Statistics of antibody binding to the spike protein explain the dependence of COVID 19 infection risk on antibody concentration and affinity

The increase of COVID-19 breakthrough infection risk with time since vaccination has a clear relationship to the decrease of antibody concentration with time. 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, leading to blocking of binding to the receptor: namely that the probability of infection is the probability that a critical number of the spike proteins protruding from the virus are unblocked. 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 infection given measured antibody concentration. It can be used to relate population breakthrough infection risk to the distribution across the population of antibody concentration, and its variation with time.