Because SARS-CoV-2 constantly mutates to escape from the immune response, there is a reduction of neutralizing capacity of antibodies initially targeting the historical strain against emerging Variants of Concerns (VoC)s. That is why the measure of the protection conferred by vaccination cannot solely rely on the antibody levels, but also requires to measure their neutralization capacity. Here we used a mathematical model to follow the humoral response in 26 individuals that received up to three vaccination doses of Bnt162b2 vaccine, and for whom both anti-S IgG and neutralisation capacity was measured longitudinally against all main VoCs. Our model could identify two independent mechanisms that led to a marked increase in humoral response over the successive vaccination doses. In addition to the already known increase in IgG levels after each dose, we identified that the neutralization capacity was significantly increased after the third vaccine administration against all VoCs, despite large inter-individual variability. Consequently, the model projects that the mean duration of detectable neutralizing capacity against non-Omicron VoC is between 366 days (Beta variant, 95% Prediction Intervals PI [323; 366]) and 606 days (Alpha variant, 95% PI [555; 638]). Despite a very low protection after three doses, the mean duration of detectable neutralizing capacity against Omicron variants varies between 184 days (BA.5 variant, 95% PI [155; 215]) and 268 days (BA.1 variant, 95% PI [238; 302]). Our model shows the benefit of incorporating the neutralization capacity in the follow-up of patients to better inform on their level of protection against the different SARS-CoV-2 variants as well as their optimal timing of vaccine administration.