a population are accompanied by a changed basic reproduction number. Here, we aim to understand how changes in values of basic parameters affect the benefits of vaccination at the direct level, of the individuals vaccinated, and at the indirect level, of the wider, unvaccinated community. We work within the framework of a Susceptible-Infected-Recovered model, and produce a metric for the benefits of vaccination, at both direct and indirect levels, in terms of the number of avoided deaths. Taking into account the initial prevalence of a SARS-CoV-2 infection, the mortality rate of the disease, the basic reproduction number, the vaccination rate, and the effectiveness of a vaccine, we explore how these basic parameters affect the benefits of vaccination. We find a range of situations where indirect benefits of vaccination outweigh direct benefits. This especially occurs at lower rates of vaccination (20% - [Formula: see text]) and intermediate values of the basic reproduction number (1-1.5). The indirect benefits can be substantial, in some cases being more than 400% of the direct benefits. For an initial prevalence of SARS-CoV-2 infection of 2%, a basic reproduction number of 1.2, a mortality rate of 2%, and a vaccine effectiveness of 95%, our findings show, for a population of 500,000 people, where 100,000 susceptible individuals are vaccinated, that approximately 2200 deaths are avoided. However, approximately 600 of these deaths are avoided amongst vaccinated individuals, while approximately 1600 deaths are avoided in the wider, unvaccinated community.