COVID 19 breakthrough infection risk: a simple physical model describing the dependence on antibody concentration

The empirically-observed dependence on blood IgG anti-receptor binding domain antibody concentration of SARS-CoV-2 vaccine efficacy against infection has a rational explanation in the statistics of binding of antibody to spike proteins on the virus surface: namely that the probability of protection is the probability of antibody binding to more than a critical number of the spike proteins protruding from the virus. The model is consistent with the observed antibody concentrations required to induce immunity and with the observed dependence of vaccine efficacy on antibody concentration and thus is a useful tool in the development of models to relate, for an individual person, risk of breakthrough infection given measured antibody concentration